,transcrib]'s ,note ,?is book uses a numb] ( a/ronomical symbols1 includ+ signs ( ! ,zodiac 71 1 1 1 1 1 1 1 1 1 1 71 symbols = planets 71 1 1 1 1 7 & = ! sun & moon 71 74 ,if ^! *>act]s d n display correctly1 y may h to use an alt]native font1 su* z ,arial ,unicode ,,ms or ,deja,vu4 ,:5 italics 7 us$ 9 ! orig9al book1 ! correspond+ text has be5 surr\nd$ by und]scores4 ,mix$ fractions h be5 display$ ) a hyph5 betwe5 :ole numb] & fraction = cl>ity4 ,sup]script$ *>act]s are prec$$ by & :5 m ?an "o "* is sup]script$1 !y are surr\nd$ by 4 ,"s corrections h be5 made to ! pr9t$ text4 ,^! are li/$ 9 a second transcrib]'s note at ! end ( ! text4 ,illu/ration3 ,! ,,orr]y1 made by ,,james ,,f]guson4 ,n4 #a4 ,! ,sun1 #b4 ,m]cury1 #c4 ,v5us1 #d4 ,! ,e>?1 #e4 ,! ,moon1 #f4 ,! ,syd]eal ,dial plate1 #g4 ,! ,h\r ,circle1 #h4 ye ,circle = ye4 ,moon's ,age1 #i4 ,! ,moon's ,orbit1 #aj4 ye ,po9t]1 ,%ew+ ! ,sun's ,place ,day ( ! ,mon?1 #aa4 ,! ,ecliptic1 #ab4 ,! ,h&le = turn+ ye :ole ma*9e ,j4 ,f]guson inv4 et del94 ,g4 ,*ild4 ,sculp4 ,,a/ronomy ,,expla9$ ,,^u ,sir ,,isaac ,,newton's ,,pr9ciples1 ,,& ,,made ,,easy ,,to ,,^? ,,:o ,,h ,,n ,,/udi$ ,,ma!matics4 ,by ,,james ,,f]guson4 ,,heb4 ,,xi4 #c4 ,! ,worlds 7 fram$ by ! ,^w ( ,,god4 ,,job ,,xxvi4 #ac4 ,by 8 ,_s he ha? g>ni%$ ! ,heav5s4 ,,! ,,second ,,edition4 ,illu/ration3 decoration ,,london3 ,pr9t$ =1 & sold by ! ,,au?or1 at ! ,,globe1 opposite ,cecil-,/reet 9 ! ,/r&4 ,,mdcclvii4 ,,to ,,! ,,"r ,,hon\rable ,,george ,,e>l ( ,,macclesfield1 ,,visc\nt ,,p>k] ( ,,ewelme 9 ,,ox=d%ire1 ,,& ,,b>on ( ,,macclesfield 9 ,,*e%ire2 ,,presid5t ( ! ,,royal ,,society ( ,,london1 ,,memb] ( ! ,,royal ,,academy ,,( ,,sci5ces at ,,p>is1 ,,( ,,! ,,imp]ial ,,academy ,,( ,,sci5ces at ,pet]sburg1 ,,& ,,"o ,,( ,,! ,,tru/ees ( ! ,,briti% ,,museum2 ,,di/+ui%$ ,by 8 ,,g5]\s ,,zeal = promot+ e ,,bran* ( ,,useful ,,k2 ,,?is ,,treatise ( ,,a/ronomy ,,is ,,inscrib$1 ,) ! ,,mo/ ,,pr(\nd ,,respect1 ,by ,,8 ,,lord%ip's ,,mo/ ,,oblig$1 ,& ,,mo/ ,,humble ,,s]vant1 ,,james ,,f]guson4 ,,! ,,cont5ts4 ,,*ap4 ,i4 ,( ,a/ronomy 9 g5]al ,page #a ,,*ap4 ,,ii4 ,a brief ,description ( ! ,,sol> ,,sy/em #e ,,*ap4 ,,iii4 ,! ,,cop]nican or ,,sol> ,,sy/em demon/rat$ to be #ca true ,,*ap4 ,,iv4 ,! ,ph5om5a ( ! ,heav5s z se5 f diff]5t #ci p>ts ( ! ,e>? ,,*ap4 ,v4 ,! ,ph5om5a ( ! ,heav5s z se5 f diff]5t #de p>ts ( ! ,sol> ,sy/em ,,*ap4 ,,vi4 ,! ,ptolemean ,sy/em refut$4 ,! ,motions & ,phases #ej ( ,m]cury & ,v5us expla9$ ,,*ap4 ,,vii4 ,! physical ,causes ( ! ,motions ( ! ,planets4 ,! #ed ,exc5tricities ( _! ,orbits4 ,! times 9 :i* ! ,action ( ,gravity w\ld br+ !m to ! ,sun4 ,,ar*im$es',s ideal ,problem = mov+ ! ,e>?4 ,! _w n et]nal ,,*ap4 ,,viii4 ,( ,light4 ,x's proportional quantities on ! #fb diff]5t ,planets4 ,x's ,refractions 9 ,wat] & ,air4 ,! ,atmosph]e1 x's ,weight & ,prop]ties4 ,! ,horizontal ,moon ,,*ap4 ,,ix4 ,! ,me?od ( f9d+ ! ,di/ances ( ! ,sun1 ,moon #gc & ,planets ,,*ap4 ,x4 ,! ,circles ( ! ,globe describ$4 ,! diff]5t #gh l5g?s ( days & nights1 & ! vicissitude ( ,seasons1 expla9$4 ,! explanation ( ! ,ph5om5a ( ,saturn's ,r+ conclud$ ,,*ap4 ,,xi4 ,! ,me?od ( f9d+ ! ,longitude by ! ,eclipses ( #hg ,jupit]'s ,satellites3 ,! amaz+ velocity ( ,light demon/rat$ by ^! ,eclipses ,,*ap4 ,,xii4 ,( ,sol> & ,sid]eal ,"t #ic ,,*ap4 ,,xiii4 ,( ! ,equation ( ,"t #ig ,,*ap4 ,,xiv4 ,( ! ,precession ( ! ,equ9oxes #ajh ,,*ap4 ,,xv4 ,! ,moon's ,surface m\nta9\s3 ,h] ,phases describ$3 #abd ,h] ,pa?1 & ! ,pa?s ( ,jupit]'s ,moons del9eat$3 ,! proportions ( ! ,diamet]s ( _! ,orbits1 & ^? ( ,saturn's ,moons to ea* o!r2 & to ! ,diamet] ( ! ,sun ,,*ap4 ,,xvi4 ,! ,ph5om5a ( ! ,h>ve/-,moon expla9$ by a #acf common ,globe3 ,! ,ye>s 9 :i* ! ,h>ve/-,moons are lea/ & mo/ b5eficial1 f #agea to #ahfa4 ,! long duration ( ,moon-light at ! ,poles 9 ,w9t] ,page ,,*ap4 ,,xvii4 ,( ! ebb+ & fl[+ ( ! ,sea #adg ,,*ap4 ,,xviii4 ,( ,eclipses3 ,_! ,numb] & ,p]iod4 ,a l>ge #aef ,catalogue ( ,anci5t & ,mod]n ,eclipses ,,*ap4 ,,xix4 ,! ,calculation ( ,new & ,full ,moons & ,eclipses4 #ahi ,! geometrical ,con/ruction ( ,sol> & ,lun> ,eclipses4 ,! exam9ation ( anci5t ,eclipses ,,*ap4 ,,xx4 ,( ! fix$ ,/>s #bcj ,,*ap4 ,,xxi4 ,( ! ,division ( ,"t4 ,a p]petual ,table ( ,new #bdh ,moons4 ,! ,times ( ! ,bir? & ,dea? ( ,,*ri/4 ,a ,table ( rem>kable ras or ,ev5ts ,,*ap4 ,,xxii4 ,a ,description ( ! ,a/ronomical ,ma*9]y s]v+ to #bfj expla9 & illu/rate ! =ego+ "p ( ?is ,treatise ,,errata4 ,9 ! ,table fac+ ,page #ca1 ! ,sun's quantity ( matt] %\ld be #bbgejj4 ,page #dj1 l4 la/1 = inf9ite read indef9ite4 ,page #ig1 l4 #bj1 = ?is read ! next4 ,page #afd1 l4 #b f ! bottom1 = )\t any accel]ation read z above1 )\t any accel]ation4 ,page #aii1 l4 #af = ,,xiv read ,,xv4 ,page #bch1 l4 #af1 = #dj read #djf4 ,page #bdj1 l4 #ae f ! bottom1 = ,tifri read ,tisri1 ,page #bdi l4 #ac2 f ! bottom = ,,xvii read ,v4 ,,a/ronomy ,,expla9$ ,,^u ,sir ,,isaac ,,newton's ,,pr9ciples4 ,,*ap4 ,i4 ,( ,a/ronomy 9 g5]al4 ,sid5ote3 ,! g5]al use ( ,a/ronomy4 #a4 ,( all ! sci5ces cultivat$ by mank9d1 ,a/ronomy is ackn[l$g$ to be1 & und\bt$ly is1 ! mo/ sublime1 ! mo/ int]e/+1 & ! mo/ useful4 ,=1 by k d]iv$ f ?is sci5ce1 n only ! bulk ( ! ,e>? is discov]$1 ! situation & ext5t ( ! c\ntries & k+doms ^u x asc]ta9$1 trade & comm]ce c>ri$ on to ! remote/ p>ts ( ! _w1 & ! v>i\s products ( sev]al c\ntries di/ribut$ = ! heal?1 com=t1 & conv5i5cy ( its inhabitants2 b our v faculties are enl>g$ ) ! gr&eur ( ! ideas x conveys1 our m9ds exalt$ above ! l[ contract$ prejudices ( ! vulg>1 & our und]/&+s cle>ly conv9c$1 & affect$ ) ! conviction1 ( ! exi/5ce1 wisdom1 p[]1 goodness1 & sup]9t5d5cy ( ! ,,supreme ,,be+6 ,s t )\t an hyp]bole1 8,an undev\t ,a/ronom] is mad#a40 #b4 ,f ?is bran* ( k we also le>n by :at means or laws ! ,almighty c>ries on1 & cont9ues ! admirable h>mony1 ord]1 & connexion obs]vable ?r\gh\t ! planet>y sy/em2 & are l$ by v p[]ful argum5ts to =m ! pleas+ d$uction1 t m9ds capable ( su* deep rese>*es n only d]ive _! orig9 f t adorable ,be+1 b are also incit$ to aspire aft] a m p]fect k ( 8 nature1 & a /rict] con=mity to 8 w4 ,sid5ote3 ,! ,e>? b a po9t z se5 f ! ,sun4 #c4 ,by ,a/ronomy we discov] t ! ,e>? is at s great a di/ance f ! ,sun1 t if se5 f !nce x w\ld appe> no bigg] ?an a po9t2 al?\gh x's circumf]5ce is kn[n to be #be1jbj miles4 ,yet t di/ance is s small1 comp>$ ) ! di/ance ( ! ,fix$ ,/>s1 t if ! ,orbit 9 :i* ! ,e>? moves r\nd ! ,sun 7 solid1 & se5 f ! ne>e/ ,/>1 x w\ld likewise appe> no bigg] ?an a po9t1 al?\gh x is at lea/ #afb millions ( miles 9 diamet]4 ,= ! ,e>? 9 go+ r\nd ! ,sun is #afb millions ( miles ne>] to "s ( ! ,/>s at "o "t ( ! ye> ?an at ano!r2 & yet _! app>5t magnitudes1 situations1 & di/ances f "o ano!r /ill rema9 ! same2 & a telescope :i* magnifies above #bjj times does n s5sibly magnify !m3 :i* proves !m to be at lea/ #djj ?\s& times f>!r f u ?an we are f ! ,sun4 ,sid5ote3 ,! ,/>s are ,suns4 #d4 ,x is n to be imag9$ t all ! ,/>s are plac$ 9 "o concave surface1 s z to be equally di/ant f u2 b t !y are scatt]$ at imm5se di/ances f "o ano!r ?r\gh unlimit$ space4 ,s t !re may be z great a di/ance betwe5 any two neighb\r+ ,/>s1 z betwe5 our ,sun & ^? :i* are ne>e/ to him4 ,!re=e an ,obs]v]1 :o is ne>e/ any fix$ ,/>1 w look ^u x alone z a real ,sun2 & consid] ! re/ z s _m %9+ po9ts1 plac$ at equal di/ances f him 9 ! ,firmam5t4 ,sid5ote3 ,& innum]able4 #e4 ,by ! help ( telescopes we discov] ?\s&s ( ,/>s :i* are invisible to ! nak$ eye2 & ! bett] our glasses are1 /ill ! m become visible3 s t we c set no limits ei!r to _! numb] or _! di/ances4 ,! celebrat$ ,,huyg5s c>ries 8 ?\ghts s f>1 z to believe x n impossible t !re may be ,/>s at su* inconceivable di/ances1 t _! light has n yet rea*$ ! ,e>? s9ce x's creation2 al?\gh ! velocity ( light be a million ( times great] ?an ! velocity ( a cannon bullet1 z %all be demon/rat$ aft]w>ds #aig1 #baf3 &1 z ,mr4 ,,addison v ju/ly obs]ves1 ?is ?\ght is f> f be+ extravagant1 :5 we consid] t ! ,univ]se is ! "w ( inf9ite p[]1 prompt$ by inf9ite goodness2 hav+ an inf9ite space to ex]t itself 92 s t our imag9ations c set no b\nds to x4 ,sid5ote3 ,:y ! ,sun appe>s bigg] ?an ! ,/>s4 #f4 ,! ,sun appe>s v bright & l>ge 9 comp>ison ( ! ,fix$ ,/>s1 because we keep con/antly ne> ! ,sun1 9 comp>ison ( our imm5se di/ance f ! ,/>s4 ,=1 a spectator1 plac$ z ne> to any ,/> z we are to ! ,sun1 w\ld see t ,/> a body z l>ge & bright z ! ,sun appe>s to u3 & a spectator1 z f> di/ant f ! ,sun z we are f ! ,/>s1 w\ld see ! ,sun z small z we see a ,/>1 dive/$ ( all its circumvolv+ ,planets2 & w\ld reckon x "o ( ! ,/>s 9 numb]+ !m4 ,sid5ote3 ,! ,/>s are n enlight5$ by ! ,sun4 #g4 ,! ,/>s1 be+ at su* imm5se di/ances f ! ,sun1 _c possibly receive f him s /rong a light z !y seem to h2 nor any brightness suffici5t to make !m visible to u4 ,= ! ,sun's rays mu/ be s scatt]$ & dissipat$ be=e !y rea* su* remote objects1 t !y c nev] be transmitt$ back to our eyes1 s z to r5d] ^! objects visible by reflection4 ,! ,/>s !re=e %9e ) _! own native & unborr[$ lu/re1 z ! ,sun does2 & s9ce ea* p>ticul> ,/>1 z well z ! ,sun1 is conf9$ to a p>ticul> portion ( space1 'tis pla9 t ! ,/>s are ( ! same nature ) ! ,sun4 ,sid5ote3 ,!y are probably surr\nd$ by ,planets4 #h4 ,x is no ways probable t ! ,almighty1 :o always acts ) inf9ite wisdom & does no?+ 9 va91 %\ld create s _m glori\s ,suns1 fit = s _m important purposes1 & place !m at su* di/ances f "o ano!r1 )\t prop] objects ne> en\gh to be b5efit$ by _! influ5ces4 ,:oev] imag9es !y 7 creat$ only to give a fa9t glimm]+ light to ! inhabitants ( ?is ,globe1 mu/ h a v sup]ficial k ( ,a/ronomy1 & a mean op9ion ( ! ,div9e ,wisdom3 s9ce1 by an inf9itely less ex]tion ( creat+ p[]1 ! ,deity c\ld h giv5 our ,e>? mu* m light by "o s+le additional ,moon4 #i4 ,in/ead !n ( "o ,sun & "o ,_w only 9 ! ,univ]se1 z ! unskilful 9 ,a/ronomy imag9e1 t ,sci5ce discov]s to u su* an inconceivable numb] ( ,suns1 ,sy/ems1 & ,worlds1 disp]s$ ?r\gh b\ndless ,space1 t if our ,sun1 ) all ! ,planets1 ,moons1 & ,comets belong+ to x 7 annihilat$1 !y w\ld be no m miss$ out ( ! ,creation ?an a gra9 ( s& f ! sea-%ore4 ,! space !y possess be+ comp>atively s small1 t x w\ld sc>ce be a s5sible blank 9 ! ,univ]se2 al?\gh ,saturn1 ! out]mo/ ( our planets1 revolves ab\t ! ,sun 9 an ,orbit ( #dhhd millions ( miles 9 circumf]5ce1 & "s ( our ,comets make excursions upw>ds ( t5 ?\s& millions ( miles beyond ,saturn's ,orbit2 & yet1 at t amaz+ di/ance1 !y are incomp>ably ne>] to ! ,sun ?an to any ( ! ,/>s2 z is evid5t f _! keep+ cle> ( ! attractive ,p[] ( all ! ,/>s1 & return+ p]iodically by virtue ( ! ,sun's attraction4 ,sid5ote3 ,! /ell> ,planets may be habitable4 #aj4 ,f :at we "k ( our own ,sy/em x may be reasonably conclud$ t all ! re/ are ) equal wisdom contriv$1 situat$1 & provid$ ) accommodations = rational inhabitants4 ,let u !re=e take a survey ( ! ,sy/em to :i* we belong2 ! only "o accessible to u2 & f !nce we %all be ! bett] enabl$ to judge ( ! nature & end ( ! o!r ,sy/ems ( ! ,univ]se4 ,= al?\gh !re is almo/ an inf9ite v>iety 9 all ! p>ts ( ! ,creation :i* we h opportunities ( exam9+2 yet !re is a g5]al analogy runn+ ?r\gh & connect+ all ! p>ts into "o s*eme1 "o design1 "o :ole6 ,sid5ote3 ,z our ,sol> ,planets are4 #aa4 ,& !n1 to an att5tive consid]]1 x w appe> highly probable1 t ! ,planets ( our ,sy/em1 toge!r ) _! att5dants call$ ,satellites or ,moons1 are mu* ( ! same nature ) our ,e>?1 & de/9$ = ! l purposes4 ,=1 !y are solid opaque ,globes1 capable ( support+ animals & vegetables4 ,"s ( !m are bigg]1 "s less1 & "s mu* ab\t ! size ( our ,e>?4 ,!y all circulate r\nd ! ,sun1 z ! ,e>? does1 9 a %ort] or long] "t accord+ to _! respective di/ances f him3 & h1 :]e x w\ld n be inconv5i5t1 regul> returns ( summ] & w9t]1 spr+ & autumn4 ,!y h w>m] & cold] climates1 z ! v>i\s productions ( our ,e>? require3 &1 9 su* z af=d a possibility ( discov]+ x1 we obs]ve a regul> motion r\nd _! ,axes l t ( our ,e>?1 caus+ an alt]nate return ( day & night2 :i* is necess>y = lab\r1 re/1 & vegetation1 & t all p>ts ( _! surfaces may be expos$ to ! rays ( ! ,sun4 ,sid5ote3 ,! f>!/ f ! ,sun h mo/ ,moons to enlight5 _! nights4 #ab4 ,su* ( ! ,planets z are f>!/ f ! ,sun1 & !re=e enjoy lea/ ( 8 light1 h t defici5cy made up by sev]al ,moons1 :i* con/antly accompany1 & revolve ab\t !m1 z our ,moon revolves ab\t ! ,e>?4 ,! remote/ ,planet has1 ov] & above1 a broad ,r+ encompass+ x2 :i* l a lucid ,zone 9 ! ,heav5s reflects ! ,sun's light v copi\sly on t ,planet3 s t if ! remot] ,planets h ! ,sun's light fa9t] by day ?an we1 !y h an addition made to x morn+ & ev5+ by "o or m ( _! ,moons1 & a great] quantity ( light 9 ! night-"t4 ,sid5ote3 ,our ,moon m\nta9\s l ! ,e>?4 #ac4 ,on ! surface ( ! ,moon1 because x is ne>] u ?an any o!r ( ! cele/ial ,bodies are1 we discov] a ne>] resemblance ( our ,e>?4 ,=1 by ! assi/ance ( telescopes we obs]ve ! ,moon to be full ( high m\nta9s1 l>ge valleys1 & deep cavities4 ,^! simil>ities leave u no room to d\bt b t all ! ,planets & ,moons 9 ! ,sy/em are design$ z commodi\s habitations = creatures end[$ ) capacities ( kn[+ & ador+ _! b5efic5t ,creator4 ,illu/ration3 ,plate ,i4 ,,! ,,sol> ,,sy/em ,j4 ,f]guson del94 ,j4 ,mynde ,sculp4 #ad4 ,s9ce ! ,fix$ ,/>s are prodigi\s sph]es ( fire1 l our ,sun1 & at inconceivable di/ances f "o ano!r1 z well z f u1 x is reasonable to conclude !y are made = ! same purposes t ! ,sun is2 ea* to be/[ light1 heat1 & vegetation on a c]ta9 numb] ( inhabit$ ,planets1 kept by gravitation )9 ! sph]e ( x's activity4 ,sid5ote3 ,numb]less ,suns & ,worlds4 #ae4 ,:at an augu/6 :at an amaz+ conception1 if human imag9ation c conceive x1 does ?is give ( ! works ( ! ,creator6 ,?\s&s ( ?\s&s ( ,suns1 multipli$ )\t end1 & rang$ all ar\nd u1 at imm5se di/ances f ea* o!r1 att5d$ by t5 ?\s& times t5 ?\s& ,worlds1 all 9 rapid motion1 yet calm1 regul>1 & h>moni\s1 inv>iably keep+ ! pa?s prescrib$ !m2 & ^! ,worlds peopl$ ) myriads ( intellig5t be+s1 =m$ = endless progression 9 p]fection & felicity4 #af4 ,if s mu* p[]1 wisdom1 goodness1 & magnific5ce is display$ 9 ! mat]ial ,creation1 :i* is ! lea/ consid]able "p ( ! ,univ]se1 h[ great1 h[ wise1 h[ good mu/ ,,he be1 :o made & gov]ns ! ,:ole6 ,,*ap4 ,,ii4 ,a brief ,description ( ! ,,sol> ,,sy/em4 ,sid5ote3 ,,plate ,i4 ,fig4 #a4 ,! ,sol> ,sy/em4 #ag4 ,! ,planets & ,comets :i* move r\nd ! ,sun z _! c5t]1 con/itute ! ,sol> ,sy/em4 ,^? ,planets :i* are ne>] ! ,sun n only f9i% _! circuits soon]1 b likewise move fa/] 9 _! respective ,orbits ?an ^? :i* are m remote f him4 ,_! motions are all p]=m$ f we/ to ea/1 9 ,orbits ne>ly circul>4 ,_! names1 di/ances1 bulks1 & p]iodical revolutions1 are z foll[s4 ,sid5ote3 ,! ,sun4 #ah4 ,! ,,sun 1 an imm5se globe ( fire1 is plac$ ne> ! common c5t]1 or r 9 ! l[]#b focus1 ( ! ,orbits ( all ! ,planets & ,comets#c2 & turns r\nd 8 axis 9 #be days #f h\rs1 z is evid5t by ! motion ( spots se5 on 8 surface4 ,8 diamet] is comput$ to be #gfc1jjj miles2 &1 by ! v>i\s attractions ( ! circumvolv+ ,planets1 he is agitat$ by a small motion r\nd ! c5t] ( gravity ( ! ,sy/em4 ,all ! ,planets1 z se5 f him1 move ! same way1 & accord+ to ! ord] ( ,signs 9 ! graduat$ ,circle c4 :i* repres5ts ! great ,ecliptic 9 ! ,heav5s3 b1 z se5 f any "o ,planet1 ! re/ appe> sometimes to g backw>d1 sometimes =w>d1 & sometimes to /& /ill2 n 9 circles nor ellipses1 b 9#d loop$ curves :i* nev] return into !mselves4 ,! ,comets come f all p>ts ( ! ,heav5s1 & move 9 all sorts ( directions4 ,sid5ote3 ,,plate ,i4 ,fig4 ,i4 ,! ,sun4 ,! ,axes ( ! ,planets1 :at4 #ai4 ,hav+ m5tion$ ! ,sun's turn+ r\nd 8 axis1 & z !re w be frequ5t occasion to speak ( ! l motion ( ! ,e>? & o!r ,planets1 x is prop] "h to in=m ! "y ,tyro 9 ,a/ronomy1 t nei!r ! ,sun nor ,planets h mat]ial axes to turn ^u1 & support !m1 z 9 ! little imp]fect ,ma*9es contriv$ to repres5t !m4 ,= ! axis ( a ,planet is a l9e conceiv$ to be drawn ?r\gh x's c5t]1 ab\t :i* x revolves z on a real axis4 ,! extremities ( ?is l9e1 t]m9at+ 9 opposite po9ts ( ! ,planet's surface1 are call$ its ,poles4 ,t :i* po9ts t[>ds ! nor!rn "p ( ! ,heav5s is call$ ! ,nor? ,pole2 & ! o!r1 po9t+ t[>ds ! s\!rn "p1 is call$ ! ,s\? ,pole4 ,a b[l :irl$ f "o's h& into ! op5 air turns r\nd su* a l9e )9 itself1 :il/ x moves =w>d2 & su* are ! l9es we mean1 :5 we speak ( ! ,axes ( ! ,heav5ly bodies4 ,sid5ote3 ,_! ,orbits are n 9 ! same plane ) ! ,ecliptic4 ,,plate ,i4 ,_! ,nodes4 ,:]e situat$4 #bj4 ,let u suppose ! ,e>?'s ,orbit to be a ?91 ev51 solid plane2 cutt+ ! ,sun ?r\gh ! c5t]1 & ext5d$ out z f> z ! ,/>ry ,heav5s1 :]e x w m>k ! great ,circle call$ ! ,ecliptic4 ,?is ,circle we suppose to be divid$ into #ab equal p>ts1 call$ ,signs2 ea* ,sign into #cj equal p>ts1 call$ ,degrees2 ea* ,degree into #fj equal p>ts1 call$ ,m9utes2 & e ,m9ute into #fj equal p>ts1 call$ ,seconds3 s t a ,second is ! #fj? "p ( a ,m9ute2 a ,m9ute ! #fj? "p ( a ,degree2 & a ,degree ! #cfj? "p ( a ,circle1 or #cj? "p ( a ,sign4 ,! ,planes ( ! ,orbits ( all ! o!r ,planets likewise cut ! ,sun 9 halves2 b ext5d$ to ! ,heav5s1 =m ,circles diff]5t f "o ano!r1 & f ! ,ecliptic2 "o half ( ea* be+ on ! nor? side1 & ! o!r on ! s\? side ( x4 ,consequ5tly ! ,orbit ( ea* ,planet crosses ! ,ecliptic 9 two opposite po9ts1 :i* are call$ ! ,planet's ,nodes4 ,^! ,nodes are all 9 diff]5t p>ts ( ! ,ecliptic2 & !re=e1 if ! planet>y ,tracks rema9$ visible 9 ! ,heav5s1 !y w\ld 9 "s measure resemble ! diff]5t rutts ( waggon-:eels cross+ "o ano!r 9 diff]5t p>ts1 b nev] go+ f> asund]4 ,t ,node1 or ,int]section ( ! ,orbit ( any ,planet ) ! ,e>?'s ,orbit1 f :i* ! ,planet asc5ds nor?w>d above ! ,ecliptic1 is call$ ! ,asc5d+ ,node ( ! ,planet2 & ! o!r1 :i* is directly opposite !reto1 is call$ x's ,desc5d+ ,node4 ,saturn's ,asc5d+ ,node is 9 #ba deg4 #ac m94 ( ,canc] 1 ,jupit]'s 9 #g deg4 #bi m94 ( ! same ,sign1 ,m>s's 9 #ag deg4 #ag m94 ( ,taurus 1 ,v5us's 9 #ac deg4 #ei m94 ( ,gem9i 1 & ,m]cury's 9 #ad deg4 #dc m94 ( ,taurus4 ,"h we consid] ! ,e>?'s ,orbit z ! /&>d1 & ! ,orbits ( all ! o!r ,planets z oblique to x4 ,sid5ote3 ,! ,planets ,orbits1 :at4 #ba4 ,:5 we speak ( ! ,planets ,orbits1 all t is meant is _! ,pa?s ?r\gh ! op5 & unresi/+ ,space 9 :i* !y move2 & are kept 91 by ! attractive p[] ( ! ,sun1 & ! projectile =ce impress$ ^u !m at fir/3 betwe5 :i* p[] & =ce !re is s exact an adju/m5t1 t )\t any solid ,orbits to conf9e ! ,planets1 !y keep _! c\rses1 & at ! end ( e revolution f9d ! po9ts f :5ce !y fir/ set out1 mu* m truly ?an c be imitat$ 9 ! be/ ma*9es made by human art4 ,sid5ote3 ,m]cury4 ,fig4 ,i4 ,may be inhabit$4 ,,plate ,i4 #bb4 ,,m]cury1 ! ne>e/ ,planet to ! ,sun1 goes r\nd him 7z 9 ! circle m>k$ 7 9 #hg days #bc h\rs ( our "t ne>ly2 :i* is ! l5g? ( 8 ye>4 ,b1 be+ seldom se51 & no spots appe>+ on 8 surface or disc1 ! "t ( 8 rotation on 8 axis1 or ! l5g? ( 8 days & nights1 is z yet unkn[n4 ,8 di/ance f ! ,sun is comput$ to be #cb millions ( miles1 & 8 diamet] #bfjj4 ,9 8 c\rse1 r\nd ! ,sun1 he moves at ! rate ( #ie ?\s& miles e h\r4 ,8 light & heat f ! ,sun are almo/ sev5 times z great z ours2 & ! ,sun appe>s to him almo/ sev5 times z l>ge z to u4 ,! great heat on ?is ,planet is no argum5t aga9/ x's be+ inhabit$2 s9ce ! ,almighty c\ld z easily suit ! bodies & con/itutions ( x's inhabitants to ! heat ( _! dwell+1 z he has done ours to ! temp]ature ( our ,e>?4 ,& x is v probable t ! p !re h su* an op9ion ( u1 z we h ( ! inhabitants ( ,jupit] & ,saturn2 namely1 t we mu/ be intol]ably cold1 & h v little light at s great a di/ance f ! ,sun4 ,sid5ote3 ,has l phases ) ! ,moon4 #bc4 ,?is ,planet appe>s to u ) all ! v>i\s phases ( ! ,moon1 :5 view$ at diff]5t times by a good telescope2 save only t he nev] appe>s q ,full1 because 8 enlight5$ side is nev] turn$ directly t[>ds u b :5 he is s ne> ! ,sun z to be lo/ to our sight 9 x's beams4 ,&1 z 8 enlight5$ side is always t[>d ! ,sun1 x is pla9 t he %9es n by any light ( 8 own2 = if he did1 he w\ld con/antly appe> r\nd4 ,t he moves ab\t ! ,sun 9 an ,orbit )9 ! ,e>?'s ,orbit is also pla9 7z w be m l>gely %ewn by & by1 #ada1 seq47 because he is nev] se5 opposite to ! ,sun1 nor above #ef times ! ,sun's bread? f 8 c5t]4 ,sid5ote3 ,8 ,orbit & ,nodes4 #bd4 ,8 ,orbit is incl9$ sev5 degrees to ! ,ecliptic2 & t ,node #bj1 f :i* he asc5ds nor?w>d above ! ,ecliptic is 9 ! #ad? degree ( ,taurus2 ! opposite1 9 ! #ad? degree ( ,scorpio4 ,! ,e>? is 9 ^! po9ts on ! #e? ( ,novemb] & #d? ( ,may1 new /yle2 & :5 ,m]cury comes to ei!r ( 8 ,nodes at 8#e inf]ior ,conjunction ab\t ^! times1 he w appe> to pass ov] ! disc or face ( ! ,sun1 l a d>k r\nd spot4 ,b 9 all o!r p>ts ( 8 ,orbit 8 ,conjunctions are invisible1 because he ei!r goes above or bel[ ! ,sun4 ,sid5ote3 ,:5 he w be se5 z if ^u ! ,sun4 #be4 ,mr4 ,,:i/on has giv5 u an acc\nt ( sev]al p]iods at :i* ,m]cury may be se5 on ! ,sun's disc1 viz4 ,9 ! ye> #aghb1 ,nov4 #ab?1 at #c h4 #dd m4 9 ! aft]noon3 #aghf1 ,may #d?1 at #f h4 #eg m4 9 ! =5oon3 #aghi1 ,dec4 #f?1 at #c h4 #ee m4 9 ! aft]noon2 & #agii1 ,may #g?1 at #b h4 #cd m4 9 ! aft]noon4 ,!re w be sev]al int]m$iate ,transits1 b none ( !m visible at ,london4 ,sid5ote3 ,fig4 ,i4 ,v5us4 #bf4 ,,v5us1 ! next ,planet 9 ord]1 is comput$ to be #ei millions ( miles f ! ,sun2 & by mov+ at ! rate ( #fi ?\s& miles e h\r 9 h] ,orbit 7z 9 ! circle m>k$ 71 %e goes r\nd ! ,sun 9 #bbd days #ag h\rs ( our "t ne>ly2 9 :i*1 ?\gh x be ! full l5g? ( h] ye>1 %e has only #i-a_/d days1 accord+ to ,,bian*9i's obs]vations2 s t 9 h]1 e day & night toge!r is z long z #bd-a_/c days & nights ) u4 ,?is odd qu>t] ( a day 9 e ye> makes e f\r? ye> a leap-ye> to ,v5us2 z ! l does to our ,e>?4 ,h] diamet] is #gijf miles2 & by h] diurnal motion ! inhabitants ab\t h] ,equator are c>ri$ #dc miles e h\r3 besides ! #fi1jjj above-m5tion$4 ,sid5ote3 ,h] ,orbit lies betwe5 ! ,e>? & ,m]cury4 #bg4 ,h] ,orbit includes t ( ,m]cury )9 x2 = at h] greate/ ,elongation1 or app>5t di/ance f ! ,sun1 %e is #if times 8 bread? f 8 c5tre2 :i* is almo/ d\ble ( ,m]cury's4 ,h] ,orbit is includ$ by ! ,e>?'s2 = if x 7 n1 %e might be se5 z (t5 9 ,opposition to ! ,sun z 9 ,conjunction ) him2 b %e 0 nev] se5 #ij degrees1 or a f\r? "p ( a ,circle1 f ! ,sun4 ,sid5ote3 ,%e is our morn+ & ev5+ ,/> by turns4 #bh4 ,:5 ,v5us appe>s we/ ( ! ,sun %e rises be=e him 9 ! morn+1 & is call$ ! ,morn+ ,/>3 :5 %e appe>s ea/ ( ! ,sun %e %9es 9 ! ev5+ aft] he sets1 & is !n call$ ! ,ev5+ ,/>3 be+ ea* 9 x's turn = #bij days4 ,x may p]haps be surpris+ at fir/1 t ,v5us %\ld keep long] on ! ea/ or we/ ( ! ,sun ?an ! :ole "t ( h] ,p]iod r\nd him4 ,b ! difficulty vani%es :5 we consid] t ! ,e>? is all ! :ile go+ r\nd ! ,sun ! same way1 ?\gh n s quick z ,v5us3 & !re=e h] relative motion to ! ,e>? mu/ 9 e ,p]iod be z mu* sl[] ?an h] absolute motion 9 h] ,orbit1 z ! ,e>? dur+ t "t advances =w>d 9 ! ,ecliptic2 :i* is #bbj degrees4 ,to u %e appe>s ?r\gh a telescope 9 all ! v>i\s %apes ( ! ,moon4 #bi4 ,! ,axis ( ,v5us is incl9$ #ge degrees to ! ,axis ( h] ,orbit2 :i* is #ea-a_/b degrees m ?an our ,e>?'s ,axis is incl9$ to ! ,axis ( ! ,ecliptic3 & !re=e ! v>iation ( h] seasons is mu* great] ?an ( ours4 ,! ,nor? ,pole ( h] ,axis incl9es t[>d ! #bj? degree ( ,aqu>ius1 our ,e>?'s to ! beg9n+ ( ,canc]2 & !re=e ! nor!rn p>ts ( ,v5us h summ] 9 ! ,signs :]e ^? ( our ,e>? h w9t]1 & vice v]s4 ,sid5ote3 ,rem>kable appe>ances4 #cj4 ,! #f;artificial day at ea* ,pole ( ,v5us is z long z #aab-a_/b #gnatural days on our ,e>?4 ,sid5ote3 ,h] ,tropics & pol> ,circles1 h[ situat$4 #ca4 ,! ,sun's greate/ ,decl9ation on ea* side ( h] ,equator am\nts to #ge degrees2 !re=e h]#h ,tropics are only #ae degrees f h] ,poles2 & h] #i,pol> ,circles z f> f h] ,equator4 ,consequ5tly1 ! ,tropics ( ,v5us are betwe5 h] ,pol> ,circles & h] ,poles2 contr>y to :at ^? ( our ,e>? are4 ,sid5ote3 ,! ,sun's daily ,c\rse4 #cb4 ,z h] annual ,revolution conta9s only #i-a_/d ( h] days1 ! ,sun w always appe> to g ?r\gh a ,sign1 or twelf? ,"p ( h] ,orbit1 9 little m t ?ree qu>t]s ( h] natural day1 or ne>ly 9 #ah-c_/d ( our days & nights4 ,sid5ote3 ,& great decl9ation4 #cc4 ,because h] day is s great a "p ( h] ye>1 ! ,sun *anges 8 ,decl9ation 9 "o day s mu*1 t if he passes v]tically1 or directly ov] head ( any giv5 place on ! ,tropic1 ! next day he w be #bf degrees f x3 & :atev] place he passes v]tically ov] :5 9 ! ,equator1 "o day's revolution w remove him #cf-a_/d degrees f x4 ,s t ! ,sun *anges 8 ,decl9ation e day 9 ,v5us ab\t #ad degrees m at a mean rate1 ?an he does 9 a qu>t] ( a ye> on our ,e>?4 ,?is appe>s to be provid5tially ord]$1 = prev5t+ ! too great effects ( ! ,sun's heat 7:i* is twice z great on ,v5us z on ! ,e>?7 s t he _c %9e p]p5dicul>ly on ! same places = two days toge!r2 & by t means1 ! heat$ places h "t to cool4 ,sid5ote3 ,to det]m9e ! po9ts ( ! ,compass at h] ,poles4 #cd4 ,if ! inhabitants ab\t ! ,nor? ,pole ( ,v5us fix _! ,s\?1 or ,m]idian ,l9e1 ?r\gh t "p ( ! ,heav5s :]e ! ,sun comes to 8 greate/ ,height1 or ,nor? ,decl9ation1 & call ^? ! ,ea/ & ,we/ po9ts ( _! ,horizon1 :i* are #ij degrees on ea* side f t po9t :]e ! ,horizon is cut by ! ,m]idian ,l9e1 ^! inhabitants w h ! foll[+ rem>kables4 ,sid5ote3 ,surpris+ appe>ances at h] ,poles2 ,! ,sun w rise #bb-a_/b degrees#aj nor? ( ! ,ea/1 & go+ on #aab-a_/b degrees1 z measur$ on ! plane ( ! #aa;,horizon1 he w cross ! ,m]idian at an altitude ( #ab-a_/b degrees2 !n mak+ an entire revolution )\t sett+1 he w cross x aga9 at an altitude ( #dh-a_/b degrees2 at ! next revolution he w cross ! ,m]idian z he comes to 8 greate/ height & decl9ation1 at ! altitude ( #ge degrees2 be+ !n only #ae degrees f ! ,z5i?1 or t po9t ( ! ,heav5s :i* is directly ov] head3 & !nce he w desc5d 9 ! l spiral mann]2 cross+ ! ,m]idian fir/ at ! altitude ( #dh-a_/b degrees2 next at ! altitude ( #ab-a_/b degrees2 & go+ on !nce #aab-a_/b degrees1 he w set #bb-a_/b degrees nor? ( ! ,we/2 s t1 aft] hav+ be5 #d-e_/h revolutions above ! ,horizon1 he desc5ds bel[ x to exhibit ! l appe>ances at ! ,s\? ,pole4 #ce4 ,at ea* ,pole1 ! ,sun cont9ues half a ye> )\t sett+ 9 summ]1 & z long )\t ris+ 9 w9t]2 consequ5tly ! pol> inhabitants ( ,v5us h only "o day & "o night 9 ! ye>2 z x is at ! ,poles ( our ,e>?4 ,b ! diff]5ce betwe5 ! heat ( summ] & cold ( w9t]1 or ( mid-day & mid-night1 on ,v5us1 is mu* great] ?an on ! ,e>?3 because 9 ,v5us1 z ! ,sun is = half a ye> toge!r above ! ,horizon ( ea* ,pole 9 x's turn1 s he is = a consid]able "p ( t "t ne> ! ,z5i?2 & dur+ ! o!r half ( ! ye>1 always bel[ ! ,horizon1 & = a great "p ( t "t at lea/ #gj degrees f x4 ,:]eas1 at ! ,poles ( our ,e>?1 al?\gh ! ,sun is = half a ye> toge!r above ! ,horizon1 yet he nev] asc5ds above1 nor desc5ds bel[ x1 m ?an #bc-a_/b degrees4 ,:5 ! ,sun is 9 ! ,equ9octial1 or 9 t ,circle :i* divides ! nor!rn half ( ! ,heav5s f ! s\!rn1 he is se5 ) "o half ( 8 ,disc above ! ,horizon ( ! ,nor? ,pole1 & ! o!r half above ! ,horizon ( ! ,s\? ,pole2 s t 8 c5t] is 9 ! ,horizon ( bo? ,poles3 & !n desc5d+ bel[ ! ,horizon ( "o1 he asc5ds gradually above t ( ! o!r4 ,h5ce1 9 a ye>1 ea* ,pole has "o spr+1 "o h>ve/1 a summ] z long z !m bo?1 & a w9t] equal 9 l5g? to ! o!r ?ree seasons4 ,sid5ote3 ,at h] pol> ,circles2 #cf4 ,at ! ,pol> ,circles ( ,v5us1 ! seasons are mu* ! same z at ! ,equator1 because !re are only #ae degrees betwixt !m1 #ca2 only ! w9t]s are n q s long1 nor ! summ]s s %ort3 b ! f\r seasons come twice r\nd e ye>4 ,sid5ote3 ,at h] ,tropics2 #cg4 ,at ,v5us's ,tropics1 ! ,sun cont9ues = ab\t fifte5 ( our weeks toge!r )\t sett+ 9 summ]2 & z long )\t ris+ 9 w9t]4 ,:il/ he is m ?an #ae degrees f ! ,equator1 he nei!r rises to ! inhabitants ( ! "o ,tropic1 nor sets to ^? ( ! o!r3 :]eas1 at our t]re/rial ,tropics he rises & sets e day ( ! ye>4 #ch4 ,at ,v5us's ,tropics1 ! ,seasons are mu* ! same z at h] ,poles2 only ! summ]s are a little long]1 & ! w9t]s a little %ort]4 ,sid5ote3 ,at h] ,equator4 #ci4 ,at h] ,equator1 ! days & nights are always ( ! same l5g?2 & yet ! diurnal & nocturnal ,ar*es are v diff]5t1 especially :5 ! ,sun's decl9ation is ab\t ! greate/3 = !n1 8 m]idian altitude may sometimes be twice z great z 8 midnight depression1 & at o!r times ! rev]se4 ,:5 ! ,sun is at 8 greate/ ,decl9ation1 ei!r ,nor? or ,s\?1 8 rays are z oblique at ,v5us's ,equator1 z !y are at ,london on ! %orte/ day ( w9t]4 ,!re=e1 at h] ,equator !re are two w9t]s1 two summ]s1 two spr+s1 & two autumns e ye>4 ,b because ! ,sun /ays = "s "t ne> ! ,tropics1 & passes s quickly ov] ! ,equator1 e w9t] !re w be almo/ twice z long z summ]3 ! f\r seasons return+ twice 9 t "t1 :i* consi/s only ( #i-a_/d days4 #dj4 ,^? p>ts ( ,v5us :i* lie betwe5 ! ,poles & ,tropics1 & betwe5 ! ,tropics & ,pol> ,circles1 & also betwe5 ! ,pol> ,circles & ,equator1 p>take m or less ( ! ,ph5om5a ( ^! ,circles1 z !y are m or less di/ant f !m4 ,sid5ote3 ,great diff]5ce ( ! ,sun's amplitude at ris+ & sett+4 #da4 ,f ! quick *ange ( ! ,sun's decl9ation x happ5s1 t :5 he rises due ea/ on any day1 he w n set due we/ on t day1 z ) u2 = if ! place :]e he rises due ea/ be on ! ,equator1 he w set on t day almo/ we/-nor?-we/2 or ab\t #ah-a_/b degrees nor? ( ! we/4 ,b if ! place be 9 #de degrees nor? latitude1 !n on ! day t ! ,sun rises due ea/ he w set nor?-we/ by we/1 or #cc degrees nor? ( ! we/4 ,& 9 #fb degrees nor? latitude :5 he rises 9 ! ea/1 he sets n 9 t revolution1 b j t\*es ! ,horizon #aj degrees to ! we/ ( ! nor? po9t2 & asc5ds aga91 cont9u+ = #c-a_/d revolutions above ! ,horizon )\t sett+4 ,!re=e1 no place has ! =5oon & aft]noon ( ! same day equally long1 unless x be on ! ,equator or at ! ,poles4 ,sid5ote3 ,! longitude ( places easily f\nd 9 ,v5us4 #db4 ,! ,sun's altitude at noon1 or any o!r "t ( ! day1 & 8 amplitude at ris+ & sett+1 be+ s diff]5t at places on ! same p>allels ( latitude1 accord+ to ! diff]5t longitudes ( ^? places1 ! longitude w be almo/ z easily f\nd on ,v5us z ! latitude is f\nd on ! ,e>?3 :i* is an advantage we c nev] enjoy1 because ! daily *ange ( ! ,sun's decl9ation is by mu* too small = t purpose4 ,sid5ote3 ,h] ,equ9oxes %ift a qu>t] ( a day =w>d e ye>4 #dc4 ,on ?is ,planet1 :]ev] ! ,sun crosses ! ,equator 9 any ye>1 he w h #i degrees ( decl9ation f t place on ! same day & h\r next ye>2 & w cross ! ,equator #ij degrees f>!r to ! we/2 :i* makes ! "t ( ! ,equ9ox a qu>t] ( a day 7almo/ equal to six ( our days7 lat] e ye>4 ,h5ce1 al?\gh ! spiral 9 :i* ! ,sun's motion is p]=m$1 be ( ! same sort e ye>1 yet x w n be ! v same1 because ! ,sun w n pass v]tically ov] ! same places till f\r annual revolutions are f9i%$4 ,sid5ote3 ,e f\r? ye> a leap-ye> to ,v5us4 ,,plate ,i4 #dd4 ,we may suppose t ! inhabitants ( ,v5us w be c>eful to add a day to "s p>ticul> "p ( e f\r? ye>2 :i* w keep ! same seasons to ! same days4 ,=1 z ! great annual *ange ( ! ,equ9oxes & ,sol/ices %ifts ! seasons a qu>t] ( a day e ye>1 !y w\ld be %ift$ ?r\gh all ! days ( ! ye> 9 #cf ye>s4 ,b by means ( ?is int]cal>y day1 e f\r? ye> w be a leap-ye>2 :i* w br+ h] "t to an ev5 reckon+1 & keep h] ,cal5d> always "r4 ,sid5ote3 ,:5 %e w appe> on ! ,sun4 #de4 ,v5us's ,orbit is incl9$ #c-a_/b degrees to ! ,e>?'s2 & crosses x 9 ! #ad? degree ( ,gem9i & ( ,sagitt>ius2 & !re=e1 :5 ! ,e>? is ab\t ^! po9ts ( ! ,ecliptic at ! "t t ,v5us is 9 h] inf]i\r conjunction1 %e w appe> l a spot on ! ,sun1 & af=d a m c]ta9 me?od ( f9d+ ! di/ances ( all ! ,planets f ! ,sun ?an any o!r yet kn[n4 ,b ^! appe>ances happ5 v seldom2 & w only be ?rice visible at ,london = ?ree hundr$ ye>s to come4 ,! fir/ "t w be 9 ! ye> #agfa1 ,june ! #f?1 at #e h\rs #ee m9utes 9 ! morn+4 ,! second #aiif1 ,june ! #i?1 at #b h\rs #ac m9utes 9 ! aft]noon4 ,& ! ?ird 9 ! ye> #bjjd1 ,june ! #f?1 at #g h\rs #ah m9utes 9 ! =5oon4 ,except+ su* ,transits z ^!1 %e %ews ! same appe>ances to u regul>ly e eight ye>s2 h] ,conjunctions1 ,elongations1 & ,times ( ris+ & sett+ be+ v ne>ly ! same1 on ! same days1 z be=e4 ,sid5ote3 ,%e may h a ,moon al?\gh we _c see x4 #df4 ,v5us may h a ,satellite or ,moon1 al?\gh x be undiscov]$ by u3 :i* w n appe> v surpris+1 if we consid] h[ inconv5i5tly we are plac$ = see+ x4 ,= x's enlight5$ side c nev] be fully turn$ t[>ds u b :5 ,v5us is beyond ! ,sun2 & !n1 z ,v5us appe>s little bigg] ?an an ord9>y ,/>1 h] ,moon may be too small to be p]ceptible at su* a di/ance4 ,:5 %e is betwe5 u & ! ,sun1 h] full ,moon has x's d>k side t[>ds u2 & !n1 we _c see x any m ?an we c our own ,moon at ! "t ( ,*ange4 ,:5 ,v5us is at h] greate/ ,elongation1 we h b "o half ( ! enlight5$ side ( h] ,full ,moon t[>ds u2 & ev5 !n x may be too f> di/ant to be se5 by u4 ,b if %e has a ,moon1 x may c]ta9ly be se5 ) h] ^u ! ,sun1 9 ! ye> #agfa1 unless x's ,orbit be consid]ably incl9$ to ! ,ecliptic3 = if x %\ld be 9 conjunction or opposition at t "t1 we c h>dly imag9e t x moves s sl[ z to be hid by ,v5us all ! six h\rs t %e w appe> on ! ,sun's ,disc4 ,sid5ote3 ,! ,e>?4 ,fig4 ,i4 ,x's diurnal & annual motion4 #dg4 ,! ,,e>? is ! next ,planet above ,v5us 9 ! ,sy/em4 ,x is #ha millions ( miles f ! ,sun1 & goes r\nd him 7z 9 ! circle 7 9 #cfe days #e h\rs #di m9utes1 f any ,equ9ox or ,sol/ice to ! same aga93 b f any fix$ ,/> to ! same aga91 z se5 f ! ,sun1 9 #cfe days #f h\rs & #i m9utes2 ! =m] be+ ! l5g? ( ! ,tropical ye>1 & ! latt] ! l5g? ( ! ,sid]eal4 ,x travels at ! rate ( #eh ?\s& miles e h\r1 :i* motion1 ?\gh #abj times swift] ?an t ( a cannon ball1 is little m ?an half z swift z ,m]cury's motion 9 8 ,orbit4 ,! ,e>?'s diamet] is #gigj miles2 & by turn+ r\nd x's ,axis e #bd h\rs f ,we/ to ,ea/1 x causes an app>5t diurnal motion ( all ! heav5ly ,bodies f ,ea/ to ,we/4 ,by ?is rapid motion ( ! ,e>? on x's ,axis1 ! inhabitants ab\t ! ,equator are c>ri$ #ajdb miles e h\r1 :il/ ^? on ! p>allel ( ,london are c>ri$ only ab\t #ehj1 besides ! #eh ?\s& miles by ! annual motion above-m5tion$1 :i* is common to all places :atev]4 ,sid5ote3 ,incl9ation ( x's ,axis4 #dh4 ,! ,e>?'s ,axis makes an angle ( #bc-a_/b degrees ) ! ,axis ( x's ,orbit2 & keeps always ! same oblique direction2 incl9+ t[>ds ! same fix$ ,/>s#ab ?r\gh\t x's annual c\rse2 :i* causes ! returns ( spr+1 summ]1 autumn1 & w9t]2 z w be expla9$ at l>ge 9 ! t5? ,*apt]4 ,sid5ote3 ,a pro( ( x's be+ r\nd4 #di4 ,! ,e>? is r\nd l a globe2 z appe>s1 #a4 f x's %ad[ 9 ,eclipses ( ! ,moon2 :i* %ad[ is always b\nd$ by a circul> l9e #cad4 #b4 ,f our see+ ! ma/s ( a %ip :il/ ! hull is hid by ! convexity ( ! wat]4 #c4 ,f x's hav+ be5 sail$ r\nd by _m navigators4 ,! hills take (f no m f ! r\ndness ( ! ,e>? 9 comp>ison1 ?an gra9s ( du/ d f ! r\ndness ( a common ,globe4 ,sid5ote3 ,x's numb] ( squ>e miles4 #ej4 ,! seas & unkn[n p>ts ( ! ,e>? 7by a measurem5t ( ! be/ ,maps7 conta9 #afj million #ebb ?\s& & #bf squ>e miles2 ! inhabit$ p>ts #ch million #iij ?\s& #efi3 ,europe #d million #def ?\s& & #fe2 ,asia #aj million #gfh ?\s& #hbc2 ,africa #i million #fed ?\s& #hjg2 ,am]ica #ad million #aaj ?\s& #hgd4 ,9 all1 #aii million #eab ?\s& #eie2 :i* is ! numb] ( squ>e miles on ! :ole surface ( our ,globe4 ,sid5ote3 ,! proportion ( l& & sea4 ,,plate ,i4 #ea4 ,dr4 ,,long1 9 ! fir/ volume ( 8 ,a/ronomy1 pag4 #afh1 m5tions an +5i\s & easy me?od ( f9d+ ne>ly :at proportion ! l& be>s to ! sea2 :i* is1 to take ! pap]s ( a l>ge t]re/rial globe1 & aft] sep>at+ ! l& f ! sea ) a pair ( sciss>s1 to weigh !m c>efully 9 scales4 ,?is supposes ! globe to be exactly del9eat$1 & ! pap]s all ( equal ?ickness4 ,! ,doctor made ! exp]im5t on ! pap]s ( ,mr4 ,,s5ex's sev5te5 in* globe2 & f\nd t ! sea pap]s weigh$ #cdi gra9s1 & ! l& only #abd3 by :i* x appe>s t almo/ ?ree f\r? p>ts ( ! surface ( our ,e>? betwe5 ! ,pol> ,circles are cov]$ ) wat]1 & t little m ?an "o f\r? is dry l&4 ,! ,doctor omitt$ weigh+ all )9 ! ,pol> ,circles2 because !re is no c]ta9 measurem5t ( ! l& !re1 s z to "k :at proportion x be>s to ! sea4 ,sid5ote3 ,! ,moon4 #eb4 ,! ,,moon is n a ,planet1 b only a ,satellite or ,att5dant ( ! ,e>?1 mov+ r\nd ! ,e>? f ,*ange to ,*ange 9 #bi days #ab h\rs & #dd m9utes2 & go+ r\nd ! ,sun ) x e ye>4 ,! ,moon's diamet] is #bahj miles2 & h] di/ance f ! ,e>? #bdj ?\s&4 ,%e goes r\nd h] ,orbit 9 #bg days #g h\rs #dc m9utes1 mov+ ab\t #bbij miles e h\r2 & turns r\nd h] ,axis exactly 9 ! "t t %e goes r\nd ! ,e>?1 :i* is ! reason ( h] keep+ always ! same side t[>ds u1 & t h] day & night tak5 toge!r is z long z our lun> mon?4 ,sid5ote3 ,h] ,phases4 #ec4 ,! ,moon is an opaque ,globe l ! ,e>?1 & %9es only by reflect+ ! light ( ! ,sun3 !re=e :il/ t half ( h] :i* is t[>d ! ,sun is enlight5$1 ! o!r half mu/ be d>k & invisible4 ,h5ce1 %e disappe>s :5 %e comes betwe5 u & ! ,sun2 because h] d>k side is !n t[>d u4 ,:5 %e is gone a little way =w>d1 we see a little ( h] enlight5$ side2 :i* /ill increases to our view1 z %e advances =w>d1 until %e comes to be opposite to ! ,sun2 & !n h] :ole enlight5$ side is t[>ds ! ,e>?1 & %e appe>s ) a r\nd1 illum9$ ,orb2 :i* we call ! ,full ,moon3 h] d>k side be+ !n turn$ away f ! ,e>?4 ,f ! ,full %e seems to decrease gradually z %e goes ?r\gh ! o!r half ( h] c\rse2 %ew+ u less & less ( h] enlight5$ side e day1 till h] next *ange or conjunction ) ! ,sun1 & !n %e disappe>s z be=e4 ,sid5ote3 ,a pro( t %e %9es n by h] own light4 ,fig4 ,i4 #ed4 ,! cont9ual *ang+ ( ! ,moon's phases or %apes demon/rates t %e %9es n by any light ( h] own3 = if %e did1 be+ globul>1 we %\ld always see h] ) a r\nd full ,orb l ! ,sun4 ,h] ,orbit is repres5t$ 9 ! ,s*eme by ! little circle m1 ^u ! ,e>?'s ,orbit 3 b x is drawn fifty times too l>ge 9 proportion to ! ,e>?'s2 & yet is almo/ too small to be se5 9 ! ,diagram4 ,sid5ote3 ,"o half ( h] always enlight5$4 #ee4 ,! ,moon has sc>ce any diff]5ce ( seasons2 h] ,axis be+ almo/ p]p5dicul> to ! ,ecliptic4 ,:at is v s+ul>1 "o half ( h] has no d>kness at all2 ! ,e>? con/antly af=d+ x a /rong light 9 ! ,sun's abs5ce2 :ile ! o!r half has a =tnight's d>kness & a =tnight's light by turns4 ,sid5ote3 ,our ,e>? is h] ,moon4 #ef4 ,our ,e>? is a ,moon to ! ,moon1 wax+ & wane+ regul>ly1 b appe>+ ?irte5 times z big1 & af=d+ h] ?irte5 times z mu* light1 z %e does to u4 ,:5 %e *anges to u1 ! ,e>? appe>s full to h]2 & :5 %e is 9 h] fir/ qu>t] to u1 ! ,e>? is 9 x's ?ird qu>t] to h]2 & vice v]s4 #eg4 ,b f "o half ( ! ,moon1 ! ,e>? is nev] se5 at all3 f ! middle ( ! o!r half1 x is always se5 ov] head2 turn+ r\nd almo/ ?irty times z quick z ! ,moon does4 ,f ! l9e :i* limits our view ( ! ,moon1 or all r\nd :at we call h] edges1 only "o half ( ! ,e>?'s side next h] is se52 ! o!r half be+ hid bel[ ! ,horizon4 ,to h]1 ! ,e>? seems to be ! bigge/ ,body 9 ! ,univ]se2 = x appe>s ?irte5 times z big z %e does to u4 ,sid5ote3 ,a ,pro( ( ! ,moon's hav+ no ,atmosph]e2 #eh4 ,! ,moon has no su* ,atmosph]e1 or body ( air surr\nd+ h] z we h3 = if %e _h1 we c\ld nev] see h] edge s well def9$ z x appe>s2 b !re w\ld be a sort ( a mi/ or haz9ess r\nd h]1 :i* w\ld make ! ,/>s look fa9t]1 :5 !y 7 se5 ?r\gh x4 ,b obs]vation proves1 t ! ,/>s :i* disappe> beh9d ! ,moon reta9 _! full lu/re until !y seem to t\* h] v edge1 & !n vani% 9 a mom5t4 ,?is has be5 (t5 obs]v$ by ,a/ronom]s1 b p>ticul>ly by ,,cass9i#ac ( ! ,/> 9 ! brea/ ( ,virgo1 :i* appe>s s+le & r\nd to ! b>e eye2 b ?r\gh a refract+ ,telescope ( #af feet appe>s to be two ,/>s s ne> toge!r1 t ! di/ance betwe5 !m seems to be b equal to "o ( _! app>5t diamet]s4 ,! ,moon 0 obs]v$ to pass ov] !m on ! #ba/ ( ,april #agbj1 ,n4 ,s4 & z h] d>k edge drew ne> to !m1 x caus$ no *ange 9 _! col\r or ,situation4 ,at #be m94 #ad sec4 pa/ #ab at night1 ! mo/ we/]ly ( ^! ,/>s 0 hid by ! d>k edge ( ! ,moon2 & 9 #cj seconds aft]w>d1 ! mo/ ea/]ly ,/> 0 hid3 ea* ( !m disappe>+ beh9d ! ,moon 9 an in/ant1 )\t any prec$+ dim9ution ( magnitude or brightness2 :i* by no means c\ld h be5 ! case if !re 7 an ,atmosph]e r\nd ! ,moon2 = !n1 "o ( ! ,/>s fall+ obliquely into x be=e ! o!r1 ought by refraction to h suff]$ "s *ange 9 its col\r1 or 9 x's di/ance f ! o!r ,/> :i* 0 n yet ent]$ into ! ,atmosph]e4 ,b no su* alt]ation c\ld be p]ceiv$ ?\gh ! obs]vation 0 p]=m$ ) ! utmo/ att5tion to t p>ticul>2 & 0 v prop] to h made su* a discov]y4 ,! fa9t light1 :i* has be5 se5 all ar\nd ! ,moon1 9 total ,eclipses ( ! ,sun1 has be5 obs]v$1 dur+ ! "t ( d>kness1 to h x's c5t] co9cid5t ) ! c5t] ( ! ,sun2 & is !re=e mu* m likely to arise f ! ,atmosph]e ( ! ,sun ?an f t ( ! ,moon2 = if x 7 ! latt]1 x's c5t] w\ld h gone along ) ! ,moon's4 ,sid5ote3 ,nor ,seas4 ,%e is full ( cav]ns & deep pits4 #ei4 ,if !re 7 seas 9 ! ,moon1 %e c\ld h no cl\ds1 ra9s1 nor /orms z we h2 because %e has no su* ,atmosph]e to support ! vap\rs :i* occasion !m4 ,& e "o kn[s1 t :5 ! ,moon is above our ,horizon 9 ! night "t1 %e is visible1 unless ! cl\ds ( our ,atmosph]e hide h] f our view2 & all p>ts ( h] appe> con/antly ) ! same cle>1 s]5e1 & calm aspect4 ,b ^? d>k p>ts ( ! ,moon1 :i* 7 =m]ly ?\ght to be seas1 are n[ f\nd to be only va/ deep cavities1 & places :i* reflect n ! ,sun's light s /rongly z o!rs1 hav+ _m cav]ns & pits ^: %ad[s fall )9 !m1 & are always d>k on ! sides next ! ,sun2 :i* demon/rates _! be+ holl[3 & mo/ ( ^! pits h little knobs l hillocks /&+ )9 !m1 & ca/+ %ad[s also2 :i* cause ^! places to appe> d>k] ?an o!rs :i* h few]1 or less rem>kable cav]ns4 ,all ^! appe>ances %ew t !re are no seas 9 ! ,moon2 = if !re 7 any1 _! surfaces w\ld appe> smoo? & ev51 l ^? on ! ,e>?4 ,sid5ote3 ,! ,/>s always visible to ! ,moon4 #fj4 ,!re be+ no ,atmosph]e ab\t ! ,moon1 ! ,heav5s 9 ! day "t h ! appe>ance ( night to a ,lun>ian :o turns 8 back t[>d ! ,sun2 & :5 he does1 ! ,/>s appe> z bright to him z !y d 9 ! night to u4 ,=1 x is entirely ow+ to our ,atmosph]e t ! ,heav5s are bright ab\t u 9 ! day4 ,sid5ote3 ,! ,e>? a ,dial to ! ,moon4 #fa4 ,z ! ,e>? turns r\nd x's ,axis1 ! sev]al cont95ts1 seas1 & isl&s appe> to ! ,moon's inhabitants l s _m spots ( diff]5t =ms & brightness1 mov+ ov] x's surface2 b mu* fa9t] at "s times ?an o!rs1 z our cl\ds cov] !m or leave !m4 ,by ^! spots ! ,lun>ians c det]m9e ! "t ( ! ,e>?'s diurnal motion1 j z we d ! motion ( ! ,sun3 & p]haps !y measure _! "t by ! motion ( ! ,e>?'s spots2 = !y _c h a tru] dial4 ,sid5ote3 ,,plate ,i4 ,h[ ! ,lun>ians may "k ! l5g? ( _! ye>4 #fb4 ,! ,moon's ,axis is s ne>ly p]p5dicul> to ! ,ecliptic1 t ! ,sun nev] removes s5sibly f h] ,equator3 & !#ad obliquity ( h] ,orbit1 :i* is next to no?+ z se5 f ! ,sun1 _c cause any s5sible decl9ation ( ! ,sun f h] ,equator4 ,yet h] inhabitants are n de/itute ( means = det]m9+ ! l5g? ( _! ye>1 ?\gh _! me?od & ours mu/ diff]4 ,= we c "k ! l5g? ( our ye> by ! return ( our ,equ9oxes2 b ! ,lun>ians1 hav+ always equal day & night1 mu/ h rec\rse to ano!r me?od2 & we may suppose1 !y measure _! ye> by obs]v+ ! ,poles ( our ,e>?2 z "o always beg9s to be enlight5$1 & ! o!r disappe>s1 at our ,equ9oxes2 !y be+ conv5i5tly situat$ = obs]v+ great tracks ( l& ab\t our ,e>?'s ,poles1 :i* are entirely unkn[n to u4 ,h5ce we may conclude1 t ! ye> is ( ! same absolute l5g? bo? to ! ,e>? & ,moon1 ?\gh v diff]5t z to ! numb] ( days3 we hav+ #cfe-a_/d natural days1 & ! ,lun>ians only #ab-g_/ai2 e day & night 9 ! ,moon be+ z long z #bi-a_/b on ! ,e>?4 ,sid5ote3 ,& ! longitudes ( _! places4 #fc4 ,! ,moon's inhabitants on ! side next ! ,e>? may z easily f9d ! longitude ( _! places z we c f9d ! latitude ( ours4 ,= ! ,e>? keep+ con/antly1 or v ne>ly s1 ov] "o ,m]idian ( ! ,moon1 ! ea/ or we/ di/ances ( places f t ,m]idian are z easily f\nd1 z we c f9d our di/ance f ! ,equator by ! ,altitude ( our cele/ial ,poles4 ,sid5ote3 ,m>s4 ,fig4 ,i4 #fd4 ,! ,planet ,,m>s is next 9 ord]1 be+ ! fir/ above ! ,e>?'s ,orbit4 ,8 di/ance f ! ,sun is comput$ to be #abc millions ( miles2 & by travell+ at ! rate ( #dg ?\s& miles e h\r1 z 9 ! circle 1 he goes r\nd ! ,sun 9 #fhg ( our days & #ag h\rs2 :i* is ! l5g? ( 8 ye>1 & conta9s #ffg-a_/d ( 8 days2 e day & night toge!r be+ #dj m9utes long] ?an ) u4 ,8 diamet] is #dddd miles1 & by 8 diurnal rotation ! inhabitants ab\t 8 ,equator are c>ri$ #eef miles e h\r4 ,8 quantity ( light & heat is equal b to "o half ( ours2 & ! ,sun appe>s b half z big to him z to u4 ,sid5ote3 ,8 ,atmosph]e & ,phases4 #fe4 ,?is ,planet be+ b a fif? "p s big z ! ,e>?1 if any ,moon att5ds him1 %e mu/ be v small1 & has n yet be5 discov]$ by our be/ telescopes4 ,he is ( a fi]y r$ col\r1 & by 8 ,appulses to "s ( ! fix$ ,/>s1 seems to be surr\nd$ by a v gross ,atmosph]e4 ,he appe>s sometimes gibb\s1 b nev] horn$2 :i* bo? %ews t 8 ,orbit includes ! ,e>?'s )9 x1 & t he %9es n by 8 own light4 #ff4 ,to ,m>s1 our ,e>? & ,moon appe> l two ,moons1 a bigg] & a less2 *ang+ places ) "o ano!r1 & appe>+ sometimes horn$1 sometimes half or ?ree qu>t]s illum9at$1 b nev] full2 nor at mo/ above a qu>t] ( a degree f ea* o!r1 al?\gh !y are #bdj ?\s& miles asund]4 ,sid5ote3 ,,plate ,i4 ,h[ ! o!r ,planets appe> to ,m>s4 #fg4 ,our ,e>? appe>s almo/ z big to ,m>s z ,v5us does to u1 & at ,m>s x is nev] se5 above #dh degrees f ! ,sun2 sometimes x appe>s to pass ov] ! ,disc ( ! ,sun1 & s d ,m]cury & ,v5us3 b ,m]cury c nev] be se5 f ,m>s by su* eyes z ours1 unassi/$ by prop] in/rum5ts2 & ,v5us w be z seldom se5 z we see ,m]cury4 ,jupit] & ,saturn are z visible to ,m>s z to u4 ,8 ,axis is p]p5dicul> to ! ,ecliptic1 & 8 ,orbit is #b degrees incl9$ to x4 ,sid5ote3 ,jupit]4 ,fig4 ,i4 #fh4 ,,jupit]1 ! bigge/ ( all ! ,planets1 is /ill high] 9 ! ,sy/em1 be+ ab\t #dbd millions ( miles f ! ,sun3 & go+ at ! rate ( #be ?\s& miles e h\r 9 8 ,orbit1 z 9 ! circle f9i%es 8 annual p]iod 9 elev5 ( our ye>s #cad days & #ah h\rs4 ,he is above #ajjj times z big z ! ,e>?1 = 8 diamet] is #ha1jjj miles2 :i* is m ?an t5 times ! diamet] ( ! ,e>?4 ,sid5ote3 ,! numb] ( days 9 8 ye>4 #fi4 ,jupit] turns r\nd 8 ,axis 9 #i h\rs #ef m9utes2 s t 8 ye> conta9s #aj ?\s& #dfd days2 & ! diurnal velocity ( 8 equatoreal p>ts is great] ?an ! swiftness ) :i* he moves 9 8 annual ,orbit2 a s+ul> circum/ance1 z f> z we "k4 ,by ?is prodigi\s quick ,rotation1 8 equatoreal inhabitants are c>ri$ #be ?\s& #ibj miles e h\r 7:i* is #ibj miles an h\r m ?an an inhabitant ( our ,e>? moves 9 tw5ty-f\r h\rs7 besides ! #be ?\s& above-m5tion$1 :i* is common to all p>ts ( 8 surface1 by 8 annual motion4 ,sid5ote3 ,8 ,belts & spots4 #gj4 ,jupit] is surr\nd$ by fa9t sub/ances1 call$ ,belts1 9 :i* s _m *anges appe>1 t !y are g5]ally ?\ght to be cl\ds3 = "s ( !m h be5 fir/ int]rupt$ & brok51 & !n h vani%$ entirely4 ,!y h sometimes be5 obs]v$ ( diff]5t bread?s1 & aft]w>ds h all become ne>ly ( ! same bread?4 ,l>ge spots h be5 se5 9 ^! ,belts2 & :5 a ,belt vani%es1 ! contigu\s spots disappe> ) x4 ,! brok5 ends ( "s ,belts h be5 g5]ally obs]v$ to revolve 9 ! same "t ) ! spots2 only ^? ne>] ! ,equator 9 some:at less "t ?an ^? ne> ! ,poles2 p]haps on acc\nt ( ! ,sun's great] heat ne> ! ,equator1 :i* is p>allel to ! ,belts & c\rse ( ! spots4 ,sev]al l>ge spots1 :i* appe> r\nd at "o "t1 gr[ oblong by degrees1 & !n divide into two or ?ree r\nd spots4 ,! p]iodical "t ( ! spots ne> ! ,equator is #i h\rs #ej m9utes1 b ( ^? ne> ! ,poles #i h\rs #ef m9utes4 ,see ,dr4 ,,smi?'s ,optics1 #ajjd seq4 ,sid5ote3 ,he has no *ange ( seasons2 #ga4 ,! ,axis ( ,jupit] is s ne>ly p]p5dicul> to 8 ,orbit1 t he has no s5sible *ange ( seasons2 :i* is a great advantage1 & wisely ord]$ by ! ,au?or ( ,nature4 ,=1 if ! ,axis ( ?is ,planet 7 incl9$ any consid]able numb] ( degrees1 j s _m degrees r\nd ea* ,pole w\ld 9 _! turn be almo/ six ( our ye>s toge!r 9 d>kness4 ,&1 z ea* degree ( a great ,circle on ,jupit] conta9s #gjf ( our miles at a mean rate1 x is easy to judge :at va/ tracts ( l& w\ld be r5d]$ un9habitable by any consid]able incl9ation ( 8 ,axis4 ,sid5ote3 ,b has f\r ,moons4 #gb4 ,! ,sun appe>s b #a_/bh "p s big to ,jupit] z to u2 & 8 light & heat are 9 ! same small proportion1 b comp5sat$ by ! quick returns !re(1 & by f\r ,moons 7"s bigg] & "s less ?an our ,e>?7 :i* revolve ab\t him3 s t !re is sc>ce any "p ( ?is huge ,planet b :at is dur+ ! :ole night enlight5$ by "o or m ( ^! ,moons1 except 8 ,poles1 :5ce only ! f>!/ ,moons c be se51 & :]e _! light is n want$1 because ! ,sun con/antly circulates 9 or ne> ! ,horizon1 & is v probably kept 9 view ( bo? ,poles by ! ,refraction ( ,jupit]'s ,atmosph]e1 :i*1 if x be l ours1 has c]ta9ly refractive p[] en\gh = t purpose4 ,sid5ote3 ,_! p]iods r\nd ,jupit]4 ,_! gr& p]iod4 #gc4 ,! ,orbits ( ^! ,moons are repres5t$ 9 ! ,s*eme ( ! ,sol> ,sy/em by f\r small circles m>k$ #a4 #b4 #c4 #d4 on ,jupit]'s ,orbit 2 b are drawn fifty times too l>ge 9 proportion to x4 ,! fir/ ,moon1 or t ne>e/ to ,jupit]1 goes r\nd him 9 #a day #ah h\rs & #cf m9utes ( our "t2 & is #bbi ?\s& miles di/ant f 8 c5t]3 ,! second p]=ms x's revolution 9 ?ree days #ac h\rs & #ae m9utes1 at #cfd ?\s& miles di/ance3 ,! ?ird 9 #g days ?ree h\rs & #ei m9utes1 at ! di/ance ( #ehj ?\s& miles3 ,& ! f\r?1 or out]mo/1 9 #af days #ah h\rs & #cj m9utes1 at ! di/ance ( "o million ( miles f 8 c5t]4 ,! ,p]iods ( ^! ,moons are s incomm5surate to "o ano!r1 t if ev] !y 7 all 9 a "r l9e betwe5 ,jupit] & ! ,sun1 x w require m ?an #c1jjj1jjj1jjj1jjj ye>s f t "t to br+ !m all into ! same "r l9e aga91 z any "o w f9d :o r$uces all _! p]iods into seconds1 !n multiplies !m into "o ano!r1 & divides ! product by #dcb2 :i* is ! highe/ numb] t w divide ! product ( all _! p]iodical times1 namely #db1jhe1cjc1cgf1ica1iid1iee1ijd seconds1 )\t a rema9d]4 ,sid5ote3 ,p>allax ( _! ,orbits1 & di/ances f ,jupit]4 ,,plate ,i4 ,h[ he appe>s to 8 ne>e/ ,moon4 #gd4 ,! ,angles "u :i* ! ,orbits ( ,jupit]'s ,moons are se5 f ! ,e>?1 at x's mean di/ance f ,jupit]1 are z foll[3 ,! fir/1 #c #ee2 ! second1 #f #ad2 ! ?ird1 #i #eh2 & ! f\r?1 #ag #cj4 ,& _! di/ances f ,jupit]1 measur$ by 8 semidiamet]s1 are ?us3 ,! fir/1 #e-b_/c2 ! second1 #i2 ! ?ird4 #ad-bc_/fj2 & ! f\r?1 #be-ah_/fjae4 ,?is ,planet1 se5 f x's ne>e/ ,moon1 appe>s #ajjj times z l>ge z our ,moon does to u2 wax+ & wane+ 9 all h] mon?ly %apes1 e #db-a_/b h\rs4 ,sid5ote3 ,two gr& discov]ies made by ! ,eclipse ( ,jupit]'s ,moons4 #ge4 ,jupit]'s ?ree ne>e/ ,moons fall into 8 %ad[1 & are eclips$ 9 e ,revolution3 b ! ,orbit ( ! f\r? ,moon is s mu* incl9$1 t x passe? by ,jupit]1 )\t fall+ into 8 %ad[1 two ye>s 9 e six4 ,by ^! ,eclipses1 ,a/ronom]s h n only discov]$ t ! ,sun's light comes to u 9 eight m9utes2 b h also det]m9$ ! longitudes ( places on ?is ,e>? ) great] c]ta9ty & facility ?an by any o!r me?od yet kn[n2 z %all be expla9$ 9 ! elev5? ,*apt]4 ,sid5ote3 ,! great diff]5ce betwe5 ! ,equatoreal & ,pol> diamet]s ( ,jupit]4 ,! diff]5ce little 9 ^? ( our ,e>?4 #gf4 ,! diff]5ce betwe5 ! ,equatoreal & ,pol> diamet]s ( ,jupit] is #fbcj miles2 = 8 equatoreal diamet] is to 8 pol> z #ac to #ab4 ,s t 8 ,poles are #caae miles ne>] 8 c5t] ?an 8 ,equator is4 ,?is results f 8 quick motion r\nd 8 ,axis2 = ! fluids1 toge!r ) ! light p>ticles1 :i* !y c c>ry or wa% away ) !m1 rec$e f ! ,poles :i* are at re/1 t[>ds ! ,equator :]e ! motion is quicke/1 until !re be a suffici5t numb] accumulat$ to make up ! defici5cy ( gravity occasion$ by ! c5trifugal =ce1 :i* always arises f a quick motion r\nd an axis3 & :5 ! weight is made up s1 z t all p>ts ( ! surface press equally heavy t[>d ! c5t]1 !re is an equilibrium1 & ! equatoreal p>ts rise no high]4 ,our ,e>? be+ b a v small ,planet1 comp>$ to ,jupit]1 & x's motion on x's ,axis be+ mu* sl[]1 x is less flatt5$ ( c\rse2 = ! diff]5ce betwe5 x's equatoreal & pol> diamet]s is only z #bcj to #bbi1 or #ce miles4 ,sid5ote3 ,place ( 8 ,nodes4 #gg4 ,jupit]'s ,orbit is #a degree #bj m9utes incl9$ to ! ,ecliptic4 ,8 ,nor? ,node is 9 ! #g? degree ( ,canc]1 & 8 ,s\? ,node 9 ! #g? degree ( ,capricorn4 ,sid5ote3 ,saturn4 ,fig4 ,i4 #gh4 ,,saturn1 ! remote/ ( all ! ,planets1 is ab\t #ggg millions ( miles f ! ,sun2 &1 travell+ at ! rate ( #ah ?\s& miles e h\r1 z 9 ! circle m>k$ 1 p]=ms 8 annual circuit 9 #bi ye>s #afg days & #e h\rs ( our "t2 :i* makes only "o ye> to t ,planet4 ,8 diamet] is #fg1jjj miles2 & !re=e he is ne> #fjj times z big z ! ,e>?4 ,sid5ote3 ,fig4 ,v4 ,8 ,r+4 ,,plate ,i4 #gi4 ,he is surr\nd$ by a ?9 broad ,r+1 z an artificial ,globe is by its ,horizon4 ,?is ,r+ appe>s d\ble :5 se5 ?r\gh a good telescope1 & is repres5t$ by ! figure 9 su* an oblique view z x is g5]ally se54 ,x is incl9$ #cj degrees to ! ,ecliptic1 & is ab\t #ba ?\s& miles 9 bread?2 :i* is equal to x's di/ance f ,saturn on all sides4 ,!re is reason to believe t ! ,r+ turns r\nd x's ,axis1 because1 :5 x is almo/ edge-wise to u1 x appe>s some:at ?ick] on "o side ( ! ,planet ?an on ! o!r2 & ! ?icke/ edge has be5 se5 on diff]5t sides at diff]5t times4 ,b ,saturn hav+ no visible spots on 8 body1 :]eby to det]m9e ! "t ( 8 turn+ r\nd 8 ,axis1 ! l5g? ( 8 days & nights1 & ! position ( 8 ,axis1 are unkn[n to u4 ,sid5ote3 ,8 five ,moons4 ,fig4 ,i4 #hj4 ,to ,saturn1 ! ,sun appe>s only #a_/ij? "p s big z to u2 & ! light & heat he receives f ! ,sun are 9 ! same proportion to ours4 ,b to comp5sate = ! small quantity ( sun-light1 he has five ,moons1 all go+ r\nd him on ! outside ( 8 ,r+1 & ne>ly 9 ! same plane ) x4 ,! fir/1 or ne>e/ ,moon to ,saturn1 goes r\nd him 9 #a day #ba h\rs #ai m9utes2 & is #adj ?\s& miles f 8 c5t]3 ,! second1 9 two days #ag h\rs #dj m9utes2 at ! di/ance ( #ahg ?\s& miles3 ,! ?ird1 9 #d days #ab h\rs #be m9utes2 at #bfc ?\s& miles di/ance3 ,! f\r?1 9 #ae days #bb h\rs #da m9utes2 at ! di/ance ( #fjj ?\s& miles3 ,& ! fif?1 or out]mo/1 at "o million #hjj ?\s& miles f ,saturn's c5t]1 goes r\nd him 9 #gi days #g h\rs #dh m9utes4 ,_! ,orbits 9 ! ,s*eme ( ! ,sol> ,sy/em are repres5t$ by ! five small circles1 m>k$ #a4 #b4 #c4 #d4 #e4 on ,saturn's ,orbit2 b ^!1 l ! ,orbits ( ! o!r ,satellites1 are drawn fifty times too l>ge 9 proportion to ! ,orbits ( _! ,prim>y ,planets4 ,sid5ote3 ,8 ,axis probably incl9$ to 8 ,r+4 #ha4 ,! ,sun %9es almo/ fifte5 ( our ye>s toge!r on "o side ( ,saturn's ,r+ )\t sett+1 & z long on ! o!r 9 x's turn4 ,s t ! ,r+ is visible to ! inhabitants ( t ,planet = almo/ fifte5 ( our ye>s1 & z long invisible by turns1 if x's ,axis has no ,incl9ation to x's ,r+3 b if ! ,axis ( ! ,planet be incl9$ to ! ,r+1 suppose ab\t #cj degrees1 ! ,r+ w appe> & disappe> once e natural day to all ! inhabitants )9 #cj degrees ( ! ,equator1 on bo? sides1 frequ5tly eclips+ ! ,sun 9 a ,saturnian day4 ,moreov]1 if ,saturn's ,axis be s incl9$ to 8 ,r+1 x is p]p5dicul> to 8 ,orbit2 & !reby ! inconv5i5ce ( diff]5t seasons to t ,planet is avoid$4 ,= consid]+ ! l5g? ( ,saturn's ye>1 :i* is almo/ equal to ?irty ( ours1 :at a dreadful condition mu/ ! inhabitants ( 8 ,pol> regions be 91 if !y be half ( t "t depriv$ ( ! light & heat ( ! ,sun8 :i* mu/ n be _! case alone1 if ! ,axis ( ! ,planet be p]p5dicul> to ! ,r+1 b also ! ,r+ mu/ hide ! ,sun f va/ tracks ( l& on ea* side ( ! ,equator = #ac or #ad ( our ye>s toge!r1 on ! s\? side & nor? side by turns1 z ! ,axis incl9es to or f ! ,sun3 ! rev]se ( :i* inconv5i5ce is ano!r good presumptive pro( ( ! ,incl9ation ( ,saturn's ,axis to x's ,r+1 & also ( 8 ,axis be+ p]p5dicul> to 8 ,orbit4 ,sid5ote3 ,h[ ! ,r+ appe>s to ,saturn & to u4 ,9 :at ,signs ,saturn appe>s to lose 8 ,r+2 & 9 :at ,signs x appe>s mo/ op5 to u4 #hb4 ,?is ,r+1 se5 f ,saturn1 appe>s l a va/ lum9\s ,ar* 9 ! ,heav5s1 z if x did n belong to ! ,planet4 ,:5 we see ! ,r+ mo/ op51 x's %ad[ ^u ! ,planet is broade/2 & f t "t ! %ad[ gr[s n>r[]1 z ! ,r+ appe>s to d to u2 until1 by ,saturn's annual motion1 ! ,sun comes to ! plane ( ! ,r+1 or ev5 ) x's edge2 :i* be+ !n direct$ t[>ds u1 becomes invisible on acc\nt ( x's ?9ness2 z %all be expla9$ m l>gely 9 ! t5? ,*apt]1 & illu/rat$ by a figure4 ,! ,r+ disappe>s twice 9 e annual ,revolution ( ,saturn1 namely1 :5 he is 9 ! #ai? degree bo? ( ,pisces & ( ,virgo4 ,& :5 ,saturn is 9 ! middle betwe5 ^! po9ts1 or 9 ! #ai? degree ei!r ( ,gem9i or ( ,sagitt>ius1 8 ,r+ appe>s mo/ op5 to u2 & !n x's longe/ diamet] is to x's %orte/ z #i to #d4 ,sid5ote3 ,no ,planet b ,saturn c be se5 f ,jupit]2 nor any f ,jupit] besides ,saturn4 #hc4 ,to su* eyes z ours1 unassi/$ by in/rum5ts1 ,jupit] is ! only ,planet t c be se5 f ,saturn2 & ,saturn ! only ,planet t c be se5 f ,jupit]4 ,s t ! inhabitants ( ^! two ,planets mu/ ei!r see mu* f>!r ?an we d1 or h equally good in/rum5ts to c>ry _! sight to remote objects1 if !y "k t !re is su* a body z our ,e>? 9 ! ,univ]se3 = ! ,e>? is no bigg] se5 f ,jupit] ?an 8 ,moons are se5 f ! ,e>?2 & if 8 l>ge body _h n fir/ attract$ our sight1 & prompt$ our curiosity to view him ) ! telescope1 we %\ld nev] h kn[n any ?+ ( 8 ,moons2 unless by *ance we _h direct$ ! telescope t[>d t small "p ( ! ,heav5s :]e !y 7 at ! "t ( obs]vation4 ,& ! l is true ( ! ,moons ( ,saturn4 ,sid5ote3 ,place ( ,saturn's ,nodes4 #hd4 ,! ,orbit ( ,saturn is #b-a_/b degrees incl9$ to ! ,ecliptic1 or ,orbit ( our ,e>?1 & int]sects x 9 ! #ba/ degree ( ,canc] & ( ,capricorn2 s t ,saturn's ,nodes are only #ad degrees f ,jupit]'s1 #gg4 ,sid5ote3 ,! ,sun's light mu* /rong] on ,jupit] & ,saturn ?an is g5]ally believ$4 ,all our heat dep5ds n on ! ,sun's rays4 #he4 ,! quantity ( light1 af=d$ by ! ,sun ( ,jupit]1 be+ b #a_/bh? "p1 & to ,saturn only #a_/ij? "p1 ( :at we enjoy2 may at fir/ ?\ght induce u to believe t ^! two ,planets are entirely unfit = rational be+s to dwell ^u4 ,b1 t _! light is n s weak z we imag9e1 is evid5t f _! brightness 9 ! night-"t2 & also1 t :5 ! ,sun is s mu* eclips$ to u z to h only ! #dj? "p ( 8 ,disc left uncov]$ by ! ,moon1 ! decrease ( light is n v s5sible3 & j at ! end ( d>kness 9 ,total ,eclipses1 :5 8 we/]n limb beg9s to be visible1 & seems no bigg] ?an a bit ( f9e silv] wire1 e "o is surpris$ at ! brightness :]e) t small "p ( him %9es4 ,! ,moon :5 ,full af=ds travell]s light en\gh to keep !m f mi/ak+ _! way2 & yet1 accord+ to ,dr4 ,,smi?#af1 x is equal to no m ?an a #ij ?\s&? "p ( ! light ( ! ,sun3 t is1 ! ,sun's light is #ij ?\s& times z /rong z ! light ( ! ,moon :5 ,full4 ,consequ5tly1 ! ,sun gives a ?\s& times z mu* light to ,saturn z ! ,full ,moon does to u2 & above ?ree ?\s& times z mu* to ,jupit]4 ,s t ^! two ,planets1 ev5 )\t any ,moons1 w\ld be mu* m enlight5$ ?an we at fir/ imag9e2 & by hav+ s _m1 !y may be v com=table places ( resid5ce4 ,_! heat1 s f> z x dep5ds on ! =ce ( ! ,sun's rays1 is c]ta9ly mu* less ?an ours2 to :i* no d\bt ! bodies ( _! inhabitants are z well adapt$ z ours are to ! seasons we enjoy4 ,& if we consid]1 t ,jupit] nev] has any w9t]1 ev5 at 8 ,poles2 :i* probably is also ! case ) ,saturn1 ! cold _c be s int5se on ^! two ,planets z is g5]ally imag9$4 ,besides1 !re may be some?+ 9 _! nature or soil mu* w>m] ?an 9 t ( our ,e>?3 & we f9d t all our heat dep5ds n on ! rays ( ! ,sun2 = if x did1 we %\ld always h ! same mon?s equally hot or cold at _! annual returns4 ,b x is f> o!rwise1 = ,febru>y is sometimes w>m] ?an ,may1 :i* mu/ be ow+ to vap\rs & exhalations f ! ,e>?4 ,sid5ote3 ,x is highly probable t all ! ,planets are inhabit$4 ,,plate ,i4 #hf4 ,e p]son :o looks ^u1 & comp>es ! ,sy/ems ( ,moons toge!r1 :i* belong to ,jupit] & ,saturn1 mu/ be amaz$ at ! va/ magnitude ( ^! two ,planets1 & ! noble att5dance !y h 9 respect ( our little ,e>?3 & c nev] br+ himself to ?9k1 t an inf9itely wise ,creator %\ld dispose ( all 8 animals & vegetables "h1 leav+ ! o!r ,planets b>e & de/itute ( rational creatures4 ,to suppose t he _h any view to our ,b5efit1 9 creat+ ^! ,moons & giv+ !m _! motions r\nd ,jupit] & ,saturn2 to imag9e t he int5d$ ^! va/ ,bodies = any advantage to u1 :5 he well knew t !y c\ld nev] be se5 b by a few ,a/ronom]s peep+ ?r\gh telescopes2 & t he gave to ! ,planets regul> returns ( days & nights1 & diff]5t seasons to all :]e !y w\ld be conv5i5t2 b ( no mann] ( s]vice to u1 except only :at imm$iately reg>ds our own ,planet ! ,e>?2 to imag9e1 ,i say1 t he did all ?is on our acc\nt1 w\ld be *>g+ him impi\sly ) hav+ done mu* 9 va93 & z absurd1 z to imag9e t he has creat$ a little ,sun & a ,planet>y ,sy/em )9 ! %ell ( our ,e>?1 & int5d$ !m = our use4 ,^! consid]ations am\nt to little less ?an a positive pro( t all ! ,planets are inhabit$3 = if !y are n1 :y all ?is c>e 9 furni%+ !m ) s _m ,moons1 to supply ^? ) light :i* are at ! great] di/ances f ! ,sun8 ,d we n see1 t ! f>!r a ,planet is f ! ,sun1 ! great] ,app>atus x has = t purpose8 save only ,m>s1 :i* be+ b a small ,planet1 may h ,moons too small to be se5 by u4 ,we "k t ! ,e>? goes r\nd ! ,sun1 & turns r\nd x's own ,axis1 to produce ! vicissitudes ( summ] & w9t] by ! =m]1 & ( day & night by ! latt] motion1 = ! b5efit ( its inhabitants4 ,may we n !n fairly conclude1 by p>ity ( reason1 t ! end & design ( all ! o!r ,planets is ! same8 & is n ?is agreeable to t beautiful h>mony :i* reigns ov] ! ,univ]se8 ,surely x is3 & raises 9 u ! mo/ magnific5t ideas ( ! ,,supreme ,,be+1 :o is e :]e1 & at all times pres5t2 display+ 8 p[]1 wisdom1 & goodness among all 8 creatures6 & di/ribut+ happ9ess to innum]able ranks ( v>i\s be+s6 ,sid5ote3 ,fig4 ,,ii4 ,h[ ! ,sun appe>s to ! diff]5t ,planets4 #hg4 ,9 ,fig4 #b;d1 we h a view ( ! proportional bread? ( ! ,sun's face or disc1 z se5 f ! diff]5t ,planets4 ,! ,sun is repres5t$ ,no #a1 z se5 f ,m]cury2 ,no #b1 z se5 f ,v5us2 ,no #c1 z se5 f ! ,e>?2 ,no #d1 z se5 f ,m>s2 ,no #e1 z se5 f ,jupit]2 & ,no #f1 z se5 f ,saturn4 ,sid5ote3 ,fig4 ,,iii4 ,fig4 ,,iv4 ,let ! circle ,b be ! ,sun z se5 f any ,planet1 at a giv5 di/ance2 to ano!r ,planet1 at d\ble t di/ance1 ! ,sun w appe> j ( half t bread?1 z ,a2 :i* conta9s only "o f\r? "p ( ! area or surface ( ,b4 ,=1 all circles1 z well z squ>e surfaces1 are to "o ano!r z ! squ>es ( _! diamet]s4 ,?us1 ! squ>e ,a is j half z broad z ! squ>e ,b2 & yet x is pla9 to sight1 t ,b conta9s f\r times z mu* surface z ,a4 ,h5ce1 9 r\nd numb]s1 ! ,sun appe>s #g times l>g] to ,m]cury ?an to u1 #ij times l>g] to u ?an to ,saturn1 & #fcj times z l>ge to ,m]cury z to ,saturn4 ,sid5ote3 ,fig4 ,v4 ,proportional bulks & di/ances ( ! ,planets4 ,,plate ,i4 #hh4 ,9 ,fig4 #e?1 we h a view ( ! bulks ( ! ,planets 9 proportion to ea* o!r1 & to a suppos$ globe ( two foot diamet] = ! ,sun4 ,! ,e>? is #bg times z big z ,m]cury1 v little bigg] ?an ,v5us1 #e times z big z ,m>s2 b ,jupit] is #ajdi times z big z ! ,e>?1 ,saturn #ehf times z big1 exclusive ( 8 ,r+2 & ! ,sun is #hgg ?\s& #fej times z big z ! ,e>?4 ,if ! ,planets 9 ?is ,figure 7 set at _! due di/ances f a ,sun ( two feet diamet]1 accord+ to _! proportional bulks1 z 9 our ,sy/em1 ,m]cury w\ld be #bh y>ds f ! ,sun's c5t]2 ,v5us #ea y>ds #a foot2 ! ,e>? #gj y>ds #b feet2 ,m>s #ajg y>ds #b feet2 ,jupit] #cgj y>ds #b feet2 & ,saturn #gfj y>ds two feet4 ,! ,comet ( ! ye> #afhj1 at x's greate/ di/ance1 #aj ?\s& #gfj y>ds4 ,9 ?is proportion1 ! ,moon's di/ance f ! c5t] ( ! ,e>? w\ld be only #g-a_/b in*es4 ,sid5ote3 ,an idea ( _! di/ances4 #hi4 ,to assi/ ! imag9ation 9 conceiv+ an idea ( ! va/ di/ances ( ! ,sun1 ,planets1 & ,/>s1 let u suppose1 t a body project$ f ! ,sun %\ld cont9ue to fly ) ! swiftness ( a cannon ball2 i4 e4 #dhj miles e h\r2 ?is body w\ld rea* ! ,orbit ( ,m]cury1 9 #g ye>s #bba days2 ( ,v5us1 9 #ad ye>s #h days2 ( ! ,e>?1 9 #ai ye>s #ia days2 ( ,m>s1 9 #bi ye>s #he days2 ( ,jupit]1 9 #ajj ye>s #bhj days2 ( ,saturn1 9 #ahd ye>s #bdj days2 to ! ,comet ( #afhj1 at x's greate/ di/ance f ! ,sun1 9 #bffj ye>s2 & to ! ne>e/ fix$ ,/>s 9 ab\t #g million #fjj ?\s& ye>s4 ,sid5ote3 ,:y ! ,planets appe> bigg] & less at diff]5t times4 #ij4 ,z ! ,e>? is n ! c5t] ( ! ,orbits 9 :i* ! ,planets move1 !y come ne>] to x & g f>!r f x & at diff]5t times2 on :i* acc\nt !y appe> bigg] & less by turns4 ,h5ce1 ! app>5t magnitudes ( ! ,planets are n always a c]ta9 rule to "k !m by4 ,sid5ote3 ,fig4 ,i4 #ia4 ,"u ,fig4 #c1 are ! names & *>act]s ( ! twelve ,signs ( ! ,zodiac1 :i* ! ,read] %\ld be p]fectly well acqua9t$ )2 s z to "k ! *>act]s )\t see+ ! names4 ,e ,sign conta9s #cj degrees1 z 9 ! ,circle b\nd+ ! ,sol> ,sy/em2 to :i* ! *>act]s ( ! ,signs are set 9 _! prop] places4 ,sid5ote3 ,! ,comets4 #ib4 ,! ,,comets are solid opaque bodies1 ) long transp>5t tra9s or tails1 issu+ f t side :i* is turn$ away f ! ,sun4 ,!y move ab\t ! ,sun1 9 v exc5tric ellipses2 & are ( a mu* great] d5sity ?an ! ,e>?2 = "s ( !m are heat$ 9 e ,p]iod to su* a degree1 z w\ld vitrify or dissipate any sub/ance kn[n to u4 ,sir ,,isaac ,,newton comput$ ! heat ( ! ,comet :i* appe>$ 9 ! ye> #afhj1 :5 ne>e/ ! ,sun1 to be #bjjj times hott] ?an r$-hot iron1 & t be+ ?us heat$1 x mu/ reta9 x's heat until x comes r\nd aga91 al?\gh x's ,p]iod %\ld be m ?an tw5ty ?\s& ye>s2 & x is comput$ to be only #ege4 ,! me?od ( comput+ ! heat ( bodies1 keep+ at any kn[n di/ance f ! ,sun1 s f> z _! heat dep5ds on ! =ce ( ! ,sun's rays1 is v easy2 & %all be expla9$ 9 ! eigh? ,*apt]4 ,sid5ote3 ,,plate ,i4 ,fig4 ,i4 ,!y prove t ! ,orbits ( ! ,planets are n solid4 ,! ,p]iods only ( ?ree are kn[n4 ,!y prove ! ,/>s to be at imm5se di/ances4 #ic4 ,"p ( ! ,pa?s ( ?ree ,comets are del9eat$ 9 ! ,s*eme ( ! ,sol> ,sy/em1 & ! ye>s m>k$ 9 :i* !y made _! appe>ance4 ,x is believ$1 t !re are at lea/ #ba ,comets belong+ to our ,sy/em1 mov+ 9 all sorts ( directions3 & all ^? :i* h be5 obs]v$1 h mov$ ?r\gh ! e!real ,regions & ! ,orbits ( ! ,planets )\t suff]+ ! lea/ s5sible resi/ance 9 _! motions2 :i* pla9ly proves t ! ,planets d n move 9 solid ,orbs4 ,( all ! ,comets1 ! ,p]iods ( ! above-m5tion$ ?ree only are kn[n ) any degree ( c]ta9ty4 ,! fir/ ( ^! ,comets appe>$ 9 ! ye>s #aeca1 #afjg1 & #afhb2 & is expect$ to appe> aga9 9 ! ye> #ageh1 & e #ge? ye> aft]w>ds4 ,! second ( !m appe>$ 9 #aecb & #affa1 & may be expect$ to return 9 #aghi & e #abi? ye> aft]w>ds4 ,! ?ird1 hav+ la/ appe>$ 9 #afhj1 & x's ,p]iod be+ no less ?an #ege ye>s1 _c return until ! ye> #bbbe4 ,?is ,comet1 at x's greate/ di/ance1 is ab\t #aa ?\s& two hundr$ millions ( miles f ! ,sun2 & at x's lea/ di/ance f ! ,sun's c5t]1 :i* is #dij1jjj miles1 is )9 less ?an a ?ird "p ( ! ,sun's semi-diamet] f 8 surface4 ,9 t "p ( x's ,orbit :i* is ne>e/ ! ,sun1 x flies ) ! amaz+ swiftness ( #hhj1jjj miles 9 an h\r2 & ! ,sun1 z se5 f x1 appe>s an hundr$ degrees 9 bread?2 consequ5tly1 #dj ?\s& times z l>ge z he appe>s to u4 ,! a/oni%+ l5g? t ?is ,comet runs out into empty ,space1 sugge/s to our m9ds an idea ( ! va/ di/ance betwe5 ! ,sun & ! ne>e/ fix$ ,/>s2 ( ^: ,attractions all ! ,comets mu/ keep cle>1 to return p]iodically1 & g r\nd ! ,sun2 & x %ews u also1 t ! ne>e/ ,/>s1 :i* are probably ^? t seem ! l>ge/1 are z big z our ,sun1 & ( ! same nature ) him2 o!rwise1 !y c\ld n appe> s l>ge & bright to u z !y d at su* an imm5se di/ance4 ,sid5ote3 ,inf]5ces drawn f ! above ph5om5a4 #id4 ,! extreme heat1 ! d5se atmosph]e1 ! gross vap\rs1 ! *aotic /ate ( ! ,comets1 seem at fir/ sight to indicate !m altoge!r unfit = ! purposes ( animal life1 & a mo/ mis]able habitation = rational be+s3 & !re=e #ag"s are ( op9ion t !y are s _m hells = torm5t+ ! damn$ ) p]petual vicissitudes ( heat & cold4 ,b1 :5 we consid]1 on ! o!r h&1 ! inf9ite p[] & goodness ( ! ,deity2 ! latt] incl9+1 & ! =m] enabl+ him to make creatures suit$ to all /ates & circum/ances2 t matt] exi/s only = ! sake ( intellig5ce2 & t :]ev] we f9d x1 we always f9d x pregnant ) life1 or necess>ily subs]vi5t !reto2 ! numb]less species1 ! a/oni%+ div]sity ( animals 9 e>?1 air1 wat]1 & ev5 on o!r animals2 e blade ( grass1 e t5d] leaf1 e natural fluid1 sw>m+ ) life2 & e "o ( ^! enjoy+ su* gratifications z ! nature & /ate ( ea* requires3 :5 we reflect moreov] t "s c5turies ago1 till exp]i5ce undeceiv$ u1 a great "p ( ! ,e>? 0 judg$ un9habitable2 ! ,torrid ,zone by reason ( excessive heat1 & ! two ,frigid ,zones because ( _! intoll]able cold2 x seems highly probable1 t su* num]\s & l>ge masses ( durable matt] z ! ,comets are1 h[ev] unlike !y be to our ,e>?1 are n de/itute ( be+s capable ( contemplat+ ) wond]1 & ackn[l$g+ ) gratitude ! wisdom1 symmetry1 & beauty ( ! ,creation2 :i* is m pla9ly to be obs]v$ 9 _! ext5sive ,t\r ?r\gh ! ,heav5s1 ?an 9 our m conf9$ ,circuit4 ,if f>!r conjecture is p]mitt$1 may we n suppose !m in/rum5tal 9 recruit+ ! exp5d$ fuel ( ! ,sun2 & supply+ ! exhau/$ moi/ure ( ! ,planets8 ,h[ev] difficult x may be1 circum/anc$ z we are1 to f9d out _! p>ticul> de/9ation1 ?is is an und\bt$ tru?1 t :]ev] ! ,deity ex]ts 8 p[]1 !re he also manife/s 8 wisdom & goodness4 ,sid5ote3 ,?is ,sy/em v anci5t1 & demon/rable4 #ie4 ,,! ,,sol> ,,sy/em "h describ$ is n a late inv5tion2 = x 0 kn[n & taught by ! wise ,samian philosoph] ,,py?agoras1 & o!rs among ! anci5ts2 b 9 latt] times 0 lo/1 'till ! #ae? c5tury1 :5 x 0 aga9 re/or$ by ! fam\s ,poli% philosoph] ,,ni*olaus ,,cop]nicus1 :o 0 born at ,?orn 9 ! ye> #adgc4 ,9 ?is1 he 0 foll[$ by ! greate/ ma!maticians & philosoph]s t h s9ce liv$2 z ,,kepl]1 ,,galileo1 ,,desc>tes1 ,,gass5dus1 & ,sir ,,isaac ,,newton2 ! la/ ( :om has e/abli%$ ?is ,sy/em on su* an ev]la/+ f\ndation ( ma!matical & physical demon/ration1 z c nev] be %ak53 & none :o und]/& him c hesitate ab\t x4 ,sid5ote3 ,! ,ptolemean ,sy/em absurd4 #if4 ,9 ! ,ptolemean ,sy/em ! ,e>? 0 suppos$ to be fix$ 9 ! ,c5t] ( ! ,univ]se2 & t ! ,moon1 ,m]cury1 ,v5us1 ! ,sun1 ,m>s1 ,jupit]1 & ,saturn mov$ r\nd ! ,e>?3 above ! ,planets1 ?is ,hypo!sis plac$ ! ,firmam5t ( ,/>s1 & !n ! two ,cry/all9e ,sph]es2 all :i* 7 includ$ 9 & receiv$ motion f ! ,primum ,mobile1 :i* con/antly revolv$ ab\t ! ,e>? 9 #bd h\rs1 f ,ea/ to ,we/4 ,b z ?is rude ,s*eme 0 f\nd incapable to /& ! te/ ( art & obs]vation1 x 0 soon reject$ by all true philosoph]s2 not)/&+ ! opposition & viol5ce ( bl9d & zeal\s bigots4 ,sid5ote3 ,! ,ty*onic ,sy/em1 p>tly true & p>tly false4 #ig4 ,! ,ty*onic ,sy/em succe$$ ! ,ptolemean1 b 0 nev] s g5]ally receiv$4 ,9 ?is ! ,e>? 0 suppos$ to /& /ill 9 ! ,c5t] ( ! ,univ]se or ,firmam5t ( ,/>s1 & ! ,sun to revolve ab\t x e #bd h\rs2 ! ,planets1 ,m]cury1 ,v5us1 ,m>s1 ,jupit]1 & ,saturn1 go+ r\nd ! ,sun 9 ! times already m5tion$4 ,b "s ( ,,ty*o's disciples suppos$ ! ,e>? to h a diurnal motion r\nd x's ,axis1 & ! ,sun ) all ! above ,planets to g r\nd ! ,e>? 9 a ye>2 ! ,planets mov+ r\nd ! ,sun 9 ! =esaid times4 ,?is hypo!sis1 be+ p>tly true & p>tly false1 0 embrac$ by few2 & soon gave way to ! only true & rational ,sy/em1 re/or$ by ,,cop]nicus & demon/rat$ by ,sir ,,isaac ,,newton4 #ih4 ,to br+ ! =ego+ p>ticul>s at once 9 view1 ) sev]al o!rs :i* foll[1 conc]n+ ! ,p]iods1 ,di/ances1 ,bulks1 c4 ( ! ,planets1 ! foll[+ ,table is ins]t$4 ,a ,,table ,( ! ,,p]iods1 ,,revolutions1 ,,magnitudes1 c4 ( ! ,,planets4 ---------------------------------------- ---------------------- ,sun & ,annual ,diurnal ,diamet] ,mean ,mean di/ance ,planets4p]iod rotation 9 diam4 zf ! ,sun r\nd on x's ,engli% se5 fr4 9 ,engli% ! ,sun4 ,axis4 miles4 ! ,sun4 miles4 ---------------------------------------- ---------------------- ,sun ---- #be;d4 #f;h4 #gfcjjj ---- ---- ,m]cury #hg;d #bc;h,unkn[n4 #bfjj #bj #cb1jjj1jjj ,v5us #bbd;d #ag;h#bd;d4 #h;h4 #gijf #cj #ei1jjj1jjj ,e>? #cfe;d #f;h #a;d4 #j;h4 #gigj #ba #ha1jjj1jjj ,moon #cfe;d #f;h#bi;d4 #ab-c_/d;h4 #bahj #f #ha1jjj1jjj ,m>s #fhf;d #bc;h#bd;h4 #djm4 #dddd #aa #abc1jjj1jjj ,jupit] #dccb;d #ab;h #i;h4 #efm4 #hajjj #cg #dbd1jjj1jjj ,saturn #ajgei;d #g;h,unkn[n4 #fgjjj #af #ggg1jjj1jjj ---------------------------------------- ---------------------- ---------------------------------------- ------------------------- ,sun & ,exc5tricity ,axis ,orbit ,place ( ,place ( ,proportion ,planets4 ( x's incl9$incl9$ x's x's ( ,orbit to to ,aphelion4,asc5d+,diamet]s4 9 miles4 ,orbit4 ,ecliptic4 ,node4 ---------------------------------------- ------------------------- ,sun ---- #h #j ---- ---- ---- #ajjjj ,m]cury #f1gbj1jjj ,unkn4 #f #ed #ac #h #ad #dc #cd-a_/aj ,v5us #dac1jjj #ge #j #c #bj #d #bj #ac #ei #ajc-a_/b ,e>? #a1cgg1jjj #bc #bi #j #j #h #a ---- #ajd-a_/b ,moon #ac1jjj #b #aj #e #h ---- ,v>iable4 #bh-a_/b ,m>s #aa1dci1jjj #j #j #a #eb #j #cb #ag #ag #eh-a_/f ,jupit] #bj1ceb1jjj #j #j #a #bj #i #aj #g #biajfa-b_/c ,saturn #db1gce1jjj ,unkn4 #b #cj #bg #ej #ba #ac #hgh-a_/i ---------------------------------------- ------------------------- ---------------------------------------- ----------------------------- ,sun & ,proportion,prop4 (,proportion,proportion,propor4 ,h\rly ,h\rly ,planets4( ,gravity ( ( quantitymotion motion ,bulk4 on ! ,d5sity4 ,light ( 9 x's( x's surface4 ,heat4 ,matt]4 ,orbit4 ,equator4 ---------------------------------------- ----------------------------- ,sun #hggfej #bd #be-a_/b #dejjj #bbgejj ---- #chah ,m]cury #a_/bg ,unkn4 ,unkn4 #f-a_/b ,unkn4 #iejjj ,unkn4 ,v5us #a ,unkn4 ,unkn4 #a-c_/d ,unkn4 #fijjj #dc ,e>? #a #a #ajj #a #a #ehjjj #ajdb ,moon #a_/ej #cd_/ajj #abc-a_/b #a #a_/dj #bbij #i-a_/b ,m>s #a_/e ,unkn4 ,unkn4 #c_/g ,unkn4 #dgjjj #eef ,jupit] #ajdi #b #ai #a_/bh #bbj #bejjj #beibj ,saturn #ehf #a-a_/b #ae #a_/ij #id #ahjjj ,unkn4 ---------------------------------------- ----------------------------- ---------------------------------------- ----------------------- ,sun & ,squ>e miles 9 ,cubic miles 9 solidity4,w\ld fall to ,planets4 surface4 ! ,sun 9 ---------------------------------------- ----------------------- ,sun #a1hbh1iaa1jjj1jjjbcb1egg1aae1acg1jjj1jj j days h4 ,m]cury #ba1bcf1hjj #i1aie1ecd1ejj #ae #ac ,v5us #fia1cfa1cjj #beh1ejg1hcb1bjj #ci #ag ,e>? #aii1heb1hfj #bfe1djd1eih1jhj #ad #aj ,moon #ad1hih1gej #e1djh1bdf1jjj #fd #aj ,m>s #fb1jch1bdj #de1ifi1cce1hdj #aba #j ,jupit] #bj1fjc1igj1jjj #bgh1aec1eie1jjj1jjj #bij #j ,saturn #ad1ajb1efb1jjj #aee1abh1ahb1jjj1jjj #gfg #j ,if ! projectile =ce 0 de/roy$4 ---------------------------------------- ----------------------- ,if ! ,moon's projectile =ce 0 de/roy$1 %e w\ld fall to ! ,e>? 9 #d days #ba h\rs4 ---------------------------------------- ------ ,jupit]'s,p]iods r\nd ,saturn's,p]iods r\nd ,moons4 ,jupit]4 ,moons4 ,saturn4 ---------------------------------------- ------ ,no ,d4 ,h4 ,m4 ,no ,d4 ,h4 ,m4 ---------------------------------------- ------ #a #a #ah #cf #a #a #ba #ai #b #c #ac #ae #b #b #ag #dj #c #g #c #ei #c #d #ab #be #d #af #ah #cj #d #ae #bb #da ----------------------- #e #gi #g #dh ----------------------- ,,*ap4 ,,iii4 ,! ,,cop]nican ,,sy/em demon/rat$ to be true4 ,sid5ote3 ,( matt] & motion4 #ii4 ,matt] is ( itself inactive1 & indiff]5t to motion or re/4 ,a body at re/ c nev] put itself 9 motion2 a body 9 motion c nev] /op nor move sl[] ( itself4 ,h5ce1 :5 we see a body 9 motion we conclude "s o!r sub/ance mu/ h giv5 x t motion2 :5 we see a body fall f motion to re/ we conclude "s o!r body or cause /opt x4 #ajj4 ,all motion is naturally rectil9eal4 ,a bullet ?r[n by ! h&1 or dis*>g$ f a cannon w\ld cont9ue to move 9 ! same direction x receiv$ at fir/1 if no o!r p[] div]t$ its c\rse4 ,!re=e1 :5 we see a body mov+ 9 a curve ( :atev] k9d1 we conclude x mu/ be act$ ^u by two p[]s at lea/3 "o to put x 9 motion1 & ano!r draw+ x (f f ! rectil9eal c\rse :i* x w\ld o!rwise h cont9u$ to move 94 ,sid5ote3 ,gravity demon/rable4 #aja4 ,! p[] by :i* bodies fall t[>ds ! ,e>? is call$ ,gravity or ,attraction4 ,by ?is p[] 9 ! ,e>? x is1 t all bodies1 on :atev] side1 fall 9 l9es p]p5dicul> to x's surface4 ,on opposite p>ts ( ! ,e>? bodies fall 9 opposite directions1 all t[>ds ! c5tre :]e ! =ce ( gravity is z x 7 accumulat$4 ,by ?is p[] con/antly act+ on bodies ne> ! ,e>? !y are kept f leav+ x altoge!r2 & ^? on its surface are kept !reto on all sides1 s t !y _c fall f x4 ,bodies ?r[n ) any obliquity are drawn by ?is p[] f a /raight l9e into a curve1 until !y fall to ! ,gr\nd3 ! great] ! =ce by :i* !y are ?r[n1 ! great] is ! di/ance !y are c>ri$ be=e !y fall4 ,if we suppose a body c>ri$ sev]al miles above ! ,e>?1 & !re project$ 9 an horizontal direction1 ) s great a velocity t x w\ld move m ?an a semidiamet] ( ! ,e>?1 9 ! "t x w\ld take to fall to ! ,e>? by gravity2 9 t case1 if !re 7 no resi/+ m$ium 9 ! way1 ! body w\ld n fall to ! ,e>? at all2 b cont9ue to circulate r\nd ! ,e>?1 keep+ always ! same pa?1 & return+ to ! po9t f :5ce x 0 project$1 ) ! same velocity z at fir/4 ,sid5ote3 ,projectile =ce demon/rable4 #ajb4 ,we f9d ! ,moon moves r\nd ! ,e>? 9 an ,orbit ne>ly circul>4 ,! ,moon !re=e mu/ be act$ on by two p[]s or =ces2 "o :i* w\ld cause h] to move 9 a "r l9e1 ano!r b5d+ h] motion f t l9e into a curve4 ,?is attractive p[] mu/ be seat$ 9 ! ,e>?2 = !re is no o!r body )9 ! ,moon's ,orbit to draw h]4 ,! attractive p[] ( ! ,e>? !re=e ext5ds to ! ,moon2 &1 9 comb9ation ) h] projectile =ce1 causes h] to move r\nd ! ,e>? 9 ! same mann] z ! circulat+ body above suppos$4 ,sid5ote3 ,! ,sun & ,planets attract ea* o!r4 #ajc4 ,! ,moons ( ,jupit] & ,saturn are obs]v$ to move r\nd _! prim>y ,planets3 !re=e !re is su* a p[] z gravity 9 ^! ,planets4 ,all ! ,planets move r\nd ! ,sun1 & respect x = _! c5tre ( motion3 !re=e ! ,sun mu/ be end[$ ) attract+ =ce1 z well z ! ,e>? & ,planets4 ,! l may be prov$ ( ! ,comets4 ,s t all ! bodies or matt] 9 ! ,sol> ,sy/em are possess$ ( ?is p[]2 & p]haps s is all matt] :atsoev]4 #ajd4 ,z ! ,sun attracts ! ,planets ) _! ,satellites1 & ! ,e>? ! ,moon1 s ! ,planets & ,satellites re-attract ! ,sun1 & ! ,moon ! ,e>?3 action & re-action be+ always equal4 ,?is is also confirm$ by obs]vation2 = ! ,moon raises tides 9 ! ocean1 ! ,satellites & ,planets di/urb "o ano!r's motions4 #aje4 ,e p>ticle ( matt] be+ possess$ ( an attract+ p[]1 ! effect ( ! :ole mu/ be 9 proportion to ! numb] ( attract+ p>ticles3 t is1 to ! quantity ( matt] 9 ! body4 ,?is is demon/rat$ f exp]im5ts on p5dulums3 =1 if !y are ( equal l5g?s1 :atev] _! weights be1 !y always vibrate 9 equal times4 ,n[1 if "o be d\ble ! weight ( ano!r1 ! =ce ( gravity or attraction mu/ be d\ble to make x oscillate ) ! same cel]ity3 if "o is ?rice ! weight or quantity ( matt] ( ano!r1 x requires ?rice ! =ce ( gravity to make x move ) ! same cel]ity4 ,h5ce x is c]ta91 t ! p[] ( gravity is always proportional to ! quantity ( matt] 9 bodies1 :atev] _! bulks or figures are4 #ajf4 ,gravity also1 l all o!r virtues or emanations issu+ f a c5tre1 decreases z ! squ>e ( ! di/ance increases3 t is1 a body at twice ! di/ance attracts ano!r ) only a f\r? "p ( ! =ce2 at f\r times ! di/ance1 ) a sixte5? "p ( ! =ce4 ,?is too is confirm$ f obs]vation1 by comp>+ ! di/ance :i* ! ,moon falls 9 a m9ute f a "r l9e t\*+ h] ,orbit1 ) ! space :i* bodies ne> ! ,e>? fall 9 ! same "t3 & also by comp>+ ! =ces :i* reta9 ,jupit]'s ,moons 9 _! ,orbits4 ,?is w be m fully expla9$ 9 ! sev5? ,*apt]4 ,sid5ote3 ,gravitation & projection exemplifi$4 #ajg4 ,! mutual attraction ( bodies may be exemplifi$ by a boat & a %ip on ! ,wat]1 ti$ by a rope4 ,let a man ei!r 9 %ip or boat pull ! rope 7x is ! same 9 effect at :i* end he pulls1 = ! rope w be equally /ret*$ ?r\gh\t17 ! %ip & boat w be drawn t[>ds "o ano!r2 b ) ?is diff]5ce1 t ! boat w move z mu* fa/] ?an ! %ip z ! %ip is heavi] ?an ! boat4 ,suppose ! boat z heavy z ! %ip1 & !y w draw "o ano!r equally 7sett+ aside ! great] resi/ance ( ! ,wat] on ! bigg] body7 & meet 9 ! middle ( ! fir/ di/ance betwe5 !m4 ,if ! %ip is a ?\s& or t5 ?\s& times heavi] ?an ! boat1 ! boat w be drawn a ?\s& or t5 ?\s& times fa/] ?an ! %ip2 & meet proportionably ne>] ! place f :i* ! %ip set out4 ,n[1 :il/ "o man pulls ! rope1 endeav\r+ to br+ ! %ip & boat toge!r1 let ano!r man1 9 ! boat1 endeav\r to r[ h] (f sidewise1 or at "r ,angles to ! rope2 & ! =m]1 in/ead ( be+ able to draw ! boat to ! %ip1 w f9d x en\gh = him to keep ! boat f go+ fur!r (f2 :il/ ! latt]1 endeav\r+ to r[ (f ! boat 9 a /raight l9e1 w1 by means ( ! o!r's pull+ x t[>ds ! %ip1 r[ ! boat r\nd ! %ip at ! rope's l5g? f h]4 ,"h1 ! p[] employ$ to draw ! %ip & boat to "o ano!r repres5ts ! mutual attraction ( ! ,sun & ,planets1 by :i* ! ,planets w\ld fall freely t[>ds ! ,sun ) a quick motion2 & w\ld also 9 fall+ attract ! ,sun t[>ds !m4 ,& ! p[] employ$ to r[ (f ! boat repres5ts ! projectile =ce impress$ on ! ,planets at "r ,angles1 or ne>ly s1 to ! ,sun's attraction2 by :i* means ! ,planets move r\nd ! ,sun1 & are kept f fall+ to x4 ,on ! o!r h&1 if x be attempt$ to make a heavy %ip g r\nd a light boat1 !y w meet soon] ?an ! %ip c get r\nd2 or ! %ip w drag ! boat aft] x4 #ajh4 ,let ! above pr9ciples be appli$ to ! ,sun & ,e>?2 & !y w ev9ce1 beyond a possibility ( d\bt1 t ! ,sun1 n ! ,e>?1 is ! c5t] ( ! ,sy/em2 & t ! ,e>? moves r\nd ! ,sun z ! o!r ,planets d4 ,sid5ote3 ,! absurdity ( suppos+ ! ,e>? at re/4 ,=1 if ! ,sun moves ab\t ! ,e>?1 ! ,e>?'s attractive p[] mu/ draw ! ,sun t[>ds x f ! l9e ( projection s1 z to b5d x's motion into a curve2 & ! ,e>? be+ at lea/ #afi ?\s& times light] ?an ! ,sun1 by be+ s mu* less z to x's quantity ( matt]1 mu/ move #afi ?\s& times fa/] t[>d ! ,sun ?an ! ,sun does t[>d ! ,e>?2 & consequ5tly w\ld fall to ! ,sun 9 a %ort "t if x _h n a v /rong projectile motion to c>ry x (f4 ,! ,e>? !re=e1 z well z e o!r ,planet 9 ! ,sy/em1 mu/ h a rectil9eal impulse to prev5t its fall+ into ! ,sun4 ,to say1 t gravitation reta9s all ! o!r ,planets 9 _! ,orbits )\t affect+ ! ,e>?1 :i* is plac$ betwe5 ! ,orbits ( ,m>s & ,v5us1 is z absurd z to suppose t six cannon bullets might be project$ upw>ds to diff]5t heights 9 ! ,air1 & t five ( !m %\ld fall d[n to ! gr\nd2 b ! six?1 :i* is nei!r ! highe/ nor ! l[e/1 %\ld rema9 susp5d$ 9 ! ,air )\t fall+2 & ! ,e>? move r\nd ab\t x4 #aji4 ,!re is no su* ?+ 9 nature z a heavy body mov+ r\nd a light "o z its c5tre ( motion4 ,a pebble fa/5$ to a mill-/one by a /r+1 may by an easy impulse be made to circulate r\nd ! mill-/one3 b no impulse c make a mill-/one circulate r\nd a loose pebble1 = ! heavie/ w\ld und\bt$ly c>ry ! lighte/ along ) x :]ev] x goes4 #aaj4 ,! ,sun is s imm5sely bigg] & heavi] ?an ! ,e>?#ah1 t if he 0 mov$ out ( 8 place1 n only ! ,e>?1 b all ! o!r ,planets if !y 7 unit$ into "o mass1 w\ld be c>ri$ along ) ! ,sun z ! pebble w\ld be ) ! mill-/one4 ,sid5ote3 ,! h>mony ( ! cele/ial motions4 ,! absurdity ( suppos+ ! ,/>s & ,planets to move r\nd ! ,e>?4 #aaa4 ,by consid]+ ! law ( gravitation1 :i* takes place ?r\gh\t ! ,sol> ,sy/em1 9 ano!r light1 x w be evid5t t ! ,e>? moves r\nd ! ,sun 9 a ye>2 & n ! ,sun r\nd ! ,e>?4 ,x has be5 %ewn 7 #ajf7 t ! p[] ( gravity decreases z ! squ>e ( ! di/ance increases3 & f ?is x foll[s ) ma!matical c]ta9ty1 t :5 two or m bodies move r\nd ano!r z _! c5tre ( motion1 ! squ>es ( _! p]iodic times w be to "o ano!r 9 ! same proportion z ! cubes ( _! di/ances f ! c5tral body4 ,?is holds precisely ) reg>d to ! ,planets r\nd ! ,sun1 & ! ,satellites r\nd ! ,planets2 ! relative di/ances ( all :i*1 are well kn[n4 ,b1 if we suppose ! ,sun to move r\nd ! ,e>?1 & comp>e its p]iod ) ! ,moon's by ! above rule1 x w be f\nd t ! ,sun w\ld take no less ?an #agc1eaj days to move r\nd ! ,e>?1 9 :i* case our ye> w\ld be #dge times z long z x n[ is4 ,to ?is we may add1 t ! aspects ( increase & decrease ( ! ,planets1 ! times ( _! seem+ to /& /ill1 & to move direct & retrograde1 answ] precisely to ! ,e>?'s motion2 b n at all to ! ,sun's )\t introduc+ ! mo/ absurd & mon/r\s suppositions1 :i* w\ld de/roy all h>mony1 ord]1 & simplicity 9 ! ,sy/em4 ,moreov]1 if ! ,e>? is suppos$ to /& /ill1 & ! ,/>s to revolve 9 free spaces ab\t ! ,e>? 9 #bd h\rs1 x is c]ta9 t ! =ces by :i* ! ,/>s revolve 9 _! ,orbits are n direct$ to ! ,e>?1 b to ! c5tres ( ! sev]al ,orbits3 t is1 ( ! sev]al p>allel ,circles :i* ! ,/>s on diff]5t sides ( ! ,equator describe e day3 & ! l inf]5ces may be drawn f ! suppos$ diurnal motion ( ! ,planets1 s9ce !y are nev] 9 ! ,equ9octial b twice1 9 _! c\rses ) reg>d to ! />ry ,heav5s4 ,b1 t =ces %\ld be direct$ to no c5tral body1 on :i* !y physically dep5d1 b to innum]able imag9>y po9ts 9 ! axe ( ! ,e>? produc$ to ! ,poles ( ! ,heav5s1 is an hypo!sis too absurd to be all[$ ( by any rational creature4 ,& x is /ill m absurd to imag9e t ^! =ces %\ld increase exactly 9 proportion to ! di/ances f ?is axe2 = ?is is an indication ( an increase to inf9ity3 :]eas ! =ce ( attraction is f\nd to decrease 9 rec$+ f ! f\nta9 f :5ce x fl[s4 ,b1 ! f>!r t any ,/> is f ! quiesc5t ,pole ! great] mu/ be ! ,orbit :i* x describes2 & yet x appe>s to g r\nd 9 ! same "t z ! ne>e/ ,/> to ! ,pole does4 ,& if we take into consid]ation ! two-fold motion obs]v$ 9 ! ,/>s1 "o diurnal r\nd ! ,axis ( ! ,e>? 9 #bd h\rs1 & ! o!r r\nd ! ,axis ( ! ,ecliptic 9 #beibj ye>s #bea1 x w\ld require an explication ( su* a p]plex$ composition ( =ces1 z c\ld by no means be reconcil$ ) any physical ,!ory4 ,sid5ote3 ,objections aga9/ ! ,e>?'s motion answ]$4 #aab4 ,!re is b "o objection ( any weight t c be made to ! ,e>?'s motion r\nd ! ,sun2 :i* is1 t 9 opposite po9ts ( ! ,e>?'s ,orbit1 x's ,axis :i* always keeps a p>allel direction w\ld po9t to diff]5t fix$ ,/>s2 :i* is n f\nd to be fact4 ,b ?is objection is easily remov$ by consid]+ ! imm5se di/ance ( ! ,/>s 9 respect ( ! diamet] ( ! ,e>?'s ,orbit2 ! latt] be+ no m ?an a po9t :5 comp>$ to ! =m]4 ,if we lay a rul] on ! side ( a table1 & along ! edge ( ! rul] view ! top ( a spire at t5 miles di/ance2 !n lay ! rul] on ! opposite side ( ! table 9 a p>allel situation to :at x _h be=e1 & ! spire w /ill appe> along ! edge ( ! rul]2 because our eyes1 ev5 :5 assi/$ by ! be/ in/rum5ts are incapable ( di/+ui%+ s small a *ange4 #aac4 ,dr4 ,,bradley1 our pres5t ,a/ronom] ,royal1 has f\nd by a long s]ies ( ! mo/ accurate obs]vations1 t !re is a small app>5t motion ( ! fix$ ,/>s1 occasion$ by ! ab]ration ( _! light1 & s exactly answ]+ to an annual motion ( ! ,e>?1 z ev9ces ! same1 ev5 to a ma!matical demon/ration4 ,^? :o are qualifi$ to read ! ,doctor's mode/ ,acc\nt ( ?is great discov]y may consult ! ,philosophical ,transactions1 ,no #djf4 ,or !y may f9d x treat$ ( at l>ge by ,drs4 ,,smi?#ai1 ,,long#bj1 ,,desaguli]s#ba1 ,,ru!rfur?1 ,mr4 ,,maclaur9#bb1 & ,m4 ,,de ,,la ,,caille#bc4 ,sid5ote3 ,:y ! ,sun appe>s to *ange 8 place4 #aad4 ,x is true t ! ,sun seems to *ange 8 place daily1 s z to make a t\r r\nd ! />ry ,heav5s 9 a ye>4 ,b :e!r ! ,e>? or ,sun moves1 ?is appe>ance w be ! same2 =1 :5 ! ,e>? is 9 any "p ( ! ,heav5s1 ! ,sun w appe> 9 ! opposite4 ,& !re=e1 ?is appe>ance c be no objection aga9/ ! motion ( ! ,e>?4 #aae4 ,x is well kn[n to e p]son :o has sail$ on smoo? ,wat]1 or be5 c>ri$ by a /ream 9 a calm1 t h[ev] fa/ ! vessel goes he does n feel its progressive motion4 ,! motion ( ! ,e>? is incomp>ably m smoo? & uni=m ?an t ( a %ip1 or any ma*9e made & mov$ by human art3 & !re=e x is n to be imag9$ t we c feel x's motion4 ,sid5ote3 ,! ,e>?'s motion on x's ,axis demon/rat$4 #aaf4 ,we f9d t ! ,sun1 & ^? ,planets on :i* !re are visible spots1 turn r\nd _! ,axes3 = ! spots move regul>ly ov] _! ,disks#bd4 ,f h5ce we may reasonably conclude t ! o!r ,planets on :i* we see no spots1 & ! ,e>? :i* is likewise a ,planet1 h su* rotations4 ,b be+ incapable ( leav+ ! ,e>?1 & view+ x at a di/ance2 & x's rotation be+ smoo? & uni=m1 we c nei!r see x move on x's ,axis z we d ! ,planets1 nor feel ourselves affect$ by x's motion4 ,yet !re is "o effect ( su* a motion :i* w enable u to judge ) c]ta9ty :e!r ! ,e>? revolves on x's ,axis or n4 ,all ,globes :i* d n turn r\nd _! ,axes w be p]fect sph]es1 on acc\nt ( ! equality ( ! weight ( bodies on _! surfaces2 especially ( ! fluid p>ts4 ,b all ,globes :i* turn on _! ,axes w be oblate sph]oids2 t is1 _! surfaces w be high]1 or f>!r f ! c5tre1 9 ! equatoreal ?an 9 ! pol> ,regions3 =1 z ! equatoreal p>ts move quicke/1 !y w rec$e f>!r f ! ,axis ( motion1 & enl>ge ! equatoreal diamet]4 ,t our ,e>? is really ( ?is figure is demon/rable f ! unequal vibrations ( a p5dulum1 & ! unequal l5g?s ( degrees 9 diff]5t latitudes4 ,s9ce !n1 ! ,e>? is high] at ! ,equator ?an at ! ,poles1 ! sea1 :i* naturally runs d[nw>d1 or t[>ds ! places :i* are ne>e/ ! c5tre1 w\ld run t[>ds ! pol> ,regions1 & leave ! equatoreal p>ts dry1 if ! c5trifugal =ce ( ^! p>ts did n raise & c>ry ! wat]s ?i!r4 ,! ,e>?'s equatoreal diamet] is #ce miles long] ?an its ,axis4 ,sid5ote3 ,all bodies heavi] at ! ,poles ?an !y w\ld be at ! ,equator4 #aag4 ,bodies ne> ! ,poles are heavi] ?an ^? t[>ds ! ,equator1 because !y are ne>] ! ,e>?'s c5tre1 :]e ! :ole =ce ( ! ,e>?'s attraction is accumulat$4 ,!y are also heavi] because _! c5trifugal =ce is less on acc\nt ( _! diurnal motion be+ sl[]4 ,= bo? ^! reasons1 bodies c>ri$ f ! ,poles t[>d ! ,equator1 gradually lose ( _! weight4 ,exp]im5ts prove t a p5dulum1 :i* vibrates seconds ne> ! ,poles vibrates sl[] ne> ! ,equator1 :i* %ews t x is light] or less attract$ !re4 ,to make x oscillate 9 ! same "t1 'tis f\nd necess>y to dim9i% x's l5g?4 ,by comp>+ ! diff]5t l5g?s ( p5dulums sw++ seconds at ! ,equator & at ,london1 x is f\nd t a p5dulum mu/ be #b-afi_/ajjj l9es %ort] at ! ,equator ?an at ! ,poles4 ,a l9e is a twelf? "p ( an in*4 ,sid5ote3 ,h[ !y might lose all _! weight4 #aah4 ,if ! ,e>? turn$ r\nd x's ,axis 9 #hd m9utes #dc seconds1 ! c5trifugal =ce w\ld be equal to ! p[] ( gravity at ! ,equator2 & all bodies !re w\ld entirely lose _! weight4 ,if ! ,e>? revolv$ quick] !y w\ld all fly (f1 & leave x4 ,sid5ote3 ,! ,e>?'s motion _c be felt4 #aai4 ,"o on ! ,e>? c no m be s5sible ( x's undi/urb$ motion on x's ,axis1 ?an "o 9 ! cab9 ( a %ip on smoo? ,wat] c be s5sible ( h] motion :5 %e turns g5tly & uni=mly r\nd4 ,x is !re=e no argum5t aga9/ ! ,e>?'s diurnal motion t we d n feel x3 nor is ! app>5t revolutions ( ! cele/ial bodies e day a pro( ( ! reality ( ^! motions2 = :e!r we or !y revolve1 ! appe>ance is ! v same4 ,a p]son look+ ?r\gh ! cab9 w9d[s ( a %ip z /rongly fancies ! objects on l& to g r\nd :5 ! %ip turns1 z if !y 7 actually 9 motion4 ,sid5ote3 ,to ! diff]5t ,planets ! ,heav5s appe> to turn r\nd on diff]5t ,axes4 #abj4 ,if we c\ld translate ourselves f ,planet to ,planet1 we %\ld /ill f9d t ! ,/>s w\ld appe> ( ! same magnitudes1 & at ! same di/ances f ea* o!r1 z !y d to u "h2 because ! wid? ( ! remote/ ,planet's ,orbit be>s no s5sible proportion to ! di/ance ( ! ,/>s4 ,b !n1 ! ,heav5s w\ld seem to revolve ab\t v diff]5t ,axes2 & consequ5tly1 ^? quiesc5t ,po9ts :i* are our ,poles 9 ! ,heav5s w\ld seem to revolve ab\t o!r po9ts1 :i*1 ?\gh app>5tly 9 motion to u on ,e>? w\ld be at re/ z se5 f any o!r ,planet4 ,?us1 ! ,axis ( ,v5us1 :i* lies almo/ at "r ,angles to ! ,axis ( ! ,e>?1 w\ld h x's motionless ,poles 9 two opposite po9ts ( ! ,heav5s ly+ almo/ 9 our ,equ9octial1 :]e ! motion appe>s quicke/ because x is p]=m$ 9 ! greate/ ,circle4 ,& ! v ,poles1 :i* are at re/ to u1 h ! quicke/ motion ( all z se5 f ,v5us4 ,to ,m>s & ,jupit] ! ,heav5s appe> to turn r\nd ) v diff]5t velocities on ! same ,axis1 ^: ,poles are ab\t #bc-a_/b degrees f ours4 ,7 we on ,jupit] we %\ld be at fir/ amaz$ at ! rapid motion ( ! ,heav5s2 ! ,sun & ,/>s go+ r\nd 9 #i h\rs #ef m9utes4 ,c\ld we g f !nce to ,v5us we %\ld be z mu* surpris$ at ! sl[ness ( ! heav5ly motions3 ! ,sun go+ b once r\nd 9 #ehd h\rs1 & ! ,/>s 9 #edj4 ,& c\ld we g f ,v5us to ! ,moon we %\ld see ! ,heav5s turn r\nd ) a yet sl[] motion2 ! ,sun 9 #gjh h\rs1 ! ,/>s 9 #fee4 ,z x is impossible ^! v>i\s circumvolutions 9 su* diff]5t times & on su* diff]5t ,axes c be real1 s x is unreasonable to suppose ! ,heav5s to revolve ab\t our ,e>? m ?an x does ab\t any o!r ,planet4 ,:5 we reflect on ! va/ di/ance ( ! fix$ ,/>s1 to :i* #afb1jjj1jjj ( miles is b a po9t1 we are fill$ ) amazem5t at ! imm5sity ( _! di/ance4 ,b if we try to frame an idea ( ! extreme rapidity ) :i* ! ,/>s mu/ move1 if !y move r\nd ! ,e>? 9 #bd h\rs1 ! ?\ght becomes s mu* too big = our imag9ation1 t we c no m conceive x ?an we d inf9ity or et]nity4 ,if ! ,sun 0 to g r\nd ! ,e>? 9 a day1 he mu/ travel upw>ds ( #cjj1jjj miles 9 a m9ute3 b ! ,/>s be+ at lea/ #aj1jjj times z f> z ! ,sun f u1 ^? ab\t ! ,equator mu/ move #aj1jjj times z quick4 ,& all ?is to s]ve no o!r purpose ?an :at c be z fully & mu* m simply obta9$ by ! ,e>?'s turn+ r\nd ea/w>d z on an ,axis1 e #bd h\rs1 caus+ !reby an app>5t diurnal motion ( ! ,sun we/w>d1 & br++ ab\t ! alt]nate returns ( day & night4 ,illu/ration3 ,pl4 ,,ii4 ,sid5ote3 ,objections aga9/ ! ,e>?'s diurnal motion answ]$4 #aba4 ,z to ! common objections aga9/ ! ,e>?'s motion on x's ,axis1 !y are all easily answ]$ & set aside4 ,t x may turn )\t be+ se5 or felt to d s1 has be5 already %ewn1 #aai4 ,b "s are apt to imag9e t if ! ,e>? turns ea/w>d 7z x c]ta9ly does if x turns at all7 a ball fir$ p]p5dicul>ly upw>d 9 ! air mu/ fall consid]ably we/w>d ( ! place x 0 project$ f4 ,?is objection1 :i* at fir/ seems to h "s weight1 w be f\nd to h none at all :5 we consid] t ! gun & ball p>take ( ! ,e>?'s motion2 & !re=e ! ball be+ c>ri$ =w>d ) ! air z quick z ! ,e>? & air turn1 mu/ fall d[n aga9 on ! same place4 ,a /one let fall f ! top ( a ma9-ma/1 if x meets ) no ob/acle1 falls on ! deck z ne> ! foot ( ! ma/ :5 ! %ip sails z :5 x does n4 ,& if an inv]t$ bottle1 full ( liquor1 be hung up to ! ciel+ ( ! cab91 & a small hole be made 9 ! cork to let ! liquor drop ?r\gh on ! floor1 ! drops w fall j z f> =w>d on ! floor :5 ! %ip sails z :5 x is at re/4 ,& gnats or flies c z easily dance among "o ano!r 9 a mov+ cab9 z 9 a fix$ *amb]4 ,z = ^? scripture expressions :i* seem to contradict ! ,e>?'s motion1 ?is g5]al answ] may be made to !m all1 viz4 'tis pla9 f _m in/ances t ! ,scriptures 7 nev] int5d$ to in/ruct u 9 ,philosophy or ,a/ronomy2 & !re=e1 on ^? subjects1 expressions are n always to be tak5 9 ! /ricte/ s5se2 b = ! mo/ "p z accommodat$ to ! common appreh5sions ( mank9d4 ,m5 ( s5se 9 all ages1 :5 n treat+ ( ! sci5ces purposely1 h foll[$ ?is me?od3 & x w\ld be 9 va9 to foll[ any o!r 9 address+ ourselves to ! vulg>1 or bulk ( any community4 ,moses calls ! ,moon ,a ,,great ,,lum9>y 7z x is 9 ! ,hebrew7 z well z ! ,sun3 b ! ,moon is kn[n to be an opaque body1 & ! smalle/ t ,a/ronom]s h obs]v$ 9 ! ,heav5s & %9es ^u u n by any inh]5t light ( x's own1 b by reflect+ ! light ( ! ,sun4 ,if ,moses _h kn[n ?is1 & told ! ,israelites s1 !y w\ld h />$ at him2 & consid]$ him r z a madman ?an z a p]son commission$ by ! ,almighty to be _! lead]4 ,,*ap4 ,,iv4 ,! ,ph5om5a ( ! ,heav5s z se5 f diff]5t p>ts ( ! ,e>?4 ,sid5ote3 ,we are kept to ! ,e>? by gravity4 ,,plate ,,ii4 ,fig4 ,i4 ,antipodes4 ,axis ( ! ,_w4 ,x's ,poles4 ,fig4 ,,ii4 #abb4 ,we are kept to ! ,e>?'s surface on all sides by ! p[] ( x's c5tral attraction2 :i*1 lay+ hold ( all bodies accord+ to _! d5sities or quantities ( matt] )\t reg>d to _! bulks1 con/itutes :at we call _! weight4 ,& hav+ ! sky ov] our heads1 g :]e we w1 & our feet t[>ds ! c5tre ( ! ,e>?1 we call x up ov] our heads1 & d[n "u our feet3 al?\gh ! same "r l9e :i* is d[n to u1 if cont9u$ ?r\gh & beyond ! opposite side ( ! ,e>?1 w\ld be up to ! inhabitants on ! opposite side4 ,=1 ! inhabitants n1 i1 e1 m1 s1 o1 q1 l /& ) _! feet t[>d ! ,e>?'s c5tre ,c2 & h ! same figure ( sky ,n1 l1 ,e1 ,m1 ,s1 ,o1 ,q1 ,l ov] _! heads4 ,!re=e1 ! po9t ,s is z directly upw>d to ! inhabitant s on ! s\? ,pole z ,n is to ! inhabitant n on ! ,nor? ,pole3 s is ,e to ! inhabitant e1 suppos$ to be on ! nor? end ( ,p]u2 & ,q to ! opposite inhabitant q on ! middle ( ! isl& ,sumatra4 ,ea* ( ^! obs]v]s is surpris$ t 8 opposite or ,antipode c /& ) 8 head hang+ d[nw>ds4 ,b let ei!r g to ! o!r1 & he w tell him t he /ood z upright & firm on ! place :]e he 0 z he n[ /&s :]e he is4 ,to all ^! obs]v]s ! ,sun1 ,moon1 & ,/>s seem to turn r\nd ! po9ts ,n & ,s z ! ,poles ( ! fix$ ,axis ,,ncs2 because ! ,e>? does really turn r\nd ! ma!matical l9e n,cs z r\nd an ,axis ( :i* n is ! ,nor? ,pole & s ! ,s\? ,pole4 ,! ,inhabitant ,u 7,fig4 ,,ii47 affirms t he is on ! upp]mo/ side ( ! ,e>?1 & wond]s h[ ano!r at ,l c /& on ! und]mo/ side ) 8 head hang+ d[nw>ds4 ,b ,u 9 ! mean "t =gets t 9 twelve h\rs "t he w be c>ri$ half r\nd ) ! ,e>?2 & !n be 9 ! v situation t ,l n[ is1 al?\gh z f> f him z be=e4 ,& yet1 :5 ,u comes !re1 he w f9d no diff]5ce z to 8 mann] ( /&+2 only he w see ! opposite half ( ! ,heav5s1 & imag9e ! ,heav5s to h gone half r\nd him4 ,sid5ote3 ,h[ our ,e>? might h an upp] & an "u side4 #abc4 ,:5 we see a globe hung up 9 a room we _c help imag9+ x to h an upp] & an "u side1 & imm$iately =m a l idea ( ! ,e>?2 f :5ce we conclude1 t x is z impossible = p]sons to /& on ! "u side ( ! ,e>? z = pebbles to lie on ! "u side ( a common ,globe1 :i* in/antly fall d[n f x to ! gr\nd2 & well !y may1 because ! attraction ( ! ,e>?1 be+ too /rong = ! attraction ( ! ,globe1 pulls !m away4 ,j s w\ld be ! case ) our ,e>?1 if x 7 plac$ ne> a ,globe mu* bigg] ?an itself1 su* z ,jupit]3 = !n x w\ld really h an upp] & an "u side ) respect to t l>ge ,globe2 :i*1 by x's ,attraction1 w\ld pull away e ?+ f ! side ( ! ,e>? next to x2 & only ^? on ! top ( ! opposite or upp] side c\ld keep ^u x4 ,b !re is no l>g] ,globe ne> en\gh our ,e>? to ov]come x's c5tral attraction2 & !re=e x has no su* ?+ z an upp] & an "u side3 = all bodies on or ne> x's surface1 ev5 to ! ,moon1 gravitate t[>ds x's c5t]4 ,sid5ote3 ,,plate ,,ii4 #abd4 ,let any man imag9e t ! ,e>? & e ?+ b himself is tak5 away1 & he left alone 9 ! mid/ ( indef9ite ,space2 he c\ld !n h no idea ( up or d[n2 & 7 8 pockets full ( gold1 he might take ! pieces "o by "o1 & ?r[ !m away on all sides ( him1 )\t any dang] ( los+ !m2 = ! attraction ( 8 body w\ld br+ !m all back by ! ways !y w5t1 & he w\ld be d[n to e "o ( !m4 ,b !n1 if a ,sun or any o!r l>ge body 7 creat$1 & plac$ 9 any "p ( ,space sev]al millions ( miles f him1 he w\ld be attract$ t[>ds x1 & c\ld n save himself f fall+ d[n to x4 ,sid5ote3 ,fig4 ,i4 ,"o half ( ! ,heav5s visible to an inhabitant on any "p ( ! ,e>?4 ,ph5om5a at ! ,poles4 ,,plate ,,ii4 #abe4 ,! ,e>?'s bulk is b a po9t1 z t at ,c1 comp>$ to ! ,heav5s2 & !re=e e inhabitant ^u x1 let him be :]e he w1 z at n1 e1 m1 s1 c4 sees "o half ( ! ,heav5s4 ,! inhabitant n1 on ! ,nor? ,pole ( ! ,e>?1 con/antly sees ! ,hemisph]e ,,enq2 & hav+ ! ,nor? ,pole ,n ( ! ,heav5s j ov] 8 head1 8 #be;,horizon co9cides ) ! ,cele/ial ,equator ,,ecq4 ,!re=e all ! ,/>s 9 ! ,nor!rn ,hemisph]e ,,enc1 betwe5 ! ,equator & ,nor? ,pole1 appe> to turn r\nd ! l9e ,,nc1 mov+ p>allel to ! ,horizon4 ,! ,equatoreal ,/>s keep 9 ! ,horizon1 & all ^? 9 ! ,s\!rn ,hemisph]e ,,esq are invisible4 ,! l ,ph5om5a are se5 by ! obs]v] s on ! ,s\? ,pole1 ) respect to ! ,hemisph]e ,,esq2 & to him ! opposite ,hemisph]e is always invisible4 ,h5ce1 "u ei!r ,pole1 only "o half ( ! ,heav5s is se52 = ^? p>ts :i* are once visible nev] set1 & ^? :i* are once invisible nev] rise4 ,b ! ,ecliptic ,,ycx or ,orbit :i* ! ,sun appe>s to describe once a ye> by ! ,e>?'s annual motion1 has ! half ,,yc con/antly above ! ,horizon ,,ecq ( ! ,nor? ,pole n2 & ! o!r half ,,cx always bel[ x4 ,!re=e :il/ ! ,sun describes ! nor!rn half ,,yc ( ! ,ecliptic he nei!r sets to ! ,nor? ,pole nor rises to ! ,s\?2 & :il/ he describes ! s\!rn half ,,cx he nei!r sets to ! ,s\? ,pole nor rises to ! ,nor?4 ,! same ?+s are true ) respect to ! ,moon2 only ) ?is diff]5ce1 t z ! ,sun describes ! ,ecliptic b once a ye>1 he is = half t "t visible to ea* ,pole 9 x's turn1 & z long invisible2 b z ! ,moon goes r\nd ! ,ecliptic 9 #bg days #h h\rs1 %e is only visible = #ac days #af h\rs1 & z long invisible to ea* ,pole by turns4 ,all ! ,planets likewise rise & set to ! ,poles1 because _! ,orbits are cut obliquely 9 halves by ! ,horizon ( ! ,poles4 ,:5 ! ,sun 79 8 app>5t way f ,x7 arrives at ,c1 :i* is on ! #bj? ( ,m>*1 he is j ris+ to an obs]v] at n on ! ,nor? ,pole1 & sett+ to ano!r at s on ! ,s\? ,pole4 ,f ,c he rises high] & high] 9 e app>5t ,diurnal revolution 'till he comes to ! highe/ po9t ( ! ,ecliptic y1 on ! #ba/ ( ,june1 & !n he is at 8 greate/ ,altitude1 :i* is #bc-a_/b degrees1 or ! ,arc ,ey1 equal to 8 greate/ ,nor? decl9ation2 & f !nce he seems to desc5d gradually 9 e app>5t ,circumvolution1 'till he sets at ,c on ! #bc;d ( ,septemb]2 & !n he goes to exhibit ! l ,appe>ances at ! ,s\? ,pole = ! o!r half ( ! ye>4 ,h5ce ! ,sun's app>5t motion r\nd ! ,e>? is n 9 p>allel ,circles1 b 9 ,spirals2 su* z might be repres5t$ by a ?read w\nd r\nd a ,globe f ,tropic to ,tropic2 ! ,spirals be+ at "s di/ance f "o ano!r ab\t ! ,equator1 b gradually ne>] to ea* o!r z !y approa* ne>] to ! ,tropics4 ,sid5ote3 ,ph5om5a at ! ,equator4 ,fig4 ,i4 #abf4 ,if ! obs]v] be any :]e on ! ,t]re/rial ,equator e,cq1 z suppose at e1 he is 9 ! ,plane ( ! ,cele/ial ,equator2 or "u ! ,equ9octial ,,ecq2 & ! ,axis ( ! ,e>? n,cs is co9cid5t ) ! ,plane ( 8 ,horizon1 ext5d$ out to ,n & ,s1 ! ,nor? & ,s\? ,poles ( ! ,heav5s4 ,z ! ,e>? turns r\nd ! l9e ,,ncs1 ! :ole ,heav5s ,m,o,ll seem to turn r\nd ! same l9e1 b ! contr>y way4 ,x is pla9 t ?is obs]v] has ! ,poles con/antly 9 8 ,horizon1 & t 8 ,horizon cuts ! ,diurnal pa?s ( all ! ,cele/ial bodies p]p5dicul>ly & 9 halves4 ,!re=e ! ,sun1 ,planets1 & ,/>s rise e day1 & asc5d p]p5dicul>ly above ! ,horizon = six h\rs1 & pass+ ov] ! ,m]idian1 desc5d 9 ! same mann] = ! six foll[+ h\rs2 !n set 9 ! ,horizon1 & cont9ue twelve h\rs bel[ x4 ,consequ5tly at ! ,equator ! days & nights are equally long ?r\gh\t ! ye>4 ,:5 ! obs]v] is 9 ! situation e1 he sees ! ,hemisph]e ,,s52 b 9 twelve h\rs aft]1 he is c>ri$ half r\nd ! ,e>?'s ,axis to q1 & !n ! ,hemisph]e ,,sqn becomes visible to him2 & ,,s5 disappe>s1 be+ hid by ! ,convexity ( ! ,e>?4 ,?us we f9d t to an obs]v] at ei!r ( ! ,poles "o half ( ! ,sky is always visible1 & ! o!r half nev] se52 b to an obs]v] on ! ,equator ! :ole ,sky is se5 e #bd h\rs4 ,! ,figure "h ref]r$ to1 repres5ts a ,cele/ial globe ( glass1 hav+ a ,t]re/rial globe )9 x2 aft] ! mann] ( ! ,glass ,sph]e inv5t$ by my g5]\s fri5d ,dr4 ,,long1 ,l[ndes's ,pr(essor ( ,a/ronomy 9 ,cambridge4 ,sid5ote3 ,rem>k4 #abg4 ,if a ,globe be held sidewise to ! eye1 at "s di/ance1 & s t nei!r ( x's ,poles c be se51 ! ,equator ,,ecq & all ,circles p>allel to x1 z ,,dl1 yzx1 ab,x1 ,,mo1 c4 w appe> to be /raight l9es1 z project$ 9 ?is ,figure2 :i* is requisite to be m5tion$ "h1 because we %all h occasion to call !m ,circles 9 ! foll[+ ,article#bf4 ,sid5ote3 ,ph5om5a betwe5 ! ,equator & ,poles4 ,! ,circles ( p]petual ,app>ition & ,occultation4 #abh4 ,let u n[ suppose t ! obs]v] has gone f ! ,equator e t[>ds ! ,nor? ,pole n1 & t he /ops at i1 f :i* place he !n sees ! ,hemisph]e ,m,el,n,l2 8 ,horizon ,,mcl hav+ %ift$ z _m #bg;,degrees f ! ,cele/ial poles ,n & ,s z he has travell$ f "u ! ,equ9octial ,e4 ,& z ! ,heav5s seem con/antly to turn r\nd ! l9e ,,ncs z an ,axis1 all ^? ,/>s :i* are z f> f ! ,nor? ,pole ,n z ! obs]v] is f "u1 ! ,equ9octial1 namely ! ,/>s nor? ( ! dott$ p>allel ,,dl1 nev] set bel[ ! ,horizon2 & ^? :i* are s\? ( ! dott$ p>allel ,,mo nev] rise above x4 ,h5ce1 ! =m] ( ^! two p>allel ,circles is call$ ! ,circle ( p]petual ,app>ition1 & ! latt] ! ,circle ( p]petual ,occultation3 b all ! ,/>s betwe5 ^! two ,circles rise & set e day4 ,let u imag9e _m ,circles to be drawn betwe5 ^! two1 & p>allel to !m2 ^? :i* are on ! nor? side ( ! ,equ9octial w be unequally cut by ! ,horizon ,,mcl1 hav+ l>g] portions above ! ,horizon ?an bel[ x2 & ! m s1 z !y are ne>] to ! ,circle ( p]petual ,app>ition2 b ! rev]se happ5s to ^? on ! s\? side ( ! ,equ9octial1 :il/ ! ,equ9octial is divid$ 9 two equal p>ts by ! ,horizon4 ,h5ce1 by ! app>5t turn+ ( ! ,heav5s1 ! nor!rn ,/>s describe great] ,arcs or ,portions ( ,circles above ! ,horizon ?an bel[ x2 & ! great] z !y are f>!r f ! ,equ9octial t[>ds ! ,circle ( p]petual ,app>ition2 :il/ ! contr>y happ5s to all ,/>s s\? ( ! ,equ9octial3 b ^? ^u x describe equal ,arcs bo? above & bel[ ! ,horizon1 & !re=e !y are j z long above z bel[ x4 ,sid5ote3 ,,plate ,,ii4 #abi4 ,an obs]v] on ! ,equator has no ,circle ( p]petual ,app>ition or ,occultation1 because all ! ,/>s1 toge!r ) ! ,sun & ,moon1 rise & set to him e day4 ,b1 z a b>e view ( ! ,figure is suffici5t to %ew t ^! two ,circles ,,dl & ,,mo are j z f> f ! ,poles ,n & ,s z ! obs]v] at i 7or "o opposite to him at o7 is f ! ,equator ,,ecq2 x is pla91 t if an obs]v] beg9s to travel f ! ,equator t[>ds ei!r ,pole1 8 ,circle ( p]petual ,app>ition rises f t ,pole z f a ,po9t1 & 8 ,circle ( p]petual ,occultation f ! o!r4 ,z ! obs]v] advances t[>d ! ne>] ,pole1 ^! two ,circles enl>ge _! diamet]s1 & come ne>] "o ano!r1 until he comes to ! ,pole2 & !n !y meet & co9cide 9 ! ,equator4 ,on diff]5t sides ( ! ,equator1 to obs]v]s at equal di/ances f x1 ! ,circle ( p]petual ,app>ition to "o is ! ,circle ( p]petual ,occultation to ! o!r4 ,sid5ote3 ,:y ! ,/>s always describe ! same p>allel ( motion1 & ! ,sun a diff]5t4 #acj4 ,because ! ,/>s nev] v>y _! di/ances f ! ,equ9octial1 s z to be s5sible 9 an age1 ! l5g?s ( _! diurnal & nocturnal ,arcs are always ! same to ! same places on ! ,e>?4 ,b z ! ,e>? goes r\nd ! ,sun e ye> 9 ! ,ecliptic1 "o half ( :i* is on ! nor? side ( ! ,equ9octial & ! o!r half on x's s\? side1 ! ,sun appe>s to *ange 8 place e day1 s z to g once r\nd ! ,circle ,,ycx e ye> #aad4 ,!re=e :il/ ! ,sun appe>s to advance nor?w>d1 f hav+ describ$ ! ,p>allel ab,x t\*+ ! ,ecliptic 9 ,x ! days cont9ually l5g!n & ! nights %ort51 until he comes to y & describes ! ,p>allel yzx1 :5 ! days are at ! longe/ & ! nights at ! %orte/3 = !n1 z ! ,sun goes no f>!r nor?w>d1 ! greate/ portion t is possible ( ! diurnal ,arc yz is above ! ,horizon ( ! inhabitant i2 & ! smalle/ portion zx bel[ x4 ,z ! ,sun decl9es s\?w>d f y he describes small] diurnal & great] nocturnal ,arcs1 or ,portions ( ,circles1 e day2 :i* cause? ! days to %ort5 & nights to l5g!n1 until he arrives aga9 at ! ,p>allel ab,x2 :i* hav+ only ! small "p ab above ! ,horizon ,,mcl1 & ! great "p b,x bel[ x1 ! days are at ! %orte/ & ! nights at ! longe/2 because ! ,sun rec$es no f>!r s\?1 b returns nor?w>d z be=e4 ,x is easy to see t ! ,sun mu/ be 9 ! ,equ9octial ,,ecq twice e ye>1 & !n ! days & nights are equally long2 t is1 #ab h\rs ea*4 ,^! h9ts s]ve at pres5t to give an idea ( "s ( ! ,appe>ances result+ f ! motions ( ! ,e>?2 :i* w be m p>ticul>ly describ$ 9 ! t5? ,*apt]4 ,sid5ote3 ,fig4 ,i4 ,p>allel1 ,oblique1 & ,"r sph]e1 :at4 #aca4 ,to an obs]v] at ei!r ,pole1 ! ,horizon & ,equ9octial are co9cid5t2 & ! ,sun & ,/>s seem to move p>allel to ! ,horizon3 !re=e1 su* an obs]v] is said to h a ,p>allel position ( ! ,sph]e4 ,to an obs]v] any :]e betwe5 ! ,poles & ,equator1 ! ,p>allels describ$ by ! ,sun & ,/>s are cut obliquely by ! ,horizon1 & !re=e he is said to h an ,oblique position ( ! ,sph]e4 ,to an obs]v] any :]e on ! ,equator1 ! ,p>allels ( ,motion1 describ$ by ! ,sun & ,/>s are cut p]p5dicul>ly1 or at ,"r angles1 by ! ,horizon2 & !re=e he is said to h a ,"r position ( ! ,sph]e4 ,& ^! ?ree are all ! diff]5t ways t ! ,sph]e c be posit$ to all p1 on ! ,e>?4 ,,*ap4 ,v4 ,! ,ph5om5a ( ! ,heav5s z se5 f diff]5t ,p>ts ( ! ,sol> ,sy/em4 #acb4 ,s va/ly great is ! di/ance ( ! />ry ,heav5s1 t if view$ f any "p ( ! ,sol> ,sy/em1 or ev5 _m millions ( miles beyond x1 its appe>ance w\ld be ! v same to u4 ,! ,sun & ,/>s w\ld all seem to be fix$ on "o concave surface1 ( :i* ! ,spectator's eye w\ld be ! c5tre4 ,b ! ,planets1 be+ mu* ne>] ?an ! ,/>s1 _! appe>ances w v>y consid]ably ) ! place f :i* !y are view$4 #acc4 ,if ! spectator is at re/ )\t _! ,orbits1 ! ,planets w seem to be at ! same di/ance z ! ,/>s2 b cont9ually *ang+ _! places ) respect to ! ,/>s1 & to "o ano!r3 assum+ v>i\s phases ( increase & decrease l ! ,moon4 ,&1 not)/&+ _! regul> motions ab\t ! ,sun1 w sometimes appe> to move quick]1 sometimes sl[]1 be z (t5 to ! we/ z to ! ea/ ( ! ,sun2 & at _! greate/ di/ances seem q /ation>y4 ,! duration1 ext5t1 & po9ts 9 ! ,heav5s :]e ^! digressions beg9 & end1 w\ld be m or less accord+ to ! respective di/ances ( ! sev]al ,planets f ! ,sun3 b 9 ! same ,planet !y w\ld cont9ue inv>iably ! same at all times2 l p5dulums ( unequal l5g?s oscillat+ toge!r1 ! %ort] move quick & g ov] a small space1 ! long] move sl[ & g ov] a l>ge space4 ,if ! obs]v] is at re/ )9 ! ,orbits ( ! ,planets1 b n ne> ! common c5t]1 _! app>5t motions w be irregul>1 b less s ?an 9 ! =m] case4 ,ea* ( ! sev]al ,planets w appe> bigg] & less by turns1 z !y approa* ne>] or rec$e f>!r f ! obs]v]2 ! ne>e/ v>y+ mo/ 9 _! size4 ,!y w also move quick] or sl[] ) reg>d to ! fix$ ,/>s1 b w nev] be retrograde or /ation>y4 #acd4 ,next1 let a spectator 9 motion view ! ,heav5s3 ! same app>5t irregul>ities w be obs]v$1 b ) "s v>iation result+ f 8 own motion4 ,if he is on a ,planet :i* has a rotation on x's ,axis1 n be+ s5sible ( 8 own motion he w imag9e ! :ole ,heav5s1 ,sun1 ,planets1 & ,/>s to revolve ab\t him 9 ! same "t t 8 ,planet turns r\nd1 b ! contr>y way2 & w n be easily conv9c$ ( ! deception4 ,if 8 ,planet moves r\nd ! ,sun1 ! same irregul>ities & aspects z above w appe> 9 ! motions ( ! ,planets3 only1 ! times ( _! be+ direct1 /ation>y & retrograde w be accel]at$ or ret>d$ z !y concur )1 or are contr>y to 8 motion3 & ! ,sun w seem to move among ! fix$ ,/>s or ,signs1 directly opposite to ^? 9 :i* 8 ,planet moves2 *ang+ x's place e day z he does4 ,9 a ^w1 :e!r our obs]v] be 9 motion or at re/1 :e!r )9 or )\t ! ,orbits ( ! ,planets1 _! motions w seem irregul>1 intricate & p]plex$1 unless he is 9 ! c5t] ( ! ,sy/em2 & f !nce1 ! mo/ beautiful ord] & h>mony w be obs]v$4 ,sid5ote3 ,! ,sun's c5t] ! only po9t f :i* ! true motions & places ( ! ,planets c\ld be se54 #ace4 ,! ,sun be+ ! c5t] ( all ! ,planets motions1 ! only place f :i* _! motions c\ld be truly se51 is ! ,sun's c5t]2 :]e ! obs]v] be+ suppos$ n to turn r\nd ) ! ,sun 7:i*1 9 ?is case1 we mu/ imag9e to be a transp>5t body7 w\ld see all ! ,/>s at re/1 & seem+ly equidi/ant f him4 ,to su* an obs]v] ! ,planets w\ld appe> to move among ! fix$ ,/>s1 9 a simple1 regul>1 & uni=m mann]2 only1 t z 9 equal times !y describe equal ,areas1 !y w\ld describe spaces some:at unequal1 because !y move 9 elliptic ,orbits #aee4 ,_! motions w\ld also appe> to be :at !y are 9 fact1 ! same way r\nd ! ,heav5s2 9 pa?s :i* cross at small ,angles 9 diff]5t p>ts ( ! ,heav5s1 & !n sep>ate a little f "o ano!r #bj4 ,s t1 if ! sol> ,a/ronom] %\ld make ! ,pa? or ,orbit ( any "o ,planet a /&>d1 & consid] x z hav+ no obliquity #bja1 he w\ld judge ! pa?s ( all ! re/ to be incl9$ to x2 ea* ,planet hav+ "o half ( x's pa? on "o side1 & ! o!r half on ! opposite side ( ! /&>d ,pa? or ,orbit4 ,& if he %\ld ev] see all ! ,planets />t f a conjunction ) ea* o!r#bh2 ,m]cury w\ld move s mu* fa/] ?an ,v5us z to ov]take h] aga9 7?\gh n 9 ! same po9t ( ! ,heav5s7 9 a quantity ( "t almo/ equal to #ade ( our days & nights2 or1 z we commonly call !m1 ,natural ,days1 :i* include bo? ! days & nights3 ,v5us w\ld move s mu* fa/] ?an ! ,e>? z to ov]take x aga9 9 #ehe natural days3 ! ,e>? s mu* fa/] ?an ,m>s z to ov]take him aga9 9 #ggh su* days3 ,m>s is mu* fa/] ?an ,jupit] z to ov]take him aga9 9 #hag su* days3 & ,jupit] s mu* fa/] ?an ,saturn z to ov]take him aga9 9 #gbcf days1 all ( our "t4 ,sid5ote3 ,! judgm5t t a sol> ,a/ronom] w\ld probably make conc]n+ ! di/ances & bulks ( ! ,planets4 #acf4 ,b z our sol> ,a/ronom] c\ld h no idea ( measur+ ! c\rses ( ! ,planets by our days1 he w\ld v probably take ! p]iod ( ,m]cury1 :i* is ! quicke/ mov+ ,planet1 = a measure to comp>e ! p]iods ( ! o!rs by4 ,z all ! ,/>s w\ld appe> quiesc5t to him1 he w\ld nev] ?9k t !y _h any dep5dance ^u ! ,sun2 b c\ld naturally imag9e t ! ,planets h1 because !y move r\nd ! ,sun4 ,& x is by no means improbable1 t he w\ld conclude ^? ,planets ^: p]iods are quicke/ to move 9 ,orbits proportionably less ?an ^? d :i* make sl[] circuits4 ,b be+ de/itute ( a me?od = f9d+ _! ,p>allaxes1 or1 m prop]ly speak+1 z !y c\ld h no ,p>allax to him1 he c\ld nev] "k any ?+ ( _! real di/ances or magnitudes4 ,_! relative di/ances he might p]haps guess at by _! p]iods1 & f !nce inf] some?+ ( tru? conc]n+ _! relative bulks1 by comp>+ _! app>5t bulks ) "o ano!r4 ,= example1 ,jupit] appe>+ bigg] to him ?an ,m>s1 he w\ld conclude x to be mu* bigg] 9 fact2 because x appe>s s1 & mu/ be f>!r f him1 on acc\nt ( x's long] p]iod4 ,m]cury w\ld seem bigg] ?an ! ,e>?2 b by comp>+ x's p]iod ) ! ,e>?'s1 he w\ld conclude t ! ,e>? is mu* f>!r f him ?an ,m]cury1 & consequ5tly t x mu/ be really bigg] ?\gh app>5tly less2 & s ( ! re/4 ,&1 z ea* ,planet w\ld appe> some:at bigg] 9 "o "p ( x's ,orbit ?an 9 ! opposite1 & to move quicke/ :5 x seems bigge/1 ! obs]v] w\ld be at no loss to det]m9e t all ! ,planets move 9 ,orbits ( :i* ! ,sun is n precisely 9 ! c5t]4 ,sid5ote3 ,! ,planet>y motions v irregul> z se5 f ! ,e>?4 ,,plate ,,iii4 #acg4 ,! app>5t magnitudes ( ! ,planets cont9ually *ange z se5 f ! ,e>?1 :i* demon/rates t !y approa* ne>] to x1 & rec$e f>!r f x by turns4 ,f ^! ,ph5om5a1 & _! app>5t motions among ! ,/>s1 !y seem to describe loop$ curves :i* nev] return into !mselves1 ,v5us's pa? except$4 ,& if we 7 to trace out all _! app>5t pa?s1 & put ! figures ( !m toge!r 9 "o diagram1 !y w\ld appe> s anomal\s & confus$1 t no man 9 8 s5ses c\ld believe !m to be repres5tations ( _! real pa?s2 b w\ld imm$iately conclude1 t su* app>5t irregul>ities mu/ be ow+ to "s ,optic illusions4 ,& aft] a good deal ( enquiry1 he might p]haps be at a loss to f9d out ! true cause ( ^! inequalities2 especially if he 7 "o ( ^? :o w\ld r1 ) ! greate/ ju/ice1 *>ge frail man ) ignorance1 ?an ! ,almighty ) be+ ! au?or ( su* confusion4 ,sid5ote3 ,^? ( ,m]cury & ,v5us repres5t$4 ,fig4 ,i4 #ach4 ,dr4 ,,long1 9 8 fir/ volume ( ,a/ronomy1 has giv5 u figures ( ! app>5t pa?s ( all ! ,planets sep>ately f ,,cass9i2 & on see+ !m ,i fir/ ?\ght ( attempt+ to trace "s ( !m by a ma*9e#bi t %ews ! motions ( ! ,sun1 ,m]cury1 ,v5us1 ! ,e>? & ,moon1 accord+ to ! ,cop]nican ,sy/em4 ,hav+ tak5 (f ! ,sun1 ,m]cury1 & ,v5us1 ,i put black-lead p5cils 9 _! places1 ) ! po9ts turn$ upw>d2 & fix$ a circul> %eet ( pa/e-bo>d s1 t ! ,e>? kept con/antly "u x's c5t] 9 go+ r\nd ! ,sun2 & ! pa/e-bo>d kept its p>allelism4 ,!n1 press+ g5tly ) "o h& ^u ! pa/e-bo>d to make x t\* ! ?ree p5cils1 ) ! o!r h& ,i turn$ ! w9* :i* moves ! :ole ma*9]y3 & z ! ,e>?1 toge!r ) ! p5cils 9 ! places ( ,m]cury & ,v5us1 _h _! prop] motions r\nd ! ,sun's p5cil1 :i* kept at re/ 9 ! c5t] ( ! ma*9e1 all ! ?ree p5cils describ$ a diagram f :i* ! fir/ ,figure ( ! ?ird ,plate is truly copi$ 9 a small] size4 ,z ! ,e>? mov$ r\nd ! ,sun1 ! ,sun's p5cil describ$ ! dott$ ,circle ( ,mon?s1 :il/ ,m]cury's p5cil drew ! curve ) ! greate/ numb] ( loops1 & ,v5us's t ) ! fewe/4 ,9 _! inf]i\r conjunctions !y come z mu* ne>] ! ,e>?1 or )9 ! ,circle ( ! ,sun's app>5t motion r\nd ! ,heav5s1 z !y g beyond x 9 _! sup]i\r conjunctions4 ,on ea* side ( ! loops !y appe> ,/ation>y2 9 t "p ( ea* loop next ! ,e>? retrograde2 & 9 all re/ ( _! pa?s direct4 ,illu/ration3 ,plate ,,iii4 ,j4 ,f]guson del94 ,j4 ,mynde ,sc4 ,sid5ote3 ,,plate ,,iii4 ,if ,cass9i's ,figures ( ! pa?s ( ! ,sun1 ,m]cury & ,v5us 7 put toge!r1 ! ,figure z above trac$ out1 w\ld be exactly l !m4 ,x repres5ts ! ,sun's app>5t motion r\nd ! ,ecliptic1 :i* is ! same e ye>2 ,m]cury's motion = sev5 ye>s2 & ,v5us's = eight2 9 :i* "t ,m]cury's pa? makes #bc loops1 cross+ itself s _m times1 & ,v5us's only five4 ,9 eight ye>s ,v5us falls s ne>ly into ! same app>5t pa? aga91 z to deviate v little f x 9 "s ages2 b 9 :at numb] ( ye>s ,m]cury & ! re/ ( ! ,planets w\ld describe ! same visible pa?s ov] aga91 ,i _c at pres5t det]m9e4 ,hav+ f9i%$ ! above ,figure ( ! pa?s ( ,m]cury & ,v5us1 ,i put ! ,ecliptic r\nd !m z 9 ! ,doctor's ,book2 & add$ ! dott$ l9es f ! ,e>? to ! ,ecliptic = %ew+ ,m]cury's app>5t or geoc5tric motion !re9 = "o ye>2 9 :i* "t 8 pa? makes ?ree loops1 & goes on a little f>!r2 :i* %ews t he has ?ree inf]i\r1 & z _m sup]i\r conjunctions ) ! ,sun 9 t "t1 & also t he is six times ,/ation>y1 & ?rice ,retrograde4 ,let u n[ trace out 8 motion = "o ye> 9 ! ,figure4 ,sid5ote3 ,fig4 ,i4 ,suppose ,m]cury to be sett+ out f ,a t[>ds ,b 7betwe5 ! ,e>? & left-h& corn] ( ! ,plate7 & z se5 f ! ,e>? 8 motion w !n be direct1 or accord+ to ! ord] ( ! ,signs4 ,b :5 he comes to ,b1 he appe>s to /& /ill 9 ! #bc;d degree ( at ,f1 z %ewn by ! l9e ,,bf4 ,:il/ he goes f ,b to ,c1 ! l9e ,,bf goes backw>d f ,f to ,e1 or contr>y to ! ord] ( ,signs2 & :5 he is at ,c he appe>s ,/ation>y at ,e2 hav+ gone back #aa-a_/b degrees4 ,n[1 suppose him ,/ation>y on ! fir/ ( ,janu>y at ,c1 on ! t5? !re( he w appe> 9 ! ,heav5s z at #bj1 ne> ,f2 on ! #bj? he w be se5 z at ,g2 on ! #ca/ at ,h2 on ! #aj? ( ,febru>y at ,i2 on ! #bj? at ,k2 & on ! #bh? at ,l2 z ! dott$ l9es %ew1 :i* are drawn ?r\gh e t5? day's motion 9 8 loop$ pa?1 & cont9u$ to ! ,ecliptic4 ,on ! #aj? ( ,m>* he appe>s at ,m2 on ! #bj? at ,n2 & on ! #ca/ at ,o4 ,on ! #aj? ( ,april he appe>s ,/ation>y at ,p2 on ! #bj? he seems to h gone back aga9 to ,o2 & on ! #cj? he appe>s ,/ation>y at ,q hav+ gone back #aa-a_/b degrees4 ,?us ,m]cury seems to g =w>d #d ,signs #aa ,degrees1 or #aca ,degrees2 & to g back only #aa or #ab ,degrees1 at a mean rate4 ,f ! #cj? ( ,april to ! #aj? ( ,may1 he seems to move f ,q to ,r2 & on ! #bj? he is se5 at ,s1 go+ =w>d 9 ! same mann] aga91 accord+ to ! ord] ( lett]s2 & backw>d :5 !y g back2 :i*1 'tis ne$less to expla9 any f>!r1 z ! read] c trace him out s easily ?r\gh ! re/ ( ! ye>4 ,! same appe>ances happ5 9 ,v5us's motion2 b z %e moves sl[] ?an ,m]cury1 !re are long] int]vals ( "t betwe5 !m4 ,hav+ already #abj4 giv5 "s acc\nt ( ! app>5t diurnal motions ( ! ,heav5s z se5 f ! diff]5t ,planets1 we %all n tr\ble ! read] any m ) t subject4 ,,*ap4 ,,vi4 ,! ,ptolemean ,sy/em refut$4 ,! ,motions & ,phases ( ,m]cury & ,v5us expla9$4 #aci4 ,! ,ty*onic ,sy/em #ig1 be+ suffici5tly refut$ by ! #aji? ,article1 we %all say no?+ m ab\t x4 #adj4 ,! ,ptolemean ,sy/em #if1 :i* ass]ts ! ,e>? to be at re/ 9 ! ,c5t] ( ! ,univ]se1 & all ! ,planets ) ! ,sun & ,/>s to move r\nd x1 is evid5tly false & absurd4 ,= if ?is hypo!sis 7 true1 ,m]cury & ,v5us c\ld nev] be hid beh9d ! ,sun1 z _! ,orbits are includ$ )9 ! ,sun's3 & aga91 ^! two ,planets w\ld always move direct1 & be z (t5 9 ,opposition to ! ,sun z 9 ,conjunction ) him4 ,b ! contr>y ( all ?is is true3 = !y are j z (t5 beh9d ! ,sun z be=e him1 appe> z (t5 to move backw>ds z =w>ds1 & are s f> f be+ se5 at any "t 9 ! side ( ! ,heav5s opposite to ! ,sun1 t !y 7 nev] se5 a qu>t] ( a circle 9 ! ,heav5s di/ant f him4 ,sid5ote3 ,appe>ances ( ,m]cury & ,v5us4 #ada4 ,^! two ,planets1 :5 view$ ) a good telescope1 appe> 9 all ! v>i\s %apes ( ! ,moon2 :i* is a pla9 pro( t !y are enlight5$ by ! ,sun1 & %9e n by any light ( _! own3 = if !y did1 !y w\ld con/antly appe> r\nd z ! ,sun does2 & c\ld nev] be se5 l d>k spots ^u ! ,sun :5 !y pass directly betwe5 him & u4 ,_! regul> ,phases demon/rate !m to be ,sph]ical bodies2 z may be %ewn by ! foll[+ exp]im5t4 ,sid5ote3 ,exp]im5t to prove !y are r\nd4 ,hang an ivory ball by a ?read1 & let any ,p]son move x r\nd ! flame ( a c&le1 at two or ?ree y>ds di/ance f y\r ,eye3 :5 ! ball is beyond ! c&le1 s z to be almo/ hid by ! flame1 x's enlight5$ side w be t[>ds y1 & appe> r\nd l ! ,full ,moon3 ,:5 ! ball is betwe5 y & ! c&le1 x's enlight5$ side w disappe>1 z ! ,moon does at ! ,*ange3 ,:5 x is half way betwe5 ^! two positions1 x w appe> half illum9at$1 l ! ,moon 9 h] ,qu>t]s3 ,b 9 e o!r place betwe5 ^! positions1 x w appe> m or less horn$ or gibb\s4 ,if ?is exp]im5t be made ) a circul> plate :i* has a flat surface1 y may make x appe> fully enlight5$1 or n enlight5$ at all2 b c nev] make x seem ei!r horn$ or gibb\s4 ,sid5ote3 ,,plate ,,ii4 ,exp]im5t to repres5t ! motions ( ,m]cury & ,v5us4 #adb4 ,if y remove ab\t six or sev5 y>ds f ! c&le1 & place y\rself s t x's flame may be j ab\t ! height ( y\r eye1 & !n desire ! o!r p]son to move ! ball sl[ly r\nd ! c&le z be=e1 keep+ x z ne> ( an equal height ) ! flame z he possibly c1 ! ball w appe> to y n to move 9 a circle1 b r to vibrate backw>d & =w>d l a p5dulum2 mov+ quicke/ :5 x is directly betwe5 y & ! c&le1 & :5 directly beyond x2 & gradually sl[] z x goes f>!r to ! "r or left side ( ! flame1 until x appe>s at ! greate/ di/ance f ! flame2 & !n1 ?\gh x cont9ues to move ) ! same velocity1 x w seem to /& /ill = a mom5t4 ,9 e ,revolution x w %ew all ! above ,phases #ada2 & if two balls1 a small] & a great]1 be mov$ 9 ?is mann] r\nd ! c&le1 ! small] ball be+ kept ne>e/ ! flame1 & c>ri$ r\nd almo/ ?ree times z (t5 z ! great]1 y w h a tol]ably good repres5tation ( ! app>5t ,motions ( ,m]cury & ,v5us2 especially1 if ! bigg] ball describes a circle almo/ twice z l>ge 9 diamet] z ! circle describ$ by ! less]4 ,sid5ote3 ,fig4 ,,iii4 ,! elongations or digressions ( ,m]cury f ! ,sun4 ,,plate ,,ii4 #adc4 ,let ,,abcde be a "p or segm5t ( ! visible ,heav5s1 9 :i* ! ,sun1 ,moon1 ,planets1 & ,/>s appe> to move at ! same di/ance f ! ,e>? ,e4 ,= !re are c]ta9 limits1 beyond :i* ! eye _c judge ( diff]5t di/ances2 z is pla9 f ! ,moon's appe>+ to be no ne>] to u ?an ! ,sun & ,/>s are4 ,let ! circle fghiklmno be ! ,orbit 9 :i* ,m]cury m moves r\nd ! ,sun ,s1 accord+ to ! ord] ( ! lett]s4 ,:5 ,m]cury is at f1 he disappe>s to ! ,e>? at ,e1 because 8 enlight5$ side is turn$ f x2 unless he be !n 9 "o ( 8 ,nodes #bj1 #be2 9 :i* case1 he w appe> l a d>k spot ^u ! ,sun4 ,:5 he is at g 9 8 ,orbit1 he appe>s at ,b 9 ! ,heav5s1 we/w>d ( ! ,sun ,s1 :i* is se5 at ,c3 :5 at h1 he appe>s at ,a1 at 8 greate/ we/]n elongation or di/ance f ! ,sun2 & !n seems to /& /ill4 ,b1 z he moves f h to i1 he appe>s to g f ,a to ,b2 & seems to be 9 ! same place :5 at i z :5 he 0 at g1 only n ne> s big3 at k he is hid f ! ,e>? ,e by ! ,sun ,s2 be+ !n 9 8 sup]i\r ,conjunction4 ,9 go+ f k to l1 he appe>s to move f ,c to ,d2 & :5 he is at n1 he appe>s /ation>y at ,e2 be+ se5 z f> ea/ f ! ,sun !n1 z he 0 we/ f him at ,a4 ,9 go+ f n to o 9 8 ,orbit1 he seems to g back aga9 9 ! ,heav5s1 f ,e to ,d2 & is se5 9 ! same place 7) respect to ! ,sun7 at o z :5 he 0 at l2 b ( a l>g] diamet] at o1 because he is !n ne>] ! ,e>? ,e3 & :5 he comes to f1 he aga9 passes by ! ,sun1 & disappe>s z be=e4 ,9 go+ f n to h 9 8 ,orbit1 he seems to g backw>d 9 ! ,heav5s f ,e to ,a2 & 9 go+ f h to n1 he seems to g =w>d f ,a to ,e4 ,z he goes on f f a little ( 8 enlight5$ side at g is se5 f ,e2 at h he appe>s half full1 because half ( 8 enlight5$ side is se52 at i1 gibb\s1 or m ?an half full2 & at k he w\ld appe> q full1 7 he n hid f ! ,e>? ,e by ! ,sun ,s4 ,at l he appe>s gibb\s aga92 at n half decreas$1 at o horn$1 & at f new l ! ,moon at h] ,*ange4 ,he goes soon] f 8 ea/]n /ation at n to 8 we/]n /ation at h ?an f h to n aga92 because he goes ?r\gh less ?an half 8 ,orbit 9 ! =m] case1 & m 9 ! latt]4 ,sid5ote3 ,fig4 ,,iii4 ,! ,elongations & ,phases ( ,v5us4 ,! greate/ ,elongations ( ,m]cury & ,v5us4 #add4 ,9 ! same ,figure1 let ,,fghiklmn be ! ,orbit 9 :i* ,v5us v moves r\nd ! ,sun ,s1 accord+ to ! ord] ( ! lett]s3 & let ,e be ! ,e>? z be=e4 ,:5 ,v5us is at ,f %e is 9 h] inf]i\r ,conjunction2 & disappe>s l ! ,new ,moon because h] d>k side is t[>d ! ,e>?4 ,at ,g %e appe>s half enlight5$ to ! ,e>?1 l ! ,moon 9 h] fir/ qu>t]3 at h %e appe>s gibb\s2 at ,i1 almo/ full2 h] enlight5$ side be+ !n ne>ly t[>ds ! ,e>?3 at ,k1 %e w\ld appe> q full to ! ,e>? ,e2 b is hid f x by ! ,sun ,s3 at ,l1 %e appe>s ^u ! decrease1 or gibb\s2 at ,m1 m s2 at ,n1 only half enlight5$2 & at ,f %e disappe>s aga94 ,9 mov+ f ,n to ,g1 %e seems to g backw>d 9 ! ,heav5s2 & f ,g to ,n1 =w>d3 b1 z %e describes a mu* great] portion ( h] ,orbit 9 go+ f ,g to ,n ?an f ,n to ,g1 %e appe>s mu* long] direct ?an retrograde 9 h] motion4 ,at ,n & ,g %e appe>s /ation>y2 z ,m]cury does at n & h4 ,m]cury1 :5 /ation>y seems to be only #bh degrees f ! ,sun2 & ,v5us :5 s1 #dg2 :i* is a demon/ration t ,m]cury's ,orbit is includ$ )9 ,v5us's1 & ,v5us's )9 ! ,e>?'s4 ,sid5ote3 ,morn+ & ,ev5+ ,/>1 :at4 #ade4 ,v5us1 f h] sup]i\r ,conjunction at ,k to h] inf]i\r ,conjunction at ,f is se5 on ! ea/ side ( ! ,sun ,s f ! ,e>?4 ,e2 & !re=e %e %9es 9 ! ,ev5+ aft] ! ,sun sets1 & is call$ ! ,ev5+ ,/>3 =1 ! ,sun be+ !n to ! we/w>d ( ,v5us1 he mu/ set fir/4 ,f h] inf]i\r ,conjunction to h] sup]i\r1 %e appe>s on ! we/ side ( ! ,sun2 & !re=e rises be=e him1 = :i* reason %e is call$ ! ,morn+ ,/>4 ,:5 %e is ab\t ,n or ,g1 %e %9es s bright1 t bodies ca/ %ad[s 9 ! night-"t4 ,sid5ote3 ,,plate ,,ii4 ,! /ation>y places ( ! ,planets v>iable4 #adf4 ,if ! ,e>? kept always at ,e1 x is evid5t t ! ,/ation>y places ( ,m]cury & ,v5us w\ld always be 9 ! same po9ts ( ! ,heav5s :]e !y 7 be=e4 ,= example2 :il/ ,m]cury m goes f h to n1 accord+ to ! ord] ( ! lett]s1 he appe>s to describe ! arc ,,abcde 9 ! ,heav5s1 direct3 & :il/ he goes f n to h1 he seems to describe ! same arc back aga91 f ,e to ,a1 retrograde3 always at n & h he appe>s /ation>y at ! same po9ts ,e & ,a z be=e4 ,b ,m]cury goes r\nd 8 ,orbit1 f f to f aga91 9 #hh days2 & yet !re are #aaf days f any "o ( 8 ,conjunctions1 or app>5t ,/ations1 to ! same aga93 & ! places ( ^! ,conjunctions & ,/ations are f\nd to be ab\t #aad degrees ea/w>d f ! po9ts ( ! ,heav5s :]e !y 7 la/ be=e2 :i* proves1 t ! ,e>? has n kept all t "t at ,e1 b has _h a progressive motion 9 x's ,orbit f ,e to t4 ,v5us also diff]s e "t 9 ! places ( h] ,conjunctions & ,/ations2 b mu* m ?an ,m]cury2 because1 z ,v5us describes a mu* l>g] ,orbit ?an ,m]cury does1 ! ,e>? advances s mu* ! f>!r 9 x's annual pa? be=e ,v5us comes r\nd aga94 ,sid5ote3 ,! ,elongations ( all ,saturn's inf]i\r ,planets z se5 f him4 #adg4 ,z ,m]cury & ,v5us1 se5 f ! ,e>?1 h _! respective ,elongations f ! ,sun1 & ,/ation>y places2 s has ! ,e>?1 se5 f ,m>s2 & ,m>s1 se5 f ,jupit]2 & ,jupit]1 se5 f ,saturn4 ,t is1 to e sup]i\r ,planet1 all ! inf]i\r ones h _! ,/ations & ,elongations2 z ,v5us & ,m]cury h to ! ,e>?4 ,z se5 f ,saturn1 ,m]cury nev] goes above #b-a_/b degrees f ! ,sun2 ,v5us #d-a_/c2 ! ,e>? #f2 ,m>s #i-a_/b2 & ,jupit] #cc-a_/d3 s t ,m]cury1 z se5 f ! ,e>?1 has almo/ z great a ,digression or ,elongation f ! ,sun1 z ,jupit] se5 f ,saturn4 ,sid5ote3 ,a pro( ( ! ,e>?'s annual motion4 #adh4 ,because ! ,e>?'s ,orbit is includ$ )9 ! ,orbits ( ,m>s1 ,jupit]1 & ,saturn1 !y are se5 on all sides ( ! ,heav5s2 & are z (t5 9 ,opposition to ! ,sun z 9 ,conjunction ) him4 ,if ! ,e>? /ood /ill1 !y w\ld always appe> direct 9 _! motions1 nev] retrograde nor /ation>y4 ,b !y seem to g j z (t5 backw>d z =w>d2 :i*1 if gravity be all[$ to exi/1 af=ds a suffici5t pro( ( ! ,e>?'s annual motion4 ,sid5ote3 ,fig4 ,,iii4 ,,plate ,,ii4 ,g5]al ,ph5om5a ( a sup]i\r ,planet to an inf]i\r4 #adi4 ,z ,v5us & ! ,e>? are sup]i\r ,planets to ,m]cury1 !y %ew mu* ! same ,appe>ances to him t ,m>s & ,jupit] d to u4 ,let ,m]cury m be at f1 ,v5us v at ,f1 & ! ,e>? at ,e2 9 :i* situation ,v5us hides ! ,e>? f ,m]cury2 b1 be+ 9 opposition to ! ,sun1 %e %9es on ,m]cury ) a full illum9$ ,orb2 ?\gh1 ) respect to ! ,e>?1 %e is 9 conjunction ) ! ,sun & invisible4 ,:5 ,m]cury is at f1 & ,v5us at ,g1 h] enlight5$ side n be+ directly t[>ds him1 %e appe>s a little gibb\s2 z ,m>s does 9 a l situation to u3 b1 :5 ,v5us is at ,i1 h] enlight5$ side is s mu* t[>ds ,m]cury at f1 t %e appe>s to him almo/ ( a r\nd figure4 ,at ,k1 ,v5us disappe>s to ,m]cury at f1 be+ !n hid by ! ,sun2 z all our sup]i\r ,planets are to u1 :5 9 conjunction ) ! ,sun4 ,:5 ,v5us has1 z x 71 em]g$ out ( ! ,sun beams1 z at ,l1 %e appe>s almo/ full to ,m]cury at f2 at ,m & ,n1 a little gibb\s2 q full at ,f1 & l>ge/ ( all2 be+ !n 9 opposition to ! ,sun1 & consequ5tly ne>e/ to ,m]cury at f2 %9+ /rongly on him 9 ! night1 because h] di/ance f him !n is some:at less ?an a fif? "p ( h] di/ance f ! ,e>?1 :5 %e appe>s r\nde/ to x betwe5 ,i & ,k1 or betwe5 ,k & ,l1 z se5 f ! ,e>? ,e4 ,consequ5tly1 :5 ,v5us is opposite to ! ,sun z se5 f ,m]cury1 %e appe>s m ?an #be times z l>ge to him z %e does to u :5 at ! fulle/4 ,our case is almo/ simil> ) respect to ,m>s1 :5 he is opposite to ! ,sun2 because he is !n s ne> ! ,e>?1 & has 8 :ole enlight5$ side t[>ds x4 ,b1 because ! ,orbits ( ,jupit] & ,saturn are v l>ge 9 proportion to ! ,e>?'s1 ^! two ,planets appe> mu* less magnifi$ at _! ,oppositions or dim9i%$ at _! ,conjunctions ?an ,m>s does1 9 proportion to _! mean app>5t ,diamet]s4 ,,*ap4 ,,vii4 ,! physical ,causes ( ! ,motions ( ! ,planets4 ,! ,exc5tricities ( _! ,orbits4 ,! ,times 9 :i* ! ,action ( ,gravity w\ld br+ !m to ! ,sun4 ,,ar*im$es's ideal ,problem = mov+ ! ,e>?4 ,! ,_w n et]nal4 ,sid5ote3 ,gravitation & ,projection4 ,fig4 ,,iv4 ,,plate ,,ii4 ,circul> ,orbits4 ,fig4 ,,iv4 #aej4 ,f ! uni=m projectile motion ( bodies 9 /raight l9es1 & ! univ]sal p[] ( attraction1 arises ! curvil9eal motions ( all ! ,heav5ly bodies4 ,if ! body ,a be project$ along ! "r l9e ,,abx1 9 op5 ,space1 :]e x meets ) no resi/ance1 & is n drawn aside by any o!r p[]1 x w = ev] g on ) ! same velocity1 & 9 ! same direction4 ,=1 ! =ce :i* moves x f ,a to ,b 9 any giv5 "t1 w c>ry x f ,b to ,x 9 z mu* m "t2 & s on1 !re be+ no?+ to ob/ruct or alt] x's motion4 ,b if1 :5 ?is projectile =ce has c>ri$ x1 suppose to ,b1 ! body ,s beg9s to attract x1 ) a p[] duly adju/$1 & p]p5dicul> to x's motion at ,b1 x w !n be drawn f ! /raight l9e ,,abx1 & =c$ to revolve ab\t ,s 9 ! ,circle ,,bytu4 ,:5 ! body ,a comes to ,u1 or any o!r "p ( x's ,orbit1 if ! small body u1 )9 ! sph]e ( ,u's attraction1 be project$ z 9 ! "r l9e ,z1 ) a =ce p]p5dicul> to ! attraction ( ,u1 !n u w g r\nd ,u 9 ! ,orbit ,w1 & accompany x 9 x's :ole c\rse r\nd ! body ,s4 ,"h1 ,s may repres5t ! ,sun1 ,u ! ,e>?1 & u ! ,moon4 #aea4 ,if a ,planet at ,b gravitates1 or is attract$1 t[>d ! ,sun1 s z to fall f ,b to y 9 ! "t t ! projectile =ce w\ld h c>ri$ x f ,b to ,x1 x w describe ! curve ,,by by ! comb9$ action ( ^! two =ces1 9 ! same "t t ! projectile =ce s+ly w\ld h c>ri$ x f ,b to ,x1 or ! gravitat+ p[] s+ly h caus$ x to desc5d f ,b to y2 & ^! two =ces be+ duly proportion$1 & p]p5dicul> to "o ano!r1 ! ,planet obey+ !m bo?1 w move 9 ! circle ,,bytu#cj4 ,sid5ote3 ,elliptical ,orbits4 ,,plate ,,ii4 #aeb4 ,b if1 :il/ ! projectile =ce c>ries ! ,planet f ,b to b1 ! ,sun's attraction 7:i* con/itutes ! ,planet's gravitation7 %\ld br+ x d[n f ,b to ,i1 ! gravitat+ p[] w\ld !n be too /rong = ! projectile =ce2 & w\ld cause ! ,planet to describe ! curve ,,bc4 ,:5 ! ,planet comes to ,c1 ! gravitat+ p[] 7:i* always increases z ! squ>e ( ! di/ance f ! ,sun ,s dim9i%es7 w be yet /rong] = ! projectile =ce2 & by conspir+ 9 "s degree !re)1 w accel]ate ! ,planet's motion all ! way f ,c to ,k2 caus+ x to describe ! arcs ,,bc1 ,,cd1 ,,de1 ,,ef1 c4 all 9 equal times4 ,hav+ x's motion ?us accel]at$1 x ga9s s mu* c5trifugal =ce1 or t5d5cy to fly (f at ,k 9 ! l9e ,kk1 z ov]comes ! ,sun's attraction3 & ! c5trifugal =ce be+ too great to all[ ! ,planet to be br\ght ne>] ! ,sun1 or ev5 to move r\nd him 9 ! ,circle ,klmn1 c4 x goes (f1 & asc5ds 9 ! curve ,,klmn1 c4 x's motion decreas+ z gradually f ,k to ,b z x increas$ f ,b to ,k1 because ! ,sun's attraction acts n[ aga9/ ! ,planet's projectile motion j z mu* z x act$ ) x be=e4 ,:5 ! ,planet has got r\nd to ,b1 x's projectile =ce is z mu* dim9i%$ f x's mean /ate ab\t ,g or ,n1 z x 0 augm5t$ at ,k2 & s1 ! ,sun's attraction be+ m ?an suffici5t to keep ! ,planet f go+ (f at ,b1 x describes ! same ,orbit ov] aga91 by virtue ( ! same =ces or laws4 ,sid5ote3 ,fig4 ,,iv4 ,! ,planets describe equal ,areas 9 equal times4 #aec4 ,a d\ble projectile =ce w always balance a quadruple p[] ( gravity4 ,let ! ,planet at ,b h twice z great an impulse f !nce t[>ds ,x1 z x _h be=e3 t is1 9 ! same l5g? ( "t t x 0 project$ f ,b to b1 z 9 ! la/ example1 let x n[ be project$ f ,b to c2 & x w require f\r times z mu* gravity to reta9 x 9 x's ,orbit3 t is1 x mu/ fall z f> z f ,b to #d 9 ! "t t ! projectile =ce w\ld c>ry x f ,b to c2 o!rwise x c\ld n describe ! curve ,,bd1 z is evid5t by ! ,figure4 ,b1 9 z mu* "t z ! ,planet moves f ,b to ,c 9 ! high] "p ( x's ,orbit1 x moves f ,i to ,k or f ,k to ,l 9 ! l[] "p !re(2 because1 f ! jo9t action ( ^! two =ces1 x mu/ always describe equal areas 9 equal times1 ?r\gh\t x's annual c\rse4 ,^! ,areas are repres5t$ by ! triangles ,,bsc1 ,,csd1 ,,dse1 ,,esf1 c4 ^: cont5ts are equal to "o ano!r1 q r\nd ! ,figure4 ,sid5ote3 ,a difficulty remov$4 #aed4 ,z ! ,planets approa* ne>] ! ,sun1 & rec$e f>!r f him1 9 e ,revolution2 !re may be "s difficulty 9 conceiv+ ! reason :y ! p[] ( gravity1 :5 x once gets ! bett] ( ! projectile =ce1 does n br+ ! ,planets ne>] & ne>] ! ,sun 9 e ,revolution1 till !y fall ^u & unite ) him4 ,or :y ! projectile =ce1 :5 x once gets ! bett] ( gravity1 does n c>ry ! ,planets f>!r & f>!r f ! ,sun1 till x removes !m q out ( ! sph]e ( 8 attraction1 & causes !m to g on 9 /raight l9es = ev] aft]w>d4 ,b by consid]+ ! effects ( ^! p[]s z describ$ 9 ! two la/ ,articles1 ?is difficulty w be remov$4 ,suppose a ,planet at ,b to be c>ri$ by ! projectile =ce z f> z f ,b to b1 9 ! "t t gravity w\ld h br\ght x d[n f ,b to #a3 by ^! two =ces x w describe ! curve ,,bc4 ,:5 ! ,planet comes d[n to ,k1 x w be b half z f> f ! ,sun ,s z x 0 at ,b2 & !re=e1 by gravitat+ f\r times z /rongly t[>ds him1 x w\ld fall f ,k to ,v 9 ! same l5g? ( "t t x w\ld h fall5 f ,b to #a 9 ! high] "p ( x's ,orbit1 t is1 ?r\gh f\r times z mu* space2 b x's projectile =ce is !n s mu* increas$ at ,k1 z w\ld c>ry x f ,k to k 9 ! same "t2 be+ d\ble ( :at x 0 at ,b1 & is !re=e too /rong = ! t5d5cy ( ! gravitat+ p[]1 ei!r to draw ! ,planet to ! ,sun1 or cause x to g r\nd him 9 ! circle ,klmn1 c4 :i* w\ld require x's fall+ f ,k to w1 ?r\gh a great] space ?an gravity c draw x :il/ ! projectile =ce is su* z w\ld c>ry x f ,k to k3 & !re=e ! ,planet asc5ds 9 x's ,orbit ,,klmn1 decreas+ 9 x's velocity = ! cause already assign$ 9 #aeb4 ,sid5ote3 ,! ,planet>y ,orbits elliptical4 ,_! ,exc5tricities4 #aee4 ,! ,orbits ( all ! ,planets are ,ellipses1 v little diff]5t f ,circles3 b ! ,orbits ( ! ,comets are v long ,ellipses2 ! l[] focus ( !m all be+ 9 ! ,sun4 ,if we suppose ! mean di/ance 7or middle betwe5 ! greate/ & lea/7 ( e ,planet & ,comet f ! ,sun to be divid$ into #ajjj equal p>ts1 ! ,exc5tricities ( _! ,orbits1 bo? 9 su* p>ts & 9 ,engli% miles1 w be z foll[s4 ,m]cury's1 #baj p>ts1 or #f1gbj1jjj miles2 ,v5us's1 #g p>ts1 or #dac1jjj miles2 ! ,e>?'s1 #ag p>ts1 or #a1cgg1jjj miles2 ,m>s's1 #ic p>ts1 or #aa1dci1jjj miles2 ,jupit]'s1 #dh p>ts1 or #bj1ceb1jjj miles2 ,saturn's1 #ee p>ts1 or #db1gce1jjj miles4 ,( ! ne>e/ ( ! ?ree =em5tion$ ,comets1 #a1deh1jjj miles2 ( ! middlemo/1 #b1jbe1jjj1jjj miles2 & ( ! out]mo/1 #f1fjj1jjj1jjj4 ,sid5ote3 ,! above laws suffici5t = motions bo? 9 circul> & elliptic ,orbits4 #aef4 ,by ! above-m5tion$ laws #aej seq4 bodies w move 9 all k9ds ( ,ellipses1 :e!r long or %ort1 if ! spaces !y move 9 be void ( resi/ance4 ,only1 ^? :i* move 9 ! long] ,ellipses1 h s mu* ! less projectile =ce impress$ ^u !m 9 ! high] p>ts ( _! ,orbits2 & _! velocities1 9 com+ d[n t[>ds ! ,sun1 are s prodigi\sly increas$ by 8 attraction1 t _! c5trifugal =ces 9 ! l[] p>ts ( _! ,orbits are s great z to ov]come ! ,sun's attraction !re1 & cause !m to asc5d aga9 t[>ds ! high] p>ts ( _! ,orbits2 dur+ :i* "t1 ! ,sun's attraction act+ s contr>y to ! motions ( ^? bodies1 causes !m to move sl[] & sl[]1 until _! projectile =ces are dim9i%$ almo/ to no?+2 & !n !y are br\ght back aga9 by ! ,sun's attraction1 z be=e4 ,sid5ote3 ,9 :at times ! ,planets w\ld fall to ! ,sun by ! p[] ( gravity4 #aeg4 ,if ! projectile =ces ( all ! ,planets & ,comets 7 de/roy$ at _! mean di/ances f ! ,sun1 _! gravities w\ld br+ !m d[n s1 z t ,m]cury w\ld fall to ! ,sun 9 #ae days #ac h\rs2 ,v5us 9 #ci days #ag h\rs2 ! ,e>? or ,moon 9 #fd days #aj h\rs2 ,m>s 9 #aba days2 ,jupit] 9 #bij2 & ,saturn 9 #gfg4 ,! ne>e/ ,comet 9 #ac ?\s& days2 ! middlemo/ 9 #bc ?\s& days2 & ! out]mo/ 9 #ff ?\s& days4 ,! ,moon w\ld fall to ! ,e>? 9 #d days #bj h\rs2 ,jupit]'s fir/ ,moon w\ld fall to him 9 #g h\rs1 8 second 9 #ae1 8 ?ird 9 #cj1 & 8 f\r? 9 #ga h\rs4 ,saturn's fir/ ,moon w\ld fall to him 9 #h h\rs2 8 second 9 #ab1 8 ?ird 9 #ai1 8 f\r? 9 #fh h\rs1 & ! fif? 9 #ccf4 ,a /one w\ld fall to ! ,e>?'s c5t]1 if !re 7 an holl[ passage1 9 #ba m9utes #i seconds4 ,mr4 ,,:i/on gives ! foll[+ ,rule = su* ,computations4 8#ca;,x is demon/rable1 t half ! ,p]iod ( any ,planet1 :5 x is dim9i%$ 9 ! sesquialt]al proportion ( ! numb] #a to ! numb] #b1 or ne>ly 9 ! proportion ( #ajjj to #bhbh1 is ! "t t x w\ld fall to ! ,c5t] ( x's ,orbit40 ,?is proportion is1 :5 a quantity or numb] conta9s ano!r once & a half z mu* m4 ,sid5ote3 ,! prodigi\s attraction ( ! ,sun & ,planets4 #aeh4 ,! quick motions ( ! ,moons ( ,jupit] & ,saturn r\nd _! ,prim>ies1 demon/rate t ^! two ,planets h /rong] attractive p[]s ?an ! ,e>? has4 ,=1 ! /rong] t "o body attracts ano!r1 ! great] mu/ be ! projectile =ce1 & consequ5tly ! quick] mu/ be ! motion ( t o!r body1 to keep x f fall+ to x's prim>y or c5tral ,planet4 ,jupit]'s second ,moon is #abd ?\s& miles f>!r f ,jupit] ?an our ,moon is f u2 & yet ?is second ,moon goes almo/ eight times r\nd ,jupit] :il/ our ,moon goes only once r\nd ! ,e>?4 ,:at a prodigi\s attractive p[] mu/ ! ,sun !n h1 to draw all ! ,planets & ,satellites ( ! ,sy/em t[>ds him2 & :at an amaz+ p[] mu/ x h requir$ to put all ^! ,planets & ,moons into su* rapid motions at fir/6 ,amaz+ inde$ to u1 because impossible to be effect$ by ! /r5g? ( all ! liv+ ,creatures 9 an unlimit$ numb] ( ,worlds1 b no ways h>d = ! ,almighty1 ^: ,planet>ium takes 9 ! :ole ,univ]se6 ,sid5ote3 ,,ar*im$es's ,problem = rais+ ! ,e>?4 #aei4 ,! celebrat$ ,,ar*im$es affirm$ he c\ld move ! ,e>? if he _h a place to /& on to manage 8 ma*9]y#cb4 ,?is ass]tion is true 9 ,!ory1 b1 ^u exam9ation1 w be f\nd absolutely impossible 9 fact1 ev5 ?\gh a prop] place & mat]ials ( suffici5t /r5g? c\ld be _h4 ,! simple/ & easie/ me?od ( mov+ a heavy body a little way is by a lev] or cr[1 :]e a small weight or p[] appli$ to ! long arm w raise a great weight on ! %ort "o4 ,b !n1 ! small weight mu/ move z mu* quick] ?an ! great weight z ! latt] is heavi] ?an ! =m]2 & ! l5g? ( ! long arm ( ! lev] to ! l5g? ( ! %ort arm mu/ be 9 ! same proportion4 ,n[1 suppose a man pulls or presses ! end ( ! long arm ) ! =ce ( #bjj p\nd weight1 & t ! ,e>? conta9s 9 r\nd ,numb]s #d1jjj1jjj1jjj1jjj1jjj1jjj1jjj or #djjj ,trillions ( cubic feet1 ea* at a mean rate weigh+ #ajj p\nd2 & t ! prop or c5t] ( motion ( ! lev] is #fjjj miles f ! ,e>?'s c5t]3 9 ?is case1 ! l5g? ( ! lev] f ! ,fulcrum or c5t] ( motion to ! mov+ p[] or weight ought to be #ab1jjj1jjj1jjj1jjj1jjj1jjj1jjj1jjj or #ab ,quadrillions ( miles2 & s _m miles mu/ ! p[] move1 9 ord] to raise ! ,e>? b "o mile1 :5ce 'tis easy to compute1 t if ,,ar*im$es or ! p[] appli$ c\ld move z swift z a cannon bullet1 x w\ld take #bg1jjj1jjj1jjj1jjj or #bg ,billions ( ye>s to raise ! ,e>? "o in*4 ,if any o!r ma*9e1 su* z a comb9ation ( :eels & screws1 0 propos$ to move ! ,e>?1 ! "t x w\ld require1 & ! space gone ?r\gh by ! h& t turn$ ! ma*9e1 w\ld be ! same z be=e4 ,h5ce we may le>n1 t h[ev] b\ndless our ,imag9ation & ,!ory may be1 ! actual op]ations ( man are conf9$ )9 n>r[ b\nds2 & m suit$ to our real wants ?an to our desires4 ,sid5ote3 ,h>d to det]m9e :at ,gravity is4 #afj4 ,! ,sun & ,planets mutually attract ea* o!r3 ! p[] by :i* !y d s we call ,gravity4 ,b :e!r ?is p[] be me*anical or no1 is v mu* disput$4 ,we are c]ta9 t ! ,planets di/urb "o ano!r's motions by x1 & t x decreases accord+ to ! squ>es ( ! di/ances ( ! ,sun & ,planets2 z light1 :i* is kn[n to be mat]ial1 likewise does4 ,h5ce ,gravity %\ld seem to arise f ! ag5cy ( "s subtile matt] press+ t[>ds ! ,sun & ,planets1 & act+1 l all me*anical causes1 by contact4 ,b on ! o!r h&1 :5 we consid] t ! degree or =ce ( ,gravity is exactly 9 proportion to ! quantities ( matt] 9 ^? bodies1 )\t any reg>d to _! bulks or quantity ( surface1 act+ z freely on _! int]nal z ext]nal p>ts1 x seems to surpass ! p[] ( me*anism2 & to be ei!r ! imm$iate ag5cy ( ! ,deity1 or effect$ by a law orig9ally e/abli%$ & impre/ on all matt] by him4 ,b "s affirm t matt]1 be+ altoge!r in]t1 _c be impress$ ) any ,law1 ev5 by almighty ,p[]3 & t ! ,deity mu/ !re=e be con/antly impell+ ! ,planets t[>d ! ,sun1 & mov+ !m ) ! same irregul>ities & di/urbances :i* ,gravity w\ld cause1 if x c\ld be suppos$ to exi/4 ,b1 if a man may v5ture to publi% 8 own ?\ghts1 7& :y %\ld n "o z well z ano!r87 x seems to me no great] absurdity1 to suppose ! ,deity capable ( sup]add+ a ,law1 or :at ,laws he pleases1 to matt]1 ?an to suppose him capable ( giv+ x exi/5ce at fir/4 ,! mann] ( bo? is equally inconceivable to u2 b nei!r ( !m imply a contradiction 9 our ideas3 & :at implies no contradiction is )9 ! p[] ( ,omnipot5ce4 ,d we n see t a human creature c prep>e a b> ( /eel s z to make x attract ne$les & fil+s ( iron2 & t he c put a /op to t p[] or virtue1 & aga9 call x =? aga9 z (t5 z he pleases8 ,to say t ! workman infuses any new p[] into ! b>1 is say+ too mu*2 s9ce ! ne$le & fil+s1 to :i* he has done no?+1 re-attract ! b>4 ,& f ?is x appe>s t ! p[] 0 orig9ally impre/ on ! matt] ( :i* ! b>1 ne$le1 & fil+s are compos$2 b does n seem to act until ! b> be prop]ly prep>$ by ! artific]3 some:at l a rope coil$ up 9 a %ip1 :i* w nev] draw a boat or any o!r ?+ t[>ds ! %ip1 unless "o end be ti$ to x1 & ! o!r end to t :i* is to be haul$ up2 & !n x is no matt] :i* end ( ! rope ! sailors pull at1 = ! rope w be equally /ret*$ ?r\gh\t1 & ! %ip & boat w move t[>ds "o ano!r4 ,to say t ! ,almighty has infus$ no su* virtue or p[] into ! mat]ials :i* compose ! b>1 b t he waits till ! op]ator be pleas$ to prep>e x by due position & friction1 & !n1 :5 ! ne$le or fil+s are br\ght pretty ne> ! b>1 ! ,deity presses !m t[>ds x1 & )draws 8 h& :5ev] ! workman ei!r = use1 curiosity or :im1 does :at appe>s to him to de/roy ! action ( ! b>1 seems q ridicul\s & trifl+2 z x supposes ,god n only to be subs]vi5t to our incon/ant wills1 b also to d :at w\ld be bel[ ! dignity ( any rational man to be employ$ ab\t4 #afa4 ,t ! projectile =ce 0 at fir/ giv5 by ! ,deity is evid5t4 ,=1 s9ce matt] c nev] put itself into motion1 & all bodies may be mov$ 9 any direction :atsoev]2 & yet all ! ,planets bo? prim>y & second>y move f we/ to ea/1 9 planes ne>ly co9cid5t2 :il/ ! ,comets move 9 all directions1 & 9 planes s diff]5t f "o ano!r2 ^! motions c be ow+ to no me*anical cause ( necessity1 b to ! free *oice & p[] ( an intellig5t ,be+4 #afb4 ,:atev] ,gravity be1 'tis pla9 t x acts e mom5t ( "t3 = %\ld x's action cease1 ! projectile =ce w\ld in/antly c>ry (f ! ,planets 9 /raight l9es f ^? p>ts ( _! ,orbits :]e ,gravity left !m4 ,b1 ! ,planets be+ once put into motion1 !re is no occasion = any new projectile =ce1 unless !y meet ) "s resi/ance 9 _! ,orbits2 nor = any m5d+ h&1 unless !y di/urb "o ano!r too mu* by _! mutual attractions4 ,sid5ote3 ,! ,planets di/urb "o ano!r's motion4 ,! consequ5ces !re(4 #afc4 ,x is f\nd t !re are di/urbances among ! ,planets 9 _! motions1 aris+ f _! mutual attractions :5 !y are 9 ! same qu>t] ( ! ,heav5s2 & t our ye>s are n always precisely ( ! same l5g?#cc4 ,besides1 !re is reason to believe t ! ,moon is some:at ne>] ! ,e>? n[ ?an %e 0 =m]ly2 h] p]iodical mon? be+ %ort] ?an x 0 9 =m] ages4 ,=1 our ,a/ronomical ,tables1 :i* 9 ! pres5t ,age %ew ! times ( ,sol> & ,lun> ,eclipses to great precision1 d n answ] s well = v anci5t ,eclipses4 ,h5ce x appe>s1 t ! ,moon does n move 9 a m$ium void ( all resi/ance1 #agd2 & !re=e h] projectile =ce be+ a little weak5$1 :il/ !re is no?+ to dim9i% h] gravity1 %e mu/ be gradually approa*+ ne>] ! ,e>?1 describ+ small] & small] ,circles r\nd x 9 e revolution1 & f9i%+ h] ,p]iod soon]1 al?\gh h] absolute motion ) reg>d to space be n s quick n[ z x 0 =m]ly3 & !re=e1 %e mu/ come to ! ,e>? at la/2 unless t ,be+1 :i* gave h] a suffici5t projectile =ce at ! beg9n+1 adds a little m to x 9 due "t4 ,&1 z all ! ,planets move 9 spaces full ( !r & light1 :i* are mat]ial sub/ances1 !y too mu/ meet ) "s resi/ance4 ,& !re=e1 if _! gravities are n dim9i%$1 nor _! projectile =ces increas$1 !y mu/ necess>ily approa* ne>] & ne>] ! ,sun1 & at l5g? fall ^u & unite ) him4 ,sid5ote3 ,! ,_w n et]nal4 #afd4 ,"h we h a /rong philosophical argum5t aga9/ ! et]nity ( ! ,_w4 ,=1 _h x exi/$ f et]nity1 & be5 left by ! ,deity to be gov]n$ by ! comb9$ actions ( ! above =ces or p[]s1 g5]ally call$ ,laws1 x _h be5 at an end long ago4 ,& if x be left to !m x mu/ come to an end4 ,b we may be c]ta9 t x w la/ z long z 0 int5d$ by x's ,au?or1 :o ought no m to be f\nd fault ) = fram+ s p]i%able a "w1 ?an = mak+ man mortal4 ,,*ap4 ,,viii4 ,( ,light4 ,x's proportional quantities on ! diff]5t ,planets4 ,x's ,refractions 9 ,wat] & ,air4 ,! ,atmosph]e2 x's weight & prop]ties4 ,! ,horizontal ,moon4 ,sid5ote3 ,! amaz+ smallness ( ! p>ticles ( light4 #afe4 ,light consi/s ( exce$+ small p>ticles ( matt] issu+ f a lum9\s body2 z f a light$ c&le su* p>ticles ( matt] cont9ually fl[ 9 all directions4 ,dr4 ,,niew5tyt#cd computes1 t 9 "o second ( "t !re fl[s #dah1ffj1jjj1jjj1jjj1jjj1jjj1jjj1jjj1jjj 1jjj1jjj1jjj1jjj1jjj p>ticles ( light out ( a burn+ c&le2 :i* numb] conta9s at lea/ #f1ccg1bdb1jjj1jjj times ! numb] ( gra9s ( s& 9 ! :ole ,e>?2 suppos+ #ajj gra9s ( s& to be equal 9 l5g? to an in*1 & consequ5tly1 e cubic in* ( ! ,e>? to conta9 "o million ( su* gra9s4 ,sid5ote3 ,! dreadful effects t w\ld ensue f _! be+ l>g]4 #aff4 ,^! amaz+ly small p>ticles1 by /rik+ ^u our eyes1 excite 9 our m9ds ! idea ( light3 &1 if !y 7 s l>ge z ! smalle/ p>ticles ( matt] disc]nible by our be/ microscopes1 in/ead ( be+ s]viceable to u1 !y w\ld soon deprive u ( sight by ! =ce aris+ f _! imm5se velocity1 :i* is above #afd ?\s& miles e second#ce1 or #a1bcj1jjj times swift] ?an ! motion ( a cannon bullet4 ,& !re=e1 if ! p>ticles ( light 7 s l>ge1 t a million ( !m 7 equal 9 bulk to an ord9>y gra9 ( l&1 we dur/ no m op5 our eyes to ! light ?an suff] s& to be %ot po9t blank aga9/ !m4 ,sid5ote3 ,h[ objects become visible to u4 ,,plate ,,ii4 #afg4 ,:5 ^! small p>ticles1 fl[+ f ! ,sun or f a c&le1 fall ^u bodies1 & are !reby reflect$ to our eyes1 !y excite 9 u ! idea ( t body by =m+ x's picture on ! ret9a#cf4 ,& s9ce bodies are visible on all sides1 light mu/ be reflect$ f !m 9 all directions4 ,sid5ote3 ,! rays ( ,light naturally move 9 /raight l9es4 ,a pro( t !y h9d] n "o ano!r's motions4 #afh4 ,a ray ( light is a cont9u$ /ream ( ^! p>ticles1 fl[+ f any visible body 9 /raight l9es4 ,t !y move 9 /raight1 & n 9 crook$ l9es1 unless !y be refract$1 is evid5t f bodies n be+ visible if we endeav\r to look at !m ?r\gh ! bore ( a b5d$ pipe2 & f _! ceas+ to be se5 by ! int]position ( o!r bodies1 z ! fix$ ,/>s by ! int]position ( ! ,moon & ,planets1 & ! ,sun :olly or 9 "p by ! int]position ( ! ,moon1 ,m]cury1 or ,v5us4 ,& t ^! rays d n int]f]e1 or jo/le "o ano!r out ( _! ways1 9 fl[+ f diff]5t bodies all ar\nd1 is pla9 f ! foll[+ ,exp]im5t4 ,make a little hole 9 a ?9 plate ( metal1 & set ! plate upright on a table1 fac+ a r[ ( light$ c&les /&+ by "o ano!r2 !n place a %eet ( pap] or pa/ebo>d at a little di/ance f ! o!r side ( ! plate1 & ! rays ( all ! c&les1 fl[+ ?r\gh ! hole1 w =m z _m specks ( light on ! pap] z !re are c&les be=e ! plate1 ea* speck z di/9ct & l>ge1 z if !re 7 only "o c&le to ca/ "o speck2 :i* %ews t ! rays are no h9d]ance to ea* o!r 9 _! motions1 al?\gh !y all cross 9 ! hole4 ,sid5ote3 ,fig4 ,,xi4 ,9 :at proportion light & heat decrease at any giv5 di/ance f ! ,sun4 ,,plate ,,ii4 #afi4 ,light1 & !re=e heat s f> z x dep5ds on ! ,sun's rays 7 #he1 t[>ds ! end7 decreases 9 proportion to ! squ>es ( ! di/ances ( ! ,planets f ! ,sun4 ,?is is easily demon/rat$ by a ,figure :i*1 toge!r ) x's description1 ,i h tak5 f ,dr4 ,,smi?'s ,optics#cg4 ,let ! light :i* fl[s f a po9t ,a1 & passes ?r\gh a squ>e hole ,b1 be receiv$ ^u a plane ,c1 p>allel to ! plane ( ! hole2 or1 if y please1 let ! figure ,c be ! %ad[ ( ! plane ,b2 & :5 ! di/ance ,c is d\ble ( ,b1 ! l5g? & bread? ( ! %ad[ ,c w be ea* d\ble ( ! l5g? & bread? ( ! plane ,b2 & treble :5 ,,ad is treble ( ,,ab2 & s on3 :i* may be easily exam9$ by ! light ( a c&le plac$ at ,a4 ,!re=e ! surface ( ! %ad[ ,c1 at ! di/ance ,,ac d\ble ( ,,ab1 is divisible into f\r squ>es1 & at a treble di/ance1 into n9e squ>es1 sev]ally equal to ! squ>e ,b1 z repres5t$ 9 ! ,figure4 ,! light !n :i* falls ^u ! plane ,b1 be+ suff]$ to pass to d\ble t di/ance1 w be uni=mly spread ov] f\r times ! space1 & consequ5tly w be f\r times ?9n] 9 e "p ( t space1 & at a treble di/ance x w be n9e times ?9n]1 & at a quadruple di/ance sixte5 times ?9n]1 ?an x 0 at fir/2 & s on1 accord+ to ! increase ( ! squ>e surfaces ,b1 ,c1 ,d1 ,e1 built ^u ! di/ances ,,ab1 ,,ac1 ,,ad1 ,,ae4 ,consequ5tly1 ! quantities ( ?is r>efi$ light receiv$ ^u a surface ( any giv5 size & %ape :atev]1 remov$ successively to ^! sev]al di/ances1 w be b "o qu>t]1 "o n9?1 "o sixte5? ( ! :ole quantity receiv$ by x at ! fir/ di/ance ,,ab4 ,or 9 g5]al words1 ! d5sities & quantities ( light1 receiv$ ^u any giv5 plane1 are dim9i%$ 9 ! same proportion z ! squ>es ( ! di/ances ( t plane1 f ! lum9\s body1 are increas$3 & on ! contr>y1 are increas$ 9 ! same proportion z ^! squ>es are dim9i%$4 ,sid5ote3 ,:y ! ,planets appe> dimm] :5 view$ ?ro' telescopes ?an by ! b>e eye4 #agj4 ,! m a telescope magnifies ! disks ( ! ,moon & ,planets1 !y appe> s mu* dimm] ?an to ! b>e eye2 because ! telescope _c magnify ! quantity ( light1 z x does ! surface2 &1 by spread+ ! same quantity ( light ov] a surface s mu* l>g] ?an ! nak$ eye beheld1 j s mu* dimm] mu/ x appe> :5 view$ by a telescope ?an by ! b>e eye4 ,sid5ote3 ,fig4 ,,viii4 ,refraction ( ! rays ( light4 #aga4 ,:5 a ray ( light passes out ( "o m$ium#ch into ano!r1 x is refract$1 or turn$ out ( x's fir/ c\rse1 m or less1 z x falls m or less obliquely on ! refract+ surface :i* divides ! two m$iums4 ,?is may be prov$ by sev]al exp]im5ts2 ( :i* we %all only give ?ree = example's sake4 #a4 ,9 a bason ,,fgh put a piece ( money z ,,db1 & !n retire f x z to ,a1 till ! edge ( ! bason at ,e j hides ! money f y\r sight3 !n1 keep+ y\r head /eady1 let ano!r p]son fill ! bason g5tly ) wat]4 ,z he fills x1 y w see m & m ( ! piece ,,db2 :i* w be all 9 view :5 ! bason is full1 & appe> z if lift$ up to ,c4 ,=1 ! ray ,,aeb1 :i* 0 /raight :il/ ! bason 0 empty1 is n[ b5t at ! surface ( ! wat] 9 ,e1 & turn$ out ( x's rectil9eal c\rse into ! direction ,,ed4 ,or1 9 o!r words1 ! ray ,,dek1 t proce$$ 9 a /raight l9e f ! edge ,d :il/ ! bason 0 empty1 & w5t above ! eye at ,a1 is n[ b5t at ,e2 & in/ead ( go+ on 9 ! rectil9eal direction ,,dek1 goes 9 ! angl$ direction ,,dea1 & by ent]+ ! eye at ,a r5d]s ! object ,,db visible4 ,or1 #b;dly1 place ! bason :]e ! ,sun %9es obliquely1 & obs]ve :]e ! %ad[ ( ! rim ,e falls on ! bottom1 z at ,b3 !n fill x ) wat]1 & ! %ad[ w fall at ,d2 :i* proves1 t ! rays ( light1 fall+ obliquely on ! surface ( ! wat]1 are refract$1 or b5t d[nw>ds into x4 #agb4 ,! less obliquely ! rays ( light fall ^u ! surface ( any m$ium1 ! less !y are refract$2 & if !y fall p]p5dicul>ly !reon1 !y are n refract$ at all4 ,=1 9 ! la/ exp]im5t1 ! high] ! ,sun rises1 ! less w be ! diff]5ce betwe5 ! places :]e ! edge ( ! %ad[ falls1 9 ! empty & full bason4 ,&1 #c;dly1 if a /ick be laid ov] ! bason1 & ! ,sun's rays be reflect$ p]p5dicul>ly into x f a look+-glass1 ! %ad[ ( ! /ick w fall ^u ! same place ( ! bottom1 :e!r ! bason be full or empty4 #agc4 ,! d5s] t any m$ium is1 ! m is light refract$ 9 pass+ ?r\gh x4 ,sid5ote3 ,! ,atmosph]e4 ,! ,air's compression & r>ity at diff]5t heights4 #agd4 ,! ,e>? is surr\nd$ by a ?9 fluid mass ( matt]1 call$ ! ,air1 or ,atmosph]e1 :i* gravitates to ! ,e>?1 revolves ) x 9 x's diurnal motion1 & goes r\nd ! ,sun ) x e ye>4 ,?is fluid is ( an ela/ic or spr+y nature1 & x's l[]mo/ p>ts be+ press$ by ! weight ( all ! ,air above !m1 are squeez$ ! clos] toge!r2 & are !re=e d5se/ ( all at ! ,e>?'s surface1 & gradually r>] ! high] up4 8,x is well kn[n#ci t ! ,air ne> ! surface ( our ,e>? possesses a space ab\t #abjj times great] ?an wat] ( ! same weight4 ,& !re=e1 a cyl9dric column ( ,air #abjj foot high is ( equal weight ) a cyl9d] ( wat] ( ! same bread? & b "o foot high4 ,b a cyl9d] ( ,air rea*+ to ! top ( ! ,atmosph]e is ( equal weight ) a cyl9d] ( wat] ab\t #cc foot high#dj2 & !re=e if f ! :ole cyl9d] ( ,air1 ! l[] "p ( #abjj foot high is tak5 away1 ! rema9+ upp] "p w be ( equal weight ) a cyl9d] ( wat] #cb foot high2 :]e=e1 at ! height ( #abjj feet or two furlongs1 ! weight ( ! incumb5t ,air is less1 & consequ5tly ! r>ity ( ! compress$ ,air is great] ?an ne> ! ,e>?'s surface 9 ! ratio ( #cc to #cb4 ,& hav+ ?is ratio we may compute ! r>ity ( ! ,air at all heights :atsoev]1 suppos+ ! expansion !re( to be reciprocally proportional to its compression2 & ?is proportion has be5 prov$ by ! exp]im5ts ( ,dr4 ,hooke & o!rs4 ,! result ( ! computation ,i h set d[n 9 ! annex$ ,table1 9 ! fir/ column ( :i* y h ! height ( ! ,air 9 miles1 :]e( #djjj make a semi-diamet] ( ! ,e>?2 9 ! second ! compression ( ! ,air or ! incumb5t weight2 9 ! ?ird x's r>ity or expansion1 suppos+ gravity to decrease 9 ! duplicate ratio ( ! di/ances f ! ,e>?'s c5t]4 ,& ! small num]al figures are "h us$ to %ew :at numb] ( cyph]s mu/ be jo9$ to ! numb]s express$ by ! l>g] figures1 z #j4agabbd = #j4jjjjjjjjjjjjjjjjjabbd1 & #bfiefae = #bfiefjjjjjjjjjjjjjjj4 ---------------------------------------- - ,,air's _/ _/ ,height4 ,compression4 ,expansion4 --------------------------------------- #j #cc #a #e #ag4heae #a4hdhf #aj #i4fgag #c4daea #bj #b4heb #aa4ega #dj #j4bebe #acf4hc #djj #j4agabbd #bfiefae #djjj #j4ajeddfe #gcijgajb #djjjj #j4aibafbh #bfbfcahi #djjjjj #j4bajghie #dagihbjg #djjjjjj #j4babihgh #ccdadbji ,inf9ite4 #j4babfjda #edfbbbji --------------------------------------- ,f ?is ,table x appe>s t ! ,air 9 proce$+ upw>ds is r>efi$ 9 su* mann]1 t a sph]e ( t ,air :i* is ne>e/ ! ,e>? b ( "o in* diamet]1 if dilat$ to an equal r>efaction ) t ( ! ,air at ! height ( t5 semi-diamet]s ( ! ,e>?1 w\ld fill up m space ?an is conta9$ 9 ! :ole ,heav5s on ?is side ! fix$ ,/>s1 accord+ to ! prec$+ computation ( _! di/ance#da40 ,& x likewise appe>s t ! ,moon does n move 9 a p]fectly free & un-resi/+ m$ium2 al?\gh ! air at a height equal to h] di/ance1 is at lea/ #cdjjjaij times ?9n] ?an at ! ,e>?'s surface2 & !re=e _c resi/ h] motion s z to be s5sible 9 _m ages4 ,sid5ote3 ,x's weight h[ f\nd4 ,,plate ,,ii4 #age4 ,! weight ( ! ,air1 at ! ,e>?'s surface1 is f\nd by exp]im5ts made ) ! air-pump2 & also by ! quantity ( m]cury t ! ,atmosph]e balances 9 ! b>omet]2 9 :i*1 at a mean /ate2 ! m]cury /&s #bi-a_/b in*es high4 ,& if ! tube 7 a squ>e in* wide1 x w\ld at t height conta9 #bi-a_/b cubic in*es ( m]cury1 :i* is j #ae p\nd weight2 & s mu* weight ( air e squ>e in* ( ! ,e>?'s surface su/a9s2 & e squ>e foot #add times z mu*1 because x conta9s #add squ>e in*es4 ,n[ z ! ,e>?'s surface conta9s ab\t #aii1dji1djj squ>e miles1 x mu/ be ( no less ?an #e1eei1bae1jaf1ifj1jjj squ>e feet2 :i*1 multipli$ by #bjaf1 ! numb] ( p\nds on e foot1 am\nts to #aa1bjg1cgg1dgd1aia1cfj1jjj2 or #aa trillion #bjg ?\s& #cgg billion #dgd ?\s& #aia million & #cfj ?\s& p\nds1 = ! weight ( ! :ole ,atmosph]e4 ,at ?is rate1 a middle siz$ man1 ^: surface may be ab\t #ad squ>e feet1 is press$ by #bh1bbd p\nd weight ( ,air all r\nd2 = fluids press equally up & d[n & on all sides4 ,b1 because ?is enorm\s weight is equal on all sides1 & c\nt]balanc$ by ! spr+ ( ! int]nal ,air 9 our blood vessels1 x is n felt4 ,sid5ote3 ,a common mi/ake ab\t ! weight ( ! ,air4 #agf4 ,(t5times ! /ate ( ! ,air is su* t we feel ourselves languid & dull2 :i* is commonly ?\ght to be occasion$ by ! ,air's be+ foggy & heavy ab\t u4 ,b t ! ,air is !n too light1 is evid5t f ! m]cury's s9k+ 9 ! b>omet]1 at :i* "t x is g5]ally f\nd t ! ,air has n suffici5t /r5g? to be> up ! vap\rs :i* compose ! ,cl\ds3 =1 :5 x is o!rwise1 ! ,cl\ds m\nt high1 ! ,air is m ela/ic & weighty ab\t u1 by :i* means x balances ! int]nal spr+ ( ! ,air )9 u1 braces up our blood-vessels & n]ves1 & makes u brisk & lively4 ,sid5ote3 ,)\t an ,atmosph]e ! ,heav5s w\ld always appe> d>k1 & we %\ld h no twilight4 #agg4 ,accord+ to #db;,dr4 ,,keill1 & o!r a/ronomical writ]s1 x is entirely ow+ to ! ,atmosph]e t ! ,heav5s appe> bright 9 ! day-"t4 ,=1 )\t an ,atmosph]e1 only t "p ( ! ,heav5s w\ld %9e 9 :i* ! ,sun 0 plac$3 & if an obs]v] c\ld live )\t ,air1 & %\ld turn 8 back t[>ds ! ,sun1 ! :ole ,heav5s w\ld appe> z d>k z 9 ! night1 & ! ,/>s w\ld be se5 z cle> z 9 ! nocturnal sky4 ,9 ?is case1 we %\ld h no twilight2 b a sudd5 transition f ! brighte/ sun%9e to ! blacke/ d>kness imm$iately aft] sun-set2 & f ! blacke/ d>kness to ! brighte/ sun-%9e at sun-ris+2 :i* w\ld be extremely inconv5i5t1 if n bl9d+1 to all mortals4 ,b1 by means ( ! ,atmosph]e1 we enjoy ! ,sun's light1 reflect$ f ! a]ial p>ticles1 be=e he rises & aft] he sets4 ,=1 :5 ! ,e>? by its rotation has )drawn ! ,sun f our sight1 ! ,atmosph]e be+ /ill high] ?an we1 has 8 light imp>t$ to x2 :i* gradually decreases until he has got #ah degrees bel[ ! ,horizon2 & !n1 all t "p ( ! ,atmosph]e :i* is above u is d>k4 ,f ! l5g? ( twilight1 ! ,doctor has calculat$ ! height ( ! ,atmosph]e 7s f> z x is d5se en\gh to reflect any light7 to be ab\t #dd miles4 ,b x is seldom d5se en\gh at two miles height to be> up ! ,cl\ds4 ,sid5ote3 ,x br+s ! ,sun 9 view be=e he rises1 & keeps him 9 view aft] he sets4 #agh4 ,! ,atmosph]e refracts ! ,sun's rays s1 z to br+ him 9 sight e cle> day1 be=e he rises 9 ! ,horizon2 & to keep him 9 view = "s m9utes aft] he is really set bel[ x4 ,=1 at "s times ( ! ye>1 we see ! ,sun t5 m9utes long] above ! ,horizon ?an he w\ld be if !re 7 no refractions3 & ab\t six m9utes e day at a mean rate4 ,sid5ote3 ,fig4 ,,ix4 ,,plate ,,ii4 #agi4 ,to illu/rate ?is1 let ,,iek be a "p ( ! ,e>?'s surface1 cov]$ ) ! ,atmosph]e ,,hgfc2 & let ,,heo be !#dc s5sible ,horizon ( an obs]v] at ,e4 ,:5 ! ,sun is at ,a1 really bel[ ! ,horizon1 a ray ( light ,,ac proce$+ f him comes /raight to ,c1 :]e x falls on ! surface ( ! ,atmosph]e1 & !re ent]+ a d5s] m$ium1 x is turn$ out ( its rectil9eal c\rse ,a,cd,g1 & b5t d[n to ! obs]v]'s eye at ,e2 :o !n sees ! ,sun 9 ! direction ( ! refract$ ray ed,e1 :i* lies above ! ,horizon1 & be+ ext5d$ out to ! ,heav5s1 %ews ! ,sun at ,b #aga4 ,sid5ote3 ,fig4 ,,ix4 #ahj4 ,! high] ! ,sun rises1 ! less 8 rays are refract$1 because !y fall less obliquely on ! surface ( ! ,atmosph]e #agb4 ,?us1 :5 ! ,sun is 9 ! direction ( ! l9e ,ef,l cont9u$1 he is s ne>ly p]p5dicul> to ! surface ( ! ,e>? at ,e1 t 8 rays are b v little b5t f a rectil9eal c\rse4 ,sid5ote3 ,! quantity ( refraction4 #aha4 ,! ,sun is ab\t #cb-a_/d m94 ( a deg4 9 bread?1 :5 at 8 mean di/ance f ! ,e>?2 & ! horizontal refraction ( 8 rays is #cc-c_/d m94 :i* be+ m ?an 8 :ole diamet]1 br+s all 8 ,disc 9 view1 :5 8 upp]mo/ edge rises 9 ! ,horizon4 ,at t5 deg4 height ! refraction is n q #e m94 at #bj deg4 only #b m94 #bf sec42 at #cj deg4 b #a m94 #cb sec42 betwe5 :i* & ! ,z5i?1 x is sc>ce s5sible3 ! quantity ?r\gh\t1 is %ewn by ! annex$ table1 calculat$ by ,sir ,,isaac ,,newton4 ---------------------------------------- --------- #ahb4 ,a ,,table %ew+ ! ,refractions ( ! ,sun1 ,moon1 & ,/>s2 adapt$ to _! app>5t ,altitudes4 ---------------------------------------- -- ,app>4 ,refrac- ,ap4 ,refrac- ,ap4 ,refrac- ,alt4 tion4 ,alt4 tion4 ,alt4 tion4 ---------------------------------------- -- ,d4 ,m4 ,m4 ,s4 ,d4 ,m4 ,s4 ,d4 ,m4 ,s4 ---------------------------------------- -- #j #j #cc #de #ba #b #ah #ef #j #cf #j #ae #cj #bd #bb #b #aa #eg #j #ce #j #cj #bg #ce #bc #b #e #eh #j #cd #j #de #be #aa #bd #a #ei #ei #j #cb #a #j #bc #g #be #a #ed #fj #j #ca ---------------------------------------- -- #a #ae #ba #bj #bf #a #di #fa #j #cj #a #cj #ai #df #bg #a #dd #fb #j #bh #a #de #ah #bb #bh #a #dj #fc #j #bg #b #j #ag #h #bi #a #cf #fd #j #bf #b #cj #ae #b #cj #a #cb #fe #j #be ---------------------------------------- -- #c #j #ac #bj #ca #a #bh #ff #j #bd #c #cj #aa #eg #cb #a #be #fg #j #bc #d #j #aj #dh #cc #a #bb #fh #j #bb #d #cj #i #ej #cd #a #ai #fi #j #ba #e #j #i #b #ce #a #af #gj #j #bj ---------------------------------------- -- #e #cj #h #ba #cf #a #ac #ga #j #ai #f #j #g #de #cg #a #aa #gb #j #ah #f #cj #g #ad #ch #a #h #gc #j #ag #g #j #f #dg #ci #a #f #gd #j #af #g #cj #f #bb #dj #a #d #ge #j #ae ---------------------------------------- -- #h #j #f #j #da #a #b #gf #j #ad #h #cj #e #dj #db #a #j #gg #j #ac #i #j #e #bb #dc #j #eh #gh #j #ab #i #cj #e #f #dd #j #ef #gi #j #aa #aj #j #d #eb #de #j #ed #hj #j #aj ---------------------------------------- -- #aa #j #d #bg #df #j #eb #ha #j #i #ab #j #d #e #dg #j #ej #hb #j #h #ac #j #c #dg #dh #j #dh #hc #j #g #ad #j #c #ca #di #j #dg #hd #j #f #ae #j #c #ag #ej #j #de #he #j #e ---------------------------------------- -- #af #j #c #d #ea #j #dd #hf #j #d #ag #j #b #ec #eb #j #db #hg #j #c #ah #j #b #dc #ec #j #dj #hh #j #b #ai #j #b #cd #ed #j #ci #hi #a #a #bj #j #b #bf #ee #j #ch #ij #j #j ---------------------------------------- -- ,sid5ote3 ,,plate ,,ii4 ,! incon/ancy ( ,refractions4 ,a v rem>kable case conc]n+ refraction4 #ahc4 ,9 all obs]vations1 to h ! true altitude ( ! ,sun1 ,moon1 or ,/>s1 ! refraction mu/ be subtract$ f ! obs]v$ altitude4 ,b ! quantity ( refraction is n always ! same at ! same altitude2 because heat dim9i%es ! air's refractive p[] & d5sity1 & cold increases bo?2 & !re=e no "o table c s]ve precisely = ! same place at all seasons1 nor ev5 at all times ( ! same day2 mu* less = diff]5t climates3 x hav+ be5 obs]v$ t ! horizontal refractions are ne> a ?ird "p less at ! ,equator ?an at ,p>is1 z m5tion$ by ,dr4 ,,smi? 9 ! #cgj? rem>k on 8 ,optics1 :]e ! foll[+ acc\nt is giv5 ( an extraord9>y refraction ( ! sun-beams by cold4 8,!re is a fam\s obs]vation ( ?is k9d made by "s ,holl&]s t w9t]$ 9 ,nova ,zembla 9 ! ye> #aeif1 :o 7 surpris$ to f9d1 t aft] a cont9ual night ( ?ree mon?s1 ! ,sun began to rise sev5te5 days soon] ?an accord+ to computation1 d$uc$ f ! ,altitude ( ! ,pole obs]v$ to be #gf3 :i* _c o!rwise be acc\nt$ =1 ?an by an extraord9>y quantity ( refraction ( ! ,sun's rays1 pass+ ?ro' ! cold d5se air 9 t climate4 ,,kepl] computes t ! ,sun 0 almo/ five degrees bel[ ! ,horizon :5 he fir/ appe>$2 & consequ5tly ! refraction ( 8 rays 0 ab\t n9e times great] ?an x is ) u40 #ahd4 ,! ,sun & ,moon appe> ( an oval figure z ,,fcgd1 j aft] _! ris+1 & be=e _! sett+3 ! reason is1 t ! refraction be+ great] 9 ! ,horizon ?an at any di/ance above x1 ! l[]mo/ limb ,g appe>s m elevat$ ?an ! upp]mo/4 ,b al?\gh ! refraction %ort5s ! v]tical ,diamet] ,,fg1 x has no s5sible effect on ! horizontal ,diamet] ,,cd1 :i* is all equally elevat$4 ,:5 ! refraction is s small z to be imp]ceptible1 ! ,sun & ,moon appe> p]fectly r\nd1 z ,,aebf4 ,sid5ote3 ,our imag9ation _c judge rightly ( ! di/ance ( inaccessible objects4 #ahe4 ,we daily obs]ve1 t ! objects :i* appe> mo/ di/9ct are g5]ally ^? :i* are ne>e/ to u2 & consequ5tly1 :5 we h no?+ b our imag9ation to assi/ u 9 e/imat+ ( di/ances1 bright objects seem ne>] to u ?an ^? :i* are less bright1 or ?an ! same objects d :5 !y appe> less bright & worse def9$1 ev5 ?\gh _! di/ance 9 bo? cases be ! same4 ,& z 9 bo? cases !y are se5 "u ! same angle#dd1 our imag9ation naturally sugge/s an idea ( a great] di/ance betwe5 u & ^? objects :i* appe> fa9t] & worse def9$ ?an ^? :i* appe> bright] "u ! same ,angles2 especially if !y be su* objects z we 7 nev] ne> to1 & ( ^: real ,magnitudes we c be no judges by sight4 ,sid5ote3 ,nor always ( ^? :i* are accessible4 #ahf4 ,b1 x is n only 9 judg+ ( ! diff]5t app>5t ,magnitudes ( ! same objects1 :i* are bett] or worse def9$ by _! be+ m or less bright1 t we may be deceiv$3 = we may make a wrong conclusion ev5 :5 we view !m "u equal degrees ( brightness1 & "u equal ,angles2 al?\gh !y be objects ^: bulks we are g5]ally acqua9t$ )1 su* z h\ses or trees3 = pro( ( :i*1 ! two foll[+ in/ances may suffice4 ,sid5ote3 ,! reason assign$4 ,,plate ,,ii4 ,fir/1 ,:5 a h\se is se5 ov] a v broad riv] by a p]son /&+ on l[ gr\nd1 :o sees no?+ ( ! riv]1 nor kn[s ( x be=eh&2 ! bread? ( ! riv] be+ hid f him1 because ! banks seem contigu\s1 he loses ! idea ( a di/ance equal to t bread?2 & ! h\se seems small1 because he ref]s x to a less di/ance ?an x really is at4 ,b1 if he goes to a place f :i* ! riv] & int]jac5t gr\nd c be se51 ?\gh no f>!r f ! h\se1 he !n p]ceives ! h\se to be at a great] di/ance ?an he imag9$2 & !re=e fancies x to be bigg] ?an he did at fir/2 al?\gh 9 bo? cases x appe>s "u ! same ,angle1 & consequ5tly makes no bigg] picture on ! ret9a ( 8 eye 9 ! latt] case ?an x did 9 ! =m]4 ,_m h be5 deceiv$1 by tak+ a r$ coat ( arms1 fix$ ^u ! iron gate 9 ,cl>e-,hall walks at ,cambridge1 = a brick h\se at a mu* great] di/ance#de4 ,sid5ote3 ,fig4 ,,xii4 ,secondly1 ,9 foggy wea!r1 at fir/ sight1 we g5]ally imag9e a small h\se1 :i* is j at h&1 to be a great ca/le at a di/ance2 because x appe>s s dull & ill def9$ :5 se5 ?r\gh ! ,mi/1 t we ref] x to a mu* great] di/ance ?an x really is at2 & !re=e1 "u ! same ,angle1 we judge x to be mu* bigg]4 ,=1 ! ne> object ,,fe1 se5 by ! eye ,,abd1 appe>s "u ! same ,angle ,,g*1 t ! remote object ,,ghi does3 & ! rays ,,gfcn & ,,hecm cross+ "o ano!r at ,c 9 ! pupil ( ! eye1 limit ! size ( ! picture ,,mn on ! ret9a2 :i* is ! picture ( ! object ,,fe1 & if ,,fe 7 tak5 away1 w\ld be ! picture ( ! object ,,ghi1 only worse def9$2 because ,,ghi1 be+ f>!r (f1 appe>s dull] & fa9t] ?an ,,fe did4 ,b if a ,fog1 z ,,kl1 comes betwe5 ! eye & ! object ,,fe1 x appe>s dull & ill def9$ l ,,ghi2 :i* causes our imag9ation to ref] ,,fe to ! great] di/ance ,,*1 in/ead ( ! small di/ance ,,ce :i* x really is at4 ,& consequ5tly1 z mis-judg+ ! di/ance does n 9 ! lea/ dim9i% ! ,angle "u :i* ! object appe>s1 ! small hay-rick ,,fe seems to be z big z ,,ghi4 ,sid5ote3 ,fig4 ,,ix4 ,:y ! ,sun & ,moon appe> bigge/ 9 ! ,horizon4 #ahg4 ,! ,sun & ,moon appe> bigg] 9 ! ,horizon ?an at any consid]able height above x4 ,^! ,lum9>ies1 al?\gh at great di/ances f ! ,e>?1 appe> float+1 z x 71 on ! surface ( our ,atmosph]e ,h,g,ffe,c1 a little way beyond ! ,cl\ds2 ( :i*1 ^? ab\t ,f1 directly ov] our heads at ,e1 are ne>] u ?an ^? ab\t ,h or e 9 ! ,horizon ,h,ee4 ,!re=e1 :5 ! ,sun or ,moon appe> 9 ! ,horizon at e1 !y are n only se5 9 a "p ( ! ,sky :i* is really f>!r f u ?an if !y 7 at any consid]able ,altitude1 z ab\t f2 b !y are also se5 ?r\gh a great] quantity ( ,air & ,vap\rs at e ?an at f4 ,"h we h two concurr+ appe>ances :i* deceive our imag9ation1 & cause u to ref] ! ,sun & ,moon to a great] di/ance at _! ris+ or sett+ ab\t e1 ?an :5 !y are consid]ably high z at f3 fir/1 _! seem+ to be on a "p ( ! ,atmosph]e at e1 :i* is really f>!r ?an f f a spectator at ,e2 & secondly1 _! be+ se5 ?r\gh a gross] m$ium :5 at e ?an :5 at f2 :i*1 by r5d]+ !m dimm]1 causes u to imag9e !m to be at a yet great] di/ance4 ,& z1 9 bo? cases1 !y are se5#df mu* "u ! same ,angle1 we naturally judge !m to be bigge/ :5 !y seem f>!/ f u2 l ! above-m5tion$ h\se #ahf1 se5 f a high] gr\nd1 :i* %ew$ x to be f>!r (f ?an x appe>$ f l[ gr\nd2 or ! hay-rick1 :i* appe>$ at a great] di/ance by means ( an int]pos+ ,fog4 ,sid5ote3 ,_! ,diamet]s are n less on ! ,m]idian ?an 9 ! ,horizon4 #ahh4 ,any "o may satisfy himself t ! ,moon appe>s "u no great] ,angle 9 ! ,horizon ?an on ! ,m]idian1 by tak+ a l>ge %eet ( pap]1 & roll+ x up 9 ! =m ( a ,tube1 ( su* a wid?1 t obs]v+ ! ,moon ?r\gh x :5 %e rises1 %e may1 z x 71 j fill ! ,tube2 !n tie a ?read r\nd x to keep x ( t size2 & :5 ! ,moon comes to ! ,m]idian1 & appe>s mu* less to ! eye1 look at h] aga9 ?r\gh ! same ,tube1 & %e w fill x j z mu*1 if n m1 ?an %e did at h] ris+4 #ahi4 ,:5 ! full ,moon is 9 p]igeo1 or at h] lea/ di/ance f ! ,e>?1 %e is se5 "u a l>g] ,angle1 & mu/ !re=e appe> bigg] ?an :5 %e is ,full at o!r times3 & if t "p ( ! ,atmosph]e :]e %e rises be m replete ) vap\rs ?an usual1 %e appe>s s mu* ! dimm]2 & !re=e we fancy h] to be /ill ! bigg]1 by ref]r+ h] to an unusually great di/ance2 kn[+ t no objects :i* are v f> di/ant c appe> big unless !y be really s4 ,illu/ration3 ,plate ,,iiii4 ,j4 ,f]guson del94 ,j4 ,mynde ,sculp4 ,,*ap4 ,,ix4 ,! ,me?od ( f9d+ ! ,di/ances ( ! ,sun1 ,moon1 & ,planets4 ,sid5ote3 ,,plate ,,iv4 #aij4 ,^? :o h n le>nt h[ to take ! #dg;,altitude ( any ,cele/ial ,ph5om5on by a common ,quadrant1 nor "k any ?+ ( ,pla9 ,trigonometry1 may pass ov] ! fir/ ,article ( ?is %ort ,*apt]1 & take ! ,a/ronom]'s ^w = x1 t ! di/ances ( ! ,sun & ,planets are z /at$ 9 ! fir/ ,*apt] ( ?is ,book4 ,b1 to e "o :o kn[s h[ to take ! ,altitude ( ! ,sun1 ! ,moon1 or a ,/>1 & c solve a pla9 "r-angl$ ,triangle1 ! foll[+ me?od ( f9d+ ! di/ances ( ! ,sun & ,moon w be easily und]/ood4 ,sid5ote3 ,fig ,i4 ,let ,,bag be "o half ( ! ,e>?1 ,,ac x's semi-diamet]1 ,s ! ,sun1 m ! ,moon1 & ,,ekol a qu>t] ( ! ,circle describ$ by ! ,moon 9 revolv+ f ! ,m]idian to ! ,m]idian aga94 ,let ,,crs be ! rational ,horizon ( an obs]v] at ,a1 ext5d$ to ! ,sun 9 ! ,heav5s1 & ,,hao 8 s5sible ,horizon2 ext5d$ to ! ,moon's ,orbit4 ,,alc is ! ,angle "u :i* ! ,e>?'s semi-diamet] ,,ac is se5 f ! ,moon at ,l1 :i* is equal to ! ,angle ,,oal1 because ! "r l9es ,,ao & ,,cl :i* include bo? ^! ,angles are p>allel4 ,,asc is ! ,angle "u :i* ! ,e>?'s semi-diamet] ,,ac is se5 f ! ,sun at ,s1 & is equal to ! ,angle ,o,af because ! l9es ,,ao & ,,crs are p>allel4 ,n[1 x is f\nd by obs]vation1 t ! ,angle ,,oal is mu* great] ?an ! ,angle ,o,af2 b ,,oal is equal to ,,alc1 & ,o,af is equal to ,,asc4 ,n[1 z ,,asc is mu* less ?an ,,alc1 x proves t ! ,e>?'s semi-diamet] ,,ac appe>s mu* great] z se5 f ! ,moon at ,l ?an f ! ,sun at ,s3 & !re=e ! ,e>? is mu* f>!r f ! ,sun ?an f ! ,moon#dh4 ,! ,quantities ( ^! ,angles are det]m9$ by obs]vation 9 ! foll[+ mann]4 ,sid5ote3 ,! ,moon's horizontal ,p>allax1 :at4 ,! ,moon's di/ance det]m9$4 ,let a graduat$ in/rum5t z ,,dae1 7! l>g] ! bett]7 hav+ a moveable ,index & ,sight-holes1 be fix$ 9 su* a mann]1 t x's plane surface may be p>allel to ! ,plan ( ! ,equator1 & x's edge ,,ad 9 ! ,m]idian3 s t :5 ! ,moon is 9 ! ,equ9octial1 & on ! ,m]idian at ,e1 %e may be se5 ?r\gh ! sight-holes :5 ! edge ( ! moveable index cuts ! beg9n+ ( ! divisions at o1 on ! graduat$ limb ,,de2 & :5 %e is s se51 let ! precise "t be not$4 ,n[1 z ! ,moon revolves ab\t ! ,e>? f ! ,m]idian to ! ,m]idian aga9 9 #bd h\rs #dh m9utes1 %e w g a f\r? "p r\nd x 9 a f\r? "p ( t "t1 viz4 9 #f h\rs #ab m9utes1 z se5 f ,c1 t is1 f ! ,e>?'s c5t] or ,pole4 ,b z se5 f ,a1 ! obs]v]'s place on ! ,e>?'s surface1 ! ,moon w seem to h gone a qu>t] r\nd ! ,e>? :5 %e comes to ! s5sible ,horizon at ,o2 = ! ,index ?r\gh ! sights ( :i* %e is !n view$ w be at d1 #ij degrees f ,d1 :]e x 0 :5 %e 0 se5 at ,e4 ,n[1 let ! exact mom5t :5 ! ,moon is se5 at ,o 7:i* w be :5 %e is 9 or ne> ! s5sible ,horizon7 be c>efully not$#di1 t x may be kn[n 9 :at "t %e has gone f ,e to ,o2 :i* "t subtract$ f #f h\rs #ab m9utes 7! "t ( h] go+ f ,e to ,l7 leaves ! "t ( h] go+ f ,o to ,l1 & af=ds an easy me?od = f9d+ ! ,angle ,,oal 7call$ ! ,moon's horizontal ,p>allax1 :i* is equal to ! ,angle ,,alc7 by ! foll[+ ,analogy3 ,z ! "t ( ! ,moon's describ+ ! arc ,,eo is to #ij degrees1 s is #f h\rs #ab m9utes to ! degrees ( ! ,arc ,dd,e1 :i* measures ! ,angle ,,eal2 f :i* subtract #ij degrees1 & !re rema9s ! ,angle ,,oal1 equal to ! ,angle ,,alc1 "u :i* ! ,e>?'s ,semi-diamet] ,,ac is se5 f ! ,moon4 ,n[1 s9ce all ! ,angles ( a "r-l9$ ,triangle are equal to #ahj degrees1 or to two "r ,angles1 & ! sides ( a ,triangle are always proportional to ! ,s9es ( ! opposite ,angles1 say1 by ! ,rule ( ,?ree1 z ! ,s9e ( ! ,angle ,,alc at ! ,moon ,l is to x's opposite side ,,ac ! ,e>?'s ,semi-diamet]1 :i* is kn[n to be #cihe miles1 s is ,radius1 viz4 ! ,s9e ( #ij degrees1 or ( ! "r ,angle ,,acl to x's opposite side ,,al1 :i* is ! ,moon's di/ance at ,l f ! obs]v]'s place at ,a on ! ,e>?'s surface2 or1 s is ! ,s9e ( ! ,angle ,,cal to its opposite side ,,cl1 :i* is ! ,moon's di/ance f ! ,e>?'s c5tre1 & comes out at a mean rate to be #bdj1jjj miles4 ,! ,angle ,,cal is equal to :at ,,oal wants ( #ij degrees4 ,sid5ote3 ,! ,sun's di/ance _c be yet s exactly det]m9$ z ! ,moon's2 ,h[ ne> ! tru? x may soon be det]m9$4 #aia4 ,! ,sun's di/ance f ! ,e>? is f\nd ! same way1 b ) mu* great] difficulty2 because 8 horizontal ,p>allax1 or ! ,angle ,,oas equal to ! ,angle ,,asc1 is s small z1 to be h>dly p]ceptible1 be+ only #aj seconds ( a m9ute1 or ! #cfj? "p ( a degree4 ,b ! ,moon's horizontal ,p>allax1 or ,angle ,,oal equal to ! ,angle ,,alc1 is v disc]nible2 be+ #eg #di1 or #cdfi at x's mean /ate2 :i* is m ?an #cdj times z great z ! ,sun's3 & !re=e1 ! di/ances ( ! heav5ly bodies be+ inv]sely z ! ,tang5ts ( _! horizontal ,p>allaxes1 ! ,sun's di/ance f ! ,e>? is at lea/ #cdj times z great z ! ,moon's2 & is r und]/at$ at #ha millions ( miles1 :5 ! ,moon's di/ance is c]ta9ly kn[n to be #bdj ?\s&4 ,b because1 accord+ to "s ,a/ronom]s1 ! ,sun's horizontal ,p>allax is #aa seconds1 & accord+ to o!rs only #aj1 ! =m] ,p>allax mak+ ! ,sun's di/ance to be ab\t #ge1jjj1jjj ( miles1 & ! latt] #hb1jjj1jjj2 we may take x = grant$1 t ! ,sun's di/ance is n less ?an z d$uc$ f ! =m]1 nor m ?an z %ewn by ! latt]3 & e "o :o is accu/om$ to make su* obs]vations1 kn[s h[ h>d x is1 if n impossible1 to avoid an error ( a second2 especially on acc\nt ( ! incon/ancy ( horizontal ,refractions4 ,& "h1 ! error ( "o second1 9 s small an ,angle1 w make an error ( #g millions ( miles 9 s great a di/ance z t ( ! ,sun's2 & mu* m 9 ! di/ances ( ! sup]i\r ,planets4 ,b ,dr4 ,,halley has %ewn u h[ ! ,sun's di/ance f ! ,e>?1 & consequ5tly ! di/ances ( all ! ,planets f ! ,sun1 may be kn[n to )9 a #ejj? "p ( ! :ole1 by a ,transit ( ,v5us ov] ! ,sun's ,disc1 :i* w happ5 on ! #f? ( ,june1 9 ! ye> #agfa2 till :i* "t we mu/ cont5t ourselves ) all[+ ! ,sun's di/ance to be ab\t #ha millions ( miles1 z commonly /at$ by ,a/ronom]s4 ,sid5ote3 ,! ,sun prov$ to be mu* bigg] ?an ! ,moon4 #aib4 ,! ,sun & ,moon appe> mu* ab\t ! same bulk3 ,& e "o :o und]/&s ,geometry kn[s h[ _! true bulks may be d$uc$ f ! app>5t1 :5 _! real di/ances are kn[n4 ,sph]es are to "o ano!r z ! ,cubes ( _! ,diamet]s2 :5ce1 if ! ,sun be #ha millions ( miles f ! ,e>?1 to appe> z big z ! ,moon1 ^: di/ance does n exce$ #bdj ?\s& miles1 he mu/1 9 solid bulk1 be #db millions #hge ?\s& times z big z ! ,moon4 #aic4 ,! horizontal ,p>allaxes are be/ obs]v$ at ! ,equator2 #a4 ,because ! heat is s ne>ly equal e day1 t ! ,refractions are almo/ con/antly ! same4 #b4 ,because ! p>allactic ,angle is great] !re z at ,a 7! di/ance f !nce to ! ,e>?'s ,axis be+ great]17 ?an ^u any p>allel ( ,latitude1 z a or b4 ,sid5ote3 ,! relative di/ances ( ! ,planets f ! ,sun are kn[n to great precision1 ?\gh _! real di/ances are n well kn[n4 #aid4 ,! ,e>?'s di/ance f ! ,sun be+ det]m9$1 ! di/ances ( all ! o!r ,planets f him are easily f\nd by ! foll[+ analogy1 _! p]iods r\nd him be+ asc]ta9$ by obs]vation4 ,z ! squ>e ( ! ,e>?'s p]iod r\nd ! ,sun is to ! cube ( x's di/ance f him1 s is ! squ>e ( ! p]iod ( any o!r ,planet to ! cube ( x's di/ance1 9 su* p>ts or measures z ! ,e>?'s di/ance 0 tak52 see #aaa4 ,?is proportion gives u ! relative mean di/ances ( ! ,planets f ! ,sun to ! greate/ degree ( exactness2 & !y are z foll[s1 hav+ be5 d$uc$ f _! p]iodical times1 accord+ to ! law j m5tion$1 :i* 0 discov]$ by ,,kepl] & demon/rat$ by ,sir ,,isaac ,,newton4 ,p]iodical ,revolution to ! same fix$ ,/> 9 days & decimal p>ts ( a day4 ,( ,m]cury ,v5us ,! ,e>? ,m>s ,jupit] ,saturn #hg4ifib #bbd4fagf #cfe4befd #fhf4ighe #dccb4ead #ajgei4bge ,relative mean di/ances f ! ,sun4 #chgaj #gbccc #ajjjjj #aebcfi #ebjjif #iedjjf ,f ^! numb]s we d$uce1 t if ! ,sun's horizontal ,p>allax be #aj1 ! real mean di/ances ( ! ,planets f ! ,sun 9 ,engli% miles are #ca1gdb1bjj #ei1cac1jfj #hb1jjj1jjj #abd1idb1ehj #dbf1dgh1gbj #ghb1bhd1ibj ,b if ! ,sun's ,p>allax be #aa _! di/ances are no m ?an #bi1jcb1ejj #ed1bch1egj #ge1jjj1jjj #aad1bgf1gej #cij1jcd1ejj #gae1ejd1ejj ,errors 9 di/ance a ris+ f ! mi/ake ( #a 9 ! ,sun's ,p>allax #b1gji1gjj #e1jgd1dij #g1jjj1jjj #aj1ffe1hcj #cf1ddd1bbj #ff1ghj1dbj #aie4 ,^! la/ numb]s %ew1 t al?\gh we h ! relative di/ances ( ! ,planets f ! ,sun to ! greate/ nicety1 yet ! be/ obs]v]s h n hi!rto be5 able to asc]ta9 _! true di/ances to )9 less ?an a twelf? "p ( :at !y really are4 ,& !re=e1 we mu/ wait ) pati5ce till ! #f? ( ,june1 ,a4 ,d4 #agfa2 wi%+ t ! ,sky may !n be cle> to all places :]e !re are good ,a/ronom]s & accurate in/rum5ts = obs]v+ ! ,transit ( ,v5us ov] ! ,sun's ,disc at t "t3 z x w n happ5 aga91 s z to be visible 9 ,europe1 9 less ?an #bce ye>s aft]4 ,sid5ote3 ,:y ! cele/ial ,poles seem to keep /ill 9 ! same po9ts ( ! ,heav5s1 not)/&+ ! ,e>?'s motion r\nd ! ,sun4 #aif4 ,! ,e>?'s ,axis produc$ to ! ,/>s1 be+ c>ri$ #ejp>allel to itself dur+ ! ,e>?'s annual revolution1 describes a circle 9 ! ,sph]e ( ! fix$ ,/>s equal to ! ,orbit ( ! ,e>?4 ,b ?is ,orbit1 ?\gh v l>ge 9 itself1 if view$ f ! ,/>s1 w\ld appe> no bigg] ?an a po9t2 & consequ5tly1 ! circle describ$ 9 ! ,sph]e ( ! ,/>s by ! ,axis ( ! ,e>? produc$1 if view$ f ! ,e>?1 mu/ appe> b z a po9t2 t is1 x's diamet] appe>s too little to be measur$ by obs]vation3 = ,dr4 ,,bradley has assur$ u1 t if x _h am\nt$ to a s+le second1 or two at mo/1 he %\ld h p]ceiv$ x 9 ! great numb] ( obs]vations he has made1 especially ^u ,dragonis2 & t x seem$ to him v probable t ! annual ,p>allax ( ?is ,/> is n s great z a s+le second3 & consequ5tly1 t x is above #djj ?\s& times f>!r f u ?an ! ,sun4 ,h5ce ! cele/ial poles seem to cont9ue 9 ! same po9ts ( ! ,heav5s ?r\gh\t ! ye>2 :i* by no means disproves ! ,e>?'s annual motion1 b pla9ly proves ! di/ance ( ! ,/>s to be exce$+ great4 ,sid5ote3 ,! amaz+ velocity ( light4 ,,plate ,,iv4 #aig4 ,! small app>5t motion ( ! ,/>s #aac1 discov]$ by t great ,a/ronom]1 he f\nd to be no ways ow+ to _! annual ,p>allax 7= x came out contr>y !reto7 b to ! ,ab]ration ( _! light1 :i* c result f no kn[n cause besides t ( ! ,e>?'s annual motion2 & z x agrees s exactly !re)1 x proves beyond dispute t ! ,e>? has su* a motion3 = ?is ,ab]ration compleats all x's v>i\s ,ph5om5a e ye>2 & proves t ! velocity ( />-light is su* z c>ries x ?r\gh a space equal to ! ,sun's di/ance f u 9 #h m9utes #ac seconds ( "t4 ,h5ce1 ! velocity ( light is #eaaj ?\s& #baj times z great z ! ,e>?'s velocity 9 x's ,orbit2 :i* velocity 7f :at we "k already ( ! ,e>?'s di/ance f ! ,sun7 may be affect$ to be at lea/ betwe5 #eg & #eh ?\s& miles e h\r3 & suppos+ x to be #ehjjj1 ?is numb] multipli$ by ! above #ajbaj1 gives #eib million #ahj ?\s& miles = ! h\rly motion ( light3 :i* la/ numb] divid$ by #cfjj1 ! numb] ( seconds 9 an h\r1 %ews t light flies at ! rate ( m ?an #afd ?\s& miles e second ( "t1 or sw+ ( a common clock p5dulum4 ,,*ap4 ,x4 ,! ,circles ( ! ,globe describ$4 ,! diff]5t l5g?s ( days & nights1 & ! vicissitudes ( seasons1 expla9$4 ,! explanation ( ! ,ph5om5a ( ,saturn's ,r+ conclud$4 7,see #ha & #hb47 ,sid5ote3 ,circles ( ! ,sph]e4 ,fig4 ,,ii ,equator1 ,tropics1 ,pol> ,circles1 & ,poles4 ,fig4 ,,ii4 ,e>?'s ,axis4 ,,plate ,,iv4 ,m]idians4 #aih4 ,if ! read] be hi!rto unacqua9t$ ) ! pr9cipal circles ( ! ,globe1 he %\ld n[ le>n to "k !m2 :i* he may d suffici5tly = 8 pres5t purpose 9 a qu>t] ( an h\r1 if he sets ! ball ( a t]re/rial ,globe be=e him1 or looks at ! ,figure ( x1 :]e9 ^! circles are drawn & nam$4 ,! ,equator is t great circle :i* divides ! nor!rn half ( ! ,e>? f ! s\!rn4 ,! ,tropics are less] circles p>allel to ! ,equator1 & ea* ( !m is #bc-a_/b degrees f x2 a degree 9 ?is s5se be+ ! #cfj? "p ( any great circle :i* divides ! ,e>? into two equal p>ts4 ,! ,tropic ( ,canc] lies on ! nor? side ( ! ,equator1 & ! ,tropic ( ,capricorn on ! s\?4 ,! ,arctic ,circle has ! ,nor? ,pole = x's c5t]1 & is j z f> f ! nor? ,pole z ! ,tropics are f ! ,equator3 & ! ,ant>ctic ,circle 7hid by ! suppos$ convexity ( ! ,figure7 is j z f> f ! ,s\? ,pole1 e way r\nd x4 ,^! ,poles are ! v nor? & s\? po9ts ( ! ,globe3 & all o!r places are d5om9at$ nor?w>d or s\?w>d accord+ to ! side ( ! ,equator !y lie on1 & ! ,pole to :i* !y are ne>e/4 ,! ,e>?'s ,axis is a /raight l9e pass+ ?r\gh ! c5t] ( ! ,e>?1 p]p5dicul> to ! ,equator1 & t]m9at+ 9 ! ,poles at x's surface4 ,?is1 9 ! real ,e>? & ,planets is only an imag9>y l9e2 b 9 artificial ,globes or ,planets x is a wire by :i* !y are support$1 & turn$ r\nd 9 ,orr]ies1 or su* l ma*9es1 by :eel-"w4 ,! circles #ab4 #a4 #b4 #c4 #d1 c4 are ,m]idians to all places !y pass ?r\gh2 & we mu/ suppose ?\s&s m to be drawn1 because e place t is ev] s little to ! ea/ or we/ ( any o!r place1 has a diff]5t ,m]idian f t o!r place4 ,all ! ,m]idians meet 9 ! ,poles2 & :5ev] ! ,sun's c5t] is pass+ ov] any ,m]idian1 9 8 app>5t motion r\nd ! ,e>?1 x is mid-day or noon to all places on t ,m]idian4 ,sid5ote3 ,zones4 #aii4 ,! broad ,space ly+ betwe5 ! ,tropics1 l a girdle surr\nd+ ! ,globe1 is call$ ! torrid ,zone1 ( :i* ! ,equator is 9 ! middle1 all ar\nd4 ,! ,space betwe5 ! ,tropic ( ,canc] & ,arctic ,circle is call$ ! ,nor? temp]ate ,zone4 ,t betwe5 ! ,tropic ( ,capricorn & ! ,ant>ctic ,circle1 ! ,s\? temp]ate ,zone4 ,& ! two circul> ,spaces b\nd$ by ! ,pol> ,circles are ! two ,frigid ,zones2 d5om9at$ nor? or s\?1 f t ,pole :i* is 9 ! c5t] ( ! "o or ! o!r ( !m4 #bjj4 ,hav+ acquir$ ?is easy bran* ( k1 ! le>n] may proce$ to make ! foll[+ exp]im5t ) 8 t]re/rial ball2 :i* w give him a pla9 idea ( ! diurnal & annual motions ( ! ,e>?1 toge!r ) ! diff]5t l5g?s ( days & nights1 & all ! beautiful v>iety ( seasons1 dep5d+ on ^? motions4 ,sid5ote3 ,fig4 ,,iii4 ,a pleasant exp]im5t %ew+ ! diff]5t l5g?s ( days & nights1 & ! v>iety ( seasons4 ,summ] ,sol/ice4 ,take ab\t sev5 feet ( /rong wire1 & b5d x into a circul> =m1 z abcd1 :i* be+ view$ obliquely1 appe>s elliptical z 9 ! ,figure4 ,place a light$ c&le on a table1 & hav+ fix$ "o end ( a silk ?read ,k1 to ! nor? pole ( a small t]re/rial ,globe ,h1 ab\t ?ree in*es diamet]1 cause ano!r p]son to hold ! wire circle s t x may be p>allel to ! table1 & z high z ! flame ( ! c&le ,i1 :i* %\ld be 9 or ne> ! c5t]4 ,!n1 hav+ twi/$ ! ?read z t[>ds ! left h&1 t by untwi/+ x may turn ! ,globe r\nd ea/w>d1 or contr>y to ! way t ! h&s ( a wat* move2 hang ! ,globe by ! ?read )9 ?is circle1 almo/ contigu\s to x2 & z ! ?read untwi/s1 ! ,globe 7:i* is enlight5$ half r\nd by ! c&le z ! ,e>? is by ! ,sun7 w turn r\nd x's ,axis1 & ! diff]5t places ^u x w be c>ri$ ?r\gh ! light & d>k ,hemisph]es1 & h ! appe>ance ( a regul> succession ( days & nights1 z our ,e>? has 9 reality by su* a motion4 ,z ! ,globe turns1 move y\r h& sl[ly s z to c>ry ! ,globe r\nd ! c&le accord+ to ! ord] ( ! lett]s abcd1 keep+ x's c5t] ev5 ) ! wire circle2 & y w p]ceive1 t ! c&le be+ /ill p]p5dicul> to ! ,equator w enlight5 ! ,globe f pole to pole 9 x's motion r\nd ! circle2 & t e place on ! ,globe goes equally ?r\gh ! light & ! d>k1 z x turns r\nd by ! untwi/+ ( ! ?read1 & !re=e has a p]petual ,equ9ox4 ,! ,globe ?us turn+ r\nd repres5ts ! ,e>? turn+ r\nd x's ,axis2 & ! motion ( ! ,globe r\nd ! c&le repres5ts ! ,e>?'s annual motion r\nd ! ,sun1 & %ews1 t if ! ,e>?'s ,orbit _h no incl9ation to x's ,axis1 all ! days & nights ( ! ye> w\ld be equally long1 & !re w\ld be no diff]5t seasons4 ,b n[1 desire ! p]son :o holds ! wire to hold x obliquely 9 ! position ,,abcd1 rais+ ! side j z mu* z he depresses ! side 1 t ! flame may be /ill 9 ! plane ( ! circle2 & twi/+ ! ?read z be=e1 t ! ,globe may turn r\nd x's ,axis ! same way z y c>ry x r\nd ! c&le2 t is1 f we/ to ea/1 let ! ,globe d[n into ! l[]mo/ "p ( ! wire circle at 1 & if ! circles be prop]ly incl9$1 ! c&le w %9e p]p5dicul>ly on ! ,tropic ( ,canc]1 & ! frigid ,zone1 ly+ )9 ! arctic or nor? pol> ,circle1 w be all 9 ! light1 z 9 ! ,figure2 & w keep 9 ! light let ! ,globe turn r\nd x's ,axis ev] s (t54 ,f ! ,equator to ! nor? pol> ,circle all ! places h long] days & %ort] nights2 b f ! ,equator to ! s\? pol> ,circle j ! rev]se4 ,! ,sun does n set to any "p ( ! nor? frigid ,zone1 z %ewn by ! c&le's %9+ on x s t ! motion ( ! ,globe c c>ry no place ( t ,zone into ! d>k3 & at ! same "t ! s\? frigid ,zone is involv$ 9 d>kness1 & ! turn+ ( ! ,globe br+s none ( x's places into ! light4 ,if ! ,e>? 7 to cont9ue 9 ! l "p ( x's ,orbit1 ! ,sun w\ld nev] set to ! inhabitants ( ! nor? frigid ,zone1 nor rise to ^? ( ! s\?4 ,at ! ,equator x w\ld be always equal day & night2 & z ! places are gradually m & m di/ant f ! ,equator1 t[>ds ! arctic ,circle1 !y w\ld h long] days & %ort] nights1 :il/ ^? on ! s\? side ( ! ,equator w\ld h _! nights long] ?an _! days4 ,9 ?is case !re w\ld be cont9ual summ] on ! nor? side ( ! ,equator1 & cont9ual w9t] on ! s\? side ( x4 ,illu/ration3 ,plate ,v4 ,j4 ,f]guson del94 ,j4 ,mynde ,sc4 ,sid5ote3 ,,plate ,,iv4 ,autumnal ,equ9ox4 ,b z ! ,globe turns r\nd x's ,axis1 move y\r h& sl[ly =w>d s z to c>ry ! ,globe f ,h t[>ds ,e1 & ! b\nd>y ( light & d>kness w approa* t[>ds ! nor? ,pole1 & rec$e t[>ds ! s\? ,pole2 ! nor!rn places w g ?r\gh less & less ( ! light1 & ! s\!rn places ?r\gh m & m ( x2 %ew+ h[ ! nor!rn days decrease 9 l5g?1 & ! s\!rn days increase1 :il/ ! ,globe proce$s f ,h to ,f4 ,:5 ! ,globe is at ,e1 x is at a mean /ate betwe5 ! l[e/ & highe/ p>ts ( x's ,orbit2 ! c&le is directly ov] ! ,equator1 ! b\nd>y ( light & d>kness j rea*es to bo? ! ,poles1 & all places on ! ,globe g equally ?r\gh ! light & d>k ,hemisph]es1 %ew+ t ! days & nights are !n equal at all places ( ! ,e>?1 ! ,poles only except$2 = ! ,sun is !n sett+ to ! nor? ,pole1 & ris+ to ! s\? ,pole4 ,sid5ote3 ,w9t] ,sol/ice4 ,cont9ue mov+ ! ,globe =w>d1 & z x goes ?r\gh ! qu>t] ,a1 ! nor? ,pole rec$es /ill f>!r into ! d>k ,hemisph]e1 & ! s\? ,pole advances m into ! light1 z ! ,globe comes ne>] to 2 & :5 x comes !re at ,f1 ! c&le is directly ov] ! ,tropic ( ,capricorn1 ! days are at ! %orte/1 & nights at ! longe/1 9 ! nor!rn ,hemisph]e1 all ! way f ! ,equator to ! arctic ,circle2 & ! rev]se 9 ! s\!rn ,hemisph]e f ! ant>ctic ,circle2 )9 :i* ,circles x is d>k to ! nor? frigid ,zone & light to ! s\?4 ,sid5ote3 ,v]nal ,equ9ox4 ,cont9ue bo? motions1 & z ! ,globe moves ?r\gh ! qu>t] ,b1 ! nor? ,pole advances t[>d ! light1 & ! s\? ,pole rec$es z fa/ f x2 ! days l5g!n 9 ! nor!rn ,hemisph]e1 & %ort5 9 ! s\!rn2 & :5 ! ,globe comes to ,g ! c&le w be aga9 ov] ! ,equator 7z :5 ! ,globe 0 at ,e7 & ! days & nights w aga9 be equal z =m]ly3 & ! nor? ,pole w be j com+ into ! light1 ! s\? ,pole go+ out ( x4 ,?us we see ! reason :y ! days l5g!n & %ort5 f ! ,equator to ! pol> ,circles e ye>2 :y !re is no day or night = sev]al turn+s ( ! ,e>?1 )9 ! pol> ,circles2 :y !re is b "o day & "o night 9 ! :ole ye> at ! ,poles2 & :y ! days & nights are equally long all ! ye> r\nd at ! ,equator1 :i* is always equally cut by ! circle b\nd+ light & d>kness4 ,sid5ote3 ,rem>k4 ,fig4 ,,iii4 ,,plate ,v4 #bja4 ,! incl9ation ( an ,axis or ,orbit is m]ely relative1 because we comp>e x ) "s o!r ,axis or ,orbit :i* we consid] z n incl9$ at all4 ,?us1 our ,horizon be+ level to u :atev] place ( ! ,e>? we are ^u1 we consid] x z hav+ no incl9ation2 & yet1 if we travel #ij degrees f t place1 we %all !n h an ,horizon p]p5dicul> to ! =m]2 b x w /ill be level to u4 ,&1 if ?is ,book be held s t ! #eb;,circle ,,abcd be p>allel to ! ,horizon1 bo? ! ,circle abcd1 & ! ,?read or ,axis ,k w be incl9$ to x4 ,b if ,book or ,plate be held1 s t ! ,?read be p]p5dicul> to ! ,horizon1 !n ! ,orbit ,,abcd w be incl9$ to ! ,?read1 & ! ,orbit abcd p]p5dicul> to x1 & p>allel to ! ,horizon4 ,we g5]ally consid] ! ,e>?'s annual ,orbit z hav+ no incl9ation1 & ! ,orbits ( all ! o!r ,planets z incl9$ to x #bj4 #bjb4 ,let u n[ take a view ( ! ,e>? 9 x's annual c\rse r\nd ! ,sun1 consid]+ x's ,orbit z hav+ no incl9ation2 & x's ,axis z incl9+ #bc-a_/b degrees f a l9e p]p5dicul> to x's ,orbit1 & keep+ ! same oblique direction 9 all p>ts ( x's annual c\rse2 or1 z commonly t]m$1 keep+ always p>allel to itself #aif4 ,sid5ote3 ,fig4 ,i4 ,a concise view ( ! seasons4 ,let a1 b1 c1 d1 e1 f1 g1 h be ! ,e>? 9 eight diff]5t p>ts ( x's ,orbit1 equidi/ant f "o ano!r2 ,ns x's ,axis1 ,n ! nor? ,pole1 s ! s\? ,pole1 & ,s ! ,sun ne>ly 9 ! c5t] ( ! ,e>?'s ,orbit #ah4 ,z ! ,e>? goes r\nd ! ,sun accord+ to ! ord] ( ! lett]s abcd1 c4 x's ,axis ,ns keeps ! same obliquity1 & is /ill p>allel to ! l9e ,m,ns4 ,:5 ! ,e>? is at a1 x's nor? ,pole incl9es t[>d ! ,sun1 & br+s all ! nor!rn places m into ! light ?an at any o!r "t ( ! ye>4 ,b :5 ! ,e>? is at e 9 ! opposite "t ( ! ye>1 ! nor? ,pole decl9es f ! ,sun1 :i* occasions ! nor!rn places to be m 9 ! d>k ?an 9 ! light2 & ! rev]se at ! s\!rn places1 z is evid5t by ! ,figure1 :i* ,i h tak5 f ,dr4 ,,long's ,a/ronomy4 ,:5 ! ,e>? is ei!r at c or g1 x's ,axis incl9es n ei!r to or f ! ,sun1 b lies sidewise to him2 & !n ! ,poles are 9 ! b\nd>y ( light & d>kness2 & ! ,sun1 be+ directly ov] ! ,equator1 makes equal day & night at all places4 ,:5 ! ,e>? is at b x is half way betwe5 ! ,summ] ,sol/ice & ,h>ve/ ,equ9ox2 :5 x is at d x is half way f ! ,h>ve/ ,equ9ox to ! ,w9t] ,sol/ice2 at f half way f ! ,w9t] ,sol/ice to ! ,spr+ ,equ9ox3 & at h half way f ! ,spr+ ,equ9ox to ! ,summ] ,sol/ice4 ,sid5ote3 ,fig4 ,,ii4 ,,plate ,v4 ,! ,ecliptic4 ,! seasons %ewn 9 ano!r view ( ! ,e>?1 & x's ,orbit4 #bjc4 ,f ?is oblique view ( ! ,e>?'s ,orbit1 let u suppose ourselves to be rais$ f> above x1 & plac$ j ov] x's c5t] ,s1 look+ d[n ^u x f x's nor? pole2 & z ! ,e>?'s ,orbit diff]s b v little f a ,circle1 we %all h x's figure 9 su* a view repres5t$ by ! ,circle ,,abcdefgh4 ,let u suppose ?is ,circle to be divid$ into #ab equal p>ts call$ ,signs1 hav+ _! names affix$ to !m2 & ea* ,sign into #cj equal p>ts call$ ,degrees1 numb]$ #aj1 #bj1 #cj1 z 9 ! out]mo/ ,circle ( ! ,figure1 :i* repres5ts ! great ,ecliptic 9 ! ,heav5s4 ,! ,e>? is %ewn 9 eight diff]5t positions 9 ?is ,circle1 & 9 ea* position is ! ,equator1 ,t ! ,tropic ( ,canc]1 ! dott$ ,circle ! p>allel ( ,london1 ,u ! arctic or nor? pol> ,circle1 & ,p ! nor? ,pole :]e all ! ,m]idians or h\r ,circles meet #aih4 ,z ! ,e>? goes r\nd ! ,sun ! nor? ,pole keeps con/antly t[>ds "o "p ( ! ,heav5s1 z x keeps 9 ! ,figure t[>ds ! "r h& side ( ! ,plate4 ,sid5ote3 ,v]nal ,equ9ox4 ,:5 ! ,e>? is at ! beg9n+ ( ,libra1 namely on ! #bj? ( ,m>*1 9 ?is ,figure 7z at g 9 ,fig4 ,i47 ! ,sun ,s z se5 f ! ,e>? appe>s at ! beg9n+ ( ,aries 9 ! opposite "p ( ! ,heav5s#ec1 ! nor? ,pole is j com+ into ! light1 ! ,sun is v]tical to ! ,equator2 :i*1 toge!r ) ! ,tropic ( ,canc]1 p>allel ( ,london1 & arctic ,circle1 are all equally cut by ! ,circle b\nd+ light & d>kness1 co9cid+ ) ! six o'clock h\r ,circle1 & !re=e ! days & nights are equally long at all places3 = e "p ( ! ,m]idian ,t,la comes into ! light at six 9 ! morn+1 & revolv+ ) ! ,e>? accord+ to ! ord] ( ! h\r-lett]s1 goes into ! d>k at six 9 ! ev5+4 ,!re are #bd ,m]idians or h\r-,circles drawn on ! ,e>? 9 ?is ,figure1 to %ew ! "t ( ,sun ris+ & sett+ at diff]5t ,seasons ( ! ,ye>4 ,sid5ote3 ,fig4 ,,ii4 ,z ! ,e>? moves 9 ! ,ecliptic accord+ to ! ord] ( ! lett]s ,,abcd1 c4 ?r\gh ! ,signs ,libra1 ,scorpio1 & ,sagitt>ius1 ! nor? ,pole comes m & m into ! light2 ! days increase z ! nights decrease 9 l5g?1 at all places nor? ( ! ,equator 2 :i* is pla9 by view+ ! ,e>? at b on ! #e? ( ,may1 :5 x is 9 ! #ae? degree ( ,scorpio#ed1 & ! ,sun z se5 f ! ,e>? appe>s 9 ! #ae? degree ( ,taurus4 ,= !n1 ! ,tropic ( ,canc] ,t is 9 ! light f a little aft] five 9 ! morn+ till almo/ sev5 9 ! ev5+2 ! p>allel ( ,london f half an h\r pa/ f\r till half an h\r pa/ sev52 ! pol> ,circle ,u f ?ree till n9e2 & a l>ge track r\nd ! nor? ,pole ,p has day all ! #bd h\rs1 = _m rotations ( ! ,e>? on x's ,axis4 ,sid5ote3 ,summ] ,sol/ice4 ,:5 ! ,e>? comes to c1 at ! beg9n+ ( ,capricorn1 & ! ,sun z se5 f ! ,e>? appe>s at ! beg9n+ ( ,canc]1 on ! #ba/ ( ,june1 z 9 ?is ,figure1 x is 9 ! position a 9 ,fig4 ,i2 & x's nor? ,pole incl9es t[>d ! ,sun1 s z to br+ all ! nor? frigid ,zone into ! light1 & ! nor!rn p>allels ( ,latitude m into ! light ?an ! d>k f ! ,equator to ! pol> ,circles2 & ! m s z !y are f>!r f ! ,equator4 ,! ,tropic ( ,canc] is 9 ! light f five 9 ! morn+ till sev5 at night1 ! p>allel ( ,london f a qu>t] be=e f\r till a qu>t] aft] eight2 & ! pol> ,circle j t\*es ! d>k1 s t ! ,sun has only ! l[] half ( 8 ,disc hid f ! inhabitants on t ,circle = a few m9utes ab\t midnight1 suppos+ no inequalities 9 ! ,horizon & no ,refractions4 ,sid5ote3 ,autumnal ,equ9ox4 ,w9t] ,sol/ice4 ,a b>e view ( ! ,figure is en\gh to %ew1 t z ! ,e>? advances f ,capricorn t[>d ,aries1 & ! ,sun appe>s to move f ,canc] t[>d ,libra1 ! nor? ,pole rec$es t[>d ! d>k1 :i* causes ! days to decrease1 & ! nights to increase 9 l5g?1 till ! ,e>? comes to ,aries1 & !n !y are equal z be=e2 = ! b\nd>y ( light & d>kness cut ! ,equator & all x's p>allels equally1 or 9 halves4 ,! nor? pole !n goes into ! d>k1 & cont9ues !re9 until ! ,e>? goes half way r\nd x's ,orbit2 or1 f ! #bc;d ( ,septemb] till ! #bj? ( ,m>*4 ,9 ! middle betwe5 ^! times1 viz4 on ! #bb;d ( ,decemb]1 ! nor? ,pole is z f> z x c be 9 ! d>k1 :i* is #bc-a_/b degrees1 equal to ! incl9ation ( ! ,e>?'s ,axis f a p]p5dicul> to x's ,orbit3 & !n1 ! nor!rn p>allels are z mu* 9 ! d>k z !y 7 9 ! light on ! #ba ( ,june2 ! w9t] nights be+ z long z ! summ] days1 & ! w9t] days z %ort z ! summ] nights4 ,x is ne$less to multiply words on ?is subject1 z we %all h occasion to m5tion ! seasons aga9 9 describ+ ! ,orr]y1 #dci4 ,only ?is mu/ be not$1 t all t has be5 said ( ! nor!rn ,hemisph]e1 ! contr>y mu/ be und]/ood ( ! s\!rn2 = on diff]5t sides ( ! ,equator ! seasons are contr>y1 because1 :5 ! nor!rn ,hemisph]e incl9es t[>d ! ,sun ! s\!rn decl9es f him4 ,sid5ote3 ,! ,ph5om5a ( ,saturn's ,r+4 ,,plate ,v4 #bjd4 ,z ,saturn goes r\nd ! ,sun1 8 obliquely posit$ r+1 l our ,e>?'s ,axis1 keeps p>allel to itself1 & is !re=e turn$ edgewise to ! ,sun twice 9 a ,saturnian ye>1 :i* is almo/ z long z #cj ( our ye>s #ha4 ,b ! r+1 ?\gh consid]ably broad1 is too ?9 to be se5 :5 x is turn$ r\nd edgewise to ! ,sun1 at :i* "t x is also edgewise to ! ,e>?2 & !re=e x disappe>s once 9 e fifte5 ye>s to u4 ,z ! ,sun %9es half a ye> on ! nor? pole ( our e>?1 !n disappe>s to x1 & %9es z long on ! s\? pole2 s1 dur+ "o half ( ,saturn's ye> ! ,sun %9es on ! nor? side ( 8 r+1 !n disappe>s to x1 & %9es z long on x's s\? side4 ,:5 ! ,e>?'s ,axis incl9es nei!r to nor f ! ,sun1 b sidewise to him1 he in/antly ceases to %9e on "o pole1 & beg9s to enlight5 ! o!r2 & :5 ,saturn's ,r+ incl9es nei!r to nor f ! ,sun1 b sidewise to him1 he ceases to %9e on ! "o side ( x1 & beg9s to %9e ^u ! o!r4 ,sid5ote3 ,fig4 ,,iii4 ,let ,s be ! ,sun1 ,,abcdefgh ,saturn's ,orbit1 & ,,iklmno ! ,e>?'s ,orbit4 ,bo? ,saturn & ! ,e>? move accord+ to ! ord] ( ! lett]s1 & :5 ,saturn is at ,a 8 r+ is turn$ edgewise to ! ,sun ,s1 & he is !n se5 f ! ,e>? z if he _h lo/ 8 r+1 let ! ,e>? be 9 any "p ( x's ,orbit :atev]1 except betwe5 ,n & ,o2 = :il/ x describes t space1 ,saturn is app>5tly s ne> ! ,sun z to be hid 9 8 beams4 ,z ,saturn goes f ,a to ,c 8 r+ appe>s m & m op5 to ! ,e>?3 at ,c ! r+ appe>s mo/ op5 ( all2 & seems to gr[ n>r[] & n>r[] z ,saturn goes f ,c to ,e2 & :5 he comes to ,e1 ! r+ is aga9 turn$ edgewise bo? to ! ,sun & ,e>?3 & z nei!r ( x's sides are illum9at$1 x is invisible to u1 because x's edge is too ?9 to be p]ceptible3 & ,saturn appe>s aga9 z if he _h lo/ 8 r+4 ,b z he goes f ,e to ,g1 8 r+ op5s m & m to our view on ! "u side2 & seems j z op5 at ,g z x 0 at ,c2 & may be se5 9 ! night-"t f ! ,e>? 9 any "p ( x's ,orbit1 except ab\t ,m1 :5 ! ,sun hides ! ,planet f our view4 ,z ,saturn goes f ,g to ,a 8 r+ turns m & m edgewise to u1 & !re=e x seems to gr[ n>r[] & n>r[]2 & at ,a x disappe>s z be=e4 ,h5ce1 :ile ,saturn goes f ,a to ,e ! ,sun %9es on ! upp] side ( 8 r+1 & ! "u side is d>k2 b :il/ he goes f ,e to ,a ! ,sun %9es on ! "u side ( 8 r+1 & ! upp] side is d>k4 ,sid5ote3 ,fig4 ,i & ,,iii4 ,x may p]haps be imag9$ t ?is ,article might h be5 plac$ m prop]ly aft] #ha ?an "h3 b :5 ! c&id read] consid]s t all ! v>i\s ,ph5om5a ( ,saturn's ,r+ dep5d ^u a cause simil> to t ( our ,e>?'s seasons1 he w readily all[ t !y are be/ expla9$ toge!r2 & t ! two ,figures s]ve to illu/rate ea* o!r4 ,sid5ote3 ,,plate ,,vi4 ,! ,e>? ne>] ! ,sun 9 w9t] ?an 9 summ]4 ,:y ! wea!r is colde/ :5 ! ,e>? is ne>e/ ! ,sun4 #bje4 ,! ,e>?'s ,orbit be+ elliptical1 & ! ,sun con/antly keep+ 9 x's l[] ,focus1 :i* is #a1cgg1jjj miles f ! middle po9t ( ! long] ,axis1 ! ,e>? comes twice s mu*1 or #b1ged1jjj miles ne>] ! ,sun at "o "t ( ! ye> ?an at ano!r3 = ! ,sun appe>+ "u a l>g] ,angle 9 our w9t] ?an summ]1 proves t ! ,e>? is ne>] ! ,sun 9 w9t]1 7see ! ,note on ,art4 #ahe47 ,b "h1 ?is natural "q w arise1 ,:y h we n ! hotte/ wea!r :5 ! ,e>? is ne>e/ ! ,sun8 ,9 answ] x mu/ be obs]v$1 t ! exc5tricity ( ! ,e>?'s ,orbit1 or #a million #cgg miles be>s no great] proportion to ! ,e>?'s mean di/ance f ! ,sun ?an #ag does to #ajjj2 & !re=e1 ?is small diff]5ce ( di/ance _c occasion any great diff]5ce ( heat or cold4 ,b ! pr9cipal cause ( ?is diff]5ce is1 t 9 w9t] ! ,sun's rays fall s obliquely ^u u1 t any giv5 numb] ( !m is spread ov] a mu* great] portion ( ! ,e>?'s surface :]e we live2 & !re=e ea* po9t mu/ !n h few] rays ?an 9 summ]4 ,moreov]1 !re comes a great] degree ( cold 9 ! long w9t] nights1 ?an !re c return ( heat 9 s %ort days2 & on bo? ^! acc\nts ! cold mu/ increase4 ,b 9 summ] ! ,sun's rays fall m p]p5dicul>ly ^u u1 & !re=e come ) great] =ce1 & 9 great] numb]s on ! same place2 & by _! long cont9uance1 a mu* great] degree ( heat is imp>t$ by day ?an c fly (f by night4 ,sid5ote3 ,fig4 ,,ii4 #bjf4 ,t a great] numb] ( rays fall on ! same place1 :5 !y come p]p5dicul>ly1 ?an :5 !y come obliquely on x1 w appe> by ! ,figure4 ,=1 let ,,ab be a c]ta9 numb] ( ! ,sun's rays fall+ on ,,cd 7:i*1 let u suppose to be ,london7 on ! #bb;d ( ,june3 b1 on ! #bb;d ( ,decemb]1 ! l9e ,,cd1 or ,london2 has ! oblique position ,cd to ! same rays2 & !re=e sc>ce a ?ird "p ( !m falls ^u x1 or only ^? betwe5 ,a & e2 all ! re/ e,b be+ exp5d$ on ! space d,p1 :i* is m ?an d\ble ! l5g? ( ,,cd or ,cd4 ,besides1 ^? p>ts :i* are once heat$1 reta9 ! heat = "s "t2 :i*1 ) ! additional heat daily imp>t$1 makes x cont9ue to increase1 ?\gh ! ,sun decl9es t[>d ! s\?3 & ?is is ! reason :y ,july is hott] ?an ,june1 al?\gh ! ,sun has )drawn f ! summ] ,tropic2 z we f9d x is g5]ally hott] at ?ree 9 ! aft]noon1 :5 ! ,sun has gone t[>d ! we/1 ?an at noon :5 he is on ! ,m]idian4 ,likewise1 ^? places :i* are well cool$ require "t to be heat$ aga92 = ! ,sun's rays d n heat ev5 ! surface ( any body till !y h be5 "s "t ^u x4 ,& !re=e we f9d ,janu>y = ! mo/ "p cold] ?an ,decemb]1 al?\gh ! ,sun has )drawn f ! w9t] ,tropic1 & beg9s to d>t 8 beams m p]p5dicul>ly ^u u1 :5 we h ! position ,,cf4 ,an iron b> is n heat$ imm$iately ^u be+ put into ! fire1 nor gr[s cold till "s "t aft] x has be5 tak5 out4 ,,*ap4 ,,xi4 ,! ,me?od ( f9d+ ! ,longitude by ! ,eclipses ( ,jupit]'s ,satellites3 ,! amaz+ ,velocity ( ,light demon/rat$ by ^! ,eclipses4 ,sid5ote3 ,fir/ ,m]idian1 & ,longitude ( places1 :at4 #bjg4 ,geograph]s arbitr>ily *oose to call ! ,m]idian ( "s rem>kable place ! fir/ ,m]idian4 ,!re !y beg9 _! reckon+2 & j s _m degrees & m9utes z any o!r place is to ! ea/w>d or we/w>d ( t ,m]idian1 s mu* ea/ or we/ ,longitude !y say x has4 ,a degree is ! #cfj? "p ( a ,circle1 be x great or small2 & a m9ute ! #fj? "p ( a degree4 ,! ,engli% ,geograph]s reckon ! ,longitude f ! ,m]idian ( ! ,royal ,obs]vatory at ,gre5wi*1 & ! ,fr5* f ! ,m]idian ( ,p>is4 ,sid5ote3 ,,plate ,v4 ,fig4 ,,ii4 ,h\r ,circles4 ,an h\r ( "t equal to #ae degrees ( motion4 #bjh4 ,if we imag9e twelve great ,circles1 "o ( :i* is ! ,m]idian ( any giv5 place1 to int]sect ea* o!r 9 ! two ,poles ( ! ,e>?1 & to cut ! ,equator at e #ae? degree1 !y w be divid$ by ! ,poles into #bd ,semicircles :i* divide ! ,equator into #bd equal p>ts2 & z ! ,e>? turns on x's ,axis1 ! planes ( ^! ,semicircles come successively aft] "o ano!r e h\r to ! ,sun4 ,z 9 an h\r ( "t !re is a revolution ( #ae degrees ( ! ,equator1 9 a m9ute ( "t !re w be a revolution ( #ae m9utes ( ! ,equator1 & 9 a second ( "t a revolution ( #ae seconds4 ,!re are two tables annex$ to ?is ,*apt]1 = r$uc+ mean sol> "t into degrees & m9utes ( ! t]re/rial ,equator2 & also = conv]t+ degrees & p>ts ( ! ,equator into mean sol> "t4 #bji4 ,because ! ,sun enlight5s only "o half ( ! ,e>? at once1 z x turns r\nd x's ,axis he rises to "s places at ! same mom5ts ( absolute ,"t t he sets to o!rs2 & :5 x is mid-day to "s places1 x is mid-night to o!rs4 ,! ,,xii on ! middle ( ! ,e>?'s enlight5$ side1 next ! ,sun1 /&s = mid-day2 & ! opposite ,,xii on ! middle ( ! d>k side1 = mid-night4 ,if we suppose ?is ,circle ( h\rs to be fix$ 9 ! plane ( ! ,equ9octial1 & ! ,e>? to turn r\nd )9 x1 any p>ticul> ,m]idian w come to ! diff]5t h\rs s1 z to %ew ! true "t ( ! day or night at all places on t ,m]idian4 ,!re=e1 ,sid5ote3 ,& consequ5tly to #ae degrees ( ,longitude4 ,lun> ,eclipses useful 9 f9d+ ! ,longitude4 #baj4 ,to e place #ae degrees ea/w>d f any giv5 ,m]idian1 x is noon an h\r soon] ?an on t ,m]idian2 because _! ,m]idian comes to ! ,sun an h\r soon]3 & to all places #ae degrees we/w>d x is noon an h\r lat] #bjh1 because _! ,m]idian comes an h\r lat] to ! ,sun2 & s on3 e #ae degrees ( motion caus+ an h\r's diff]5ce 9 "t4 ,!re=e !y :o h noon an h\r lat] ?an we1 h _! ,m]idian1 t is1 _! ,longitude #ae degrees we/w>d f u2 & !y :o h noon an h\r soon] ?an we1 h _! ,m]idian #ae degrees ea/w>d f ours3 & s = e h\r's diff]5ce ( "t #ae degrees diff]5ce ( ,longitude4 ,consequ5tly1 if ! beg9n+ or end+ ( a ,lun> ,eclipse be obs]v$1 suppose at ,london1 to be exactly at mid-night1 & 9 "s o!r place at #aa at night1 t place is #ae degrees we/w>d f ! ,m]idian ( ,london3 if ! same ,eclipse be obs]v$ at "o 9 ! morn+ at ano!r place1 t place is #ae degrees ea/w>d f ! said ,m]idian4 ,sid5ote3 ,eclipses ( ,jupit]'s ,satellites mu* bett] = t purpose4 #baa4 ,b z x is n easy to det]m9e ! exact mom5t ei!r ( ! beg9n+ or end+ ( a ,lun> ,eclipse1 because ! ,e>?'s %ad[ ?r\gh :i* ! ,moon passes is fa9t & ill def9$ ab\t ! edges2 we h rec\rse to ! ,eclipses ( ,jupit]'s ,satellites1 :i* disappe> s in/antane\sly z !y ent] into ,jupit]'s %ad[1 & em]ge s sudd5ly out ( x1 t we may fix ! ph5om5on to half a second ( "t4 ,! fir/ or ne>e/ ,satellite to ,jupit] is ! mo/ advantage\s = ?is purpose1 because x's motion is quick] ?an ! motion ( any ( ! re/1 & !re=e x's imm]sions & em]sions are m frequ5t4 ,sid5ote3 ,h[ to solve ?is important problem4 ,,plate ,v4 #bab4 ,! ,engli% ,a/ronom]s h made ,tables = %ew+ ! times ( ! ,eclipses ( ,jupit]'s ,satellites to great precision1 = ! ,m]idian ( ,gre5wi*4 ,n[1 let an obs]v]1 :o has ^! ,tables ) a good ,telescope & a well-regulat$ ,clock at any o!r place ( ! ,e>?1 obs]ve ! beg9n+ or end+ ( an ,eclipse ( "o ( ,jupit]'s ,satellites1 & note ! precise mom5t ( "t t he saw ! ,satellite ei!r imm]ge into1 or em]ge out ( ! %ad[1 & comp>e t "t ) ! "t %ewn by ! ,tables = ,gre5wi*2 !n1 #ae degrees diff]5ce ( ,longitude be+ all[$ = e h\r's diff]5ce ( "t1 w give ! ,longitude ( t place f ,gre5wi*1 z above #baj2 & if !re be any odd m9utes ( "t1 = e m9ute a qu>t] ( a degree1 ea/ or we/ mu/ be all[$1 z ! "t ( obs]vation is be=e or aft] ! "t %ewn by ! ,tables4 ,su* ,eclipses are v conv5i5t = ?is purpose at l&1 because !y happ5 almo/ e day2 b are ( no use at sea1 because ! roll+ ( ! %ip h9d]s all nice telescopical obs]vations4 ,sid5ote3 ,fig4 ,,ii4 ,illu/rat$ by an example4 #bac4 ,to expla9 ?is by a ,figure1 let ,j be ,jupit]1 ,k1 ,l1 ,m1 ,n 8 f\r ,satellites 9 _! respective ,orbits #a1 #b1 #c1 #d2 & let ! ,e>? be at f 7suppose 9 ,novemb]1 al?\gh t mon? is no o!rways mat]ial ?an to f9d ! ,e>? readily 9 ?is s*eme1 :]e x is %ewn 9 eight diff]5t p>ts ( x's ,orbit47 ,let ,q be a place on ! ,m]idian ( ,gre5wi*1 & ,r a place on "s o!r ,m]idian4 ,let a p]son at ,r obs]ve ! in/antane\s vani%+ ( ! fir/ ,satellite ,k into ,jupit]'s %ad[1 suppose at ?ree o'clock 9 ! morn+2 b by ! ,tables he f9ds ! imm]sion ( t ,satellite to be at midnight at ,gre5wi*3 he c !n imm$iately det]m9e1 t z !re are ?ree h\rs diff]5ce ( "t betwe5 ,q & ,r1 & t ,r is ?ree h\rs =w>d] 9 reckon+ ?an ,q1 x mu/ be #de degrees ( ea/ ,longitude f ! ,m]idian ( ,q4 ,7 ?is me?od z practicable at sea z at l&1 any sailor might almo/ z easily1 & ) equal c]ta9ty1 f9d ! ,longitude z ! ,latitude4 ,sid5ote3 ,fig4 ,,ii4 ,we seldom see ! beg9n+ & end ( ! same ,eclipse ( any ( ,jupit]'s ,moons4 #bad4 ,:il/ ! ,e>? is go+ f ,c to ,f 9 x's ,orbit1 only ! imm]sions ( ,jupit]'s ,satellites into 8 %ad[ are g5]ally se52 & _! em]sions out ( x :ile ! ,e>? goes f ,g to ,b4 ,inde$1 bo? ^! appe>ances may be se5 ( ! second1 ?ird1 & f\r? ,satellite :5 eclips$1 :il/ ! ,e>? is betwe5 ,d & ,e1 or betwe5 ,g & ,a2 b nev] ( ! fir/ ,satellite1 on acc\nt ( ! smallness ( x's ,orbit & ! bulk ( ,jupit]2 except only :5 ,jupit] is directly opposite to ! ,sun2 t is1 :5 ! ,e>? is at g3 & ev5 !n1 /rictly speak+1 we _c see ei!r ! imm]sions or em]sions ( any ( 8 ,satellites1 because 8 body be+ directly betwe5 u & 8 conical %ad[1 8 ,satellites are hid by 8 body a few mom5ts be=e !y t\* 8 %ad[2 & are q em]g$ f !nce be=e we c see !m1 z x 71 j dropp+ f him4 ,& :5 ! ,e>? is at c1 ! ,sun be+ betwe5 x & ,jupit] hides bo? him & 8 ,moons f u4 ,9 ?is ,diagram1 ! ,orbits ( ,jupit]'s ,moons are drawn 9 true proportion to 8 diamet]2 b1 9 proportion to ! ,e>?'s ,orbit !y are drawn #ha times too l>ge4 ,sid5ote3 ,,plate ,,vi4 ,jupit]'s conjunctions ) ! ,sun1 or oppositions to him1 are e ye> 9 diff]5t p>ts ( ! ,heav5s4 #bae4 ,9 :atev] mon? ( ! ye> ,jupit] is 9 conjunction ) ! ,sun1 or 9 opposition to him1 9 ! next ye> x w be a mon? lat] at lea/4 ,= :il/ ! ,e>? goes once r\nd ! ,sun1 ,jupit] describes a twelf? "p ( 8 ,orbit4 ,& !re=e1 :5 ! ,e>? has f9i%$ x's annual p]iod f be+ 9 a l9e ) ! ,sun & ,jupit]1 x mu/ g z mu* =w>d] z ,jupit] has mov$ 9 t "t1 to ov]take him aga93 j l ! m9ute h& ( a wat*1 :i* mu/1 f any conjunction ) ! h\r h&1 g once r\nd ! dial-plate & some:at above a twelf? "p m1 to ov]take ! h\r h& aga94 ,sid5ote3 ,! surpris+ velocity ( light4 #baf4 ,x is f\nd by obs]vation1 t :5 ! ,e>? is betwe5 ! ,sun & ,jupit]1 z at g1 8 ,satellites are eclips$ ab\t #h m9utes soon] ?an !y %\ld be accord+ to ! ,tables3 & :5 ! ,e>? is at ,b or ,c1 ^! ,eclipses happ5 ab\t #h m9utes lat] ?an ! ,tables pr$ict !m4 ,h5ce x is und5iably c]ta91 t ! motion ( light is n in/antane\s1 s9ce x takes ab\t #af-a_/b m9utes ( "t to g ?r\gh a space equal to ! diamet] ( ! ,e>?'s ,orbit1 :i* is #afb millions ( miles 9 l5g?3 & consequ5tly ! p>ticles ( light fly ab\t #afd ?\s& #did miles e second ( "t1 :i* is above a million ( times swift] ?an ! motion ( a cannon bullet4 ,& z light is #af-a_/b m9utes 9 travell+ across ! ,e>?'s ,orbit1 x mu/ be #h-a_/d m9utes 9 com+ f ! ,sun to u3 !re=e1 if ! ,sun 7 annihilat$ we %\ld see him = #h-a_/d m9utes aft]2 & if he 7 aga9 creat$ he w\ld be #h-a_/d m9utes old be=e we c\ld see him4 ,sid5ote3 ,fig4 ,v4 ,illu/rat$ by a ,figure4 #bag4 ,to illu/rate ?is progressive motion ( light1 let ,a & ,b be ! ,e>? 9 two diff]5t p>ts ( x's ,orbit1 ^: di/ance is #ha millions ( miles1 equal to ! ,e>?'s di/ance f ! ,sun ,s4 ,x is pla91 t if ! motion ( light 7 in/antane\s1 ! ,satellite #a w\ld appe> to ent] into ,jupit]'s %ad[ ,,ff at ! same mom5t ( "t to a spectator 9 ,a z to ano!r 9 ,b4 ,b by _m ye>s obs]vations x has be5 f\nd1 t ! imm]sion ( ! ,satellite into ! %ad[ is se5 #h-a_/d m9utes soon] :5 ! ,e>? is at ,b1 ?an :5 x is at ,a4 ,& s1 z ,mr4 ,,rom] fir/ discov]$1 ! motion ( light is !reby prov$ to be progressive1 & n in/antane\s1 z 0 =m]ly believ$4 ,x is easy to compute 9 :at "t ! ,e>? moves f ,a to ,b2 = ! *ord ( #fj degrees ( any ,circle is equal to ! ,semidiamet] ( t ,circle2 & z ! ,e>? goes ?r\gh all ! #cfj degrees ( x's ,orbit 9 a ye>1 x goes ?r\gh #fj ( ^? degrees 9 ab\t #fa days4 ,!re=e1 if on any giv5 day1 suppose ! fir/ ( ,june1 ! ,e>? is at ,a1 on ! fir/ ( ,augu/ x w be at ,b3 ! *ord1 or /raight l9e ,,ab1 be+ equal to ,,ds ! ,radius ( ! ,e>?'s ,orbit1 ! same ) ,,z x's di/ance f ! ,sun4 #bah4 ,z ! ,e>? moves f ,d to ,c1 ?r\gh ! side ,,ab ( x's ,orbit1 x is con/antly meet+ ! light ( ,jupit]'s ,satellites soon]1 :i* occasions an app>5t accel]ation ( _! ,eclipses3 & z x moves ?r\gh ! o!r half ,h ( x's ,orbit1 f ,c to ,d1 x is rec$+ f _! light1 :i* occasions an app>5t ret>dation ( _! ,eclipses1 because _! light is !n long] ere x ov]takes ! ,e>?4 #bai4 ,t ^! accel]ations ( ! imm]sions ( ,jupit]'s ,satellites into 8 %ad[1 z ! ,e>? approa*es t[>ds ,jupit]1 & ! ret>dations ( _! em]sions out ( 8 %ad[1 z ! ,e>? is go+ f him1 are n occasion$ by any inequality aris+ f ! motions ( ! ,satellites 9 exc5tric ,orbits1 is pla91 because x affects !m all alike1 9 :atev] p>ts ( _! ,orbits !y are eclips$4 ,besides1 !y g (t5 r\nd _! ,orbits e ye>1 & _! motions are no way comm5surate to ! ,e>?'s4 ,!re=e1 a ,ph5om5on n to be acc\nt$ = f ! real motions ( ! ,satellites1 b s easily d$ucible f ! ,e>?'s motion1 & s answ]able !reto1 mu/ be all[$ to result f x4 ,?is af=ds "o v good pro( ( ! ,e>?'s annual motion4 #bbj4 ,,tables = conv]t+ mean sol> ,,"t into ,degrees & ,p>ts ( ! t]re/rial ,,equator2 & also = conv]t+ ,degrees & ,p>ts ( ! ,,equator into mean sol> ,"t4 ---------------------------------------- ----- ,,table ,i4 ,= conv]t+ ,"t into ,degrees & ,p>ts ( ! ,equator4 ---------------------------------------- 99,m4 ,d4 ,m4 99,m4 ,d4 ,m4 ,h\rs,degrees ,s4 ,m4 ,s4 ,s4 ,m4 ,s4 ,t4 ,s4 ,t4 ,t4 ,s4 ,t4 ---------------------------------------- #a #ae #a #j #ae #ca #g #de #b #cj #b #j #cj #cb #h #j #c #de #c #j #de #cc #h #ae #d #fj #d #a #j #cd #h #cj #e #ge #e #a #ae #ce #h #de ---------------------------------------- #f #ij #f #a #cj #cf #i #j #g #aje #g #a #de #cg #i #ae #h #abj #h #b #j #ch #i #cj #i #ace #i #b #ae #ci #i #de #aj #aej #aj #b #cj #dj #aj #j ---------------------------------------- #aa #afe #aa #b #de #da #aj #ae #ab #ahj #ab #c #j #db #aj #cj #ac #aie #ac #c #ae #dc #aj #de #ad #baj #ad #c #cj #dd #aa #j #ae #bbe #ae #c #de #de #aa #ae ---------------------------------------- #af #bdj #af #d #j #df #aa #cj #ag #bee #ag #d #ae #dg #aa #de #ah #bgj #ah #d #cj #dh #ab #j #ai #bhe #ai #d #de #di #ab #ae #bj #cjj #bj #e #j #ej #ab #cj ---------------------------------------- #ba #cae #ba #e #ae #ea #ab #de #bb #ccj #bb #e #cj #eb #ac #j #bc #cde #bc #e #de #ec #ac #ae #bd #cfj #bd #f #j #ed #ac #cj #be #cge #be #f #ae #ee #ac #de ---------------------------------------- #bf #cij #bf #f #cj #ef #ad #j #bg #dje #bg #f #de #eg #ad #ae #bh #dbj #bh #g #j #eh #ad #cj #bi #dce #bi #g #ae #ei #ad #de #cj #dej #cj #g #cj #fj #ae #j ---------------------------------------- ---------------------------------------- ----------- ,,table ,,ii4 ,= conv]t+ ,degrees & ,p>ts ( ! ,equator into ,"t4 ---------------------------------------- ----- 99,d4 ,h4 ,m4 99,d4 ,h4 ,m4 ,m4 ,m4 ,s4 ,m4 ,m4 ,s4 ,degrees,h\rs,m9utes ,s4 ,s4 ,t4 ,s4 ,s4 ,t4 ---------------------------------------- ----- #a #j #d #ca #b #d #gj #d #dj #b #j #h #cb #b #h #hj #e #bj #c #j #ab #cc #b #ab #ij #f #j #d #j #af #cd #b #af #ajj #f #dj #e #j #bj #ce #b #bj #aaj #g #bj ---------------------------------------- ----- #f #j #bd #cf #b #bd #abj #h #j #g #j #bh #cg #b #bh #acj #h #dj #h #j #cb #ch #b #cb #adj #i #bj #i #j #cf #ci #b #cf #aej #aj #j #aj #j #dj #dj #b #dj #afj #aj #dj ---------------------------------------- ----- #aa #j #dd #da #b #dd #agj #aa #bj #ab #j #dh #db #b #dh #ahj #ab #j #ac #j #eb #dc #b #eb #aij #ab #dj #ad #j #ef #dd #b #ef #bjj #ac #bj #ae #a #j #de #c #j #baj #ad #j ---------------------------------------- ----- #af #a #d #df #c #d #bbj #ad #dj #ag #a #h #dg #c #h #bcj #ae #bj #ah #a #ab #dh #c #ab #bdj #af #j #ai #a #af #di #c #af #bej #af #dj #bj #a #bj #ej #c #bj #bfj #ag #bj ---------------------------------------- ----- #ba #a #bd #ea #c #bd #bgj #ah #j #bb #a #bh #eb #c #bh #bhj #ah #dj #bc #a #cb #ec #c #cb #bij #ai #bj #bd #a #cf #ed #c #cf #cjj #bj #j #be #a #dj #ee #c #dj #caj #bj #dj ---------------------------------------- ----- #bf #a #dd #ef #c #dd #cbj #ba #bj #bg #a #dh #eg #c #dh #ccj #bb #j #bh #a #eb #eh #c #eb #cdj #bb #dj #bi #a #ef #ei #c #ef #cej #bc #bj #cj #b #j #fj #d #j #cfj #bd #j ---------------------------------------- ----- ,^! are ! ,tables m5tion$ 9 ! #bjh? ,article1 & are s easy t !y sc>ce require any f>!r explanation ?an to in=m ! read]1 t if1 9 ,table ,i4 he reckons ! columns m>k$ ) ,a/]isks to be m9utes ( "t1 ! o!r columns give ! equatoreal p>ts or motion 9 degrees & m9utes2 if he reckons ! ,a/]isk columns to be seconds1 ! o!rs give ! motion 9 m9utes & seconds ( ! ,equator2 if ?irds1 9 seconds & ?irds3 ,& if 9 ,table ,,ii4 he reckons ! ,a/]isk columns to be degrees ( motion1 ! o!rs give ! "t answ]+ !reto 9 h\rs & m9utes2 if m9utes ( motion1 ! "t is m9utes & seconds2 if seconds ( motion1 ! correspond+ "t is giv5 9 seconds & ?irds4 ,an example 9 ea* case w make ! :ole v pla94 ,,example ,i4 ,,example ,,ii4 ,9 #aj h\rs #ae m9utes #bd ,9 :at "t w #aec degrees seconds #bj ?irds1 ,qu4 ,h[ #ea m9utes #e seconds ( ! mu* ( ! ,equator revolves ,equator revolve ?r\gh ! ?r\gh ! ,m]idian8 ,m]idian8 ,deg4 ,m4 ,s4 ,h4 ,m4 ,s4 ,t4 ,h\rs #aj #aej #j #j ,deg4 #aej #aj #j #j #j ,m94 #ae #c #de #j #c #ab #j #j ,sec4 #bd #f #j ,m94 #ea #c #bd #j ,?irds #bj #e ,sec4 #e #bj ------------ ------------ ,answ] #aec #ea #e ,answ] #aj #ae #bd #bj ,,*ap4 ,,xii4 ,( ,sol> & ,sid]eal ,"t4 ,sid5ote3 ,sid]eal days %ort] ?an sol> days1 & :y4 #bba4 ,! fix$ ,/>s appe> to g r\nd ! ,e>? 9 #bc h\rs #ef m9utes #d seconds1 & ! ,sun 9 #bd h\rs3 s t ! ,/>s ga9 ?ree m9utes #ef seconds ^u ! ,sun e day1 :i* am\nts to "o diurnal revolution 9 a ye>2 & !re=e1 9 #cfe days z measur$ by ! returns ( ! ,sun to ! ,m]idian1 !re are #cff days z measur$ by ! ,/>s return+ to x3 ! =m] are call$ ,sol> ,days1 & ! latt] ,sid]eal4 ,sid5ote3 ,,plate ,,iii4 ,! diamet] ( ! ,e>?'s ,orbit is b a physical po9t 9 proportion to ! di/ance ( ! ,/>s2 = :i* reason1 & ! ,e>?'s uni=m motion on x's ,axis1 any giv5 ,m]idian w revolve f any ,/> to ! same ,/> aga9 9 e absolute turn ( ! ,e>? on x's ,axis1 )\t ! lea/ p]ceptible diff]5ce ( "t %ewn by a clock :i* goes exactly true4 ,if ! ,e>? _h only a diurnal motion1 )\t an annual1 any giv5 ,m]idian w\ld revolve f ! ,sun to ! ,sun aga9 9 ! same quantity ( "t z f any ,/> to ! same ,/> aga92 because ! ,sun w\ld nev] *ange 8 place ) respect to ! ,/>s4 ,b1 z ! ,e>? advances almo/ a degree ea/w>d 9 x's ,orbit 9 ! "t t x turns ea/w>d r\nd its ,axis1 :atev] ,/> passes ov] ! ,m]idian on any day ) ! ,sun1 w pass ov] ! same ,m]idian on ! next day :5 ! ,sun is almo/ a degree %ort ( x2 t is1 #c m9utes #ef seconds soon]4 ,if ! ye> conta9$ only #cfj days z ! ,ecliptic does #cfj degrees1 ! ,sun's app>5t place1 s f> z 8 motion is equable1 w\ld *ange a degree e day2 & !n ! sid]eal days w\ld be j f\r m9utes %ort] ?an ! sol>4 ,sid5ote3 ,fig4 ,,ii4 ,let ,,abcdefghiklm be ! ,e>?'s ,orbit1 9 :i* x goes r\nd ! ,sun e ye>1 accord+ to ! ord] ( ! lett]s1 t is1 f we/ to ea/1 & turns r\nd x's ,axis ! same way f ! ,sun to ! ,sun aga9 e #bd h\rs4 ,let ,s be ! ,sun1 & ,r a fix$ ,/> at su* an imm5se di/ance t ! diamet] ( ! ,e>?'s ,orbit be>s no s5sible proportion to t di/ance4 ,let ,nm be any p>ticul> ,m]idian ( ! ,e>?1 & ,n a giv5 po9t or place ^u t ,m]idian4 ,:5 ! ,e>? is at ,a1 ! ,sun ,s hides ! ,/> ,r1 :i* w\ld always be hid if ! ,e>? nev] remov$ f ,a2 & consequ5tly1 z ! ,e>? turns r\nd x's ,axis1 ! po9t ,n w\ld always come r\nd to ! ,sun & ,/> at ! same "t4 ,b :5 ! ,e>? has advanc$1 suppose a twelf? "p ( x's ,orbit f ,a to ,b1 x's motion r\nd x's ,axis w br+ ! po9t ,n a twelf? "p ( a day or two h\rs soon] to ! ,/> ?an to ! ,sun2 = ! ,angle ,n,bn is equal to ! ,angle ,,asb3 & !re=e1 any ,/> :i* comes to ! ,m]idian at noon ) ! ,sun :5 ! ,e>? is at ,a1 w come to ! ,m]idian at #aj 9 ! =5oon :5 ! ,e>? is at ,b4 ,:5 ! ,e>? comes to ,c ! po9t ,n w h ! ,/> on x's ,m]idian at #h 9 ! morn+1 or f\r h\rs soon] ?an x comes r\nd to ! ,sun2 = x mu/ revolve f ,n to n1 be=e x has ! ,sun 9 x's ,m]idian4 ,:5 ! ,e>? comes to ,d1 ! po9t ,n w h ! ,/> on x's ,m]idian at six 9 ! morn+1 b t po9t mu/ revolve six h\rs m f ,n to n1 be=e x has mid-day by ! ,sun3 = n[ ! ,angle ,,asd is a "r ,angle1 & s is ,n,dn2 t is1 ! ,e>? has advanc$ #ij degrees 9 x's ,orbit1 & mu/ turn #ij degrees on its ,axis to c>ry ! po9t ,n f ! ,/> to ! ,sun3 = ! ,/> always comes to ! ,m]idian :5 ,nm is p>allel to ,,rsa2 because ,,ds is b a po9t 9 respect ( ,,rs4 ,:5 ! ,e>? is at ,e1 ! ,/> comes to ! ,m]idian at #d 9 ! morn+2 at ,f1 at two 9 ! morn+2 & at ,g1 ! ,e>? hav+ gone half r\nd x's ,orbit1 ,n po9ts to ! ,/> ,r at midnight1 be+ !n directly opposite to ! ,sun2 & !re=e1 by ! ,e>?'s diurnal motion ! ,/> comes to ! ,m]idian #ab h\rs be=e ! ,sun4 ,:5 ! ,e>? is at ,h1 ! ,/> comes to ! ,m]idian at #aj 9 ! ev5+2 at ,i x comes to ! ,m]idian at #h1 t is1 #af h\rs be=e ! ,sun2 at ,k #ah h\rs be=e him2 at ,l #bj h\rs2 at ,m #bb2 & at ,a equally ) ! ,sun aga94 ,a ,,table1 %ew+ h[ mu* ( ! ,cele/ial ,equator passes ov] ! ,m]idian 9 any "p ( a mean ,,sol> ,,day2 & h[ mu* ! ,,fix$ ,,/>s ga9 ^u ! mean ,,sol> ,,"t e ,day1 = a ,mon?4 ---------------------------------------- ---------- ,"t ,motion4 ,"t ,motion4 ,"t ,motion4 ---------------------------------------- ---------- ,h\rs ,d4 ,m4 ,s4 99,m4 ,d4 ,m4 ,s4 99,m4 ,d4 ,m4 ,s4 ,s4 ,m4 ,s4 ,t4 ,s4 ,m4 ,s4 ,t4 ,t4 ,s4 ,t4 ,t4 ,s4 ,t4 ---------------------------------------- ---------- #a #ae #b #bh #a #j #ae #b #ca #g #df #af #b #cj #d #ef #b #j #cj #e #cb #h #a #ai #c #de #g #bd #c #j #de #g #cc #h #af #ba #d #fj #i #ea #d #a #j #aj #cd #h #ca #bd #e #ge #ab #ai #e #a #ae #ab #ce #h #df #bf ---------------------------------------- ---------- #f #ij #ad #dg #f #a #cj #ae #cf #i #a #bi #g #aje #ag #ae #g #a #de #ag #cg #i #af #ca #h #abj #ai #dc #h #b #j #bj #ch #i #ca #cd #i #ace #bb #aa #i #b #ae #bb #ci #i #df #cf #aj #aej #bd #ch #aj #b #cj #be #dj #aj #a #ci ---------------------------------------- ---------- #aa #afe #bg #f #aa #b #de #bg #da #aj #af #da #ab #ahj #bi #cd #ab #c #j #cj #db #aj #ca #dc #ac #aie #cb #b #ac #c #ae #cb #dc #aj #df #df #ad #baj #cd #cj #ad #c #cj #cd #dd #aa #a #dh #ae #bbe #cf #eh #ae #c #de #cg #de #aa #af #ea ---------------------------------------- ---------- #af #bdj #ci #bf #af #d #j #ci #df #aa #ca #ec #ag #bee #da #ec #ag #d #ae #da #dg #aa #df #ef #ah #bgj #dd #ba #ah #d #cj #dd #dh #ab #a #eh #ai #bhe #df #di #ai #d #de #dg #di #ab #ag #a #bj #cjj #di #ag #bj #e #j #di #ej #ab #cb #c ---------------------------------------- ---------- #ba #cae #ea #de #ba #e #ae #eb #ea #ab #dg #f #bb #ccj #ed #ac #bb #e #cj #ed #eb #ac #b #h #bc #cde #ef #dj #bc #e #de #eg #ec #ac #ag #aa #bd #cfj #ei #h #bd #f #j #ei #ed #ac #cb #ac #be #cgf #a #cf #be #f #af #b #ee #ac #dg #af ---------------------------------------- ---------- #bf #cia #d #d #bf #f #ca #d #ef #ad #b #ah #bg #djf #f #cb #bg #f #df #g #eg #ad #ag #ba #bh #dba #i #j #bh #g #a #i #eh #ad #cb #bc #bi #dcf #aa #bh #bi #g #af #aa #ei #ad #dg #bf #cj #dea #ac #ef #cj #g #ca #ad #fj #ae #b #bh ---------------------------------------- ---------- ,accel]ations ( ! ,fix$ ,/>s4 -------------- ,d4 ,h4 ,m4 ,s4 -------------- #a #j #c #ef #b #j #g #eb #c #j #aa #dh #d #j #ae #dd #e #j #ai #ci -------------- #f #j #bc #ce #g #j #bg #ca #h #j #ca #bg #i #j #ce #bc #aj #j #ci #ai -------------- #aa #j #dc #ae #ab #j #dg #aa #ac #j #ea #g #ad #j #ee #c #ae #j #eh #eh -------------- #af #a #b #ed #ag #a #f #ej #ah #a #aj #df #ai #a #ad #db #bj #a #ah #ch -------------- #ba #a #bb #cd #bb #a #bf #cj #bc #a #cj #bf #bd #a #cd #bb #be #a #ch #ag -------------- #bf #a #db #ac #bg #a #df #i #bh #a #ej #e #bi #a #ed #a #cj #a #eg #eg -------------- ,sid5ote3 ,,plate ,,iii4 ,an absolute ,turn ( ! ,e>? on x's ,axis nev] f9i%es a sol> day4 ,fig4 ,,ii4 #bbb4 ,?us x is pla91 t an absolute turn ( ! ,e>? on x's ,axis 7:i* is always complet$ :5 ! same ,m]idian comes to be p>allel to x's situation at any "t ( ! day be=e7 nev] br+s ! same ,m]idian r\nd f ! ,sun to ! ,sun aga92 b t ! ,e>? requires z mu* m ?an "o turn on x's ,axis to f9i% a natural day1 z x has gone =w>d 9 t "t2 :i*1 at a mean /ate is a #cfe? "p ( a ,circle4 ,h5ce1 9 #cfe days ! ,e>? turns #cff times r\nd x's ,axis2 & !re=e1 z a turn ( ! ,e>? on x's ,axis compleats a sid]eal day1 !re mu/ be "o sid]eal day m 9 a ye> ?an ! numb] ( sol> days1 be ! numb] :at x w1 on ! ,e>?1 or any o!r ,planet4 ,"o turn be+ lo/ ) respect to ! numb] ( sol> days 9 a ye>1 by ! ,planet's go+ r\nd ! ,sun2 j z x w\ld be lo/ to a travell]1 :o1 9 go+ r\nd ! ,e>?1 w\ld lose "o day by foll[+ ! app>5t diurnal motion ( ! ,sun3 & consequ5tly1 w\ld reckon "o day less at 8 return 7let him take :at "t he w\ld to g r\nd ! ,e>?7 ?an ^? :o rema9$ all ! :ile at ! place f :i* he set out4 ,s1 if !re 7 two ,e>?s revolv+ equably on _! ,axes1 & if "o rema9$ at ,a until ! o!r travell$ r\nd ! ,sun f ,a to ,a aga91 t ,e>? :i* kept x's place at ,a w\ld h x's sol> & sid]eal days always ( ! same l5g?2 & s1 w\ld h "o sol> day m ?an ! o!r at x's return4 ,h5ce1 if ! ,e>? turn$ b once r\nd x's ,axis 9 a ye>1 & if t turn 0 made ! same way z ! ,e>? goes r\nd ! ,sun1 !re w\ld be cont9ual day on "o side ( ! ,e>?1 & cont9ual night on ! o!r4 ,sid5ote3 ,to "k by ! ,/>s :e!r a ,clock goes true or n4 #bbc4 ,! fir/ "p ( ! prec$+ ,table %ews h[ mu* ( ! cele/ial ,equator passes ov] ! ,m]idian 9 any giv5 "p ( a mean sol> day1 & is to be und]/ood ! same way z ! ,table 9 ! #bbj? article4 ,! latt] "p1 intitl$1 ,accel]ations ( ! fix$ ,/>s1 af=ds u an easy me?od ( kn[+ :e!r or no our clocks & wat*es g true3 ,= if1 ?r\gh a small hole 9 a w9d[-%utt]1 or 9 a ?9 plate ( metal fix$ to a w9d[1 we obs]ve at :at "t any ,/> disappe>s beh9d a *imney1 or corn] ( a h\se1 at a little di/ance2 & if ! same ,/> disappe>s ! next night #c m9utes #ef seconds soon] by ! clock or wat*2 & on ! second night1 #g m9utes #eb seconds soon]2 ! ?ird night #aa m9utes #dh seconds soon]2 & s on1 e night1 z 9 ! ,table1 :i* %ews ?is diff]5ce = #cj natural days1 x is an infallible ,sign t ! ma*9e goes true2 o!rwise x does n g true2 & mu/ be regulat$ accord+ly3 & z ! disappe>+ ( a ,/> is in/antane\s1 we may dep5d on ?is in=mation to half a second4 ,illu/ration3 ,pl4 ,,vi4 ,j4 ,f]guson inv4 et del94 ,j4 ,mynde ,sc4 ,,*ap4 ,,xiii4 ,( ! ,equation ( ,"t4 ,sid5ote3 ,! ,sun & ,clocks equal only on f\r days ( ! ye>4 #bbd4 ,! ,e>?'s motion on x's ,axis be+ p]fectly uni=m1 & equal at all times ( ! ye>1 ! sid]eal days are always precisely ( ! same l5g?2 & s w\ld ! sol> or natural days be1 if ! ,e>?'s orbit 7 a p]fect ,circle1 & x's ,axis p]p5dicul> to x's orbit4 ,b ! ,e>?'s diurnal motion on an incl9$ ,axis1 & x's annual motion 9 an elliptic orbit1 cause ! ,sun's app>5t motion 9 ! ,heav5s to be unequal3 = sometimes he revolves f ! ,m]idian to ! ,m]idian aga9 9 some:at less ?an #bd h\rs1 %ewn by a well regulat$ clock2 & at o!r times 9 some:at m3 s t ! "t %ewn by an equal go+ clock & a true ,sun-dial is nev] ! same b on ! #ae? ( ,april1 ! #af? ( ,june1 ! #ca/ ( ,augu/1 & ! #bd? ( ,decemb]4 ,! clock1 if x goes equally & true all ! ye> r\nd1 w be be=e ! ,sun f ! #bd? ( ,decemb] till ! #ae? ( ,april2 f t "t till ! #af? ( ,june ! ,sun w be be=e ! clock2 f ! #af? ( ,june till ! #ca/ ( ,augu/ ! clock w be aga9 be=e ! ,sun2 & f !nce to ! #bd? ( ,decemb] ! ,sun w be fa/] ?an ! clock4 ,sid5ote3 ,use ( ! ,equation ,table4 #bbe4 ,! ,tables ( ! ,equation ( natural days1 at ! end ( ! next ,*apt]1 %ew ! "t t ought to be po9t$ out by a well regulat$ clock or wat* e day ( ! ye> at ! precise mom5t ( sol> noon2 t is1 :5 ! ,sun's c5tre is on ! ,m]idian1 or :5 a true ,sun-dial %ews x to be precisely ,twelve4 ,?us1 on ! #e? ( ,janu>y 9 ,leap-ye>1 :5 ! ,sun is on ! ,m]idian1 x ought to be #e m9utes #ea seconds pa/ twelve by ! clock2 & on ! #ae? ( ,may1 :5 ! ,sun is on ! ,m]idian1 ! "t by ! clock %\ld be b #ee m9utes #eg seconds pa/ elev52 9 ! =m] case1 ! clock is #e m9utes #ea seconds be=eh& ) ! ,sun2 & 9 ! latt] case1 ! ,sun is #d m9utes #c seconds fa/] ?an ! clock4 ,! column at ! "r h& ( ea* mon? %ews ! daily diff]5ce ( ?is equation1 z x increases or decreases4 ,b )\t a ,m]idian ,l9e1 or a ,transit-,in/rum5t fix$ 9 ! plane ( ! ,m]idian1 we _c set a ,sun-dial true4 ,sid5ote3 ,h[ to draw a ,m]idian ,l9e4 #bbf4 ,! easie/ & mo/ exp$iti\s way ( draw+ a ,m]idian ,l9e is ?is3 ,make f\r or five conc5tric ,circles1 ab\t a qu>t] ( an in* f "o ano!r1 on a flat bo>d ab\t a foot 9 bread?2 & let ! outmo/ ,circle be b little less ?an ! bo>d w conta94 ,fix a p9 p]p5dicul>ly 9 ! c5t]1 & ( su* a l5g? t x's :ole %ad[ may fall )9 ! inn]mo/ ,circle = at lea/ f\r h\rs 9 ! middle ( ! day4 ,! p9 ought to be ab\t an eigh? "p ( an in* ?ick1 ) a r\nd blunt po9t4 ,! bo>d be+ set exactly level 9 a place :]e ! ,sun %9es1 suppose f eight 9 ! morn+ till f\r 9 ! aft]noon1 ab\t :i* h\rs ! end ( ! %ad[ %\ld fall )\t all ! ,circles2 wat* ! times 9 ! =5oon1 :5 ! extremity ( ! %ort5+ %ad[ j t\*es ! sev]al ,circles1 & !re make m>ks4 ,!n1 9 ! aft]noon ( ! same day1 wat* ! l5g!n+ %ad[1 & :]e x's end t\*es ! sev]al ,circles 9 go+ ov] !m1 make m>ks also4 ,la/ly1 ) a pair ( compasses1 f9d exactly ! middle po9t betwe5 ! two m>ks on any ,circle1 & draw a /raight l9e f ! c5t] to t po9t2 :i* ,l9e w be cov]$ at noon by ! %ad[ ( a small upright wire1 :i* %\ld be put 9 ! place ( ! p94 ,! reason = draw+ sev]al ,circles is1 t 9 case "o "p ( ! day %\ld prove cle>1 & ! o!r "p some:at cl\dy1 if y miss ! "t :5 ! po9t ( ! %ad[ %\ld t\* "o ,circle1 y may p]haps cat* x 9 t\*+ ano!r4 ,! be/ "t = draw+ a ,m]idian ,l9e 9 ?is mann] is ab\t ! middle ( summ]2 because ! ,sun *anges 8 ,decl9ation sl[e/ & 8 ,altitude fa/e/ 9 ! longe/ days4 ,if ! casem5t ( a w9d[ on :i* ! ,sun %9es at noon be q upright1 y may draw a l9e along ! edge ( x's %ad[ on ! floor1 :5 ! %ad[ ( ! p9 is exactly on ! ,m]idian ,l9e ( ! bo>d3 & z ! motion ( ! %ad[ ( ! casem5t w be mu* m s5sible on ! ,floor1 ?an t ( ! %ad[ ( ! p9 on ! bo>d1 y may "k to a few seconds :5 x t\*es ! ,m]idian ,l9e on ! floor1 & s regulate y\r clock = ! day ( obs]vation by t l9e & ! ,equation ,tables above-m5tion$ #bbe4 ,sid5ote3 ,equation ( natural days expla9$4 #bbg4 ,z ! ,equation ( "t1 or diff]5ce betwe5 ! "t %ewn by a well regulat$ ,clock & a true ,sun-dial1 dep5ds ^u two causes1 namely1 ! obliquity ( ! ,ecliptic1 & ! unequal motion ( ! ,e>? 9 x1 we %all fir/ expla9 ! effects ( ^! causes sep>ately consid]$1 & !n ! unit$ effects result+ f _! comb9ation4 ,sid5ote3 ,,plate ,,vi4 ,! fir/ "p ( ! ,equation ( "t4 #bbh4 ,! ,e>?'s motion on x's ,axis be+ p]fectly equable1 or always at ! same rate1 & ! #eeplane ( ! ,equator be+ p]p5dicul> to x's ,axis1 'tis evid5t t 9 equal times equal portions ( ! ,equator pass ov] ! ,m]idian2 & s w\ld equal portions ( ! ,ecliptic if x 7 p>allel to or co9cid5t ) ! ,equator4 ,b1 z ! ,ecliptic is oblique to ! ,equator1 ! equable motion ( ! ,e>? c>ries unequal portions ( ! ,ecliptic ov] ! ,m]idian 9 equal times1 ! diff]5ce be+ proportionate to ! obliquity2 & z "s p>ts ( ! ,ecliptic are mu* m oblique ?an o!rs1 ^? diff]5ces are unequal among !mselves4 ,!re=e1 if two ,suns %\ld />t ei!r f ! beg9n+ ( ,aries or ,libra1 & cont9ue to move ?r\gh equal arcs 9 equal times1 "o 9 ! ,equator1 & ! o!r 9 ! ,ecliptic1 ! equatoreal ,sun w\ld always return to ! ,m]idian 9 #bd h\rs "t1 z measur$ by a well regulat$ clock2 b ! ,sun 9 ! ,ecliptic w\ld return to ! ,m]idian sometimes soon]1 & sometimes lat] ?an ! equatoreal ,sun2 & only at ! same mom5ts ) him on f\r days ( ! ye>2 namely1 ! #bj? ( ,m>*1 :5 ! ,sun ent]s ,aries2 ! #ba/ ( ,june1 :5 he ent]s ,canc]2 ! #bc;d ( ,septemb]1 :5 he ent]s ,libra2 & ! #ba/ ( ,decemb]1 :5 he ent]s ,capricorn4 ,b1 z !re is only "o ,sun1 & 8 app>5t motion is always 9 ! ,ecliptic1 let u h5ce=? call him ! real ,sun1 & ! o!r :i* is suppos$ to move 9 ! ,equator ! fictiti\s2 to :i* la/1 ! motion ( a well regulat$ clock always answ]s4 ,sid5ote3 ,fig4 ,,iii4 ,let ,zz be ! ,e>?1 ,z,f,rz x's ,axis1 abcde c4 ! ,equator1 ,,abcde c4 ! nor!rn half ( ! ,ecliptic f to on ! side ( ! ,globe next ! eye1 & ,,mnop c4 ! s\!rn half on ! opposite side f to 4 ,let ! po9ts at ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 c4 q r\nd f to aga9 b\nd equal portions ( ! ,ecliptic1 gone ?r\gh 9 equal times by ! real ,sun2 & ^? at a1 b1 c1 d1 e1 f1 c4 equal portions ( ! ,equator describ$ 9 equal times by ! fictiti\s ,sun2 & let ,zz be ! ,m]idian4 ,z ! real ,sun moves obliquely 9 ! ,ecliptic1 & ! fictiti\s ,sun directly 9 ! ,equator1 ) respect to ! ,m]idian1 a degree1 or any numb] ( degrees1 betwe5 & ,f on ! ,ecliptic1 mu/ be ne>] ! ,m]idian ,zz1 ?an a degree1 or any correspond+ numb] ( degrees on ! ,equator f to f2 & ! m s1 z !y are ! m oblique3 & !re=e ! true ,sun comes soon] to ! ,m]idian :il/ he is 9 ! quadrant ,f1 ?an ! fictiti\s ,sun does 9 ! quadrant f2 = :i* reason1 ! sol> noon prec$es noon by ! ,clock1 until ! real ,sun comes to ,f1 & ! fictiti\s to f2 :i* two po9ts1 be+ equidi/ant f ! ,m]idian1 bo? ,suns w come to x precisely at noon by ! ,clock4 ,:il/ ! real ,sun describes ! second quadrant ( ! ,ecliptic ,,fghikl f to 2 he comes lat] to ! ,m]idian e day1 ?an ! fictiti\s ,sun mov+ ?r\gh ! second quadrant ( ! ,equator f f to 2 = ! po9ts at ,g1 ,h1 ,i1 ,k1 & ,l be+ f>!r f ! ,m]idian ?an _! correspond+ po9ts at g1 h1 i1 k1 & l1 !y mu/ be lat] ( com+ to x3 & z bo? ,suns come at ! same mom5t to ! po9t 1 !y come to ! ,m]idian at ! mom5t ( noon by ! ,clock4 ,9 dep>t+ f ,libra1 ?r\gh ! ?ird quadrant1 ! real ,sun go+ ?r\gh ,,mnopq t[>ds at ,r1 & ! fictiti\s ,sun ?r\gh mnopq t[>ds r1 ! =m] comes to ! ,m]idian e day soon] ?an ! latt]1 until ! real ,sun comes to 1 & ! fictiti\s to r1 & !n !y bo? come to ! ,m]idian at ! same "t4 ,la/ly1 z ! real ,sun moves equably ?r\gh ,,/uvw1 f t[>ds 2 & ! fictiti\s ,sun ?r\gh /uvw1 f r t[>ds 1 ! =m] comes lat] e day to ! ,m]idian ?an ! latt]1 until !y bo? arrive at ! po9t 1 & !n !y make noon at ! same "t ) ! clock4 ,sid5ote3 ,a ,table ( ! ,equation ( ,"t dep5d+ on ! ,sun's place 9 ! ,ecliptic4 ,,plate ,,vi4 #bbi4 ,! annex$ ,table %ews h[ mu* ! ,sun is fa/] or sl[] ?an ! clock ought to be1 s f> z ! diff]5ce dep5ds ^u ! obliquity ( ! ,ecliptic2 ( :i* ! ,signs ( ! fir/ & ?ird quadrants are at ! head ( ! ,table1 & _! ,degrees at ! left h&2 & 9 ^! ! ,sun is fa/] ?an ! ,clock3 ! ,signs ( ! second & f\r? quadrants are at ! foot ( ! ,table1 & _! degrees at ! "r h&2 9 all :i* ! ,sun is sl[] ?an ! ,clock3 s t ent]+ ! ,table ) ! giv5 ,sign ( ! ,sun's place at ! head ( ! ,table1 & ! ,degree ( 8 place 9 t ,sign at ! left h&2 or ) ! giv5 ,sign at ! foot ( ! ,table1 & ,degree at ! "r h&2 9 ! ,angle ( meet+ is ! numb] ( m9utes & seconds t ! ,sun is fa/] or sl[] ?an ! clock3 or 9 o!r words1 ! quantity ( "t 9 :i* ! real ,sun1 :5 9 t "p ( ! ,ecliptic1 comes soon] or lat] to ! ,m]idian ?an ! fictiti\s ,sun 9 ! ,equator4 ,?us1 :5 ! ,sun's place is ,taurus #ab degrees1 he is #i m9utes #di seconds fa/] ?an ! clock2 & :5 8 place is ,canc] #ah degrees1 he is #f m9utes #b seconds sl[]4 ---------------------------------------- ----- ,sun fa/] ?an ! ,clock 9 ---------------------------------------- - #a/ ,q4 #c;d ,q4 -------------------------------- ,degrees ,deg4 ---------------------------------------- - #j #j #j #h #bd #h #df #cj #a #j #bj #h #ce #h #cf #bi #b #j #dj #h #de #h #be #bh #c #a #j #h #ed #h #ad #bg #d #a #ai #i #c #h #a #bf #e #a #ci #i #aa #g #di #be #f #a #ei #i #ah #g #ce #bd #g #b #ah #i #bd #g #ba #bc #h #b #cg #i #ca #g #f #bb #i #b #ef #i #cf #f #ea #ba #aj #c #af #i #da #f #ce #bj #aa #c #cd #i #de #f #ai #ai #ab #c #ec #i #di #f #b #ah #ac #d #aa #i #ea #e #de #ag #ad #d #bi #i #ec #e #bg #af #ae #d #dg #i #ed #e #i #ae #af #e #d #i #ee #d #ej #ad #ag #e #ba #i #ee #d #ca #ac #ah #e #ch #i #ed #d #ab #ab #ai #e #ed #i #eb #c #eb #aa #bj #f #aj #i #ej #c #cb #aj #ba #f #bf #i #dg #c #ab #i #bb #f #da #i #dc #b #ea #h #bc #f #ee #i #ch #b #cj #g #bd #g #i #i #cc #b #i #f #be #g #bc #i #bg #a #dh #e #bf #g #cf #i #bj #a #bg #d #bg #g #di #i #ac #a #e #c #bh #h #a #i #e #j #dc #b #bi #h #ac #h #ef #j #bb #a #cj #h #bd #h #df #j #j #j ---------------------------------------- - #b;d ,q4 ,deg4 #d? ,q4 ---------------------------------------- - ,sun sl[] ?an ! ,clock 9 ---------------------------------------- ----- ,sid5ote3 ,fig4 ,,iii4 #bcj4 ,?is "p ( ! ,equation ( "t may p]haps be some:at difficult to und]/& by a ,figure1 because bo? halves ( ! ,ecliptic seem to be on ! same side ( ! ,globe2 b x may be made v easy to any p]son :o has a real ,globe be=e him1 by putt+ small pat*es on e t5? or fifte5? degree bo? ( ! ,equator & ,ecliptic2 & !n1 turn+ ! ball sl[ly r\nd we/w>d1 he w see all ! pat*es f ,aries to ,canc] come to ! braz5 ,m]idian soon] ?an ! correspond+ pat*es on ! ,equator2 all ^? f ,canc] to ,libra w come lat] to ! ,m]idian ?an _! correspond+ pat*es on ! ,equator2 ^? f ,libra to ,capricorn soon]1 & ^? f ,capricorn to ,aries lat]3 & ! pat*es at ! beg9n+s ( ,aries1 ,canc]1 ,libra1 & ,capricorn1 be+ also on ! ,equator1 %ew t ! two ,suns meet !re1 & come to ! ,m]idian toge!r4 ,sid5ote3 ,a ma*9e = %ew+ ! sid]eal1 ! equal1 & ! sol> ,"t4 ,,plate ,,vi4 #bca4 ,let u suppose t !re are two little balls mov+ equably r\nd a cele/ial ,globe by clock-"w1 "o always keep+ 9 ! ,ecliptic1 & gilt ) gold1 to repres5t ! real ,sun2 & ! o!r keep+ 9 ! ,equator1 & silv]$1 to repres5t ! fictiti\s ,sun3 & t :il/ ^! balls move once1 r\nd ! ,globe accord+ to ! ord] ( ,signs1 ! ,clock turns ! ,globe #cff times r\nd x's ,axis we/w>d4 ,! ,/>s w make #cff diurnal revolutions f ! bras5 ,m]idian to x aga92 & ! two balls repres5t+ ! real & fictiti\s ,sun always go+ f>!r ea/w>d f any giv5 ,/>1 w come lat] ?an x to ! ,m]idian e foll[+ day2 & ea* ball w make #cfe revolutions to ! ,m]idian2 com+ equally to x at ! beg9n+s ( ,aries1 ,canc]1 ,libra1 & ,capricorn3 b 9 e o!r po9t ( ! ,ecliptic1 ! gilt ball w come ei!r soon] or lat] to ! ,m]idian ?an ! silv]$ ball1 l ! pat*es above-m5tion$4 ,?is w\ld be a pretty-en\gh way ( %ew+ ! reason :y any giv5 ,/>1 :i*1 on a c]ta9 day ( ! ye>1 comes to ! ,m]idian ) ! ,sun1 passes ov] x s mu* soon] e foll[+ day1 z on t day twelvemon? to come to ! ,m]idian ) ! ,sun aga92 & also to %ew ! reason :y ! real ,sun comes to ! ,m]idian sometimes soon]1 sometimes lat]1 ?an x is noon by ! clock2 &1 on f\r days ( ! ye>1 at ! same "t2 :il/ ! fictiti\s ,sun always comes to ! ,m]idian :5 x is twelve at noon by ! clock4 ,?is w\ld be no difficult task = an arti/ to p]=m2 = ! gold ball might be c>ri$ r\nd ! ,ecliptic by a wire f x's nor? ,pole1 & ! silv] ball r\nd ! ,equator by a wire f x's s\? ,pole1 ) a few :eels to ea*2 :i* might be easily add$ to my improvem5t ( ! cele/ial ,globe1 describ$ 9 ,no #dhc ( ! ,philosophical ,transactions2 & ( :i* ,i %all give a description 9 ! latt] "p ( ?is ,book1 f ! #c;d ,figure ( ! #c;d plate4 ,sid5ote3 ,fig4 ,,iii4 #bcb4 ',tis pla9 t if ! ,ecliptic 7 m obliquely posit$ to ! ,equator1 z ! dott$ ,circle x1 ! equal divisions f to x w\ld come /ill soon] to ! ,m]idian ,z#j ?an ^? m>k$ ,a1 ,b1 ,c1 ,d1 & ,e d3 = two divisions conta9+ #cj degrees1 f to ! second dott1 a little %ort ( ! figure #a1 come soon] to ! ,m]idian ?an "o division conta9+ only #ae degrees f to ,a does1 z ! ,ecliptic n[ /&s2 & ^? ( ! second quadrant f x to w\ld be s mu* lat]4 ,! ?ird quadrant w\ld be z ! fir/1 & ! f\r? z ! second4 ,& x is likewise pla91 t :]e ! ,ecliptic is mo/ oblique1 namely ab\t ,aries & ,libra1 ! diff]5ce w\ld be greate/3 & lea/ ab\t ,canc] & ,capricorn1 :]e ! obliquity is lea/4 ,sid5ote3 ,! second "p ( ! ,equation ( ,"t4 ,,plate ,,vi4 #bcd4 ,hav+ expla9$ "o cause ( ! diff]5ce ( "t %ewn by a well-regulat$ ,clock & a true ,sun-dial2 & consid]$ ! ,sun1 n ! ,e>?1 z mov+ 9 ! ,ecliptic2 we n[ proce$ to expla9 ! o!r cause ( ?is diff]5ce1 namely1 ! inequality ( ! ,sun's app>5t motion #bje1 :i* is sl[e/ 9 summ]1 :5 ! ,sun is f>!/ f ! ,e>?1 & swifte/ 9 w9t] :5 he is ne>e/ to x4 ,b ! ,e>?'s motion on x's ,axis is equable all ! ye> r\nd1 & is p]=m$ f we/ to ea/2 :i* is ! way t ! ,sun appe>s to *ange 8 place 9 ! ,ecliptic4 #bce4 ,if ! ,sun's motion 7 equable 9 ! ,ecliptic1 ! :ole diff]5ce betwe5 ! equal "t z %ewn by a ,clock1 & ! unequal "t z %ewn by ! ,sun1 w\ld arise f ! obliquity ( ! ,ecliptic4 ,b ! ,sun's motion sometimes exce$s a degree 9 #bd h\rs1 ?\gh g5]ally x is less3 & :5 8 motion is sl[e/ any p>ticul> ,m]idian w revolve soon] to him ?an :5 8 motion is quicke/2 = x w ov]take him 9 less "t :5 he advances a less space ?an :5 he moves ?r\gh a l>g]4 #bcf4 ,n[1 if !re 7 two ,suns mov+ 9 ! plane ( ! ,ecliptic1 s z to g r\nd x 9 a ye>2 ! "o describ+ an equal arc e #bd h\rs1 & ! o!r describ+ sometimes a less arc 9 #bd h\rs1 & at o!r times a l>g]2 ga9+ at "o "t ( ! ye> :at x lo/ at ! opposite2 'tis evid5t t ei!r ( ^! ,suns w\ld come soon] or lat] to ! ,m]idian ?an ! o!r z x happ5$ to be beh9d or be=e ! o!r3 & :5 !y 7 bo? 9 conjunction !y w\ld come to ! ,m]idian at ! same mom5t4 ,sid5ote3 ,fig4 ,,iv4 #bcg4 ,z ! real ,sun moves unequably 9 ! ,ecliptic1 let u suppose a fictiti\s ,sun to move equably 9 x4 ,let ,,abcd be ! ,ecliptic or ,orbit 9 :i* ! real ,sun moves1 & ! dott$ ,circle abcd ! imag9>y ,orbit ( ! fictiti\s ,sun2 ea* go+ r\nd 9 a ye> accord+ to ! ord] ( lett]s1 or f we/ to ea/4 ,let ,,hikl be ! ,e>? turn+ r\nd x's ,axis ! same way e #bd h\rs2 & suppose bo? ,suns to />t f ,a & a1 9 a "r l9e ) ! plane ( ! ,m]idian ,,eh1 at ! same mom5t3 ! real ,sun at ,a1 be+ !n at 8 greate/ di/ance f ! ,e>?1 at :i* "t 8 motion is sl[e/2 & ! fictiti\s ,sun at a1 ^: motion is always equable because 8 di/ance f ! ,e>? is suppos$ to be always ! same4 ,9 ! "t t ! ,m]idian revolves f ,h to ,h aga91 accord+ to ! ord] ( ! lett]s ,,hikl1 ! real ,sun has mov$ f ,a to ,f2 & ! fictiti\s ) a quick] motion f a to f1 ?r\gh a l>g] arc3 !re=e1 ! ,m]idian ,,eh w revolve soon] f ,h to h "u ! real ,sun at ,f1 ?an f ,h to k "u ! fictiti\s ,sun at f2 & consequ5tly x w be noon by ! ,sun-dial soon] ?an by ! ,clock4 ,sid5ote3 ,,plate ,,vi4 ,z ! real ,sun moves f ,a t[>ds ,c1 ! swiftness ( 8 motion increases all ! way to ,c1 :]e x is at ! quicke/4 ,b not)/&+ ?is1 ! fictiti\s ,sun ga9s s mu* ^u ! real1 soon aft] 8 dep>t+ f ,a1 t ! increas+ velocity ( ! real ,sun does n br+ him up ) ! equally mov+ fictiti\s ,sun till ! =m] comes to ,c1 & ! latt] to c1 :5 ea* has gone half r\nd x's respective orbit2 & !n be+ 9 conjunction1 ! ,m]idian ,,eh revolv+ to ,,ek comes to bo? ,suns at ! same "t1 & !re=e x is noon by !m bo? at ! same mom5t4 ,b ! increas$ velocity ( ! real ,sun1 n[ be+ at ! quicke/1 c>ries him be=e ! fictiti\s2 & !re=e1 ! same ,m]idian w come to ! fictiti\s ,sun soon] ?an to ! real3 = :il/ ! fictiti\s ,sun moves f c to g1 ! real ,sun moves ?r\gh a great] arc f ,c to ,g3 consequ5tly ! po9t ,k has x's fictiti\s noon :5 x comes to k1 b n x's real noon till x comes to l4 ,& al?\gh ! velocity ( ! real ,sun dim9i%es all ! way f ,c to ,a1 & ! fictiti\s ,sun by an equable motion is /ill com+ ne>] to ! real ,sun1 yet !y are n 9 conjunction till ! "o comes to ,a & ! o!r to a2 & !n x is noon by !m bo? at ! same mom5t4 ,& ?us x appe>s1 t ! real noon by ! ,sun is always lat] ?an ! fictiti\s noon by ! clock :il/ ! ,sun goes f ,c to ,a1 soon] :il/ he goes f ,a to ,c1 & at ^! two po9ts ! ,sun & ,clock be+ equal1 x is noon by !m bo? at ! same mom5t4 ,sid5ote3 ,apogee1 ,p]igee1 & ,apsides1 :at4 ,fig4 ,,iv4 #bch4 ,! po9t ,a is call$ ! ,sun's ,apogee1 because :5 he is !re he is at 8 greate/ di/ance f ! ,e>?2 ! po9t ,c 8 ,p]igee1 because :5 9 x he is at 8 lea/ di/ance f ! ,e>?3 & a "r l9e1 z ,,aec1 drawn ?r\gh ! ,e>?'s c5t]1 f "o ( ^! po9ts to ! o!r1 is call$ ! l9e ( ! ,apsides4 ,sid5ote3 ,mean ,anomaly1 :at4 #bci4 ,! di/ance t ! ,sun has gone 9 any "t f 8 ,apogee 7n ! di/ance he has to g to x ?\gh ev] s little7 is call$ 8 mean ,anomaly1 & is reckon$ 9 ,signs & ,degrees1 all[+ #cj ,degrees to a ,sign4 ,?us1 :5 ! ,sun has gone suppose #agd degrees f 8 ,apogee at ,a1 he is said to be #e ,signs #bd ,degrees f x1 :i* is 8 mean ,anomaly3 & :5 he is gone suppose #cee degrees f 8 ,apogee1 he is said to be #aa ,signs #be ,degrees f x1 al?\gh he be b #e ,degrees %ort ( ,a 9 com+ r\nd to x aga94 #bdj4 ,f :at 0 said above x appe>s1 t :5 ! ,sun's ,anomaly is less ?an #f ,signs1 t is1 :5 he is any :]e betwe5 ,a & ,c1 9 ! half ,,abc ( 8 orbit1 ! true noon prec$es ! fictiti\s2 b :5 8 ,anomaly is m ?an #f ,signs1 t is1 :5 he is any :]e betwe5 ,c & ,a1 9 ! half ,,cda ( 8 ,orbit1 ! fictiti\s noon prec$es ! true4 ,:5 8 ,anomaly is #j ,signs #j ,degrees1 t is1 :5 he is 9 8 ,apogee at ,a2 or #f ,signs #j ,degrees1 :i* is :5 he is 9 8 ,p]igee at ,c2 he comes to ! ,m]idian at ! mom5t t ! fictiti\s ,sun does1 & !n x is noon by !m bo? at ! same in/ant4 ---------------------------------------- ------------------ ,sun fa/] ?an ! ,clock if 8 ,anomaly be ---------------------------------------- ----------- #j ,signs #a #b #c #d #e ,d4 ---------------------------------------- --- ---------------------------------------- ----------- #j #j #j #c #dh #f #ci #g #de #f #dg #c #eg #cj #a #j #h #c #ee #f #dc #g #de #f #dc #c #ej #bi #b #j #af #c #b #f #dg #g #de #f #ci #c #dc #bh #c #j #bd #d #i #f #ea #g #de #f #ce #c #ce #bg #d #j #cb #d #af #f #ed #g #de #f #cj #c #bh #bf #e #j #dj #d #bb #f #eh #g #dd #f #bf #c #bj #be #f #j #dh #d #bi #g #a #g #dd #f #ba #c #ac #bd #g #j #ef #d #ce #g #e #g #dc #f #af #c #e #bc #h #a #c #d #db #g #h #g #db #f #aa #b #eh #bb #i #a #aa #d #dh #g #aa #g #da #f #f #b #ej #ba #aj #a #ai #d #ed #g #ad #g #dj #f #a #b #db #bj #aa #a #bg #e #j #g #ag #g #ch #e #ef #b #ce #ai #ab #a #ce #e #f #g #bj #g #cg #e #ea #b #bg #ah #ac #a #dc #e #ab #g #bb #g #ce #e #de #b #ai #ag #ad #a #ej #e #ah #g #be #g #cd #e #dj #b #aa #af #ae #a #eh #e #bd #g #bg #g #cb #e #cd #b #c #ae #af #b #f #e #cj #g #bi #g #cj #e #bh #a #ee #ad #ag #b #ac #e #ce #g #ca #g #bh #e #bb #a #dg #ac #ah #b #ba #e #da #g #cc #g #be #e #af #a #ci #ab #ai #b #bh #e #df #g #ce #g #bc #e #aj #a #ca #aa #bj #b #cf #e #eb #g #cf #g #bj #e #d #a #bb #aj #ba #b #dc #e #eg #g #ch #g #ah #d #eh #a #ad #i #bb #b #ea #f #b #g #ci #g #ae #d #ea #a #f #h #bc #b #eh #f #g #g #da #g #ab #d #de #j #eh #g #bd #c #f #f #ab #g #db #g #i #d #ch #j #ej #f #be #c #ac #f #af #g #dc #g #e #d #ca #j #da #e #bf #c #bj #f #ba #g #dc #g #b #d #be #j #cc #d #bg #c #bg #f #bf #g #dd #f #eh #d #ah #j #be #c #bh #c #cd #f #cj #g #dd #f #ee #d #aa #j #ag #b #bi #c #da #f #cd #g #de #f #ea #d #d #j #h #a #cj #c #dh #f #ci #g #de #f #dg #c #eg #j #j #j ---------------------------------------- ----------- #aa ,signs #aj #i #h #g #f ,d4 ---------------------------------------- ----------- ,sun sl[] ?an ! ,clock if 8 ,anomaly be ---------------------------------------- ------------------ ,sid5ote3 ,a ,table ( ! ,equation ( ,"t1 dep5d+ on ! ,sun's ,anomaly4 #bda4 ,! annex$ ,table %ews ! ,v>iation1 or ,equation ( "t dep5d+ on ! ,sun's ,anomaly1 & aris+ f 8 unequal motion 9 ! ,ecliptic2 z ! =m] ,table #bbi %ews ! ,v>iation dep5d+ on ! ,sun's place1 & result+ f ! obliquity ( ! ,ecliptic3 ?is is to be und]/ood ! same way z ! o!r1 namely1 t :5 ! ,signs are at ! head ( ! ,table1 ! ,degrees are at ! left h&2 b :5 ! ,signs are at ! foot ( ! ,table ! respective ,degrees are at ! "r h&2 & 9 bo? cases ! ,equation is 9 ! ,angle ( meet+4 ,:5 bo? ! above-m5tion$ ,equations are ei!r fa/] or sl[]1 _! sum is ! absolute ,equation ( ,"t2 b :5 ! "o is fa/]1 & ! o!r sl[]1 x is _! diff]5ce4 ,?us1 suppose ! ,equation dep5d+ on ! ,sun's place1 be #f m9utes #da seconds too sl[1 & ! ,equation dep5d+ on ! ,sun's ,anomaly1 be #d m9utes #bj seconds too sl[1 _! ,sun is #aa m9utes #a second too sl[4 ,b if ! "o _h be5 #f m9utes #da seconds too fa/1 & ! o!r #d m9utes #bj seconds too sl[1 _! diff]5ce _h be5 #b m9utes #ba seconds too fa/1 because ! great] quantity is too fa/4 #bdb4 ,! obliquity ( ! ,ecliptic to ! ,equator1 :i* is ! fir/ m5tion$ cause ( ! ,equation ( ,"t1 w\ld make ! ,sun & ,clocks agree on f\r days ( ! ye>2 :i* are1 :5 ! ,sun ent]s ,aries1 ,canc]1 ,libra1 & ,capricorn3 b ! o!r cause1 n[ expla9$1 w\ld make ! ,sun & ,clocks equal only twice 9 a ye>2 t is1 :5 ! ,sun is 9 8 ,apogee & ,p]igee4 ,consequ5tly1 :5 ^! two po9ts fall 9 ! beg9n+s ( ,canc] & ,capricorn1 or ( ,aries & ,libra1 !y concur 9 mak+ ! ,sun & ,clocks equal 9 ^! po9ts4 ,b ! ,apogee at pres5t is 9 ! #i? degree ( ,canc]1 & ! ,p]igee 9 ! #i? degree ( ,capricorn2 & !re=e ! ,sun & ,clocks _c be equal ab\t ! beg9n+ ( ^! ,signs1 nor at any "t ( ! ye>1 except :5 ! swiftness or sl[ness ( ,equation result+ f "o cause j balances ! sl[ness or swiftness aris+ f ! o!r4 #bdc4 ,! la/ ,table b "o1 at ! end ( ?is ,*apt]1 %ews ! ,sun's place 9 ! ,ecliptic at ! noon ( e day by ! clock1 = ! second ye> aft] leap-ye>2 & also ! ,sun's ,anomaly to ! ne>e/ degree1 neglect+ ! odd m9utes ( a degree4 ,_! use is only to assi/ 9 %ew+ ! me?od ( mak+ a g5]al ,equation ,table f ! two =e-m5tion$ ,tables ( ,equation dep5d+ on ! ,sun's ,place & ,anomaly #bbi1 #bda2 conc]n+ :i* me?od we %all give a few examples pres5tly4 ,! foll[+ ,tables are su* z might be made f ^! two2 & %ew ! absolute ,equation ( ,"t result+ f ! comb9ation ( bo? x's causes2 9 :i* ! m9utes1 z well z degrees1 bo? ( ! ,sun's ,place & ,anomaly are consid]$4 ,! use ( ^! ,tables is already expla9$1 #bbe2 & !y s]ve = e day 9 leap-ye>1 & ! fir/1 second1 & ?ird ye>s aft]3 ,= on mo/ ( ! same days ( all ^! ye>s ! ,equation diff]s1 because ( ! odd six h\rs m ?an ! #cfe days ( :i* ! ye> consi/s4 ,sid5ote3 ,examples = mak+ ,equation ,tables4 ,,example ,i4 ,on ! #ae? ( ,april ! ,sun is 9 ! #be? degree ( ,aries1 & 8 ,anomaly is #i ,signs #ae ,degrees2 ! ,equation result+ f ! =m] is #g m9utes #bc seconds ( "t too fa/ #bbi2 & f ! latt]1 #g m9utes #bg seconds too sl[1 #bda2 ! diff]5ce is #d seconds t ! ,sun is too sl[ at ! noon ( t day2 tak+ x 9 gross = ! degrees ( ! ,sun's ,place & ,anomaly1 )\t mak+ proportionable all[ance = ! odd m9utes4 ,h5ce1 at noon ! swiftness ( ! "o ,equation balanc+ s ne>ly ! sl[ness ( ! o!r1 makes ! ,sun & ,clocks equal on "s "p ( t day4 ,,example ,,ii4 ,on ! #af? ( ,june1 ! ,sun is 9 ! #be? degree ( ,gem9i1 & 8 ,anomaly is #aa ,signs #af ,degrees2 ! ,equation aris+ f ! =m] is #a m9ute #dh seconds too fa/2 & f ! latt] #a m9ute #ej seconds too sl[2 :i* balanc+ "o ano!r at noon to #b seconds1 ! ,sun & ,clocks are aga9 equal on t day4 ,,example ,,iii4 ,on ! #ca/ ( ,augu/ ! ,sun's place is #g degrees #eb m9utes ( ,virgo 7:i* we %all call ! #h? degree1 z x is s ne>7 & 8 ,anomaly is #b ,signs #j ,degrees2 ! ,equation aris+ f ! =m] is #f m9utes #da seconds too sl[2 & f ! latt] #f m9utes #ci seconds too fa/2 ! diff]5ce be+ only #b seconds too sl[ at noon1 & decreas+ t[>ds an equality w make ! ,sun & ,clocks equal 9 ! aft]noon ( t day4 ,,example4 ,,iv4 ,on ! #bc;d ( ,decemb] ! ,sun's place is #a degree #da m9utes 7call x #b degrees7 ( ,capricorn1 & 8 ,anomaly is #e ,signs #bc ,degrees2 ! ,equation = ! =m] is #dc seconds too sl[1 & = ! latt] #eh seconds too fa/2 ! diff]5ce is #ae seconds too fa/ at noon2 :i* decreas+ w come to an equality1 & s make ! ,sun & ,clocks equal 9 ! ev5+ ( t day4 ,& ?us we f9d1 t on "s "p ( ea* ( ! above-m5tion$ f\r days1 ! ,sun & ,clocks are equal2 b if we "w examples = all o!r days ( ! ye> we %all f9d !m diff]5t4 ,&1 ,sid5ote3 ,rem>k4 #bdd4 ,on ^? days :i* are equidi/ant f any ,equ9ox or ,sol/ice1 we d n f9d t ! ,equation is z mu* too fa/ or too sl[1 on ! "o side1 z x is too sl[ or too fa/ on ! o!r4 ,! reason is1 t ! l9e ( ! ,apsides #bch1 does n1 at pres5t1 fall ei!r into ! ,equ9octial or ,sol/icial po9ts #bdb4 ,sid5ote3 ,! reason :y ,equation ,tables are b tempor>y4 #bde4 ,if ! l9e ( ! ,apsides1 toge!r ) ! ,equ9octial & ,sol/icial po9ts1 7 immoveable1 a g5]al ,equation ,table might be made f ! prec$+ ,equation ,tables1 :i* w\ld always keep true1 because ^! ,tables !mselves are p]man5t4 ,b1 ) respect to ! fix$ ,/>s1 ! l9e ( ! ,apsides moves =w>ds #ab seconds ( a degree e ye>1 & ! above po9ts #ej seconds backw>d4 ,s t if 9 any giv5 ye>1 ! ,equ9octial po9ts1 & l9e ( ! ,apsides 7 co9cid5t1 9 #ajj ye>s aft]w>d !y w\ld be sep>at$ #a degree #dc m9utes #bj seconds2 & consequ5tly 9 #ebbe4h ye>s !y w\ld be sep>at$ #ij degrees1 & c\ld n meet aga91 s t ! same ,equ9octial po9t %\ld fall aga9 into ! ,apogee 9 less ?an #bj1ijc ye>s3 & ?is is ! %orte/ ,p]iod 9 :i* ! ,equation ( ,"t c be re/or$ to ! same /ate aga91 ) respect to ! same seasons ( ! ye>4 ,,*ap4 ,,xiv4 ,( ! ,precession ( ! ,equ9oxes4 #bdf4 ,x has be5 already obs]v$1 #aaf1 t by ! ,e>?'s motion on x's ,axis1 !re is m matt] accumulat$ all r\nd ! equatoreal p>ts ?an any :]e else on ! ,e>?4 ,! ,sun & ,moon1 by attract+ ?is r$undancy ( matt]1 br+ ! ,equator soon] "u !m 9 e return t[>ds x ?an if !re 0 no su* accumulation4 ,!re=e1 if ! ,sun sets out1 z f any ,/>1 or o!r fix$ po9t 9 ! ,heav5s1 ! mom5t he is dep>t+ f ! ,equ9octial or ei!r ,tropic1 he w come to ! same aga9 be=e he compleats 8 annual c\rse1 s z to arrive at ! same fix$ ,/> or ,po9t f :5ce he set out4 ,:5 ! ,sun arrives at ! same #ef;,equ9octial or ,sol/itial ,po9t1 he f9i%es :at we call ! ,tropical ,ye>1 :i*1 by long obs]vation1 is f\nd to conta9 #cfe days #e h\rs #dh m9utes #eg seconds3 & :5 he arrives at ! same fix$ ,/> aga91 z se5 f ! ,e>?1 he compleats ! ,sid]eal ,ye>2 :i* is f\nd to conta9 #cfe days #f h\rs #i m9utes #ad-a_/b seconds4 ,! ,sid]eal ,ye> is !re=e #bj m9utes #ag-a_/b seconds long] ?an ! ,sol> or ,tropical ye>1 & #i m9utes #ad-a_/b seconds long] ?an ! ,julian or ,civil ye>1 :i* we /ate at #cfe days #f h\rs3 s t ! ,civil ye> is almo/ a mean betwixt ! ,sid]eal & ,tropical4 ,sid5ote3 ,,plate ,,vi4 #bdg4 ,z ! ,sun describes ! :ole ,ecliptic1 or #cfj degrees1 9 a ,tropical ye>1 he moves #ei #h ( a degree e day2 & consequ5tly #ej ( a degree 9 #bj m9utes #ag-a_/b seconds ( "t3 !re=e1 he w arrive at ! same ,equ9ox or ,sol/ice :5 he is #ej ( a degree %ort ( ! same ,/> or fix$ po9t 9 ! ,heav5s f :i* he set out 9 ! ye> be=e4 ,s t1 ) respect to ! fix$ ,/>s1 ! ,sun & ,equ9octial po9ts fall back 7z x 77 #cj degrees 9 #bafj ye>s2 :i* w make ! ,/>s appe> to h gone #cj deg4 =w>d1 ) respect to ! ,signs ( ! ,ecliptic 9 t "t3 = ! same ,signs always keep 9 ! same po9ts ( ! ,ecliptic1 )\t reg>d to ! con/ellations4 ---------------------------------------- -------------------------- ,a ,,table %ew+ ! ,precession ( ! ,equ9octial ,po9ts 9 ! ,heav5s1 bo? 9 ,motion & ,"t2 & ! ,anticipation ( ! ,equ9oxes on ,e>?4 ---------------------------------------- ----------------------- ,precession ( ! ,equ9octial ,anticipation ( ,po9ts 9 ! ,heav5s4 ! ,equ9oxes ,julian ------------------------------------- on ! ,e>?4 ye>s4 ,motion4 ,"t4 ---------------------------------------- -------------- ,s4 ,days ,h4 ,m4 ,s4 ,d4 ,h4 ,m4 ,s4 ---------------------------------------- ---------------------- #a #j #j #j #ej #j #j #bj #ag-a_/b #j #j #aa #c #b #j #j #a #dj #j #j #dj #ce #j #j #bb #f #c #j #j #b #cj #j #a #j #eb-a_/b #j #j #cc #i #d #j #j #c #bj #j #a #ba #aj #j #j #dd #ab #e #j #j #d #aj #j #a #da #bg-a_/b #j #j #ee #ae ---------------------------------------- ---------------------- #f #j #j #e #j #j #b #a #de #j #a #f #ah #g #j #j #e #ej #j #b #bb #b-a_/b #j #a #ag #ba #h #j #j #f #dj #j #b #db #bj #j #a #bh #bd #i #j #j #g #cj #j #c #b #cg-a_/b #j #a #ci #bg #aj #j #j #h #bj #j #c #bb #ee #j #a #ej #cj ---------------------------------------- ---------------------- #bj #j #j #af #dj #j #f #de #ej #j #c #da #j #cj #j #j #be #j #j #aj #h #de #j #e #ca #cj #dj #j #j #cc #bj #j #ac #ca #dj #j #g #bb #j #ej #j #j #da #dj #j #af #ed #ce #j #i #ab #cj #fj #j #j #ej #j #j #bj #ag #cj #j #aa #c #j ---------------------------------------- ---------------------- #gj #j #j #eh #bj #j #bc #dj #be #j #ab #ec #cj #hj #j #a #f #dj #a #c #c #bj #j #ad #dd #j #ij #j #a #ae #j #a #f #bf #ae #j #af #cd #cj #ajj #j #a #bc #bj #a #i #di #aj #j #ah #be #j #bjj #j #b #df #dj #b #ai #ch #bj #a #ab #ej #j ---------------------------------------- ---------------------- #cjj #j #d #aj #j #d #e #bg #cj #b #g #ae #j #djj #j #e #cc #bj #e #ae #af #dj #c #a #dj #j #ejj #j #f #ef #dj #g #a #e #ej #c #bj #e #j #fjj #j #h #bj #j #h #aj #ee #j #d #ad #cj #j #gjj #j #i #dc #bj #i #bj #dd #aj #e #h #ee #j ---------------------------------------- ---------------------- #hjj #j #aa #f #dj #aa #f #cc #bj #f #c #bj #j #ijj #j #ab #bi #j #ab #af #bb #cj #f #ba #de #j #ajjj #j #ac #ec #bj #ad #b #aa #dj #g #af #aj #j #bjjj #j #bg #df #dj #bh #d #bc #bj #ae #h #bj #j #cjjj #a #aa #dj #j #db #f #ce #j #bc #j #cj #j ---------------------------------------- ---------------------- #djjj #a #be #cc #bj #ef #h #df #dj #cj #af #dj #j #ejjj #b #i #bf #dj #gj #aj #eh #bj #ch #h #ej #j #fjjj #b #bc #bj #j #hd #ac #aj #j #df #a #j #j #gjjj #c #g #ac #bj #ih #ae #ba #dj #ec #ag #aj #j #hjjj #c #ba #f #dj #aab #ag #cc #bj #fa #i #bj #j ---------------------------------------- ---------------------- #ijjj #d #e #j #j #abf #ai #de #j #fi #a #cj #j #ajjjj #d #ah #ec #bj #adj #ba #ef #dj #gf #ag #dj #j #bjjjj #i #g #df #dj #bha #ai #ec #bj #aec #aa #bj #j #beibj #ab #j #j #j #cfe #f #j #j #aih #ba #cf #j ---------------------------------------- ---------------------- ,sid5ote3 ,fig4 ,,iv4 ,to expla9 ?is by a ,figure1 let ! ,sun be 9 conjunction ) a fix$ ,/> at ,s1 suppose 9 ! #cj? degree ( 1 on ! #bj? day ( ,may #agef4 ,!n1 mak+ #bafj revolutions ?r\gh ! ,ecliptic ,,vwx1 at ! end ( s _m ,sid]eal ye>s1 he w be f\nd aga9 at ,s3 b at ! end ( s _m ,julian ye>s1 he w be f\nd at ,m1 %ort ( ,s3 & at ! end ( s _m ,tropical ye>s1 he w be f\nd %ort ( ,m1 9 ! #cj? deg4 ( ,taurus at ,t1 :i* has rec$$ back f ,s to ,t 9 t "t1 by ! ,precession ( ! ,equ9octial po9ts ,aries & ,libra4 ,! ,arc ,,/ w be equal to ! am\nt ( ! ,precession ( ! ,equ9ox 9 #bafj ye>s1 at ! rate ( #ej ( a degree1 or #bj m94 #ag-a_/b sec4 ( "t1 annually3 ?is1 9 s _m ye>s1 makes #cj days1 #aj-a_/b h\rs2 :i* is ! diff]5ce betwe5 #bafj ,sid]eal & ,tropical ye>s3 ,& ! ,arc ,,mt w be equal to ! space mov$ ?r\gh by ! ,sun 9 #bafj times #aa m94 #c sec4 or #af days1 #ac h\rs #dh m9utes1 :i* is ! diff]5ce betwe5 #bafj ,julian & ,tropical ye>s4 #bdh4 ,f ! %ift+ ( ! ,equ9octial po9ts1 & ) !m all ! ,signs ( ! ,ecliptic1 x foll[s t ^? ,/>s :i* 9 ! infancy ( a/ronomy 7 9 ,aries are n[ got into ,taurus2 ^? ( ,taurus into ,gem9i1 c4 ,h5ce likewise x is1 t ! ,/>s :i* rose or set at any p>ticul> season ( ! ye>1 9 ! "t ( ,,hesiod1 ,,eudoxus1 ,,virgil1 ,,pl9y1 c4 by no means answ] at ?is "t to _! descriptions4 ,! prec$+ table %ews ! quantity ( ?is %ift+ bo? 9 ! heav5s & on ! e>?1 = any numb] ( ye>s to #be1ibj2 :i* compleats ! gr& cele/ial p]iod3 )9 :i* any numb] & its quantity is easily f\nd2 z 9 ! foll[+ example1 = #egfc ye>s2 :i* at ! ,autumnal ,equ9ox1 ,a4 ,d4 #agef1 is ?\ght to be ! age ( ! _w4 ,s t ) reg>d to ! fix$ ,/>s1 ! ,equ9octial po9ts 9 ! heav5s1 h rec$$ #bs #bj #b #cj s9ce ! creation2 :i* is z mu* z ! ,sun moves 9 #ha;d #e;h #jm #ebs4 ,& s9ce t "t1 or 9 #egfc ye>s1 ! ,equ9oxes ) u h fall5 back #dd;d #e;h #bam #is2 h5ce1 reckon+ f ! "t ( ! ,julian ,equ9ox1 ,a4 ,d4 #agef1 viz4 ,sept4 #ab?1 x appe>s t ! ,autumnal ,equ9ox at ! creation 0 on ! #bf? ( ,octob]4 ---------------------------------------- ------------------- ,precession ( ! ,equ9octial ,anticipation ,po9ts 9 ! ,heav5s4 ( ! ,julian --------------------------------- ,equ9oxes on ye>s4 ,motion4 ,"t4 ! ,e>?4 ---------------------------------------- --------- ,s4 ,d4 ,h4 ,m4 ,s4 ,d4 ,h4 ,m4 ,s4 ---------------------------------------- ------------------ #ejjj #b #i #bf #dj #gj #aj #eh #bj #ch #h #ej #j #gjj #j #i #dc #bj #i #bj #dd #aj #e #h #ee #j #fj #j #j #ej #j #j #bj #ag #cj #j #aa #c #j #c #j #j #b #cj #j #a #j #eb #j #j #cc #i ---------------------------------------- ------------------ #egfc #b #bj #b #cj #ha #e #j #eb #dd #e #ba #i ---------------------------------------- ------------------ ,sid5ote3 ,! anticipation ( ! ,equ9oxes & ,seasons4 ,,plate ,,vi4 #bdi4 ,! anticipation ( ! ,equ9oxes1 & consequ5tly ( ! seasons1 is by no means ow+ to ! ,precession ( ! ,equ9octial & ,sol/icial po9ts 9 ! ,heav5s1 7:i* c only affect ! app>5t motions1 places & decl9ations ( ! fix$ ,/>s7 b to ! diff]5ce betwe5 ! ,civil & ,sol> ye>1 :i* is #aa m9utes #c seconds2 ! ,civil ye> conta9+ #cfe days #f h\rs1 & ! ,sol> ye> #cfe days #e h\rs #dh m9utes #eg seconds4 ,! foll[+ table %ews ! l5g?1 & consequ5tly ! diff]5ce ( any numb] ( ,sid]eal1 ,civil1 & ,sol> ye>s f #a to #aj1jjj4 ,sid5ote3 ,! reason = alt]+ ! ,/yle4 #bej4 ,! above #aa m9utes #c seconds1 by :i* ! ,civil or ,julian ye> exce$s ! ,sol>1 am\nts to #aa days 9 #adcc ye>s3 & s mu* our seasons h fall5 back ) respect to ! days ( ! mon?s1 s9ce ! "t ( ! ,nic5e ,c\ncil 9 ,a4,d4 #cbe1 & !re=e 9 ord] to br+ back all ! ,fa/s & ,fe/ivals to ! days !n settl$1 x 0 requisite to suppress #aa nom9al days4 ,& t ! same seasons might be kept to ! same times ( ! ye> = ! future1 to leave out ! ,bissextile day 9 ,febru>y at ! end ( e c5tury ( ye>s n divisible by #d2 reckon+ !m only common ye>s1 z ! #ag?1 #ah? & #ai? c5turies1 viz4 ! ye>s #agjj1 #ahjj1 #aijj1 c4 because a day int]calat$ e f\r? ye> 0 too mu*1 & reta9+ ! ,bissextile-day at ! end ( ^? ,c5turies ( ye>s :i* are divisible by #d1 z ! #af?1 #bj? & #bd? ,c5turies2 viz4 ! ye>s #afjj1 #bjjj1 #bdjj1 c4 ,o!rwise1 9 l5g? ( "t ! seasons w\ld h be5 q rev]s$ ) reg>d to ! mon?s ( ! ye>s2 ?\gh x w\ld h requir$ ne> #bc1ghc ye>s to h br\ght ab\t su* a total *ange4 ,if ! ,e>? _h made exactly #cfe-a_/d diurnal rotations on its axis1 :il/ x revolv$ f any ,equ9octial or ,sol/itial po9t to ! same aga91 ! ,civil & ,sol> ye>s w\ld always h kept pace toge!r2 & ! /yle w\ld nev] h ne$$ any alt]ation4 ,sid5ote3 ,! ,precession ( ! ,equ9octial ,po9ts4 #bea4 ,hav+ already m5tion$ ! cause ( ! ,precession ( ! ,equ9octial po9ts 9 ! heav5s1 #bdf1 :i* occasions a fl[ deviation ( ! e>?'s axis f its p>allelism1 & !reby a *ange ( ! decl9ation ( ! ,/>s f ! ,equator1 toge!r ) a sl[ app>5t motion ( ! ,/>s =w>d ) respect to ! ,signs ( ! ,ecliptic2 we %all n[ describe ! ,ph5om5a by a ,diagram4 ,sid5ote3 ,fig4 ,v4 ,let ,,nzsvl be ! ,e>?1 ,,sona its ,axis produc$ to ! />ry ,heav5s1 & t]m9at+ 9 ,a1 ! pres5t nor? ,pole ( ! ,heav5s1 :i* is v]tical to ,n ! nor? ,pole ( ! ,e>?4 ,let ,,eoq be ! ,equator1 ,t,z ! ,tropic ( ,canc]1 & ,,vt ! ,tropic ( ,capricorn3 ,,voz ! ,ecliptic1 & ,,bo its ,axis1 bo? :i* are immoveable among ! ,/>s4 ,b1 z #eg! ,equ9octial po9ts rec$e 9 ! ,ecliptic1 ! ,e>?'s ,axis ,,son is 9 motion ^u ! ,e>?'s c5t] ,o1 9 su* a mann] z to describe ! d\ble ,cone ,n,on & ,s,os1 r\nd ! ,axis ( ! ,ecliptic ,,bo1 9 ! "t t ! ,equ9octial po9ts move q r\nd ! ,ecliptic1 :i* is #be1ibj ye>s2 & 9 t l5g? ( "t1 ! nor? ,pole ( ! ,e>?'s ,axis produc$1 describes ! ,circle ,,abcda 9 ! />ry ,heav5s1 r\nd ! ,pole ( ! ,ecliptic1 :i* keeps immoveable 9 ! c5t] ( t ,circle4 ,! ,e>?'s ,axis be+ #bc-a_/b degrees incl9$ to ! ,axis ( ! ,ecliptic1 ! ,circle ,,abcda1 describ$ by ! nor? ,pole ( ! ,e>?'s ,axis produc$ to ,a1 is #dg degrees 9 diamet]1 or d\ble ! incl9ation ( ! ,e>?'s ,axis4 ,9 consequ5ce ( ?is1 ! po9t ,a1 :i* at pres5t is ! ,nor? ,pole ( ! ,heav5s1 & ne> to a ,/> ( ! second magnitude 9 ! tail ( ! con/ellation call$ ! ,little ,be>1 mu/ be des]t$ by ! ,e>?'s ,axis2 :i* mov+ backw>ds a degree e #gb ye>s1 w be direct$ t[>ds ! ,/> or ,po9t ,b 9 #fdhj ye>s h5ce3 & 9 d\ble ( t "t1 or #ab1ifj ye>s1 x w be direct$ t[>ds ! ,/> or ,po9t ,c2 :i* w !n be ! ,nor? ,pole ( ! ,heav5s1 al?\gh x is at pres5t #h-a_/b degrees s\? ( ! ,z5i? ( ,london ,l4 ,! pres5t position ( ! ,equator ,,eoq w !n be *ang$ into e,oq1 ! ,tropic ( ,canc] ,t,z into ,vt1 & ! ,tropic ( ,capricorn ,,vt into t,z2 z is evid5t by ! ,figure4 ,& ! ,sun1 9 ! same "p ( ! ,heav5s :]e he is n[ ov] ! e>?ly ,tropic ( ,capricorn1 & makes ! %orte/ days & longe/ nights 9 ! ,nor!rn ,hemisph]e1 w !n be ov] ! e>?ly ,tropic ( ,canc]1 & make ! days longe/1 & nights %orte/4 ,s t x w require #ab1ifj ye>s yet m1 or #be1ibj f ! pres5t "t1 to br+ ! ,nor? ,pole ,n q r\nd1 s z to be direct$ t[>d t po9t ( ! ,heav5s :i* is v]tical to x at pres5t4 ,& !n1 & n till !n1 ! same ,/>s :i* at pres5t describe ! ,equator1 ,tropics1 pol> ,circles1 & ,poles1 by ! ,e>?'s diurnal motion1 w describe !m ov] aga94 ,a ,,table %ew+ ! ,"t conta9$ 9 any numb] ( ,sid]eal1 ,julian1 & ,sol> ,ye>s1 f #a to #ajjjj4 ---------------------------------------- ---------------------------------- ,sid]eal ,ye>s4 ,julian ,ye>s4 ,sol> ,ye>s4 ---------------------------------------- ---------------------------- ,ye>s ,days ,h4 ,m4 ,s4 ,days ,h4 ,days ,h4 ,m4 ,s4 ---------------------------------------- -------------------------- ,conta9 ,conta9 ,conta9 #a #cfe #f #i #ad-a_/b #cfe #f #cfe #e #dh #eg #b #gcj #ab #ah #bi #gcj #ab #cgj #aa #cg #ed #c #ajie #ah #bg #dc-a_/b #ajie #ah #ajie #ag #bf #ea #d #adfa #j #cf #eh #adfa #j #adfj #bc #ae #dh #e #ahbf #f #df #ab-a_/b #ahbf #f #ahbf #e #d #de ---------------------------------------- -------------------------- #f #baia #ab #ee #bg #baia #ab #baia #aj #ec #db #g #beef #ai #e #da-a_/b #beef #ah #beef #af #db #ci #h #bibb #a #ac #ef #bibb #j #biba #bb #ca #cf #i #cbhg #g #bc #aj-a_/b #cbhg #f #cbhg #d #bj #cc #aj #cfeb #ac #cb #be #cfeb #ab #cfeb #aj #i #cj ---------------------------------------- -------------------------- #bj #gcje #c #d #ej #gcje #j #gcjd #bj #ai #j #cj #ajieg #af #cg #ae #ajieg #ab #ajieg #f #bh #cj #dj #adfaj #f #i #dj #adfaj #j #adfji #af #ch #j #ej #ahbfb #ai #db #e #ahbfb #ab #ahbfb #b #dg #cj #fj #baiae #i #ad #cj #baiae #j #baiad #ab #eg #j ---------------------------------------- -------------------------- #gj #beefg #bb #df #ee #beefg #ab #beeff #bc #f #cj #hj #bibbj #ab #ai #bj #bebbj #j #bibai #i #af #j #ij #cbhgc #a #ea #de #cbhgb #ab #cbhga #ai #be #cj #ajj #cfebe #ae #bd #aj #cfebe #cfebd #e #ce #bjj #gcjea #f #dh #bj #gcjej #gcjdh #aa #aj ---------------------------------------- -------------------------- #cjj #ajiegf #bb #ab #cj #ajiege #ajiegb #af #de #djj #adfajb #ac #cf #dj #adfajj #adfjif #bb #bj #ejj #ahbfbh #e #j #ej #ahbfbe #ahbfba #c #ee #fjj #baiaec #bj #be #baiaej #baiade #i #cj #gjj #beefgi #aa #di #aj #beefge #beeffi #ae #e ---------------------------------------- -------------------------- #hjj #bibbje #c #ac #bj #bibbjj #bibaic #bj #aj #ijj #cbhgcj #ah #cg #cj #cbhgbe #cbhgah #b #ae #ajjj #cfebef #aj #a #dj #cfebej #cfebdb #g #ej #bjjj #gcjeab #bj #c #bj #gcjejj #gcjdhd #ae #dj #cjjj #ajiegfi #f #e #ajiegej #ajiegbf #bc #cj ---------------------------------------- -------------------------- #djjj #adfajbe #af #f #dj #adfajjj #adfjifi #g #bj #ejjj #ahbfbhb #b #h #bj #ahbfbej #ahbfbaa #ae #aj #fjjj #baiaech #ab #aj #baiaejj #baiadec #ad #dj #gjjj #beefgid #bb #aa #dj #beefgej #beeffif #f #ej #hjjj #bibbjea #h #ac #bj #bibbjjj #bibaich #ad #dj ---------------------------------------- -------------------------- #ijjj #cbhgjcg #ah #ae #cbhgbej #cbhgahj #bb #cj #ajjjj #cfebefd #d #af #dj #cfebejj #cfebdbc #f #bj ---------------------------------------- -------------------------- ---------------------------------------- ---------------------------------------- -------- ,a ,,table %ew+ ! ,sun's true ,place1 & ,di/ance f 8 ,apogee1 = ! second ,ye> aft] ,leap-ye>4 ---------------------------------------- ---------------------------------------- -- ,janu>y ,febru>y ,m>* ,april ,may ,june ---------------------------------------- -------------------------------- ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ---------------------------------------- -------------------------------- ,days,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4 ---------------------------------------- ------------------------------------ #a #aa #g #f #bab #ci #g #caj #ec #h #jaa #dj #i #aaj #egaj #jaj #dfaa #a #b #ab #h #f #cac #dj #g #daa #ec #h #aab #ci #i #baa #eeaj #aaa #ddaa #b #c #ac #i #f #dad #da #g #eab #ec #h #bac #ch #i #cab #ecaj #bab #daaa #c #d #ad #aj #f #eae #db #g #fac #ec #h #cad #cg #i #dac #eaaj #cac #chaa #d #e #ae #aa #f #faf #dc #g #gad #ec #h #dae #cf #i #ead #diaj #dad #ceaa #e ---------------------------------------- ------------------------------------ #f #af #ab #f #gag #dc #g #h #e #ec #h #eaf #ce #i #fae #dgaj #eae #ccaa #f #g #ag #ad #f #hah #dd #g #iaf #ec #h #fag #cd #i #gaf #deaj #faf #cjaa #g #h #ah #ae #f #iai #de #g #ajag #ec #h #gah #cc #i #hag #dcaj #gag #bhaa #h #i #ai #af #f #ajbj #df #g #aaah #ec #h #hai #cb #i #iah #daaj #hah #beaa #i #aj #bj #ag #f #aaba #df #g #abai #ec #h #ibj #cj #i #ajai #ciaj #iai #bbaa #aj ---------------------------------------- ------------------------------------ #aa #ba #ah #f #abbb #dg #g #acbj #eb #h #ajba #bi #i #aabj #cgaj #ajbj #bjaa #aa #ab #bb #ai #f #acbc #dg #g #adba #eb #h #aabb #bh #i #abba #cdaj #aaba #agaa #ab #ac #bc #ba #f #adbd #dh #g #aebb #eb #h #abbc #bf #i #acbb #cbaj #abbb #adaa #ac #ad #bd #bb #f #aebe #dh #g #afbc #eb #h #acbd #be #i #adbc #cjaj #acbc #aaaa #ad #ae #be #bc #f #afbf #di #g #agbd #ea #h #adbe #bd #i #aebd #bhaj #adbd #haa #ae ---------------------------------------- ------------------------------------ #af #bf #bd #f #agbg #di #g #ahbe #ea #h #aebf #bb #i #afbe #bfaj #aebe #faa #af #ag #bg #be #f #ahbh #ej #g #aibf #ea #h #afbg #ba #i #agbf #bcaj #afbf #caa #ag #ah #bh #bf #f #aibi #ej #g #bjbg #ej #h #agbh #ai #i #ahbg #baaj #agbg #jaa #ah #ai #bi #bg #f #bj #ea #g #babh #ej #h #ahbi #ah #i #aibh #aiaj #ahbg #ehaa #ah #bj #bh #f #ba #a #ea #g #bbbi #di #h #ai #af #i #bjbi #afaj #aibh #eeaa #ai ---------------------------------------- ------------------------------------ #ba #a #bi #f #bb #b #ea #g #bc #di #h #bj #a #ae #i #ba #aeaj #bjbi #ebaa #bj #bb #b #cj #f #bc #c #eb #g #bd #a #dh #h #ba #b #ac #i #bb #a #aaaj #ba #diaa #ba #bc #c #ca #f #bd #d #eb #g #be #b #dg #h #bb #c #aa #i #bc #b #iaj #bb #a #dfaa #bb #bd #d #cb #f #be #e #eb #g #bf #c #dg #h #bc #d #aj #i #bd #c #faj #bc #b #ddaa #bc #be #e #cc #f #bf #f #eb #g #bg #d #df #h #bd #e #h #i #be #d #daj #bd #c #daaa #bd ---------------------------------------- ------------------------------------ #bf #f #cd #f #bg #g #ec #g #bh #e #de #h #be #f #f #i #bf #e #baj #be #d #chaa #be #bg #g #ce #f #bh #h #ec #g #bi #f #de #h #bf #g #d #i #bg #e #eiaj #bf #e #ceaa #bf #bh #h #cf #f #bi #i #ec #h #j #g #dd #h #bg #h #c #i #bh #f #efaj #bg #f #cbaa #bg #bi #i #cg #g #j #h #dc #h #bh #i #a #i #bi #g #edaj #bh #g #cjaa #bh #cj #aj #ch #g #a #i #db #h #bi #i #ei #i #bi #h #eaaj #bi #h #bgaa #bi ---------------------------------------- ------------------------------------ #ca #aa #ci #g #b #aj #da #i #j #i #dhaa #j ---------------------------------------- ------------------------------------ ---------------------------------------- ---------------------------------------- -------- ,a ,,table %ew+ ! ,sun's true ,place1 & ,di/ance f 8 ,apogee1 = ! second ,ye> aft] ,leap-ye>4 ---------------------------------------- ---------------------------------------- -- ,july ,augu/ ,septemb] ,octob] ,novemb] ,decemb] ---------------------------------------- -------------------------------- ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ---------------------------------------- -------------------------------- ,days,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4 ---------------------------------------- ------------------------------------ #a #i #bd #j #j #h #ei #a #j #h #ea #b #a #h #aj #c #a #i #j #d #b #i #ah #e #a #b #aj #ba #j #a #i #eg #a #a #i #di #b #b #i #i #c #b #aj #j #d #caj #ai #e #b #c #aa #ah #j #baj #ed #a #baj #dg #b #caj #h #c #c #aa #j #d #daa #bj #e #c #d #ab #ae #j #caa #eb #a #caa #de #b #daa #h #c #d #ab #a #d #eab #ba #e #d #e #ac #ac #j #dab #di #a #dab #dc #b #eab #g #c #e #ac #a #d #fac #bb #e #e ---------------------------------------- ------------------------------------ #f #ad #aj #j #eac #dg #a #eac #db #b #fac #f #c #f #ad #a #d #gad #bc #e #f #g #ae #g #j #fad #dd #a #fad #dj #b #gad #f #c #g #ae #b #d #hae #bd #e #g #h #af #d #j #gae #db #a #gae #ci #b #hae #e #c #h #af #b #d #iaf #be #e #h #i #ag #a #j #haf #ci #a #haf #cg #b #iaf #d #c #i #ag #b #d #ajag #bf #e #i #aj #ag #ei #j #hag #cg #a #iag #ce #b #ajag #d #c #aj #ah #c #d #aaah #bg #e #aj ---------------------------------------- ------------------------------------ #aa #ah #ef #j #iah #ce #a #ajah #cd #b #aaah #c #c #aa #ai #c #d #abai #bh #e #aa #ab #ai #ec #j #ajai #cb #a #aaai #cb #b #abai #c #c #ab #bj #d #d #acbj #bi #e #ab #ac #bj #ej #j #aabj #cj #a #abbj #ca #b #acbj #b #c #ac #ba #d #d #adba #cj #e #ac #ad #ba #dg #j #abba #bh #a #acba #bi #b #adba #b #c #ad #bb #e #d #aebb #ca #e #ad #ae #bb #de #j #acbb #be #a #adbb #bh #b #aebb #b #c #ae #bc #e #d #afbc #cb #e #ae ---------------------------------------- ------------------------------------ #af #bc #db #j #adbc #bc #a #aebc #bg #b #afbc #a #c #af #bd #f #d #agbd #cc #e #af #ag #bd #ci #j #aebd #ba #a #afbd #be #b #agbd #a #c #ag #be #g #d #ahbe #cd #e #ag #ah #be #cf #j #afbe #ai #a #agbe #bd #b #ahbe #a #c #ah #bf #g #d #aibf #ce #e #ah #ai #bf #cd #j #agbf #ag #a #ahbf #bc #b #aibf #j #c #ai #bg #h #d #bjbg #cf #e #ai #bj #bg #ca #j #ahbg #ad #a #aibg #ba #b #bjbg #j #c #bj #bh #i #d #babh #ch #e #bj ---------------------------------------- ------------------------------------ #ba #bh #bh #j #aibh #ab #a #bjbh #bj #b #babh #j #c #ba #bi #i #d #bbbi #ci #e #ba #bb #bi #bf #j #bjbi #aj #a #babi #ai #b #bbbi #j #c #bb #aj #d #bc #dj #e #bb #bc #bc #j #ba #h #a #bb #ah #b #bc #j #c #bc #a #aa #d #bd #a #da #e #bc #bd #a #bj #j #bb #a #f #a #bc #a #ag #b #bd #a #j #c #bd #b #ab #d #be #b #db #e #bd #be #b #ah #j #bc #b #d #a #bd #b #af #b #be #b #j #c #be #c #ab #d #bf #c #dd #e #be ---------------------------------------- ------------------------------------ #bf #c #ae #j #bd #c #b #a #be #c #ae #b #bf #c #j #c #bf #d #ac #d #bg #d #de #e #bf #bg #d #ab #j #be #d #j #a #bf #d #ad #b #bg #d #j #c #bg #e #ad #d #bh #e #df #e #bg #bh #e #aj #j #bf #d #eh #a #bg #e #ac #b #bh #e #j #c #bh #f #ae #d #bi #f #dg #e #bh #bi #f #g #j #bg #e #ef #a #bh #f #ab #b #bi #f #j #c #bi #g #af #d #bi #g #dh #e #bi #cj #g #e #j #bh #f #ed #a #bi #g #aa #c #j #g #j #d #j #h #ag #e #j #h #di #f #j ---------------------------------------- ------------------------------------ #ca #h #b #j #bi #g #eb #b #j #h #j #d #a #i #ea #f #a ---------------------------------------- ------------------------------------ ---------------------------------------- ---------------------------------------- -------- ,a ,,table ( ! ,equation ( natural ,days1 %ew+ :at ,"t x ought to be by ! ,clock :5 ! ,sun is on ! ,m]idian4 ---------------------------------------- ---------------------------------------- -------- ,! ,bissextile1 or ,leap-ye>4 ---------------------------------------- ------------------------------------ ,days,janu>y ,dif4,febru>y,dif4 ,m>* ,dif4 ,april ,dif4 ,may ,dif4 ,june ,dif4 ---------------------------------------- -------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------ ,inc4 ,inc4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #d #j #ab #ad #e #ab #ab #cf #ab #c #dh #aa #ef #dg #aa #eg #bb #bh #g #ac #ah #g #i #b #ab #d #bh #ab #ad #ab #ab #ab #bc #ab #c #cj #aa #ef #dj #aa #eg #ca #bh #g #ac #ai #g #i #c #ab #d #ef #ab #ad #ai #ab #ab #aj #ab #c #aa #aa #ef #cc #aa #eg #dj #bh #f #ad #ah #f #aj #d #ab #e #bd #ab #ad #be #ab #aa #ef #ab #b #ec #aa #ef #bg #aa #eg #ej #bg #e #ad #ah #f #aj #e #ab #e #ea #ab #ad #cj #ab #aa #db #ab #b #ce #aa #ef #ba #aa #eh #j ------------ #bg -------- #d -------- #ad -------- #ah -------- #e -------- #aa #f #ab #f #ah #ab #ad #cd #ab #aa #bh #ab #b #ag #aa #ef #af #aa #eh #aa #bf #c #ae #ag #d #aa #g #ab #f #dd #ab #ad #cg #ab #aa #ac #ab #b #j #aa #ef #ab #aa #eh #bb #bf #c #ae #ag #d #aa #h #ab #g #aj #ab #ad #dj #ab #aj #eh #ab #a #dc #aa #ef #h #aa #eh #cc #be #b #af #ag #d #aa #i #ab #g #ce #ab #ad #db #ab #aj #db #ab #a #bf #aa #ef #d #aa #eh #dd #be #a #af #ag #c #ab #aj #ab #h #j #ab #ad #dc #ab #aj #df #ab #a #i #aa #ef #a #aa #eh #ef ------------ #bd --------,dec4-------- #af -------- #af -------- #b -------- #ab #aa #ab #h #bd #ab #ad #dd #ab #aj #aj #ab #j #ec #aa #ee #ei #aa #ei #h #bc #a #ag #af #a #ab #ab #ab #h #dg #ab #ad #dc #ab #i #ec #ab #j #cg #aa #ee #eh #aa #ei #bj #bc #a #ag #af #a #ab #ac #ab #i #aj #ab #ad #db #ab #i #cf #ab #j #ba #aa #ee #eg #aa #ei #cb #bb #b #ag #ae ,inc4 #ab #ad #ab #i #cb #ab #ad #dj #ab #i #ai #ab #j #f #aa #ee #ef #aa #ei #dd #bb #c #ag #ae #a #ac #ae #ab #i #ed #ab #ad #cg #ab #i #b #aa #ei #ea #aa #ee #eg #aa #ei #eg ------------ #ba -------- #d -------- #ah -------- #ae -------- #a -------- #ac #af #ab #aj #ae #ab #ad #cc #ab #h #dd #aa #ei #cf #aa #ee #eh #ab #j #aj #bj #d #ah #ae #a #ac #ag #ab #aj #ce #ab #ad #bi #ab #h #bf #aa #ei #ba #aa #ee #ei #ab #j #bc #ai #e #ah #ad #b #ab #ah #ab #aj #ed #ab #ad #bd #ab #h #h #aa #ei #g #aa #ef #a #ab #j #ce #ai #e #ah #ac #b #ac #ai #ab #aj #ac #ab #ad #ai #ab #g #ej #aa #eh #ed #aa #ef #c #ab #j #dh #ah #f #ah #ac #c #ac #bj #ab #aj #ca #ab #ad #ac #ab #g #cb #aa #eh #da #aa #ef #f #ab #a #a ------------ #ag -------- #g -------- #ah -------- #ac -------- #c -------- #ac #ba #ab #aa #dh #ab #ad #f #ab #g #ad #aa #eh #bh #aa #ef #i #ab #a #ad #ag #h #ai #ab #d #ac #bb #ab #ab #e #ab #ac #eh #ab #f #ee #aa #eh #af #aa #ef #ac #ab #a #bg #af #h #ai #ab #e #ac #bc #ab #ab #ba #ab #ac #ej #ab #f #cf #aa #eh #d #aa #ef #ah #ab #a #dj #ae #i #ai #ab #e #ac #bd #ab #ab #cf #ab #ac #da #ab #f #ag #aa #eg #eb #aa #ef #bc #ab #a #ec #ad #i #ai #aa #f #ac #be #ab #ab #ej #ab #ac #cb #ab #e #eh #aa #eg #da #aa #ef #bi #ab #b #f ------------ #ac -------- #aj -------- #ah -------- #aj -------- #f -------- #ab #bf #ab #ac #c #ab #ac #bb #ab #e #dj #aa #eg #ca #aa #ef #ce #ab #b #ah #ab #aa #ai #aj #g #ac #bg #ab #ac #ae #ab #ac #aa #ab #e #ba #aa #eg #ba #aa #ef #db #ab #b #ca #ab #aa #ai #i #g #ab #bh #ab #ac #bg #ab #ac #j #ab #e #b #aa #eg #ab #aa #ef #di #ab #b #dc #aa #ab #ah #i #g #ab #bi #ab #ac #ch #ab #ab #dh #ab #d #dd #aa #eg #c #aa #ef #ef #ab #b #ee #aj #ab #ai #h #h #ab #cj #ab #ac #dh #ab #d #be #aa #ef #ee #aa #eg #d #ab #c #g ------------ #i -------------------- #ai -------- #h -------- #i -------- #aa #ca #ab #ac #eg #ab #d #f #aa #eg #ac #h #ah #i ---------------------------------------- ------------------------------------ ,incr4 #i #eg ,incr4 #j #ci ,decr4 #h #cj ,decr4 #f #ec ,decr4 #j #ej ,incr4 #e #de ,decr4 #a #ef ,incr4 #a #ag ---------------------------------------- ---------------------------------------- --------- ,a ,,table ( ! ,equation ( natural ,days1 %ew+ :at ,"t x ought to be by ! ,clock :5 ! ,sun is on ! ,m]idian4 ---------------------------------------- ---------------------------------------- --------- ,! ,bissextile1 or ,leap-ye>4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,augu/ ,dif4,septemb],dif4 ,octob],dif4,novemb],dif4,decemb],dif4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #ah #ab #e #df #aa #ei #cc #aa #di #bh #aa #dc #di #aa #di #db #aa #d #ai #ah #a #bd #b #ab #c #bi #ab #e #db #aa #ei #ad #aa #di #aj #aa #dc #dh #aa #ej #f #aa #e #ai #ah ,inc4 #bd #c #ab #c #dj #ab #e #cg #aa #eh #ee #aa #dh #eb #aa #dc #di #aa #ej #cj #aa #e #ai #ah #a #be #d #ab #c #ea #ab #e #cb #aa #eh #cf #aa #dh #cd #aa #dc #ej #aa #ej #ee #aa #f #ai #ah #b #be #e #ab #d #b #ab #e #bf #aa #eh #ag #aa #dh #af #aa #dc #eb #aa #ea #bj ------------ #aj -------- #f --------- #bj -------- #ag -------- #c -------- #bf #f #ab #d #ab #ab #e #bj #aa #eg #eg #aa #dg #ei #aa #dc #ee #aa #ea #df #aj #g #bj #ag #d #bf #g #ab #d #bb #ab #e #ac #aa #eg #cg #aa #dg #db #aa #dc #ei #aa #eb #ab #i #h #bj #af #e #bf #h #ab #d #ca #ab #e #e #aa #eg #ag #aa #dg #bf #aa #dd #d #aa #eb #ch #i #h #bj #ae #f #bh #i #ab #d #dj #ab #d #eg #aa #ef #eg #aa #dg #aa #aa #dd #aj #aa #ec #f #h #i #ba #ae #f #bg #aj #ab #d #dh #ab #d #dh #aa #ef #cf #aa #df #ef #aa #dd #af #aa #ec #cc ------------ #h -------- #i --------- #ba -------- #ae -------- #g -------- #bh #aa #ab #d #ef #ab #d #ci #aa #ef #ae #aa #df #da #aa #dd #bc #aa #ed #a #h #aj #ba #ae #h #bi #ab #ab #e #d #ab #d #bi #aa #ee #ed #aa #df #bf #aa #dd #ca #aa #ed #cj #g #aj #ba #ad #i #bi #ac #ab #e #aa #ab #d #ai #aa #ee #cc #aa #df #ab #aa #dd #dj #aa #ed #ei #g #aa #ba #ac #aj #bi #ad #ab #e #ah #ab #d #h #aa #ee #ab #aa #de #ei #aa #dd #ej #aa #ee #bh #f #ab #ba #ac #aa #bi #ae #ab #e #bd #ab #c #ef #aa #ed #ea #aa #de #df #aa #de #a #aa #ee #eg ------------ #f -------- #ab --------- #ba -------- #ab -------- #ab -------- #bi #af #ab #e #cj #ab #c #dd #aa #ed #cj #aa #de #cd #aa #de #ac #aa #ef #bf #e #ab #bj #aa #ac #cj #ag #ab #e #ce #ab #c #cb #aa #ed #aj #aa #de #bc #aa #de #bf #aa #ef #ef #e #ac #ba #aa #ac #cj #ah #ab #e #dj #ab #c #ai #aa #ec #di #aa #de #ab #aa #de #ci #aa #eg #bf #d #ac #ba #aa #ad #cj #ai #ab #e #dd #ab #c #f #aa #ec #bh #aa #de #a #aa #de #ec #aa #eg #ef #d #ad #ba #aj #ae #cj #bj #ab #e #dh #ab #b #eb #aa #ec #g #aa #dd #ea #aa #df #h #aa #eh #bf ------------ #c -------- #ad --------- #ba -------- #i -------- #af -------- #cj #ba #ab #e #ea #ab #b #ch #aa #eb #df #aa #dd #db #aa #df #bd #aa #eh #ef #b #ae #ba #i #af #cj #bb #ab #e #ec #ab #b #bc #aa #eb #be #aa #dd #cc #aa #df #dj #aa #ei #bf #b #ae #bj #h #ag #cj #bc #ab #e #ee #ab #b #h #aa #eb #e #aa #dd #be #aa #df #eg #aa #ei #ef #b #af #bj #g #ah #cj #bd #ab #e #eg #ab #a #eb #aa #ea #de #aa #dd #ah #aa #dg #ae #ab #j #bf #a #af #bj #g #ai #cj #be #ab #e #eh #ab #a #cf #aa #ea #be #aa #dd #aa #aa #dg #cd #ab #j #ef ------------ #a -------- #ag --------- #bj -------- #f -------- #bj -------- #cj #bf #ab #e #ei #ab #a #ai #aa #ea #e #aa #dd #e #aa #dg #ed #ab #a #bf ,dec4 #ag #bj #e #bj #cj #bg #ab #e #eh #ab #a #b #aa #ej #de #aa #dd #j #aa #dh #ad #ab #a #ef #a #ag #bj #d #ba #bi #bh #ab #e #eg #ab #j #de #aa #ej #be #aa #dc #ef #aa #dh #ce #ab #b #be #b #ag #ai #c #bb #bi #bi #ab #e #ee #ab #j #bh #aa #ej #f #aa #dc #ec #aa #dh #eg #ab #b #ed #b #ah #ai #b #bb #bi #cj #ab #e #ec #ab #j #aj #aa #di #dg #aa #dc #ea #aa #di #ai #ab #c #bc ------------ #c -------- #ah --------- #ai -------- #a -------- #bc -------- #bi #ca #ab #e #ej #aa #ei #eb #aa #dc #ej #ab #c #eb #d #ai #a ---------------------------------------- ------------------------------------- ,incr4 #b #da ,decr4 #e #ed ,decr4 #i #df ,decr4 #e #ch ,decr4 #j #a ,incr4 #ad #aj ,decr4 #j #h ,incr4 #e #cj ---------------------------------------- ---------------------------------------- --------- ,a ,,table ( ! ,equation ( natural ,days1 %ew+ :at ,"t x ought to be by ! ,clock :5 ! ,sun is on ! ,m]idian4 ---------------------------------------- ---------------------------------------- --------- ,! ,bissextile1 or ,leap-ye>4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,augu/ ,dif4,septemb],dif4 ,octob],dif4,novemb],dif4,decemb],dif4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #ah #ab #e #df #aa #ei #cc #aa #di #bh #aa #dc #di #aa #di #db #aa #d #ai #ah #a #bd #b #ab #c #bi #ab #e #db #aa #ei #ad #aa #di #aj #aa #dc #dh #aa #ej #f #aa #e #ai #ah ,inc4 #bd #c #ab #c #dj #ab #e #cg #aa #eh #ee #aa #dh #eb #aa #dc #di #aa #ej #cj #aa #e #ai #ah #a #be #d #ab #c #ea #ab #e #cb #aa #eh #cf #aa #dh #cd #aa #dc #ej #aa #ej #ee #aa #f #ai #ah #b #be #e #ab #d #b #ab #e #bf #aa #eh #ag #aa #dh #af #aa #dc #eb #aa #ea #bj ------------ #aj -------- #f --------- #bj -------- #ag -------- #c -------- #bf #f #ab #d #ab #ab #e #bj #aa #eg #eg #aa #dg #ei #aa #dc #ee #aa #ea #df #aj #g #bj #ag #d #bf #g #ab #d #bb #ab #e #ac #aa #eg #cg #aa #dg #db #aa #dc #ei #aa #eb #ab #i #h #bj #af #e #bf #h #ab #d #ca #ab #e #e #aa #eg #ag #aa #dg #bf #aa #dd #d #aa #eb #ch #i #h #bj #ae #f #bh #i #ab #d #dj #ab #d #eg #aa #ef #eg #aa #dg #aa #aa #dd #aj #aa #ec #f #h #i #ba #ae #f #bg #aj #ab #d #dh #ab #d #dh #aa #ef #cf #aa #df #ef #aa #dd #af #aa #ec #cc ------------ #h -------- #i --------- #ba -------- #ae -------- #g -------- #bh #aa #ab #d #ef #ab #d #ci #aa #ef #ae #aa #df #da #aa #dd #bc #aa #ed #a #h #aj #ba #ae #h #bi #ab #ab #e #d #ab #d #bi #aa #ee #ed #aa #df #bf #aa #dd #ca #aa #ed #cj #g #aj #ba #ad #i #bi #ac #ab #e #aa #ab #d #ai #aa #ee #cc #aa #df #ab #aa #dd #dj #aa #ed #ei #g #aa #ba #ac #aj #bi #ad #ab #e #ah #ab #d #h #aa #ee #ab #aa #de #ei #aa #dd #ej #aa #ee #bh #f #ab #ba #ac #aa #bi #ae #ab #e #bd #ab #c #ef #aa #ed #ea #aa #de #df #aa #de #a #aa #ee #eg ------------ #f -------- #ab --------- #ba -------- #ab -------- #ab -------- #bi #af #ab #e #cj #ab #c #dd #aa #ed #cj #aa #de #cd #aa #de #ac #aa #ef #bf #e #ab #bj #aa #ac #cj #ag #ab #e #ce #ab #c #cb #aa #ed #aj #aa #de #bc #aa #de #bf #aa #ef #ef #e #ac #ba #aa #ac #cj #ah #ab #e #dj #ab #c #ai #aa #ec #di #aa #de #ab #aa #de #ci #aa #eg #bf #d #ac #ba #aa #ad #cj #ai #ab #e #dd #ab #c #f #aa #ec #bh #aa #de #a #aa #de #ec #aa #eg #ef #d #ad #ba #aj #ae #cj #bj #ab #e #dh #ab #b #eb #aa #ec #g #aa #dd #ea #aa #df #h #aa #eh #bf ------------ #c -------- #ad --------- #ba -------- #i -------- #af -------- #cj #ba #ab #e #ea #ab #b #ch #aa #eb #df #aa #dd #db #aa #df #bd #aa #eh #ef #b #ae #ba #i #af #cj #bb #ab #e #ec #ab #b #bc #aa #eb #be #aa #dd #cc #aa #df #dj #aa #ei #bf #b #ae #bj #h #ag #cj #bc #ab #e #ee #ab #b #h #aa #eb #e #aa #dd #be #aa #df #eg #aa #ei #ef #b #af #bj #g #ah #cj #bd #ab #e #eg #ab #a #eb #aa #ea #de #aa #dd #ah #aa #dg #ae #ab #j #bf #a #af #bj #g #ai #cj #be #ab #e #eh #ab #a #cf #aa #ea #be #aa #dd #aa #aa #dg #cd #ab #j #ef ------------ #a -------- #ag --------- #bj -------- #f -------- #bj -------- #cj #bf #ab #e #ei #ab #a #ai #aa #ea #e #aa #dd #e #aa #dg #ed #ab #a #bf ,dec4 #ag #bj #e #bj #cj #bg #ab #e #eh #ab #a #b #aa #ej #de #aa #dd #j #aa #dh #ad #ab #a #ef #a #ag #bj #d #ba #bi #bh #ab #e #eg #ab #j #de #aa #ej #be #aa #dc #ef #aa #dh #ce #ab #b #be #b #ag #ai #c #bb #bi #bi #ab #e #ee #ab #j #bh #aa #ej #f #aa #dc #ec #aa #dh #eg #ab #b #ed #b #ah #ai #b #bb #bi #cj #ab #e #ec #ab #j #aj #aa #di #dg #aa #dc #ea #aa #di #ai #ab #c #bc ------------ #c -------- #ah --------- #ai -------- #a -------- #bc -------- #bi #ca #ab #e #ej #aa #ei #eb #aa #dc #ej #ab #c #eb #d #ai #a ---------------------------------------- ------------------------------------- ,incr4 #b #da ,decr4 #e #ed ,decr4 #i #df ,decr4 #e #ch ,decr4 #j #a ,incr4 #ad #aj ,decr4 #j #h ,incr4 #e #cj ---------------------------------------- ---------------------------------------- --------- ,a ,,table ( ! ,equation ( natural ,days1 %ew+ :at ,"t x ought to be by ! ,clock :5 ! ,sun is on ! ,m]idian4 ---------------------------------------- ---------------------------------------- --------- ,! fir/ aft] ,leap-ye>4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,augu/ ,dif4,septemb],dif4 ,octob],dif4,novemb],dif4,decemb],dif4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #ae #ab #e #dh #aa #ei #ch #aa #di #cc #aa #dc #di #aa #di #cf #ab #d #ai #ai #j #bd #b #ab #c #bg #ab #e #dd #aa #ei #ai #aa #di #ad #aa #dc #di #aa #ej #j #aa #e #ai #ai ,inc4 #bd #c #ab #c #ch #ab #e #ci #aa #ei #j #aa #dh #ee #aa #dc #di #aa #ej #bd #aa #e #ai #ah #a #be #d #ab #c #di #ab #e #cd #aa #eh #da #aa #dh #cg #aa #dc #ej #aa #ej #di #aj #f #bj #ag #b #be #e #ab #c #ei #ab #e #bh #aa #eh #ba #aa #dh #bj #aa #dc #eb #aa #ea #ad ------------ #aj -------- #f --------- #bj -------- #ag -------- #c -------- #bf #f #ab #d #i #ab #e #bb #aa #eh #a #aa #dh #c #aa #dc #ee #aa #ea #dj #aj #g #bj #ag #c #bf #g #ab #d #ai #ab #e #ae #aa #eg #da #aa #dg #df #aa #dc #eh #aa #eb #f #aj #g #bj #ag #d #bg #h #ab #d #bi #ab #e #h #aa #eg #ba #aa #dg #bi #aa #dd #b #aa #eb #cc #i #h #bj #af #e #bg #i #ab #d #ch #ab #e #j #aa #eg #a #aa #dg #ac #aa #dd #g #aa #ec #j #h #i #bj #ae #f #bg #aj #ab #d #df #ab #d #ea #aa #ef #da #aa #df #eh #aa #dd #ac #aa #ec #bg ------------ #h -------- #i --------- #bj -------- #ae -------- #g -------- #bh #aa #ab #d #ed #ab #d #db #aa #ef #ba #aa #df #dc #aa #dd #bj #aa #ec #ce #h #aj #ba #ad #h #bh #ab #ab #e #b #ab #d #cb #aa #ef #j #aa #df #bi #aa #dd #bh #aa #ed #bc #h #aj #ba #ac #i #bi #ac #ab #e #aj #ab #d #bb #aa #ee #ci #aa #df #af #aa #dd #cg #aa #ed #eb #g #aa #ba #ac #aj #bi #ad #ab #e #ag #ab #d #aa #aa #ee #ah #aa #df #c #aa #dd #dg #aa #ee #ba #f #aa #ba #ac #aa #bi #ae #ab #e #bc #ab #d #j #aa #ed #eg #aa #de #ej #aa #dd #eh #aa #ee #ej ------------ #f -------- #ab --------- #ba -------- #ac -------- #ab -------- #cj #af #ab #e #bi #ab #c #dh #aa #ed #cf #aa #de #cg #aa #de #aj #aa #ef #ai #e #ab #ba #ab #ac #cj #ag #ab #e #cd #ab #c #cf #aa #ed #ae #aa #de #be #aa #de #bc #aa #ef #di #e #ac #ba #aa #ac #cj #ah #ab #e #ci #ab #c #bc #aa #ec #ed #aa #de #ad #aa #de #cf #aa #eg #ai #d #ac #ba #aa #ad #cj #ai #ab #e #dc #ab #c #aj #aa #ec #cc #aa #de #c #cc #de #ej #aa #eg #di #d #ad #ba #aj #ad #cj #bj #ab #e #dg #ab #b #ef #aa #ec #ab #aa #dd #ec #aa #df #d #aa #eh #ai ------------ #d -------- #ad --------- #ba -------- #aj -------- #ae -------- #cj #ba #ab #e #ea #ab #b #db #aa #eb #ea #aa #dd #dc #aa #df #ai #aa #eh #di #c #ae #bj #i #af #cj #bb #ab #e #ed #ab #b #ag #aa #eb #ca #aa #dd #cd #aa #df #ce #aa #ei #ai #b #ae #bj #h #ag #cj #bc #ab #e #ef #ab #b #ab #aa #eb #aa #aa #dd #bf #aa #df #eb #aa #ei #di #a #af #ba #g #ah #cj #bd #ab #e #eg #ab #a #ef #aa #ea #ej #aa #dd #ai #aa #dg #aj #ab #j #ai #a #af #ba #f #ai #cj #be #ab #e #eh #ab #a #dj #aa #ea #bi #aa #dd #ac #aa #dg #bi #ab #j #di ------------,dec4-------- #af --------- #bj -------- #f -------- #ai -------- #cj #bf #ab #e #ei #ab #a #bd #aa #ea #i #aa #dd #g #aa #dg #dh #ab #a #ai #a #ag #bj #e #bj #cj #bg #ab #e #eh #ab #a #g #aa #ej #dj #aa #dd #b #aa #dh #h #ab #a #di #a #ag #ai #d #ba #bi #bh #ab #e #eg #ab #a #ej #aa #ej #cj #aa #dc #eh #aa #dh #bi #ab #b #ah #b #ah #ai #c #bb #bi #bi #ab #e #ee #ab #a #cb #aa #ej #aa #aa #dc #ee #aa #dh #ea #ab #b #dg #b #ah #ai #c #bb #bi #cj #ab #e #ec #ab #j #ad #aa #di #eb #aa #dc #eb #aa #di #ac #ab #c #af ------------ #b -------- #ah --------- #ai -------- #b -------- #bc -------- #bi #ca #ab #e #ea #aa #ei #ef #aa #dc #ej #ab #c #de #c #ah #a #bi ---------------------------------------- ------------------------------------- ,incr4 #b #dc ,decr4 #e #eb ,decr4 #i #df ,decr4 #e #dc ,decr4 #j #j ,incr4 #ad #i ,decr4 #j #h ,incr4 #e #bd ---------------------------------------- ---------------------------------------- -------- ,a ,,table ( ! ,equation ( natural ,days1 %ew+ :at ,"t x ought to be by ! ,clock :5 ! ,sun is on ! ,m]idian4 ---------------------------------------- ---------------------------------------- -------- ,! second aft] ,leap-ye>4 ---------------------------------------- ------------------------------------ ,days ,janu>y,dif4,febru>y,dif4 ,m>* ,dif4 ,april ,dif4 ,may ,dif4 ,june ,dif4 ---------------------------------------- -------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------ ,inc4 ,dec4 ,inc4 ,dec4 ,dec4 ,inc4 #a #ab #d #ad #ab #ad #i #ab #ab #db #ab #c #ef #aa #ef #ej #aa #eg #af #bh #g #ac #ah #h #i #b #ab #d #db #ab #ad #af #ab #ab #bj #ab #c #ch #aa #ef #db #aa #eg #be #bh #f #ac #ah #g #aj #c #ab #e #aj #ab #ad #bb #ab #ab #af #ab #c #bj #aa #ef #ce #aa #eg #ce #bg #e #ac #ah #f #aj #d #ab #e #cg #ab #ad #bg #ab #ab #c #ab #c #b #aa #ef #bi #aa #eg #de #bg #e #ad #ah #f #aj #e #ab #f #d #ab #ad #cb #ab #aa #di #ab #b #dd #aa #ef #bc #aa #eg #ee ------------ #bg -------- #d -------- #ad -------- #ah -------- #e -------- #aj #f #ab #f #cj #ab #ad #cf #ab #aa #ce #ab #b #bf #aa #ef #ah #aa #eh #e #bf #c #ae #ag #e #aa #g #ab #f #ef #ab #ad #ci #ab #aa #bj #ab #b #i #aa #ef #bc #aa #eh #af #bf #b #ae #ag #d #aa #h #ab #g #bb #ab #ad #da #ab #aa #e #ab #a #eb #aa #ef #i #aa #eh #bg #be #b #ae #ag #c #aa #i #ab #g #dg #ab #ad #dc #ab #aj #ej #ab #a #ce #aa #ef #f #aa #eh #ch #bd #a #af #ag #c #ab #aj #ab #h #aa #ab #ad #dd #ab #aj #cd #ab #a #ah #aa #ef #c #aa #eh #ej ------------ #bd --------,dec4-------- #af -------- #ag -------- #b -------- #ab #aa #ab #h #ce #ab #ad #dd #ab #aj #ah #ab #a #a #aa #ef #a #aa #ei #b #bc #a #ag #af #b #ab #ab #ab #h #eh #ab #ad #dc #ab #aj #a #ab #j #de #aa #ee #ei #aa #ei #ad #bb #b #ag #af #b #ab #ac #ab #i #bj #ab #ad #da #ab #i #dd #ab #j #bi #aa #ee #eg #aa #ei #bf #bb #c #ag #af #a #ab #ad #ab #i #db #ab #ad #ch #ab #i #bg #ab #j #ac #aa #ee #ef #aa #ei #ch #ba #c #ag #ae ,inc4 #ab #ae #ab #aj #c #ab #ad #ce #ab #i #aj #aa #ei #eh #aa #ee #ef #aa #ei #ej ------------ #ba -------- #d -------- #ah -------- #ae -------- #a -------- #ac #af #ab #aj #bd #ab #ad #ca #ab #h #eb #aa #ei #dc #aa #ee #eg #ab #j #c #bj #d #ah #ad #a #ac #ag #ab #aj #dd #ab #ad #bg #ab #h #cd #aa #ei #bi #aa #ee #eh #ab #j #af #ai #e #ah #ad #b #ac #ah #ab #aa #c #ab #ad #bb #ab #h #af #aa #ei #ae #aa #ef #j #ab #j #bi #ah #f #ah #ad #b #ac #ai #ab #aa #ba #ab #ad #af #ab #g #eh #aa #ei #a #aa #ef #b #ab #j #db #ah #g #ah #ad #c #ac #bj #ab #aa #ci #ab #ad #i #ab #g #dj #aa #eh #dg #aa #ef #e #ab #j #ee ------------ #ag -------- #g -------- #ah -------- #ac -------- #c -------- #ac #ba #ab #aa #ef #ab #ad #b #ab #g #bb #aa #eh #cd #aa #ef #h #ab #a #h #af #h #ah #ab #c #ac #bb #ab #ab #ab #ab #ac #ed #ab #g #d #aa #eh #bb #aa #ef #aa #ab #a #ba #ae #i #ai #ab #d #ac #bc #ab #ab #bg #ab #ac #de #ab #f #de #aa #eh #aj #aa #ef #ae #ab #a #cd #ae #i #ai #ab #e #ac #bd #ab #ab #db #ab #ac #cf #ab #f #bf #aa #eg #eh #aa #ef #bj #ab #a #dg #ad #aj #ai #aa #f #ab #be #ab #ab #ef #ab #ac #bf #ab #f #g #aa #eg #dg #aa #ef #bf #ab #a #ei ------------ #ac -------- #aj -------- #ai -------- #aa -------- #f -------- #ac #bf #ab #ac #i #ab #ac #af #ab #e #dh #aa #eg #cf #aa #ef #cb #ab #b #ab #ab #aa #ai #aj #f #ac #bg #ab #ac #ba #ab #ac #e #ab #e #bi #aa #eg #bf #aa #ef #ch #ab #b #be #aa #aa #ai #aj #g #ab #bh #ab #ac #cb #ab #ab #ed #ab #e #aj #aa #eg #af #aa #ef #de #ab #b #cg #aj #ab #ai #i #g #ab #bi #ab #ac #db #ab #d #ea #aa #eg #g #aa #ef #eb #ab #b #di #aj #ah #i #h #ab #cj #ab #ac #eb #ab #d #cc #aa #ef #eh #aa #eg #j #ab #c #a ------------ #i -------------------- #ah -------- #h -------- #h -------- #aa #ca #ab #ad #a #ab #d #ae #aa #eg #h #h #ah #h ---------------------------------------- ------------------------------------ ,incr4 #i #dg ,incr4 #j #ce ,decr4 #h #bg ,decr4 #f #eh ,decr4 #j #ed ,incr4 #e #de ,decr4 #a #ej ,incr4 #a #ab ---------------------------------------- ---------------------------------------- --------- ,a ,,table ( ! ,equation ( natural ,days1 %ew+ :at ,"t x ought to be by ! ,clock :5 ! ,sun is on ! ,m]idian4 ---------------------------------------- ---------------------------------------- --------- ,! second aft] ,leap-ye>4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,augu/ ,dif4,septemb],dif4 ,octob],dif4,novemb],dif4,decemb],dif4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #ab #ab #e #dh #aa #ei #dc #aa #di #cg #aa #dc #di #aa #di #cj #ab #d #ai #ai #a #bc #b #ab #c #bd #ab #e #dd #aa #ei #bd #aa #di #ah #aa #dc #dh #aa #di #ec #aa #d #ai #ah ,inc4 #bd #c #ab #c #ce #ab #e #dj #aa #ei #e #aa #di #j #aa #dc #di #aa #ej #ag #aa #e #ai #ah #a #be #d #ab #c #df #ab #e #ce #aa #eh #df #aa #dh #db #aa #dc #ej #aa #ej #db #aa #e #bj #ah #b #be #e #ab #c #eg #ab #e #cj #aa #eh #bf #aa #dh #bd #aa #dc #eb #aa #ea #g ------------- #aj -------- #f --------- #bj -------- #ag -------- #c -------- #bf #f #ab #d #g #ab #e #bd #aa #eh #f #aa #dh #g #aa #dc #ee #aa #ea #cc #aj #g #bj #ag #c #bf #g #ab #d #ag #ab #e #ag #aa #eg #df #aa #dg #ej #aa #dc #eh #aa #ea #ei #i #g #bj #ag #d #bf #h #ab #d #bf #ab #e #aj #aa #eg #bf #aa #dg #cc #aa #dd #b #aa #eb #be #i #h #ba #af #e #bg #i #ab #d #ce #ab #e #b #aa #eg #e #aa #dg #ag #aa #dd #g #aa #eb #eb #i #i #bj #af #f #bh #aj #ab #d #dd #ab #d #ec #aa #ef #de #aa #dg #a #aa #dd #ac #aa #ec #bj ------------ #h -------- #i --------- #ba -------- #ae -------- #g -------- #bh #aa #ab #d #eb #ab #d #dd #aa #ef #bd #aa #df #df #aa #dd #bj #aa #ec #dh #h #i #ba #ad #h #bh #ab #ab #e #j #ab #d #ce #aa #ef #c #aa #df #cb #aa #dd #bh #aa #ed #af #h #aj #ba #ad #i #bh #ac #ab #e #h #ab #d #be #aa #ee #db #aa #df #ah #aa #dd #cg #aa #ed #dd #g #aa #bj #ac #i #bi #ad #ab #e #ae #ab #d #ac #aa #ee #bb #aa #df #e #aa #dd #df #aa #ed #ac #f #aa #bj #ac #aj #bi #ae #ab #e #ba #ab #d #c #aa #ee #b #aa #de #eb #aa #dd #ef #aa #ee #db ------------ #f -------- #ab --------- #ba -------- #ac -------- #aa -------- #bi #af #ab #e #bg #ab #c #ea #aa #ed #da #aa #de #ci #aa #de #g #aa #ef #aa #f #ab #ba #ab #ab #cj #ag #ab #e #cc #ab #c #ci #aa #ed #bj #aa #de #bg #aa #de #ai #aa #ef #da #e #ab #ba #aa #ac #cj #ah #ab #e #ch #ab #c #bg #aa #ec #ei #aa #de #af #aa #de #cb #aa #eg #aa #d #ac #bj #aj #ad #cj #ai #ab #e #db #ab #c #ad #aa #ec #ci #aa #de #f #aa #de #df #aa #eg #da #d #ad #ba #aj #ae #cj #bj #ab #e #df #ab #c #j #aa #ec #ah #aa #dd #ef #aa #df #a #aa #eh #aa ------------ #c -------- #ad --------- #ba -------- #aj -------- #ae -------- #cj #ba #ab #e #di #ab #b #df #aa #eb #eg #aa #dd #df #aa #df #af #aa #eh #da #c #ae #bj #i #af #cj #bb #ab #e #eb #ab #b #ca #aa #eb #cg #aa #dd #cg #aa #df #cb #aa #ei #aa #b #ae #ba #h #ag #cj #bc #ab #e #ed #ab #b #af #aa #eb #af #aa #dd #bi #aa #df #di #aa #ei #da #b #ae #ba #g #ah #cj #bd #ab #e #ef #ab #b #a #aa #ea #ee #aa #dd #bb #aa #dg #g #ab #j #aa #b #af #ba #g #ah #cj #be #ab #e #eh #ab #a #de #aa #ea #cd #aa #dd #ae #aa #dg #be #ab #j #da ------------ #a -------- #af --------- #bj -------- #f -------- #ai -------- #cj #bf #ab #e #ei #ab #a #bi #aa #ea #ad #aa #dd #i #aa #dg #dd #ab #a #aa ,dec4 #ag #bj #e #bj #cj #bg #ab #e #eh #ab #a #ab #aa #ej #ed #aa #dd #d #aa #dh #d #ab #a #da #a #ag #bj #e #ba #cj #bh #ab #e #eg #ab #j #ee #aa #ej #cd #aa #dc #ei #aa #dh #be #ab #b #aa #a #ah #ai #d #ba #bi #bi #ab #e #ef #ab #j #cg #aa #ej #ae #aa #dc #ee #aa #dh #df #ab #b #dj #b #ah #ai #c #bb #bi #cj #ab #e #ed #ab #j #ai #aa #di #ef #aa #dc #eb #aa #di #h #ab #c #i ------------ #c -------- #ah --------- #ai -------- #b -------- #bb -------- #bi #ca #ab #e #ea #ab #j #a #aa #dc #ej #ab #c #ch #c #ah #a #bi ---------------------------------------- ------------------------------------- ,incr4 #b #df ,decr4 #e #dg ,decr4 #i #dg ,decr4 #e #dg ,decr4 #j #a ,incr4 #ad #h ,decr4 #j #h ,incr4 #e #ai ---------------------------------------- ---------------------------------------- -------- ,a ,,table ( ! ,equation ( natural ,days1 %ew+ :at ,"t x ought to be by ! ,clock :5 ! ,sun is on ! ,m]idian4 ---------------------------------------- ---------------------------------------- -------- ,! ?ird aft] ,leap-ye>4 ---------------------------------------- ------------------------------------ ,days ,janu>y,dif4,febru>y,dif4 ,m>* ,dif4 ,april ,dif4 ,may ,dif4 ,june ,dif4 ---------------------------------------- -------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------ ,inc4 ,inc4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #d #g #ab #ad #f #ab #ab #dd #ab #d #a #aa #ef #eb #aa #eg #ae #bh #g #ab #ah #h #i #b #ab #d #ce #ab #ad #ac #ab #ab #cb #ab #c #dc #aa #ef #dd #aa #eg #bd #bh #g #ac #ah #g #i #c #ab #e #c #ab #ad #bj #ab #ab #ai #ab #c #be #aa #ef #cg #aa #eg #cc #bg #f #ac #ah #g #i #d #ab #e #cj #ab #ad #bf #ab #ab #f #ab #c #g #aa #ef #cj #aa #eg #db #bg #e #ad #ah #f #aj #e #ab #e #eg #ab #ad #ca #ab #aa #eb #ab #b #di #aa #ef #bd #aa #eg #eb ------------ #bg -------- #d -------- #ad -------- #ah -------- #e -------- #aj #f #ab #f #bd #ab #ad #ce #ab #aa #ch #ab #b #ca #aa #ef #ai #aa #eh #b #bf #c #ad #ah #e #aa #g #ab #f #ej #ab #ad #ch #ab #aa #bd #ab #b #ac #aa #ef #ad #aa #eh #ac #be #b #ae #ah #d #aa #h #ab #g #ae #ab #ad #da #ab #aa #i #ab #a #ee #aa #ef #aj #aa #eh #bd #be #a #af #ag #d #aa #i #ab #g #dj #ab #ad #dc #ab #aj #ec #ab #a #ch #aa #ef #f #aa #eh #ce #be #a #af #ag #c #aa #aj #ab #h #e #ab #ad #dd #ab #aj #cg #ab #a #ba #aa #ef #c #aa #eh #df ------------ #bd --------,dec4-------- #af -------- #af -------- #b -------- #ab #aa #ab #h #bi #ab #ad #dd #ab #aj #ba #ab #a #e #aa #ef #a #aa #eh #eh #bc #a #af #af #b #ab #ab #ab #h #eb #ab #ad #dc #ab #aj #e #ab #j #di #aa #ee #ei #aa #ei #aj #bc #b #ag #af #b #ab #ac #ab #i #ae #ab #ad #da #ab #aj #dh #ab #j #cc #aa #ee #eg #aa #ei #bb #bb #b #ag #af #a #ab #ad #ab #i #cg #ab #ad #ci #ab #i #ca #ab #j #ag #aa #ee #ef #aa #ei #cd #ba #c #ag #ae ,inc4 #ac #ae #ab #i #eh #ab #ad #cf #ab #i #ad #ab #j #b #aa #ee #ef #aa #ei #dg ------------ #ba -------- #d -------- #ag -------- #ae -------- #a -------- #ac #af #ab #aj #ai #ab #ad #cb #ab #h #eg #aa #ei #dg #aa #ee #eg #ab #j #j #bj #d #ah #ae #a #ac #ag #ab #aj #ci #ab #ad #bh #ab #h #ci #aa #ei #cb #aa #ee #eh #ab #j #ac #ai #e #ah #ad #a #ac #ah #ab #aj #eh #ab #ad #bc #ab #h #ba #aa #ei #ah #aa #ee #ei #ab #j #bf #ah #f #ah #ad #b #ac #ai #ab #aa #af #ab #ad #ag #ab #h #c #aa #ei #d #aa #ef #a #ab #j #ci #ah #g #ah #ad #b #ac #bj #ab #aa #cd #ab #ad #aj #ab #g #de #aa #eh #ej #aa #ef #c #ab #j #eb ------------ #ag -------- #g -------- #ah -------- #ac -------- #c -------- #ac #ba #ab #aa #ea #ab #ad #c #ab #g #bg #aa #eh #cg #aa #ef #f #ab #a #e #af #h #ai #ac #d #ab #bb #ab #ab #g #ab #ac #ee #ab #g #h #aa #eh #bd #aa #ef #aj #ab #a #ag #af #h #ai #ab #d #ac #bc #ab #ab #bc #ab #ac #dg #ab #f #di #aa #eh #ab #aa #ef #ad #ab #a #cj #ae #i #ai #ab #e #ac #bd #ab #ab #ch #ab #ac #ch #ab #f #cj #aa #eh #j #aa #ef #ai #ab #a #dc #ad #i #ai #aa #e #ac #be #ab #ab #eb #ab #ac #bi #ab #f #aa #aa #eg #di #aa #ef #bd #ab #a #ef ------------ #ac -------- #aj -------- #ah -------- #aa -------- #f -------- #ac #bf #ab #ac #e #ab #ac #ai #ab #e #ec #aa #eg #ch #aa #ef #cj #ab #b #i #ab #aa #ai #aj #f #ac #bg #ab #ac #ag #ab #ac #h #ab #e #cd #aa #eg #bh #aa #ef #cf #ab #b #bb #aa #ab #ai #aj #g #ab #bh #ab #ac #bh #ab #ab #ef #ab #e #ae #aa #eg #ah #aa #ef #dc #ab #b #cd #aa #ab #ah #i #g #ab #bi #ab #ac #ci #ab #d #eg #aa #eg #i #aa #ef #ej #ab #b #df #aj #ai #i #h #ab #cj #ab #ac #di #ab #d #ch #aa #eg #j #aa #ef #eh #ab #b #eh ------------ #i -------------------- #ai -------- #h -------- #h -------- #ab #ca #ab #ac #eh #ab #d #ai #aa #eg #f #h #ah #i ---------------------------------------- ------------------------------------ ,incr4 #i #ea ,incr4 #j #ch ,decr4 #h #be ,decr4 #g #a ,decr4 #j #ef ,incr4 #e #dc ,decr4 #a #dh ,incr4 #a #aj ---------------------------------------- ---------------------------------------- --------- ,a ,,table ( ! ,equation ( natural ,days1 %ew+ :at ,"t x ought to be by ! ,clock :5 ! ,sun is on ! ,m]idian4 ---------------------------------------- ---------------------------------------- --------- ,! ?ird aft] ,leap-ye>4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,augu/ ,dif4,septemb],dif4 ,octob],dif4,novemb],dif4,decemb],dif4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #aj #ab #e #di #aa #ei #dg #aa #di #db #aa #dc #di #aa #di #be #aa #d #ai #ah #a #bc #b #ab #c #ba #ab #e #de #aa #ei #bh #aa #di #bd #aa #dc #dh #aa #di #dh #aa #d #ai #ah ,inc4 #bd #c #ab #c #cb #ab #e #da #aa #ei #i #aa #di #f #aa #dc #dh #aa #ej #ab #aa #e #ai #ah #a #bd #d #ab #c #dc #ab #e #cf #aa #eh #ej #aa #dh #dh #aa #dc #di #aa #ej #cf #aa #e #ai #ah #b #be #e #ab #c #ed #ab #e #ca #aa #eh #ca #aa #dh #cj #aa #dc #ea #aa #ea #a ------------ #aj -------- #f --------- #bj -------- #ah -------- #b -------- #be #f #ab #d #d #ab #e #be #aa #eh #aa #aa #dh #ab #aa #dc #ec #aa #ea #bf #aj #g #bj #ag #c #bf #g #ab #d #ad #ab #e #ah #aa #eg #ea #aa #dg #ee #aa #dc #ef #aa #eb #eb #aj #g #bj #af #d #bg #h #ab #d #bd #ab #e #aa #aa #eg #ca #aa #dg #ci #aa #dd #j #aa #eb #ai #i #g #bj #af #e #bg #i #ab #d #cc #ab #e #d #aa #eg #aa #aa #dg #bc #aa #dd #e #aa #eb #df #i #h #bj #af #f #bg #aj #ab #d #db #ab #d #ef #aa #ef #ea #aa #dg #g #aa #dd #aa #aa #ec #ac ------------ #h -------- #h --------- #bj -------- #ae -------- #g -------- #bh #aa #ab #d #ej #ab #d #dh #aa #ef #ca #aa #df #eb #aa #dd #ah #aa #ec #da #h #i #ba #ae #h #bh #ab #ab #d #eh #ab #d #cg #aa #ef #aj #aa #df #cg #aa #dd #bf #aa #ed #i #h #aj #ba #ad #h #bh #ac #ab #e #f #ab #d #bg #aa #ee #di #aa #df #bc #aa #dd #cd #aa #ed #cg #g #aj #ba #ad #i #bi #ad #ab #e #ac #ab #d #ag #aa #ee #bh #aa #df #i #aa #dd #dc #aa #ee #f #f #aa #ba #ac #aj #cj #ae #ab #e #ai #ab #d #f #aa #ee #g #aa #de #ef #aa #dd #ec #aa #ee #cf ------------ #f -------- #ab --------- #bj -------- #ab -------- #aa -------- #bi #af #ab #e #be #ab #c #ed #aa #ed #dg #aa #de #dd #aa #de #d #aa #ef #f #f #ab #ba #ab #ab #cj #ag #ab #e #ca #ab #c #db #aa #ed #bf #aa #de #cb #aa #de #af #aa #ef #cf #e #ac #ba #ab #ac #cj #ah #ab #e #cf #ab #c #bi #aa #ed #e #aa #de #bj #aa #de #bi #aa #eg #f #e #ac #ba #aa #ad #bi #ai #ab #e #da #ab #c #af #aa #ec #dd #aa #de #i #aa #de #dc #aa #eg #ce #d #ac #ba #aj #ad #cj #bj #ab #e #de #ab #c #c #aa #ec #bc #aa #dd #ei #aa #de #eg #aa #eh #e ------------ #d -------- #ad --------- #bj -------- #i -------- #ae -------- #cj #ba #ab #e #di #ab #b #di #aa #ec #c #aa #dd #ej #aa #df #ab #aa #eh #cd #c #ae #ba #i #af #cj #bb #ab #e #eb #ac #b #cd #aa #eb #db #aa #dd #da #aa #df #bh #aa #ei #d #c #ae #ba #i #ag #cj #bc #ab #e #ee #ab #b #ai #aa #eb #ba #aa #dd #cb #aa #df #de #aa #ei #cd #b #ae #bj #h #ag #cj #bd #ab #e #eg #ab #b #d #aa #eb #a #aa #dd #bd #aa #dg #b #ab #j #d #a #af #ba #g #ah #cj #be #ab #e #eh #ab #a #dh #aa #ea #dj #aa #dd #ag #aa #dg #bj #ab #j #cd ------------ #a -------- #af --------- #bj -------- #f -------- #ai -------- #cj #bf #ab #e #ei #ab #a #cb #aa #ea #bj #aa #dd #aa #aa #dg #ci #ab #a #d ,dec4 #af #bj #e #bj #cj #bg #ab #e #eh #ab #a #af #aa #ea #j #aa #dd #f #aa #dg #ei #ab #a #cd #a #ag #bj #e #bj #cj #bh #ab #e #eg #ab #j #ei #aa #ej #dj #aa #dd #a #aa #dh #ai #ab #b #d #a #ag #bj #d #ba #bi #bi #ab #e #ef #ab #j #db #aa #ej #bj #aa #dc #eg #aa #dh #dj #ab #b #cc #b #ah #ai #c #bb #bi #cj #ab #e #ed #ab #j #bd #aa #ej #a #aa #dc #ed #aa #di #b #ab #c #b ------------ #b -------- #ah --------- #ai -------- #c -------- #bc -------- #bi #ca #ab #e #eb #ab #j #f #aa #dc #ea #ab #c #ca #c #ai #b #bi ---------------------------------------- ------------------------------------- ,incr4 #b #dh ,decr4 #e #dc ,decr4 #i #df ,decr4 #e #ea ,decr4 #j #a ,incr4 #ad #f ,decr4 #j #g ,incr4 #e #ad ,,*ap4 ,,xv4 ,! ,moon's surface m\nta9\s3 ,h] ,phases describ$3 ,h] pa?1 & ! pa?s ( ,jupit]'s ,moons del9eat$3 ,! proportions ( ! ,diamet]s ( _! ,orbits1 & ^? ( ,saturn's ,moons1 to ea* o!r2 & to ! ,diamet] ( ! ,sun4 ,sid5ote3 ,,pl4 ,,vii4 ,! ,moon's surface m\nta9\s4 #beb4 ,by look+ at ! ,moon ) an ord9>y telescope we p]ceive t h] surface is div]sifi$ ) long tracts ( prodigi\s high m\nta9s & deep cavities4 ,"s ( h] m\nta9s1 by comp>+ _! height ) h] diamet] 7:i* is #bahj miles7 are f\nd to be ?ree times high] ?an ! highe/ hills on our ,e>?4 ,?is rugg$ness ( ! ,moon's surface is ( great use to u1 by reflect+ ! ,sun's light to all sides3 = if ! ,moon 7 smoo? & poli%$ l a look+-glass1 or cov]$ ) wat]1 %e c\ld nev] di/ribute ! ,sun's light all r\nd2 only 9 "s positions %e w\ld %ew u 8 image1 no bigg] ?an a po9t1 b ) su* a lu/re z w\ld be hurtful to our eyes4 ,sid5ote3 ,:y no hills appe> on h] edge4 #bec4 ,! ,moon's surface be+ s unev51 _m h wond]$ :y h] edge appe>s n jagg$1 z well z ! curve b\nd+ ! light & d>k places4 ,b if we consid]1 t :at we call ! edge ( ! ,moon's ,disc is n a s+le l9e set r\nd ) m\nta9s1 9 :i* case x w\ld appe> irregul>ly ind5t$1 b a l>ge ,zone hav+ _m m\nta9s ly+ beh9d "o ano!r f ! obs]v]'s eye1 we %all f9d t ! m\nta9s 9 "s r[s w be opposite to ! vales 9 o!rs2 & s fill up ! inequalities z to make h] appe> q r\nd3 j z :5 "o looks at an orange1 al?\gh x's r\ghness be v disc]nible on ! side next ! eye1 especially if ! ,sun or a ,c&le %9es obliquely on t side1 yet ! l9e t]m9at+ ! visible "p /ill appe>s smoo? & ev54 ,illu/ration3 ,plate ,,vii4 ,j4 ,f]guson del94 ,j4 ,mynde ,sculp4 ,sid5ote3 ,! ,moon has no twilight4 ,fig4 ,i4 #bed4 ,z ! ,sun c only enlight5 t half ( ! ,e>? :i* is at any mom5t turn$ t[>ds him1 & be+ )drawn f ! opposite half leaves x 9 d>kness2 s he likewise do? to ! ,moon3 only ) ?is diff]5ce1 t ! ,e>? be+ surr\nd$ by an ,atmosph]e1 & ! ,moon hav+ none1 we h twilight aft] ! ,sun sets2 b ! ,lun> ,inhabitants h an imm$iate transition f ! brighte/ ,sun-%9e to ! blacke/ d>kness #agg4 ,=1 let tkrsw be ! ,e>?1 & ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 ,h ! ,moon 9 eight diff]5t p>ts ( h] ,orbit4 ,z ! ,e>? turns r\nd its ,axis1 f we/ to ea/1 :5 any place comes to t ! twilight beg9s !re1 & :5 x revolves f !nce to r ! ,sun ,s rises2 :5 ! place comes to s ! ,sun sets1 & :5 x comes to w ! twilight ends4 ,b z ! ,moon turns r\nd h] ,axis1 :i* is only once a mon?1 ! mom5t t any po9t ( h] surface comes to r 7see ! ,moon at ,g7 ! ,sun rises !re )\t any previ\s w>n+ by twilight2 & :5 ! same po9t comes to s ! ,sun sets1 & t po9t goes into d>kness z black z at midnight4 ,sid5ote3 ,! ,moon's ,phases4 #bee4 ,! ,moon be+ an opaque sph]ical body1 7= h] hills take (f no m f h] r\ndness ?an ! inequalities on ! surface ( an orange takes (f f its r\ndness7 we c only see t "p ( ! enlight5$ half ( h] :i* is t[>ds ! ,e>?4 ,& !re=e1 :5 ! ,moon is at ,a1 9 conjunction ) ! ,sun ,s1 h] d>k half is t[>ds ! ,e>?1 & %e disappe>s z at a1 !re be+ no light on t half to r5d] x visible4 ,:5 %e comes to h] fir/ ,octant at ,b1 or has gone an eigh? "p ( h] orbit f h] ,conjunction1 a qu>t] ( h] enlight5$ side is t[>ds ! ,e>?1 & %e appe>s horn$ z at b4 ,:5 %e has gone a qu>t] ( h] orbit f betwe5 ! ,e>? & ,sun to ,c1 %e %ews u "o half ( h] enlight5$ side z at c1 & we say1 %e is a qu>t] old4 ,at ,d %e is 9 h] second ,octant1 & by %ew+ u m ( h] enlight5$ side %e appe>s gibb\s z at d4 ,at ,e h] :ole enlight5$ side is t[>ds ! ,e>?1 & !re=e %e appe>s r\nd z at e1 :5 we say1 x is ,full ,moon4 ,9 h] ?ird ,octant at ,f1 "p ( h] d>k side be+ t[>ds ! ,e>?1 %e aga9 appe>s gibb\s1 & is on ! decrease1 z at f4 ,at ,g we see j "o half ( h] enlight5$ side1 & %e appe>s half decreas$1 or 9 h] ?ird ,qu>t]1 z at g4 ,at ,h we only see a qu>t] ( h] enlight5$ side1 be+ 9 h] f\r? ,octant1 :]e %e appe>s horn$ z at h4 ,& at ,a1 hav+ compleat$ h] c\rse f ! ,sun to ! ,sun aga91 %e disappe>s2 & we say1 x is ,new ,moon4 ,?us 9 go+ f ,a to ,e ! ,moon seems cont9ually to increase2 & 9 go+ f ,e to ,a1 to decrease 9 ! same proportion2 hav+ l ,phases at equal di/ances f ,a or ,e1 b z se5 f ! ,sun ,s1 %e is always ,full4 ,sid5ote3 ,! ,moon's ,disc n always q r\nd :5 full4 #bef4 ,! ,moon appe>s n p]fectly r\nd :5 %e is ,full 9 ! highe/ or l[e/ "p ( h] ,orbit1 because we h n a direct view ( h] enlight5$ side at t "t4 ,:5 ,full 9 ! highe/ "p ( h] orbit1 a small defici5cy appe>s on h] l[] edge2 & ! contr>y :5 ,full 9 ! l[e/ "p ( h] ,orbit4 ,sid5ote3 ,! ,phases ( ! ,e>? & ,moon contr>y4 #beg4 ',tis pla9 by ! ,figure1 t :5 ! ,moon *anges to ! ,e>?1 ! ,e>? appe>s ,full to ! ,moon2 & vice v]s4 ,= :5 ! ,moon is at ,a1 ,new to ! ,e>?1 ! :ole enlight5$ side ( ! ,e>? is t[>ds ! ,moon3 & :5 ! ,moon is at ,e1 ,full to ! ,e>?1 x's d>k side is t[>ds h]4 ,h5ce a ,new ,moon answ]s to a ,full ,e>?1 & a ,full ,moon to a ,new ,e>?4 ,! ,qu>t]s are also rev]s$ to ea* o!r4 ,sid5ote3 ,an agreeable ,ph5om5on4 #beh4 ,betwe5 ! ?ird ,qu>t] & ,*ange1 ! ,moon is frequ5tly visible 9 ! =5oon1 ev5 :5 ! ,sun %9es2 & !n %e af=ds u an opportunity ( see+ a v agreeable appe>ance1 :]ev] we f9d a globul> /one above ! level ( ! eye1 z suppose on ! top ( a gate4 ,=1 if ! ,sun %9es on ! /one1 & we place ourselves s z ! upp] "p ( ! /one may j seem to t\* ! po9t ( ! ,moon's l[]mo/ horn1 we %all !n see ! enlight5$ "p ( ! /one exactly ( ! same %ape ) ! ,moon2 horn$ z %e is1 & incl9+ ! same way to ! ,horizon4 ,! reason is pla92 = ! ,sun enlight5s ! /one ! same way z he does ! ,moon3 & bo? be+ ,globes1 :5 we put ourselves into ! above situation1 ! ,moon & /one h ! same position to our eyes2 & !re=e we mu/ see z mu* ( ! illum9at$ "p ( ! "o z ( ! o!r4 ,sid5ote3 ,! nonagesimal ,degree1 :at4 #bei4 ,! position ( ! ,moon's ,cusps1 or a "r l9e t\*+ ! po9ts ( h] horns1 is v diff]5tly incl9$ to ! ,horizon at diff]5t h\rs ( ! same days ( h] age4 ,sometimes %e /&s1 z x 71 upright on h] l[] horn1 & !n su* a l9e is p]p5dicul> to ! ,horizon3 :5 ?is1 happ5s1 %e is 9 :at ! ,a/ronom]s call ! ,nonagesimal ,degree2 :i* is ! highe/ po9t ( ! ,ecliptic above ! ,horizon at t "t1 & is #ij degrees f bo? sides ( ! ,horizon :]e x is !n cut by ! ,ecliptic4 ,b ?is nev] happ5s :5 ! ,moon is on ! ,m]idian1 except :5 %e is at ! v beg9n+ ( ,canc] or ,capricorn4 ,sid5ote3 ,h[ ! incl9ation ( ! ,ecliptic may be f\nd by ! position ( ! ,moon horns4 ,,pl4 ,,vii4 #bfj4 ,! incl9ation ( t "p ( ! ,ecliptic to ! ,horizon 9 :i* ! ,moon is at any "t :5 horn$1 may be kn[n by ! position ( h] horns2 = a "r l9e t\*+ _! po9ts is p]p5dicul> to ! ,ecliptic4 ,& z ! ,angle t ! ,moon's orbit makes ) ! ,ecliptic c nev] raise h] above1 nor depress h] bel[ ! ,ecliptic1 m ?an two m9utes ( a degree1 z se5 f ! ,sun2 x c h no s5sible effect ^u ! position ( h] horns4 ,!re=e1 if a ,quadrant be held up1 s z "o ( x's edges may seem to t\* ! ,moon's horns1 ! graduat$ side be+ kept t[>ds ! eye1 & z f> f ! eye z x c be conv5i5tly held1 ! arc betwe5 ! ,plumb-l9e & t edge ( ! ,quadrant :i* seems to t\* ! ,moon's horns w %ew ! incl9ation ( t "p ( ! ,ecliptic to ! ,horizon4 ,& ! arc betwe5 ! o!r edge ( ! ,quadrant & ,plumb-l9e w %ew ! incl9ation ( ! ,moon's horns to ! ,horizon at t "t also4 ,sid5ote3 ,fig4 ,i4 ,:y ! ,moon appe>s z big z ! ,sun4 #bfa4 ,! ,moon g5]ally appe>s z l>ge z ! ,sun2 = ! ,angle vk,a1 "u :i* ! ,moon is se5 f ! ,e>?1 is ! same ) ! ,angle ,lk,m1 "u :i* ! ,sun is se5 f x4 ,& !re=e ! ,moon may hide ! ,sun's :ole ,disc f u1 z %e sometimes does 9 sol> ,eclipses4 ,! reason :y %e does n eclipse ! ,sun at e ,*ange %all be expla9$ aft]w>ds4 ,if ! ,moon 7 f>!r f ! ,e>? z at a1 %e c\ld nev] hide ! :ole ( ! ,sun f u2 = !n %e w\ld appe> "u ! ,angle ,nk,o1 eclips+ only t "p ( ! ,sun :i* lies betwe5 ,n & ,o3 7 %e /ill fur!r f ! ,e>?1 z at ,x1 %e w\ld appe> "u ! small ,angle ,tk,w1 l a spot on ! ,sun1 hid+ only ! "p ,,tw f our sight4 ,sid5ote3 ,a pro( ( ! ,moon's turn+ r\nd h] ,axis4 #bfb4 ,! ,moon turns r\nd h] ,axis 9 ! "t t %e goes r\nd h] orbit2 :i* is evid5t f h5ce1 t a spectator at re/1 )\t ! p]iph]y ( ! ,moon's orbit1 w\ld see all h] sides turn$ regul>ly t[>ds him 9 t "t4 ,%e turns r\nd h] ,axis f any ,/> to ! same ,/> aga9 9 #bg days #h h\rs2 f ! ,sun to ! ,sun aga9 9 #bi-a_/b days3 ! =m] is ! l5g? ( h] sid]eal day1 & ! latt] ! l5g? ( h] sol> day4 ,a body mov+ r\nd ! ,sun w\ld h a sol> day 9 e revolution1 )\t turn+ on x's ,axis2 ! same z if x _h kept all ! :ile at re/1 & ! ,sun mov$ r\nd x3 b )\t turn+ r\nd x's ,axis x c\ld nev] h "o sid]eal day1 because x w\ld always keep ! same side t[>ds any giv5 ,/>4 ,sid5ote3 ,h] p]iodical & synodical ,revolution4 #bfc4 ,if ! ,e>? _h no annual motion1 ! ,moon w\ld g r\nd x s z to compleat a ,lunation1 a sid]eal1 & a sol> day1 all 9 ! same "t4 ,b1 because ! ,e>? goes =w>d 9 x's orbit :ile ! ,moon goes r\nd ! ,e>? 9 h] orbit1 ! ,moon mu/ g z mu* m ?an r\nd h] orbit f ,*ange to ,*ange 9 compleat+ a sol> day z ! ,e>? has gone =w>d 9 x's orbit dur+ t "t1 i4 e4 almo/ a twelf? "p ( a ,circle4 ,sid5ote3 ,famili>ly repres5t$4 ,a ,table %ew+ ! times t ! h\r & m9ute h&s ( a wat* are 9 conjunction4 ,a ma*9e = %ew+ ! motions ( ! ,sun & ,moon4 ,,pl4 ,,vii4 #bfd4 ,! ,moon's p]iodical & synodical revolution may be famili>ly repres5t$ by ! motions ( ! h\r & m9ute h&s ( a wat* r\nd x's dial-plate1 :i* is divid$ into #ab equal p>ts or h\rs1 z ! ,ecliptic is divid$ into #ab ,signs1 & ! ye> into #ab mon?s4 ,let u suppose ^! #ab h\rs to be #ab mon?s1 ! h\r h& ! ,sun1 & ! m9ute h& ! ,moon2 !n w ! =m] g r\nd once 9 a ye>1 & ! latt] once 9 a mon?2 b ! ,moon1 or m9ute h& mu/ g m ?an r\nd f any po9t ( ! ,circle :]e x 0 la/ conjo9$ ) ! ,sun1 or h\r h&1 to ov]take x aga93 = ! h\r h& be+ 9 motion1 c nev] be ov]tak5 by ! m9ute h& at t po9t f :i* !y />t$ at _! la/ conjunction4 ,! fir/ column ( ! annex$ ,table %ews ! numb] ( conjunctions :i* ! h\r & m9ute h& make :il/ ! h\r h& goes once r\nd ! dial-plate2 & ! o!r columns %ew ! times :5 ! two h&s meet at e conjunction4 ,?us1 suppose ! two h&s to be 9 conjunction at ,,xii1 z !y always are2 !n1 at ! fir/ foll[+ conjunction x is #e m9utes #bg seconds #af ?irds #ba f\r?s #di-a_/aa fif?s pa/ ,i :]e !y meet2 at ! second conjunction x is #aj m9utes #ed seconds #cb ?irds #dc f\r?s #ch-a_/b fif?s pa/ ,,ii2 & s on4 ,?is1 ?\gh an easy illu/ration ( ! motions ( ! ,sun & ,moon1 is n precise z to ! times ( _! conjunctions2 because1 :ile ! ,sun goes r\nd ! ,ecliptic1 ! ,moon makes #ab-a_/c conjunctions ) him2 b ! m9ute h& ( a wat* or clock makes only #aa conjunctions ) ! h\r h& 9 "o p]iod r\nd ! dial-plate4 ,b if1 in/ead ( ! common :eel-"w at ! back ( ! dial-plate1 ! ,axis ( ! m9ute h& _h a p9ion ( #f leaves turn+ a :eel ( #dj1 & ?is la/ turn+ ! h\r h&1 9 e revolution x makes r\nd ! dial-plate ! m9ute h& w\ld make #ab-a_/c conjunctions ) x2 & s w\ld be a pretty device = %ew+ ! motions ( ! ,sun & ,moon2 especially1 z ! sl[e/ mov+ h& might h a little ,sun fix$ on x's po9t1 & ! quicke/ a little ,moon4 ,besides1 ! plate1 in/ead ( h\rs & qu>t]s1 might h a ,circle ( mon?s1 ) ! #ab ,signs & _! ,degrees2 & if a plate ( #bi-a_/b equal p>ts = ! days ( ! ,moon's age 7 fix$ to ! ,axis ( ! ,sun-h&1 & bel[ x1 s z ! ,sun always kept at ! #a_/b day ( t plate1 ! ,moon-h& w\ld %ew ! ,moon's age ^u t plate = e day po9t$ out by ! ,sun-h& 9 ! ,circle ( mon?s2 & bo? ,sun & ,moon w\ld %ew _! places 9 ! ,ecliptic3 = ! ,sun w\ld g r\nd ! ,ecliptic 9 #cfe ,days & ! ,moon 9 #bg-a_/c days1 :i* is h] p]iodical revolution2 b f ! ,sun to ! ,sun aga91 or f ,*ange to ,*ange1 9 #bi-a_/b days1 :i* is h] synodical revolution4 ------------------------------------ ,conj4 ,h4 ,m4 ,s4 v pts4 ------------------------------------ #a ,i #e #bg #af #ba #di-a_/aa #b ,,ii #aj #ed #cb #dc #ch-b_/aa #c ,,iii #af #ba #di #e #bg-c_/aa #d ,,iiii #ba #di #e #bg #af-d_/aa #e ,v #bg #af #ba #di #e-e_/aa #f ,,vi #cb #dc #ch #aj #ed-f_/aa #g ,,vii #ch #aj #ed #cb #dc-g_/aa #h ,,viii #dc #ch #aj #ed #cb-h_/aa #i ,,ix #di #e #bg #af #ba-i_/aa #aj ,x #ed #cb #dc #ch #aj-aj_/aa #aa ,,xii #j #j #j #j #j ------------------------------------ ,sid5ote3 ,! ,moon's motion ?ro' op5 space describ$4 #bfe4 ,if ! ,e>? _h no annual motion1 ! ,moon's motion r\nd ! ,e>?1 & h] track 9 absolute space1 w\ld be always ! same#eh4 ,b z ! ,e>? & ,moon move r\nd ! ,sun1 ! ,moon's real pa? 9 ! ,heav5s is v diff]5t f h] pa? r\nd ! ,e>?3 ! latt] be+ 9 a progressive ,circle1 & ! =m] 9 a curve ( diff]5t degrees ( concavity1 :i* w\ld always be ! same 9 ! same p>ts ( ! ,heav5s1 if ! ,moon p]=m$ a compleat numb] ( ,lunations 9 a ye>4 ,sid5ote3 ,an idea ( ! ,e>?'s pa? & ! ,moon's4 #bff4 ,let a nail 9 ! end ( ! axle ( a *>iot-:eel repres5t ! ,e>?1 & a p9 9 ! nave ! ,moon2 if ! body ( ! *>iot be propp$ up s z to keep t :eel f t\*+ ! gr\nd1 & ! :eel be !n turn$ r\nd by h&1 ! p9 w describe a ,circle bo? r\nd ! nail & 9 ! space x moves ?r\gh4 ,b if ! props be tak5 away1 ! horses put to1 & ! *>iot driv5 ov] a piece ( gr\nd :i* is circul>ly convex2 ! nail 9 ! axle w describe a circul> curve1 & ! p9 9 ! nave w /ill describe a circle r\nd ! progressive nail 9 ! axle1 b n 9 ! space ?r\gh :i* x moves4 ,9 ?is case1 ! curve describ$ by ! nail w resemble 9 m9iature z mu* ( ! ,e>?'s annual pa? r\nd ! ,sun1 z x describes :il/ ! ,moon goes z (t5 r\nd ! ,e>? z ! p9 does r\nd ! nail3 & ! curve describ$ by ! nail w h "s resemblance ( ! ,moon's pa? dur+ s _m ,lunations4 ,sid5ote3 ,fig4 ,,ii4 ,,pl4 ,,vii4 ,let u n[ suppose t ! ,radius ( ! circul> curve describ$ by ! nail 9 ! axle is to ! ,radius ( ! ,circle :i* ! p9 9 ! nave describes r\nd ! axle z #ccg-a_/b to #a2 :i* is ! proportion ( ! ,radius or ,semidiamet] ( ! ,e>?'s ,orbit to t ( ! ,moon's2 or ( ! circul> curve ,a #a #b #c #d #e #f #g ,b c4 to ! little ,circle a2 & !n1 :il/ ! progressive nail describes ! said curve f ,a to ,e1 ! p9 w g once r\nd ! nail ) reg>d to ! c5t] ( x's pa?1 & 9 do+ s1 w describe ! curve abcde4 ,! =m] w be a true repres5tation ( ! ,e>?'s pa? = "o ,lunation1 & ! latt] ( ! ,moon's = t "t4 ,"h we may set aside ! inequalities ( ! ,moon's ,moon1 & also ! ,e>?'s mov+ r\nd x's common c5t] ( gravity & ! ,moon's3 all :i*1 if !y 7 truly copi$ 9 ?is exp]im5t1 w\ld n s5sibly alt] ! figure ( ! pa?s describ$ by ! nail & p91 ev5 ?\gh !y %\ld rub aga9/ a pla9 upright surface all ! way1 & leave _! tracks visible4 ,& if ! *>iot %\ld be driv5 =w>d on su* a convex piece ( gr\nd1 s z to turn ! :eel sev]al times r\nd1 ! track ( ! p9 9 ! nave w\ld /ill be concave t[>d ! c5t] ( ! circul> curve describ$ by ! p9 9 ! ,axle2 z ! ,moon's pa? is always concave to ! ,sun 9 ! c5t] ( ! ,e>?'s annual ,orbit4 ,sid5ote3 ,proportion ( ! ,moon's ,orbit to ! ,e>?'s4 ,9 ?is ,diagram1 ! ?icke/ curve l9e ,,abcd1 ) ! num]al figures set to x1 repres5ts z mu* ( ! ,e>?'s annual ,orbit z x describes 9 #cb days f we/ to ea/2 ! little ,circles at a1 b1 c1 d1 e %ew ! ,moon's ,orbit 9 due proportion to ! ,e>?'s2 & ! smalle/ curve abcdef repres5ts ! l9e ( ! ,moon's pa? 9 ! ,heav5s = #cb days1 acc\nt$ f any p>ticul> ,new ,moon at a4 ,! ma*9e1 ,fig4 #e? is = del9eat+ ! ,moon's pa?1 & w be describ$1 ) ! re/ ( my ,a/ronomical ma*9]y1 9 ! la/ ,*apt]4 ,! ,sun is suppos$ to be 9 ! c5t] ( ! curve ,a #a #b #c #d #e #f #g ,b c4 & ! small dott$ ,circles ^u x repres5t ! ,moon's ,orbit1 ( :i* ! ,radius is 9 ! same proportion to ! ,e>?'s pa? 9 ?is s*eme1 t ! ,radius ( ! ,moon's ,orbit 9 ! ,heav5s be>s to ! ,radius ( ! ,e>?'s annual pa? r\nd ! ,sun2 t is1 z #bdj1jjj to #ha1jjj1jjj1 or z #a to #ccg-a_/b4 ,sid5ote3 ,fig4 ,,ii4 ,:5 ! ,e>? is at ,a ! ,new ,moon is at a2 & 9 ! sev5 days t ! ,e>? describes ! curve #a #b #c #d #e #f #g1 ! ,moon 9 accompany+ ! ,e>? describes ! curve ab2 & is 9 h] fir/ ,qu>t] at b :5 ! ,e>? is at ,b4 ,z ! ,e>? describes ! curve ,b #h #i #aj #aa #ab #ac #ad ! ,moon describes ! curve bc2 & is opposite to ! ,sun at c1 :5 ! ,e>? is at ,c4 ,:il/ ! ,e>? describes ! curve ,c #ae #af #ag #ah #ai #bj #ba #bb ! ,moon describes ! curve cd2 & is 9 h] ?ird ,qu>t] at d :5 ! ,e>? is at ,d4 ,once m1 :il/ ! ,e>? describes ! curve ,d #bc #bd #be #bf #bg #bh #bi ! ,moon describes ! curve de2 & is aga9 9 conjunction at e ) ! ,sun :5 ! ,e>? is at ,e1 betwe5 ! #bi? & #cj? day ( ! ,moon's age1 acc\nt$ by ! num]al ,figures f ! ,new ,moon at ,a4 ,9 describ+ ! curve abcde1 ! ,moon goes r\nd ! progressive ,e>? z really z if %e _h kept 9 ! dott$ ,circle ,a1 & ! ,e>? cont9u$ immoveable 9 ! c5t] ( t ,circle4 ,sid5ote3 ,! ,moon's motion always concave t[>ds ! ,sun4 ,& ?us we see1 t al?\gh ! ,moon goes r\nd ! ,e>? 9 a ,circle1 ) respect to ! ,e>?'s c5t]1 h] real pa? 9 ! ,heav5s is n v diff]5t 9 appe>ance f ! ,e>?'s pa?4 ,to %ew t ! ,moon's pa? is concave to ! ,sun1 ev5 at ! "t ( ,*ange1 x is c>ri$ on a little f>!r into a second ,lunation1 z to f4 ,sid5ote3 ,h[ h] motion is alt]nately ret>d$ & accel]at$4 #bfg4 ,! ,moon's absolute motion f h] ,*ange to h] fir/ ,qu>t]1 or f a to b1 is s mu* sl[] ?an ! ,e>?'s1 t %e falls #bdj ?\s& miles 7equal to ! ,semidiamet] ( h] ,orbit7 beh9d ! ,e>? at h] fir/ ,qu>t] 9 b1 :5 ! ,e>? is 9 ,b2 t is1 %e falls back a space equal to h] di/ance f ! ,e>?4 ,f t "t h] motion is gradually accel]at$ to h] ,opposition or ,full at c1 & !n %e is come up z f> z ! ,e>?1 hav+ rega9$ :at %e lo/ 9 h] fir/ ,qu>t] f a to b4 ,f ! ,full to ! la/ ,qu>t] at d h] motion cont9ues accel]at$1 s z to be j z f> be=e ! ,e>? at ,d1 z %e 0 beh9d x at h] fir/ ,qu>t] 9 b4 ,b1 f d to e h] motion is ret>d$ s1 t %e loses z mu* ) respect to ! ,e>? z is equal to h] di/ance f x1 or to ! ,semidiamet] ( h] ,orbit2 & by t means %e comes to e1 & is !n 9 conjunction ) ! ,sun z se5 f ! ,e>? at ,e4 ,h5ce we f9d1 t ! ,moon's absolute motion is sl[] ?an ! ,e>?'s f h] ?ird ,qu>t] to h] fir/2 & swift] ?an ! ,e>?'s f h] fir/ ,qu>t] to h] ?ird3 h] pa? be+ less curv$ ?an ! ,e>?'s 9 ! =m] case1 & m 9 ! latt]4 ,yet x is /ill b5t ! same way t[>ds ! ,sun2 = if we imag9e ! concavity ( ! ,e>?'s ,orbit to be measur$ by ! l5g? ( a p]p5dicul> l9e ,cg1 let d[n f ! ,e>?'s place ^u ! /raight l9e bgd at ! ,full ( ! ,moon1 & connect+ ! places ( ! ,e>? at ! end ( ! ,moon's fir/ & ?ird ,qu>t]s1 t l5g? w be ab\t #fdj ?\s& miles2 & ! ,moon :5 ,new only approa*+ ne>] to ! ,sun by #bdj ?\s& miles ?an ! ,e>? is1 ! l5g? ( ! p]p5dicul> let d[n f h] place at t "t ^u ! same /raight l9e1 & :i* %ews ! concavity ( t "p ( h] pa?1 w be ab\t #djj ?\s& miles4 ,sid5ote3 ,a difficulty remov$4 ,,pl4 ,,vii4 #bfh4 ,! ,moon's pa? be+ concave to ! ,sun ?r\gh\t1 demon/rates t h] gravity t[>ds ! ,sun1 at h] conjunction1 exce$s h] gravity t[>ds ! ,e>?4 ,& if we consid] t ! quantity ( matt] 9 ! ,sun is almo/ #bcj ?\s& times z great z ! quantity ( matt] 9 ! ,e>?1 & t ! attraction ( ea* body dim9i%es z ! squ>e ( ! di/ance f x increases1 we %all soon f9d1 t ! po9t ( equal attraction :]e ^! two p[]s w\ld be equally /rong1 is ab\t #gj ?\s& miles ne>] ! ,e>? ?an ! ,moon is at h] ,*ange4 ,x may n[ appe> surpris+ t ! ,moon does n ab&on ! ,e>? :5 %e is betwe5 x & ! ,sun1 because %e is consid]ably m attract$ by ! ,sun ?an by ! ,e>? at t "t4 ,b ?is difficulty vani%es :5 we consid]1 t ! ,moon is s ne> ! ,e>? 9 proportion to ! ,e>?'s di/ance f ! ,sun1 t %e is b v little m attract$ by ! ,sun at t "t ?an ! ,e>? is2 & :il/ ! ,e>?'s attraction is great] ^u ! ,moon ?an ! diff]5ce ( ! ,sun's attraction ^u ! ,e>? & h] 7& t x is always mu* great] is demon/rable7 !re is no dang] ( ! ,moon's leav+ ! ,e>?2 = if %e %\ld fall t[>ds ! ,sun1 ! ,e>? w\ld foll[ h] almo/ ) equal spe$4 ,! absolute attraction ( ! ,e>? ^u a drop ( fall+ ra9 is mu* great] ?an ! absolute attraction ( ! p>ticles ( t drop ^u ea* o!r1 or ( x's c5t] ^u all p>ts ( x's circumf]5ce2 b !n ! side ( ! drop next ! ,e>? is attract$ ) s v little m =ce ?an x's c5t]1 or ev5 x's opposite side2 t ! attraction ( ! c5t] ( ! drop ^u x's side next ! ,e>? is mu* great] ?an ! diff]5ce ( =ce by :i* ! ,e>? attracts x's ne>] surface & c5t]3 on :i* acc\nt ! drop pres]ves x's r\nd figure1 & might be project$ ab\t ! ,e>? by a /rong circulat+ w9d s z to be kept f fall+ to ! ,e>?4 ,x is mu* ! same ) ! ,e>? & ,moon 9 respect to ! ,sun2 = if we %\ld suppose ! ,moon's ,orbit to be fill$ ) a fluid ,globe1 ( :i* all ! p>ts w\ld be attract$ t[>ds ! ,e>? 9 x's c5t]1 b ! :ole ( x mu* m attract$ by ! ,sun2 "o "p ( x c\ld n fall to ! ,sun )\t ! o!r1 & a suffici5t projectile =ce w\ld c>ry ! :ole fluid ,globe r\nd ! ,sun4 ,a %ip1 at ! di/ance ( ! ,moon1 sail+ r\nd ! ,e>? on ! surface ( ! fluid ,globe1 c\ld no m be tak5 away by ! ,sun :5 x is on ! side next him1 ?an ! ,e>? c\ld be tak5 away f x :5 x is on ! opposite side2 :i* c\ld nev] happ5 unless ! ,e>?'s projectile motion 7 /opt2 & if x 7 /opt1 ! ,%ip ) ! :ole fluid ,globe1 ,e>? & all toge!r1 w\ld z naturally fall to ! ,sun z a drop ( ra9 9 calm air falls to ! ,e>?4 ,h5ce we may see1 t ! ,e>? is 9 no m dang] ( be+ left by ! ,moon at ! ,*ange1 ?an ! ,moon is ( be+ left by ! ,e>? at ! ,full3 ! diamet] ( ! ,moon's ,orbit be+ s small 9 comp>ison ( ! ,sun's di/ance1 t ! ,moon is b little m or less attract$ ?an ! ,e>? at any "t4 ,& z ! ,moon's projectile =ce keeps h] f fall+ to ! ,e>?1 s ! ,e>?'s projectile =ce keeps x f fall+ to ! ,sun4 ,sid5ote3 ,fig4 ,,iii4 #bfi4 ,all ! curves :i* ,jupit]'s ,satellites describe1 are diff]5t f ! pa? describ$ by our ,moon1 al?\gh ^! ,satellites g r\nd ,jupit]1 z ! ,moon goes r\nd ! ,e>?4 ,let ,,abcde c4 be z mu* ( ,jupit]'s ,orbit z he describes 9 #ah days f ,a to ,t2 & ! curves a1 b1 c1 d w be ! pa?s ( 8 f\r ,moons go+ r\nd him 9 8 progressive motion4 ,sid5ote3 ,! absolute ,pa? ( ,jupit] & 8 ,satellites del9eat$4 ,fig4 ,,iii4 ,n[ let u suppose all ^! ,moons to set out f a conjunction ) ! ,sun1 z se5 f ,jupit]4 ,:5 ,jupit] is at ,a 8 fir/ or ne>e/ ,moon w be at a1 8 second at b1 8 ?ird at c1 & 8 f\r? at d4 ,at ! end ( #bd t]re/rial h\rs aft] ?is conjunction1 ,jupit] has mov$ to ,b1 8 fir/ ,moon or ,satellite has describ$ ! curve a#a1 8 second ! curve b#a1 8 ?ird c#a1 & 8 f\r? d#a4 ,! next day :5 ,jupit] is at ,c1 8 fir/ ,satellite has describ$ ! curve a#b f its conjunction1 8 second ! curve b#b1 8 ?ird ! curve c#b1 & 8 f\r? ! curve d#b1 & s on4 ,! num]al ,figures "u ! capital lett]s %ew ,jupit]'s place 9 8 pa? e day = #ah days1 acc\nt$ f ,a to ,t2 & ! l ,figures set to ! pa?s ( 8 ,satellites1 %ew :]e !y are at ! l times4 ,! fir/ ,satellite1 almo/ "u ,c1 is /ation>y at z se5 f ! ,sun2 & retrograde f to #b3 at #b x appe>s /ation>y aga91 & !nce x moves =w>d until x has pa/ #c1 be+ twice /ation>y1 & once retrograde betwe5 #c & #d4 ,! pa? ( ?is ,satellite int]sects itself e #db-a_/b h\rs ( our "t1 mak+ su* loops z 9 ! ,diagram at #b4 #c4 #e4 #g4 #i4 #aj4 #ab4 #ad4 #af4 #ah1 a little aft] e ,conjunction4 ,! second ,satellite b1 mov+ sl[]1 b>ely crosses x's pa? e #c days #ac h\rs2 z at #d4 #g4 #aa4 #ad4 #ah1 mak+ only five loops & z _m conjunctions 9 ! "t t ! fir/ makes t54 ,! ?ird ,satellite c mov+ /ill sl[]1 & hav+ describ$ ! curve c #a4 #b4 #c4 #d4 #e4 #f4 #g1 comes to an ,angle at #g 9 conjunction ) ! ,sun at ! end ( #g days #d h\rs2 & s goes on to describe su* ano!r curve #g4 #h4 #i4 #aj4 #aa4 #ab4 #ac4 #ad1 & is at #ad 9 x's next conjunction4 ,! f\r? ,satellite d is always progressive1 mak+ nei!r loops nor angles 9 ! ,heav5s2 b comes to x's next conjunction at e betwe5 ! num]al figures #af & #ag1 or 9 #af days #ah h\rs4 ,9 ord] to h a tol]ably good figure ( ! pa?s ( ^! ,satellites1 ,i took ! foll[+ me?od4 ,sid5ote3 ,fig4 ,,iv4 ,,pl4 ,,vii4 ,h[ to del9eate ! pa?s ( ,jupit]'s ,moons4 ,& ,saturn's4 ,hav+ drawn _! ,orbits on a ,c>d1 9 proportion to _! relative di/ances f ,jupit]1 ,i measur$ ! radius ( ! ,orbit ( ! f\r? ,satellite1 :i* 0 an in* & a t5? "p2 !n multipli$ ?is by #dbd = ! radius ( ,jupit]'s ,orbit1 because ,jupit] is #dbd times z f> f ! ,sun's c5t] z 8 f\r? ,satellite is f 8 c5t]2 & ! product !nce aris+ 0 #dff-d_/aj in*es4 ,!n tak+ a small cord ( ?is l5g?1 & fix+ "o end ( x to ! floor ( a long room by a nail1 ) a black lead p5cil at ! o!r end ,i drew ! curve ,,abcd c4 & set (f a degree & an half !reon1 f ,a to ,t2 because ,jupit] moves only s mu*1 :il/ 8 out]mo/ ,satellite goes once r\nd him1 & some:at m2 s t ?is small portion ( s l>ge a circle diff]s b v little f a /raight l9e4 ,?is done1 ,i divid$ ! space ,,at into #ah equal p>ts1 z ,,ab1 ,,bc1 c4 = ! daily progress ( ,jupit]2 & ea* "p into #bd = 8 h\rly progress4 ,! ,orbit ( ea* ,satellite 0 also divid$ into z _m equal p>ts z ! ,satellite is h\rs 9 f9i%+ x's synodical p]iod r\nd ,jupit]4 ,!n draw+ a "r l9e ?r\gh ! c5t] ( ! ,c>d1 z a diamet] to all ! #d ,orbits ^u x1 ,i put ! c>d ^u ! l9e ( ,jupit]'s motion1 & transf]r$ x to e hor>y division !reon1 keep+ always ! said diamet]-l9e on ! l9e ( ,jupit]'s pa?2 & runn+ a p9 ?r\gh ea* hor>y division 9 ! ,orbit ( ea* ,satellite z ! c>d 0 gradually transf]r$ along ! ,l9e ,,abcd etc4 ( ,jupit]'s motion1 ,i m>k$ po9ts = e h\r ?r\gh ! ,c>d = ! ,curves describ$ by ! ,satellites z ! prim>y planet 9 ! c5t] ( ! ,c>d 0 c>ri$ =w>d on ! l9e3 & s f9i%$ ! ,figure1 by draw+ ! l9es ( ea* ,satellite's motion1 ?r\gh ^? 7almo/ innum]able7 po9ts3 by :i* means1 ?is is p]haps z true a ,figure ( ! pa?s ( ^! ,satellites z c be desir$4 ,& 9 ! same mann] might ^? = ,saturn's ,satellites be del9eat$4 ,sid5ote3 ,! gr& ,p]iod ( ,jupit]'s ,moons4 #bgj4 ,x appe>s by ! s*eme1 t ! ?ree fir/ ,satellites come almo/ into ! same l9e or position e sev5? day2 ! fir/ be+ only a little beh9d ) ! second1 & ! second beh9d ) ! ?ird4 ,b ! p]iod ( ! f\r? ,satellite is s incomm5surate to ! p]iods ( ! o!r ?ree1 t x _c be guess$ at by ! diagram :5 x w\ld fall aga9 into a l9e ( conjunction ) !m1 betwe5 ,jupit] & ! ,sun4 ,& no wond]2 = suppos+ !m all to h be5 once 9 conjunction1 x w require #c1jhg1jdc1dic1bfj ye>s to br+ !m 9 a conjunction aga93 ,see #gc4 ,sid5ote3 ,fig4 ,,iv4 ,! proportions ( ! ,orbits ( ! ,planets & ,satellites4 #bga4 ,9 ,fig4 #d? we h ! proportions ( ! ,orbits ( ,saturn's five ,satellites1 & ( ,jupit]'s f\r1 to "o ano!r1 to our ,moon's ,orbit1 & to ! ,disc ( ! ,sun4 ,s is ! ,sun2 ,m m ! ,moon's ,orbit 7! ,e>? suppos$ to be at ,e27 ,j ,jupit]2 #a4 #b4 #c4 #d ! ,orbits ( 8 f\r ,moons or ,satellites2 ,sat ,saturn2 & #a4 #b4 #c4 #d4 #e ! ,orbits ( 8 five ,moons4 ,h5ce x appe>s1 t ! ,sun w\ld mu* m ?an fill ! :ole ,orbit ( ! ,moon2 = ! ,sun's diamet] is #gfc1jjj miles1 & ! diamet] ( ! ,moon's ,orbit only #dhj1jjj4 ,9 proportion to all ^! ,orbits ( ! ,satellites1 ! ,radius ( ,saturn's annual ,orbit w\ld be #ba-a_/d y>ds1 ( ,jupit]'s orbit #aa-b_/c1 & ( ! ,e>?'s #b-a_/d1 tak+ !m 9 r\nd numb]s4 #bgb4 ,! annex$ table %ews at once :at proportion ! ,orbits1 ,revolutions1 & ,velocities1 ( all ! ,satellites be> to ^? ( _! prim>y ,planets1 & :at sort ( curves ! sev]al ,satellites describe4 ,=1 ^? ,satellites ^: velocities r\nd _! prim>ies are great] ?an ! velocities ( _! prim>ies 9 op5 space1 make loops at _! conjunctions #bfi2 appe>+ retrograde z se5 f ! ,sun :il/ !y describe ! inf]ior p>ts ( _! ,orbits1 & direct :il/ !y describe ! sup]ior4 ,?is is ! case ) ,jupit]'s fir/ & second ,satellites1 & ) ,saturn's fir/4 ,b ^? ,satellites ^: velocities are less ?an ! velocities ( _! prim>y planets move direct 9 _! :ole circumvolutions2 :i* is ! case ( ! ?ird & f\r? ,satellites ( ,jupit]1 & ( ! second1 ?ird1 f\r?1 & fif? ,satellites ( ,saturn1 z well z ( our ,satellite ! ,moon3 ,b ! ,moon is ! only ,satellite ^: motion is always concave to ! ,sun4 ,!re is a table ( ?is sort 9 ,de la ,caile's ,a/ronomy1 b x is v diff]5t f ! above1 :i* ,i h comput$ f our ,engli% acc\nts ( ! p]iods & di/ances ( ^! ,planets & ,satellites4 ---------------------------------------- --------------------------- ,proportion ( ,proportion ( ,proportion ( ! ,radius ( ! ,"t ( ! ,velocity ( ,! ! ,planet's ! ,planet's ea* ,satellite ,satellites ,orbit to ! ,revolution to to ! ,velocity ,radius ( ! ! ,revolution ( its prim>y ,orbit ( ea* ( ea* ,planet4 ,satellite4 ,satellite4 ---------------------------------------- --------------------------- ( ,saturn #a ,z #ecbb to #a ,z #egch to #a ,z #egch to #ecbb #b #daee #a #ciab #a #ciab #daee #c #bied #a #bcdg #a #bcdg #bied #d #abie #a #fgd #a #fgd #abie #e #dcb #a #acd #a #acd #dcb ---------------------------------------- --------------------------- ( ,jupit] #a ,z #ahea to #a ,z #bdde to #a ,z #bdde to #ahea #b #aafe #a #abai #a #abai #aafe #c #gca #a #fjd #a #fjd #gca #d #dbd #a #beh #a #beh #dbd ---------------------------------------- --------------------------- ,! ,moon ,z #ccg-a_/b to #a ,z #ab-a_/c to #a ,z #ab-a_/c to #ccg-a_/b ---------------------------------------- --------------------------- ,,*ap4 ,,xvi4 ,! ,ph5om5a ( ! ,h>ve/-,moon expla9$ by a common ,globe3 ,! ye>s 9 :i* ! ,h>ve/-,moons are lea/ & mo/ b5eficial f #agea1 to #ahfa4 ,! long duration ( ,moon-light at ! ,poles 9 w9t]4 ,sid5ote3 ,no ,h>ve/-,moon at ! ,equator4 #bgc4 ,x is g5]ally believ$ t ! ,moon rises ab\t #dh m9utes lat] e day ?an on ! prec$+2 b ?is is true only ) reg>d to places on ! ,equator4 ,9 places ( consid]able ,latitude !re is a rem>kable diff]5ce1 especially 9 ! h>ve/ "t2 ) :i* ,f>m]s 7 bett] acqua9t$ ?an ,a/ronom]s till ( late2 & gratefully ascrib$ ! e>ly ris+ ( ! ,full ,moon at t "t ( ! ye> to ! goodness ( ,god1 n d\bt+ t he _h ord]$ x s on purpose to give !m an imm$iate supply ( moon-light aft] sun-set = _! great] conv5i5cy 9 reap+ ! fruits ( ! e>?4 ,sid5ote3 ,b rem>kable accord+ to ! di/ance ( places f x4 ,9 ?is in/ance ( ! h>ve/-moon1 z 9 _m o!rs discov]able by ,a/ronomy1 ! wisdom & b5efic5ce ( ! ,deity is conspicu\s1 :o really ord]$ ! c\rse ( ! ,moon s1 z to be/[ m or less light on all p>ts ( ! e>? z _! sev]al circum/ances & seasons r5d] x m or less s]viceable4 ,ab\t ! ,equator1 :]e !re is no v>iety ( seasons1 & ! wea!r *anges seldom1 & at /at$ times1 ,moon-light is n necess>y = ga!r+ 9 ! produce ( ! gr\nd2 & !re ! moon rises ab\t #dh m9utes lat] e day or night ?an on ! =m]4 ,at consid]able di/ances f ! ,equator1 :]e ! wea!r & seasons are m unc]ta91 ! autumnal ,full ,moons rise v soon aft] sun-set = sev]al ev5+s toge!r4 ,at ! pol> circles1 :]e ! mild season is ( v %ort duration1 ! autumnal ,full ,moon rises at ,sun-set f ! fir/ to ! ?ird qu>t]4 ,& at ! ,poles1 :]e ! ,sun is = half a ye> abs5t1 ! w9t] ,full moons %9e con/antly )\t sett+ f ! fir/ to ! ?ird qu>t]4 ,sid5ote3 ,! reason ( ?is4 ,x is soon said t all ^! ,ph5om5a are ow+ to ! diff]5t ,angles made by ! ,horizon & diff]5t p>ts ( ! ,moon's orbit2 & t ! ,moon c be full b once or twice 9 a ye> 9 ^? p>ts ( h] orbit :i* rise ) ! lea/ angles4 ,b to expla9 ?is subject intelligibly we mu/ dwell mu* long] ^u x4 ,sid5ote3 ,,plate ,,iii4 #bgd4 ,! #eiplane ( ! ,equ9octial is p]p5dicul> to ! ,e>?'s ,axis3 & !re=e1 z ! ,e>? turns r\nd its ,axis1 all p>ts ( ! ,equ9octial make equal ,angles ) ! ,horizon bo? at ris+ & sett+2 s t equal portions ( x always rise or set 9 equal times4 ,consequ5tly1 if ! ,moon's motion 7 equable1 & 9 ! ,equ9octial1 at ! rate ( #ab degrees f ! ,sun e day1 z x is 9 h] orbit1 %e w\ld rise & set #dh m9utes lat] e day ?an on ! prec$+3 = #ab degrees ( ! ,equ9octial rise or set 9 #dh m9utes ( "t 9 all ,latitudes4 ,sid5ote3 ,fig4 ,,iii4 #bge4 ,b ! ,moon's motion is s ne>ly 9 ! ,ecliptic t we may consid] h] at pres5t z mov+ 9 x4 ,n[ ! diff]5t p>ts ( ! ,ecliptic1 on acc\nt ( its obliquity to ! ,e>?'s ,axis1 make v diff]5t ,angles ) ! ,horizon z !y rise or set4 ,^? p>ts or ,signs :i* rise ) ! smalle/ ,angles set ) ! greate/1 & vice v]s4 ,9 equal times1 :5ev] ?is ,angle is lea/1 a great] portion ( ! ,ecliptic rises ?an :5 ! ,angle is l>g]2 z may be se5 by elevat+ ! pole ( a ,globe to any consid]able ,latitude1 & !n turn+ x r\nd its ,axis 9 ! ,horizon4 ,consequ5tly1 :5 ! ,moon is 9 ^? ,signs :i* rise or set ) ! smalle/ ,angles1 %e rises or sets ) ! lea/ diff]5ce ( "t2 & ) ! greate/ diff]5ce 9 ^? ,signs :i* rise or set ) ! greate/ ,angles4 ,sid5ote3 ,fig4 ,,iii4 ,! diff]5t ,angles made by ! ,ecliptic & ,horizon4 ,b1 because all :o read ?is ,treatise may n be provid$ ) ,globes1 ?\gh 9 ?is case x is requisite to "k h[ to use !m1 we %all sub/itute ! ,figure ( a ,globe2 9 :i* ,,fup is ! ,axis1 ,,tr ! ,tropic ( ,canc]1 ,,lt ! ,tropic ( ,capricorn1 ,,eu ! ,ecliptic t\*+ bo? ! ,tropics :i* are #dg degrees f ea* o!r1 & ,,ab ! ,horizon4 ,! ,equator1 be+ 9 ! middle betwe5 ! ,tropics1 is cut by ! ,ecliptic 9 two opposite po9ts1 :i* are ! beg9n+s ( ,aries & ,libra4 ,k is ! ,h\r circle ) its ,index1 ,f ! ,nor? pole ( ! ,globe elevat$ to ! ,latitude ( ,london#fj1 namely #ea-a_/b degrees above ! ,horizon2 & ,p ! ,s\? ,pole depress$ z mu* bel[ x4 ,because ( ! oblique position ( ! ,sph]e 9 ?is ,latitude1 ! ,ecliptic has ! high elevation ,n above ! ,horizon1 mak+ ! ,angle ,,nu ( #fb degrees ) x :5 ,canc] is on ! ,m]idian1 at :i* "t ,libra rises 9 ! ,ea/4 ,b let ! ,globe be turn$ half r\nd its ,axis1 till ,capricorn comes to ! ,m]idian & ,aries rises 9 ! ,ea/1 & !n ! ,ecliptic w h ! l[ elevation ,,nl above ! ,horizon mak+ only an ,angle ,,nul ( #ae degrees1 ) x2 :i* is #dg degrees less ?an ! =m] ,angle1 equal to ! di/ance betwe5 ! ,tropics4 ,sid5ote3 ,lea/ & greate/1 :54 #bgf4 ,! smalle/ ,angle made by ! ,ecliptic & ,horizon is :5 ,aries rises1 at :i* "t ,libra sets3 ! greate/ :5 ,libra rises1 at :i* "t ,aries sets4 ,f ! ris+ ( ,aries to ! ris+ ( ,libra 7:i* is twelve #fa,sid]eal h\rs7 ! angle increases2 & f ! ris+ ( ,libra to ! ris+ ( ,aries x decreases 9 ! same proportion4 ,by ?is article & ! prec$+1 x appe>s t ! ,ecliptic rises fa/e/ ab\t ,aries & sl[e/ ab\t ,libra4 ---------------------------------- ,signs ,ris+ ,sett+ ,diff4 ,diff4 ,days ----------------- ,degrees ,h4 ,m4 ,h4 ,m4 ---------------------------------- #a #ac #a #e #j #ej #b #bf #a #aj #j #dc #c #aj #a #ad #j #cg #d #bc #a #ag #j #cb #e #f #a #af #j #bh #f #ai #a #ae #j #bd #g #b #a #ae #j #bj #h #ae #a #ae #j #ah #i #bh #a #ae #j #ag #aj #ab #a #ae #j #bb #aa #be #a #ad #j #cj #ab #h #a #ac #j #ci #ac #ba #a #aj #j #dg #ad #d #a #d #j #ef #ae #ag #j #df #a #e #af #a #j #dj #a #h #ag #ad #j #ce #a #ab #ah #bg #j #cj #a #ae #ai #aj #j #be #a #af #bj #bc #j #bj #a #ag #ba #g #j #ag #a #af #bb #bj #j #ag #a #ae #bc #c #j #bj #a #ae #bd #af #j #bd #a #ae #be #bi #j #cj #a #ad #bf #ac #j #dj #a #ac #bg #bf #j #ej #a #g #bh #i #a #j #a #eh ---------------------------------- ,sid5ote3 ,quantity ( ?is ,angle at ,london4 #bgg4 ,on ! ,p>allel ( ,london1 z mu* ( ! ,ecliptic rises ab\t ,pisces & ,aries 9 two h\rs z ! ,moon goes ?r\gh 9 six days3 & !re=e :il/ ! ,moon is 9 ^! ,signs1 %e diff]s b two h\rs 9 ris+ = six days toge!r2 t is1 #bj m9utes lat] e day or night ?an on ! prec$+4 ,b 9 f\rte5 days aft]w>ds1 ! ,moon comes to ,virgo & ,libra2 :i* are ! opposite ,signs to ,pisces & ,aries2 & !n %e diff]s almo/ f\r times z mu* 9 ris+2 namely1 "o h\r & ab\t fifte5 m9utes lat] e day or night ?an ! =m]1 :il/ %e is 9 ^! ,signs2 = by #bge _! ris+ ,angle is at lea/ f\r times z great z t ( ,pisces & ,aries4 ,! annex$ ,table %ews ! daily mean diff]5ce ( ! ,moon's ris+ & sett+ on ! ,p>allel ( ,london1 = #bh days2 9 :i* "t ! ,moon f9i%es h] p]iod r\nd ! ,ecliptic1 & gets #i degrees into ! same ,sign f ! beg9n+ ( :i* %e set out4 ,s x appe>s by ! ,table1 t :ile ! ,moon is 9 & %e rises an h\r & a qu>t] lat] e day ?an ! =m]2 & diff]s only #bd1 #bj1 #ah or #ag m9utes 9 sett+4 ,b1 :5 %e comes to & 1 %e is only #bj or #ag m9utes lat] ( ris+2 & an h\r & a qu>t] lat] 9 sett+4 #bgh4 ,all ^! ?+s w be made pla9 by putt+ small pat*es on ! ,ecliptic ( a ,globe1 z f> f "o ano!r z ! ,moon moves f any ,po9t ( ! cele/ial ,ecliptic 9 #bd h\rs1 :i* at a mean rate is #fbac-a_/f degrees2 & !n 9 turn+ ! globe r\nd1 obs]ve ! ris+ & sett+ ( ! pat*es 9 ! ,horizon1 z ! ,index po9ts out ! diff]5t times 9 ! h\r circle4 ,a few ( ^! pat*es are repres5t$ by dots at #j #a #b #c c4 on ! ,ecliptic1 :i* has ! position ,,lui :5 ,aries rises 9 ! ,ea/2 & by ! dots #j #a #b #c1 c4 :5 ,libra rises 9 ! ,ea/1 at :i* "t ! ,ecliptic has ! position ,,eu3 mak+ an angle ( #fb degrees ) ! ,horizon 9 ! latt] case1 & an angle ( no m ?an #ae degrees ) x 9 ! =m]2 suppos+ ! ,globe rectifi$ to ! ,latitude ( ,london4 #bgi4 ,hav+ rectifi$ ! ,globe1 turn x until ! pat* at #j1 ab\t ! beg9n+ ( ,pisces on ! half ,,lui ( ! ,ecliptic1 comes to ! ,ea/]n side ( ! ,horizon2 & !n keep+ ! ball /eady1 set ! h\r ,index to ,,xii1 because t h\r may p]haps be m easily remembr$ ?an any o!r4 ,!n1 turn ! ,globe r\nd we/w>d1 & 9 t "t1 suppose ! pat* #j to h mov$ !nce to #a1 #ac-a_/f degrees1 :il/ ! ,e>? turns once r\nd its ,axis1 & y w see t #a rises only ab\t #bj m9utes lat] ?an #j did on ! day be=e4 ,turn ! ,globe r\nd aga91 & 9 t "t suppose ! same pat* to h mov$ f #a to #b2 & x w rise only #bj m9utes lat] by ! h\r-index ?an x did at #a on ! day or turn be=e4 ,at ! end ( ! next turn1 suppose ! pat* to h gone f #b to #c at ,u1 & x w rise #bj m9utes lat] ?an x did at #b4 ,& s on = six turns1 9 :i* "t !re w sc>ce be two h\rs diff]5ce3 ,nor w\ld !re h be5 s mu* if ! #f degrees ( ! ,sun's motion 9 t "t _h be5 all[$ =4 ,at ! fir/ ,turn ! pat* rises s\? ( ! ,ea/1 at ! middle ,turn due ,ea/1 & at ! la/ ,turn nor? ( ! ,ea/4 ,b ^! pat*es w be #i h\rs ( sett+ on ! we/]n side ( ! ,horizon1 :i* %ews t ! ,moon w be s mu* lat] ( sett+ 9 t week 9 :i* %e moves ?r\gh ^! two ,signs4 ,! cause ( ?is diff]5ce is evid5t2 = ,pisces & ,aries make only an ,angle ( #ae degrees ) ! ,horizon :5 !y rise2 b !y make an ,angle ( #fb degrees ) x :5 !y set #bge4 ,z ! ,signs ,taurus1 ,gem9i1 ,canc]1 ,leo1 ,virgo1 & ,libra rise successively1 ! ,angle increases gradually :i* !y make ) ! ,horizon2 & decreases 9 ! same proportion z !y set4 ,& = t reason1 ! ,moon diff]s gradually m 9 ! "t ( h] ris+ e day :il/ %e is 9 ^! ,signs1 & less 9 h] sett+3 ,aft] :i*1 ?r\gh ! o!r six ,signs1 viz4 ,scorpio1 ,sagitt>y1 ,capricorn1 ,aqu>ius1 ,pisces1 & ,aries1 ! ris+ diff]5ce becomes less e day1 until x be at ! lea/ ( all1 namely1 9 ,pisces & ,aries4 #bhj4 ,! ,moon goes r\nd ! ,ecliptic 9 #bg days #h h\rs2 b n f ,*ange to ,*ange 9 less ?an #bi days #ab h\rs3 s t %e is 9 ,pisces & ,aries at lea/ once 9 e ,lunation1 & 9 "s ,lunations twice4 ,sid5ote3 ,:y ! ,moon is always ,full 9 diff]5t ,signs4 ,h] p]iodical & synodical ,revolution exemplifi$4 #bha4 ,if ! ,e>? _h no annual motion1 ! ,sun w\ld nev] appe> to %ift 8 place 9 ! ,ecliptic4 ,& !n e ,new ,moon w\ld fall 9 ! same ,sign & degree ( ! ,ecliptic1 & e ,full ,moon 9 ! opposite3 = ! ,moon w\ld g precisely r\nd ! ,ecliptic f ,*ange to ,*ange4 ,s t if ! ,moon 0 once ,full 9 ,pisces1 or ,aries1 %e w\ld always be ,full :5 %e came r\nd to ! same ,sign & ,degree aga94 ,& z ! ,full ,moon rises at ,sun-set 7because :5 any po9t ( ! ,ecliptic sets ! opposite po9t rises7 %e w\ld con/antly rise )9 two h\rs ( ,sun-set dur+ ! week 9 :i* %e 7 ,full4 ,b 9 ! "t t ! ,moon goes r\nd ! ,ecliptic f any conjunction or opposition1 ! ,e>? goes almo/ a ,sign =w>d2 & !re=e ! ,sun w seem to g z f> =w>d 9 t "t1 namely #bg-a_/b degrees3 s t ! ,moon mu/ g #bg-a_/b degrees m ?an r\nd2 & z mu* f>!r z ! ,sun advances 9 t int]val1 :i* is #b-a_/ae degrees1 be=e %e c be 9 conjunction )1 or opposite to ! ,sun aga94 ,h5ce x is evid5t1 t !re c be b "o conjunction or opposition ( ! ,sun & ,moon 9 a ye> 9 any p>ticul> "p ( ! ,ecliptic4 ,?is may be famili>ly exemplifi$ by ! h\r & m9ute h&s ( a wat*1 :i* are nev] 9 conjunction or opposition 9 t "p ( ! dial-plate :]e !y 7 s la/ be=e4 ,& inde$ if we comp>e ! twelve h\rs on ! dial-plate to ! twelve ,signs ( ! ,ecliptic1 ! h\r-h& to ! ,sun & ! m9ute-h& to ! ,moon1 we %all h a tol]ably ne> resemblance 9 m9iature to ! motions ( our great cele/ial ,lum9>ies4 ,! only diff]5ce is1 t :il/ ! ,sun goes once r\nd ! ,ecliptic ! ,moon makes #ab-a_/c conjunctions ) him3 b :il/ ! h\r-h& goes r\nd ! dial-plate ! m9ute-h& makes only #aa conjunctions ) x2 because ! m9ute h& moves sl[] 9 respect ( ! h\r-h& ?an ! ,moon does ) reg>d to ! ,sun4 ,sid5ote3 ,! ,h>ve/ & ,hunt]'s ,moon4 #bhb4 ,z ! ,moon c nev] be full b :5 %e is opposite to ! ,sun1 & ! ,sun is nev] 9 ,virgo & ,libra b 9 our autumnal mon?s1 'tis pla9 t ! ,moon is nev] full 9 ! opposite ,signs1 ,pisces & ,aries1 b 9 ^! two mon?s4 ,& !re=e we c h only two ,full ,moons 9 ! ye>1 :i* rise s ne> ! "t ( ,sun-set = a week toge!r z above-m5tion$4 ,! =m] ( ^! is call$ ! ,h>ve/ ,moon1 & ! latt] ! ,hunt]'s ,moon4 ,sid5ote3 ,:y ! ,moon's regul> ris+ is nev] p]ceiv$ b 9 ,h>ve/4 #bhc4 ,"h x w probably be ask$1 :y we nev] obs]ve ?is rem>kable ris+ ( ! ,moon b 9 h>ve/1 s9ce %e is 9 ,pisces & ,aries at lea/ twelve times 9 ! ye> besides2 & mu/ !n rise ) z little diff]5ce ( "t z 9 h>ve/8 ,! answ] is pla93 = 9 w9t] ^! ,signs rise at noon2 & be+ !n only a ,qu>t] ( a ,circle di/ant f ! ,sun1 ! ,moon 9 !m is 9 h] fir/ ,qu>t]3 b :5 ! ,sun is above ! ,horizon ! ,moon's ris+ is nei!r reg>d$ nor p]ceiv$4 ,9 spr+ ^! ,signs rise ) ! ,sun because he is !n 9 !m2 & z ! ,moon *ange? 9 !m at t "t ( ! ye>1 %e is q invisible4 ,9 summ] !y rise ab\t mid-night1 & ! ,sun be+ !n ?ree ,signs1 or a ,qu>t] ( a ,circle be=e !m1 ! ,moon is 9 !m ab\t h] ?ird ,qu>t]2 :5 ris+ s late1 & giv+ b v little light1 h] ris+ passes unobs]v$4 ,& 9 autumn1 ^! ,signs be+ opposite to ! ,sun1 rise :5 he sets1 ) ! ,moon 9 opposition1 or at ! ,full1 :i* makes h] ris+ v conspicu\s4 #bhd4 ,at ! ,equator1 ! ,nor? & ,s\? ,poles lie 9 ! ,horizon2 & !re=e ! ,ecliptic makes ! same ,angle s\?w>d ) ! ,horizon :5 ,aries rises z x does nor?w>d :5 ,libra rises4 ,consequ5tly1 z ! ,moon at all ! =e-m5tion$ pat*es rises & sets ne>ly at equal ,angles ) ! ,horizon all ! ye> r\nd2 & ab\t #dh m9utes lat] e day or night ?an on ! prec$+1 !re c be no p>ticul> ,h>ve/ ,moon at ! ,equator4 #bhe4 ,! f>!r t any place is f ! ,equator1 if x be n beyond ! ,pol> ,circle1 ! ,angle gradually dim9i%es :i* ! ,ecliptic & ,horizon make :5 ,pisces & ,aries rise2 & !re=e :5 ! ,moon is 9 ^! ,signs %e rises ) a ne>ly proportionable diff]5ce lat] e day ?an on ! =m]2 & is = t reason ! m rem>kable ab\t ! ,full1 until we come to ! ,pol> ,circles1 or #ff degrees f ! ,equator2 9 :i* ,latitude ! ,ecliptic & ,horizon become co9cid5t1 e day = a mom5t1 at ! same sid]eal h\r 7or #c m9utes #ef seconds soon] e day ?an ! =m]7 & ! v next mom5t "o half ( ! ,ecliptic conta9+ ,capricorn1 ,aqu>ius1 ,pisces1 ,aries1 ,taurus1 & ,gem9i rises1 & ! opposite half sets4 ,!re=e1 :il/ ! ,moon is go+ f ! beg9n+ ( ,capricorn to ! beg9n+ ( ,canc]1 :i* is almo/ #ad days1 %e rises at ! same sid]eal h\r2 & 9 autumn j at ,sun-set1 because all t half ( ! ,ecliptic 9 :i* ! ,sun is at t "t sets at ! same sid]eal h\r1 & ! opposite half rises3 t is1 #c m9utes #ef seconds1 ( mean sol> "t1 soon] e day ?an on ! day be=e4 ,s :il/ ! ,moon is go+ f ,capricorn to ,canc] %e rises e>li] e day ?an on ! prec$+2 contr>y to :at %e does at all places betwe5 ! pol> ,circles4 ,b dur+ ! above f\rte5 days1 ! ,moon is #bd sid]eal h\rs lat] 9 sett+2 = ! six ,signs :i* rise all at once on ! ea/]n side ( ! ,horizon are #bd h\rs 9 sett+ on ! we/]n side ( x3 z any "o may see by mak+ *alk-m>ks at ! beg9n+ ( ,capricorn & ( ,canc]1 & !n1 hav+ elevat$ ! ,pole #ff-a_/b degrees1 turn ! ,globe sl[ly r\nd x's ,axis1 & obs]ve ! ris+ & sett+ ( ! ,ecliptic4 ,z ! beg9n+ ( ,aries is equally di/ant f ! beg9n+ ( ,canc] & ( ,capricorn1 x is 9 ! middle ( t half ( ! ,ecliptic :i* rises all at once4 ,& :5 ! ,sun is at ! beg9n+ ( ,libra1 he is 9 ! middle ( ! o!r half4 ,!re=e1 :5 ! ,sun is 9 ,libra & ! ,moon 9 ,capricorn1 ! ,moon is a ,qu>t] ( a ,circle be=e ! ,sun2 opposite to him1 & consequ5tly full 9 ,aries1 & a ,qu>t] ( a ,circle beh9d him :5 9 ,canc]4 ,b :5 ,libra rises ,aries sets1 & all t half ( ! ,ecliptic ( :i* ,aries is ! middle4 ,& !re=e1 at t "t ( ! ye> ! ,moon rises at ,sun-set f h] fir/ to h] ?ird ,qu>t]4 ,sid5ote3 ,! ,h>ve/ ,moons regul> on bo? sides ( ! ,equator4 #bhf4 ,9 nor!rn ,latitudes1 ! autumnal ,full ,moons are 9 ,pisces & ,aries2 & ! v]nal ,full ,moons 9 ,virgo & ,libra3 9 s\!rn ,latitudes j ! rev]se because ! seasons are contr>y4 ,b ,virgo & ,libra rise at z small ,angles ) ! ,horizon 9 s\!rn ,latitudes z ,pisces & ,aries d 9 ! nor!rn2 & !re=e ! ,h>ve/ ,moons are j z regul> on "o side ( ! ,equator z on ! o!r4 #bhg4 ,z ^! ,signs :i* rise ) ! lea/ ,angles set ) ! greate/1 ! v]nal ,full ,moons diff] z mu* 9 _! times ( ris+ e night z ! autumnal ,full ,moons diff] 9 _! times ( sett+2 & set ) z little diff]5ce z ! autumnal ,full ,moons rise3 ! "o be+ 9 all cases ! rev]se ( ! o!r4 ,sid5ote3 ,! ,moon's ,nodes4 #bhh4 ,hi!rto1 = ! sake ( pla9ness1 we h suppos$ ! ,moon to move 9 ! ,ecliptic1 f :i* ! ,sun nev] deviates4 ,b ! orbit 9 :i* ! ,moon really moves is diff]5t f ! ,ecliptic3 "o half be+ elevat$ #e-a_/c degrees above x1 & ! o!r half z mu* depress$ bel[ x4 ,! ,moon's orbit !re=e int]sects ! ,ecliptic 9 two po9ts diametrically opposite to ea* o!r3 & ^! int]sections are call$ ! ,moon's ,nodes4 ,s ! ,moon c nev] be 9 ! ,ecliptic b :5 %e is 9 ei!r ( h] ,nodes1 :i* is at lea/ twice 9 e c\rse f ,*ange to ,*ange1 & sometimes ?rice4 ,=1 z ! ,moon goes almo/ a :ole ,sign m ?an r\nd h] ,orbit f ,*ange to ,*ange2 if %e passes by ei!r ,node ab\t ! "t ( ,*ange1 %e w pass by ! o!r 9 ab\t f\rte5 days aft]1 & come r\nd to ! =m] ,node two days aga9 be=e ! next ,*ange4 ,t ,node f :i* ! ,moon beg9s to asc5d nor?w>d1 or above ! ,ecliptic1 9 nor!rn ,latitudes1 is call$ ! ,asc5d+ ,node2 & ! o!r ! ,desc5d+ ,node1 because ! ,moon1 :5 %e passes by x1 desc5ds bel[ ! ,ecliptic s\?w>d4 #bhi4 ,! ,moon's oblique motion ) reg>d to ! ,ecliptic causes "s diff]5ce 9 ! times ( h] ris+ & sett+ f :at is already m5tion$4 ,= :il/ %e is nor?w>d ( ! ,ecliptic1 %e rises soon] & sets lat] ?an if %e mov$ 9 ! ,ecliptic3 & :5 %e is s\?w>d ( ! ,ecliptic %e rises lat] & sets soon]4 ,?is diff]5ce is v>iable ev5 9 ! same ,signs1 because ! ,nodes %ift backw>d ab\t #ai-b_/c degrees 9 ! ,ecliptic e ye>2 & s g r\nd x contr>y to ! ord] ( ,signs 9 #ah ye>s #bbe days4 #bij4 ,:5 ! ,asc5d+ ,node is 9 ,aries1 ! s\!rn half ( ! ,moon's ,orbit makes an ,angle ( #e-a_/c degrees less ) ! ,horizon ?an ! ,ecliptic does1 :5 ,aries rises 9 nor!rn ,latitudes3 = :i* reason ! ,moon rises ) less diff]5ce ( "t :il/ %e is 9 ,pisces & ,aries ?an !re w\ld be if %e kept 9 ! ,ecliptic4 ,b 9 #i ye>s & #aab days aft]w>d1 ! ,desc5d+ ,node comes to ,aries2 & !n ! ,moon's ,orbit makes an ,angle #e-a_/c degrees great] ) ! ,horizon :5 ,aries rises1 ?an ! ,ecliptic does at t "t2 :i* causes ! ,moon to rise ) great] diff]5ce ( "t 9 ,pisces & ,aries ?an if %e mov$ 9 ! ,ecliptic4 #bia4 ,to be a little m p>ticul>1 :5 ! ,asc5d+ ,node is 9 ,aries1 ! ,angle is only #i-b_/c degrees on ! p>allel ( ,london :5 ,aries rises4 ,b :5 ! ,desc5d+ ,node comes to ,aries1 ! ,angle is #bj-a_/c degrees2 ?is occasions z great a diff]5ce ( ! ,moon's ris+ 9 ! same ,signs e #i ye>s1 on ! p>allel ( ,london1 z !re w\ld be on two p>allels #aj-b_/c degrees f "o ano!r1 if ! ,moon's c\rse 7 9 ! ,ecliptic4 ,! foll[+ ,table %ews h[ mu* ! obliquity ( ! ,moon's ,orbit affects h] ris+ & sett+ on ! p>allel ( ,london f ! #ab? to ! #ah? day ( h] age2 suppos+ h] to be ,full at ! autumnal ,equ9ox2 & !n1 ei!r 9 ! ,asc5d+ ,node1 highe/ "p ( h] ,orbit1 ,desc5d+ ,node1 or l[e/ "p ( h] ,orbit4 ,m signifies morn+1 ,a aft]noon2 & ! l9e at ! foot ( ! ,table %ews a week's diff]5ce 9 ris+ & sett+4 ---------------------------------------- ---------------------------- ,full 9 h] ,9 ! ,full 9 h] ,9 ! l[e/ ,asc5d+ highe/ "p ,desc5d+ "p ( h] node4 ( h] ,orbit4 node4 ,orbit4 ,moon's ---------------------------------------- ----------------- ,age ,rises ,sets ,rises ,sets ,rises ,sets ,rises ,sets at at at at at at at at ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ---------------------------------------- ------------------------ ,a ,m ,a ,m ,a ,m ,a ,m #ab #e #ae #c #bj #d #cj #c #ae #d #cb #c #dj #e #af #c #j #ac #e #cb #d #be #d #ej #d #de #e #ae #d #bj #f #j #d #ae #ad #e #dh #e #cj #e #ae #f #j #e #de #e #dj #f #bj #e #bh #ae #f #e #g #j #e #db #g #bj #f #ae #f #ef #f #de #f #cb #af #f #bj #h #ae #f #b #h #ce #f #df #h #j #g #h #g #de #ag #f #cf #i #ab #f #bf #i #de #g #ah #i #ae #g #cj #i #ae #ah #f #ed #aj #cj #g #j #aj #dj #h #j #aj #bj #g #eb #aj #j ---------------------------------------- ------------------------ ,dif4 #a #ci #g #aj #b #cj #g #be #c #bh #f #dj #b #cf #g #j ---------------------------------------- ------------------------ ,?is ,table 0 n comput$1 b only e/imat$ z ne> z c\ld be done f a common ,globe1 on :i* ! ,moon's ,orbit 0 del9eat$ ) a black lead p5cil4 ,x may at fir/ sight appe> errone\s2 s9ce z we h suppos$ ! ,moon to be full 9 ei!r ,node at ! autumnal ,equ9ox1 %e ought by ! ,table to rise j at six o'clock1 or at ,sun-set1 on ! #ae? day ( h] age2 be+ 9 ! ,ecliptic at t "t4 ,b x mu/ be consid]$1 t ! ,moon is only #ad-a_/d days old :5 %e is ,full2 & !re=e 9 bo? cases %e is a little pa/ ! ,node on ! #ae? day1 be+ above x at "o "t1 & bel[ x at ! o!r4 ,sid5ote3 ,! p]iod ( ! ,h>ve/ ,moons4 #bib4 ,z !re is a compleat revolution ( ! ,nodes 9 #ah-b_/c ye>s1 !re mu/ be a regul> p]iod ( all ! ,v>ieties :i* c happ5 9 ! ris+ & sett+ ( ! ,moon dur+ t "t4 ,b ?is %ift+ ( ! ,nodes nev] affects ! ,moon's ris+ s mu*1 ev5 9 h] quicke/ desc5d+ ,latitude1 z n to all[ u /ill ! b5efit ( h] ris+ ne>] ! "t ( ,sun-set = a few days toge!r ab\t ! ,full 9 ,h>ve/1 ?an :5 %e is ,full at any o!r "t ( ! ye>4 ,! foll[+ ,table %ews 9 :at ye>s ! ,h>ve/-,moons are lea/ b5eficial z to ! times ( _! ris+1 & 9 :at ye>s mo/1 f #agea to #ahfa4 ,! column ( ye>s "u ! lett] ,l are ^? 9 :i* ! ,h>ve/-,moons are lea/ ( all b5eficial1 because !y fall ab\t ! ,desc5d+ ,node3 & ^? "u ,m are ! mo/ ( all b5eficial1 because !y fall ab\t ! ,asc5d+ ,node4 ,9 all ! columns f ,n to ,s ! ,h>ve/-,moons desc5d gradually 9 ! ,lun> ,orbit1 & rise to less heights above ! ,horizon4 ,f ,s to ,n !y asc5d 9 ! same proportion1 & rise to great] heights above ! ,horizon4 ,9 bo? ! columns "u ,s ! ,h>ve/-,moons are 9 ! l[e/ "p ( ! ,moon's ,orbit1 t is1 f>!/ ,s\? ( ! ,ecliptic2 & !re=e /ay %orte/ ( all above ! ,horizon3 9 ! columns "u ,n j ! rev]se4 ,& 9 bo? cases1 _! ris+1 ?\gh n at ! same times1 are ne>ly ! same ) reg>d to diff]5ce ( "t1 z if ! ,moon's ,orbit 7 co9cid5t ) ! ,ecliptic4 ---------------------------------------- -------------------- ,ye>s 9 :i* ! ,h>ve/-,moons are lea/ b5eficial4 ,n ,l ,s #agea #ageb #agec #aged #agee #agef #ageg #ageh #agei #aggj #agga #aggb #aggc #aggd #agge #aggf #aggg #aggh #aghh #aghi #agij #agia #agib #agic #agid #agie #agif #agig #ahjg #ahjh #ahji #ahaj #ahaa #ahab #ahac #ahad #ahae #ahbf #ahbg #ahbh #ahbi #ahcj #ahca #ahcb #ahcc #ahcd #ahdd #ahde #ahdf #ahdg #ahdh #ahdi #ahej #ahea #aheb ,ye>s 9 :i* !y are mo/ b5eficial4 ,s ,m ,n #agfj #agfa #agfb #agfc #agfd #agfe #agff #agfg #agfh #agfi #aggi #aghj #agha #aghb #aghc #aghd #aghe #aghf #aghg #agih #agii #ahjj #ahja #ahjb #ahjc #ahjd #ahje #ahjf #ahaf #ahag #ahah #ahai #ahbj #ahba #ahbb #ahbc #ahbd #ahbe #ahce #ahcf #ahcg #ahch #ahci #ahdj #ahda #ahdb #ahdc #ahec #ahed #ahee #ahef #aheg #aheh #ahei #ahfj #ahfa ---------------------------------------- -------------------- ,sid5ote3 ,,pl4 ,,viii4 #bic4 ,at ! ,pol> ,circles1 :5 ! ,sun t\*es ! ,summ] ,tropic1 he cont9ues #bd h\rs above ! ,horizon2 & #bd h\rs bel[ x :5 he t\*es ! ,w9t] ,tropic4 ,= ! same reason ! ,full ,moon nei!r rises 9 ,summ]1 nor sets 9 ,w9t]1 consid]+ h] z mov+ 9 ! ,ecliptic4 ,= ! ,w9t] ,full ,moon be+ z high 9 ! ,ecliptic z ! ,summ] ,sun1 mu/ !re=e cont9ue z long above ! ,horizon2 & ! ,summ] ,full ,moon be+ z l[ 9 ! ,ecliptic z ! ,w9t] ,sun1 c no m rise ?an he does4 ,b ^! are only ! two ,full ,moons :i* happ5 ab\t ! ,tropics1 = all ! o!rs rise & set4 ,9 ,summ] ! ,full ,moons are l[1 & _! /ay is %ort above ! ,horizon1 :5 ! nights are %ort1 & we h lea/ occasion = ,moon-light3 9 ,w9t] !y g high1 & /ay long1 above ! ,horizon :5 ! nights are long1 & we want ! greate/ quantity ( ,moon-light4 ,sid5ote3 ,! long cont9uance ( ,moon-light at ! ,poles4 ,fig4 ,v4 #bid4 ,at ! ,poles1 "o half ( ! ,ecliptic nev] sets1 & ! o!r half nev] rises3 & !re=e1 z ! ,sun is always half a ye> 9 describ+ "o half ( ! ,ecliptic1 & z long 9 go+ ?r\gh ! o!r half1 'tis natural to imag9e t ! ,sun cont9ues half a ye> toge!r above ! ,horizon ( ea* ,pole 9 x's turn1 & z long bel[ x2 ris+ to "o ,pole :5 he sets to ! o!r4 ,?is w\ld be exactly ! case if !re 7 no refraction3 b by ! ,atmosph]e's refract+ ! ,sun's rays1 he becomes visible "s days soon] #ahc1 & cont9ues "s days long] 9 sight ?an he w\ld o!rwise d3 s t he appe>s above ! ,horizon ( ei!r ,pole be=e he has got bel[ ! ,horizon ( ! o!r4 ,&1 z he nev] goes m ?an #bc-a_/b degrees bel[ ! ,horizon ( ! ,poles1 !y h v little d>k night3 x be+ twilight !re z well z at all o!r places till ! ,sun be #ah degrees bel[ ! ,horizon1 #agg4 ,! ,full ,moon be+ always opposite to ! ,sun1 c nev] be se5 :ile ! ,sun is above ! ,horizon1 except :5 ! ,moon falls 9 ! nor!rn half ( h] ,orbit2 = :5ev] any po9t ( ! ,ecliptic rises ! opposite po9t sets4 ,!re=e1 z ! ,sun is above ! ,horizon ( ! nor? ,pole f ! #bj? ( ,m>* till ! #bc;d ( ,septemb]1 x is pla9 t ! ,moon1 :5 ,full1 be+ opposite to ! ,sun1 mu/ be bel[ ! ,horizon dur+ t half ( ! ye>4 ,b :5 ! ,sun is 9 ! s\!rn half ( ! ,ecliptic he nev] rises to ! nor? ,pole1 dur+ :i* half ( ! ye>1 e ,full ,moon happ5s 9 "s "p ( ! nor!rn half ( ! ,ecliptic1 :i* nev] sets4 ,consequ5tly1 z ! pol> ,inhabitants nev] see ! ,full ,moon 9 ,summ]1 !y h h] always 9 ! ,w9t]1 be=e1 at1 & aft] ! ,full1 %9+ = #ad ( our days & nights4 ,& :5 ! ,sun is at 8 greate/ depression bel[ ! ,horizon1 be+ !n 9 ,capricorn1 ! ,moon is at h] ,fir/ ,qu>t] 9 ,aries1 ,full 9 ,canc]1 & at h] ,?ird ,qu>t] 9 ,libra4 ,& z ! beg9n+ ( ,aries is ! ris+ po9t ( ! ,ecliptic1 ,canc] ! highe/1 & ,libra ! sett+ po9t1 ! ,moon rises at h] ,fir/ ,qu>t] 9 ,aries1 is mo/ elevat$ above ! ,horizon1 & ,full 9 ,canc]1 & sets at ! beg9n+ ( ,libra 9 h] ,?ird ,qu>t]1 hav+ cont9u$ visible = #ad diurnal rotations ( ! ,e>?4 ,?us ! ,poles are suppli$ "o half ( ! w9t] "t ) con/ant ,moon-light 9 ! ,sun's abs5ce2 & only lose sight ( ! ,moon f h] ,?ird to h] ,fir/ ,qu>t]1 :ile %e gives b v little light2 & c\ld be b ( little1 & sometimes ( no s]vice to !m4 ,a b>e view ( ! ,figure w make ?is pla92 9 :i* let ,s be ! ,sun1 e ! ,e>? 9 ,summ] :5 x's nor? ,pole n incl9es t[>d ! ,sun1 & ,e ! ,e>? 9 ,w9t]1 :5 x's nor? ,pole decl9es f him4 ,,s5 & ,,nws is ! ,horizon ( ! nor? ,pole1 :i* is co9cid5t ) ! ,equator2 &1 9 bo? ^! positions ( ! ,e>?1 is ! ,moon's ,orbit1 9 :i* %e goes r\nd ! ,e>?1 accord+ to ! ord] ( ! lett]s abcd1 ,,abcd4 ,:5 ! ,moon is at a %e is 9 h] ,?ird ,qu>t] to ! ,e>? at e1 & j ris+ to ! nor? ,pole n2 at b %e *anges1 & is at ! greate/ height above ! ,horizon1 z ! ,sun likewise is2 at c %e is 9 h] ,fir/ ,qu>t]1 sett+ bel[ ! ,horizon2 & is l[e/ ( all "u x at d1 :5 opposite to ! ,sun1 & h] enlight5$ side t[>d ! ,e>?4 ,b !n %e is full 9 view to ! s\? ,pole p2 :i* is z mu* turn$ f ! ,sun z ! nor? ,pole incl9es t[>ds him4 ,?us 9 our ,summ]1 ! ,moon is above ! ,horizon ( ! nor? ,pole :il/ %e describes ! nor!rn half ( ! ,ecliptic 1 or f h] ,?ird ,qu>t] to h] ,fir/2 & bel[ ! ,horizon dur+ ! progress ?r\gh ! s\!rn half 2 highe/ at ! ,*ange1 mo/ depress$ at ! ,full4 ,b 9 w9t]1 :5 ! ,e>? is at ,e1 & x's nor? ,pole decl9es f ! ,sun1 ! ,new ,moon at ,d is at h] greate/ depression bel[ ! ,horizon ,,nws1 & ! ,full ,moon at ,b at h] greate/ height above x2 ris+ at h] ,fir/ ,qu>t] ,a1 & keep+ above ! ,horizon till %e comes to h] ,?ird ,qu>t] ,c4 ,at a mean /ate %e is #bc-a_/b degrees above ! ,horizon at ,b & b1 & z mu* bel[ x at ,d & d1 equal to ! incl9ation ( ! ,e>?'s ,axis ,f4 ,s & ,s are1 z x 71 a ray ( light proce$+ f ! ,sun to ! ,e>?2 & %ews t :5 ! ,e>? is at e1 ! ,sun is above ! ,horizon1 v]tical to ! ,tropic ( ,canc]2 & :5 ! ,e>? is at ,e1 he is bel[ ! ,horizon1 v]tical to ! ,tropic ( ,capricorn4 ,illu/ration3 ,plate ,,viii4 ,j4 ,f]guson del94 ,j4 ,mynde ,sculp4 ,illu/ration3 ,plate ,,ix4 ,j4 ,f]guson del94 ,j4 ,mynde ,sculp4 ,,*ap4 ,,xvii4 ,( ! ebb+ & fl[+ ( ! ,sea4 ,sid5ote3 ,! cause ( ! ,tides discov]$ by ,,kepl]4 ,,plate ,,ix4 ,_! ,!ory improv$ by ,sir ,,isaac ,,newton4 #bie4 ,! cause ( ! ,tides 0 discov]$ by ,,kepl]1 :o1 9 8 ,introduction to ! ,physics ( ! ,heav5s1 ?us expla9s x3 8,! ,orb ( ! attract+ p[]1 :i* is 9 ! ,moon1 is ext5d$ z f> z ! ,e>?2 & draws ! wat]s "u ! torrid ,zone1 act+ ^u places :]e x is v]tical1 ins5sibly on conf9$ seas & bays1 b s5sibly on ! ocean ^: b$s are l>ge1 & ! wat]s h ! lib]ty ( reciprocation2 t is1 ( ris+ & fall+40 ,& 9 ! #gj? page ( 8 ,lun> ,a/ronomy----8,b ! cause ( ! ,tides ( ! ,sea appe>s to be ! bodies ( ! ,sun & ,moon draw+ ! wat]s ( ! ,sea40 ,?is h9t be+ giv51 ! immortal ,sir ,,isaac ,,newton improv$ x1 & wrote s amply on ! subject1 z to make ! ,!ory ( ! ,tides 9 a mann] q 8 own2 by discov]+ ! cause ( _! ris+ on ! side ( ! ,e>? opposite to ! ,moon4 ,= ,,kepl] believ$ t ! pres5ce ( ! ,moon occasion$ an impulse :i* caus$ ano!r 9 h] abs5ce4 ,sid5ote3 ,expla9$ on ! ,newtonian pr9ciples4 ,fig4 ,i4 ,fig4 ,i4 #bif4 ,x has be5 already %ewn #ajf1 t ! p[] ( gravity dim9i%es z ! squ>e ( ! di/ance increases2 & !re=e ! wat]s at ,z on ! side ( ! ,e>? ,,abcdefgh next ! ,moon ,m are m attract$ ?an ! c5tral p>ts ( ! ,e>? ,o by ! ,moon1 & ! c5tral p>ts are m attract$ by h] ?an ! wat]s on ! opposite side ( ! ,e>? at n3 & !re=e ! di/ance betwe5 ! ,e>?'s c5t] & ! wat]s on x's surface "u & opposite to ! ,moon w be increas$4 ,=1 let !re be ?ree bodies at ,h1 ,o1 & ,d3 if !y are all equally attract$ by ! body ,m1 !y w all move equally fa/ t[>d x1 _! mutual di/ances f ea* o!r cont9u+ ! same4 ,if ! attraction ( ,m is unequal1 !n t body :i* is mo/ /rongly attract$ w move fa/e/1 & ?is w increase x's di/ance f ! o!r body4 ,!re=e1 by ! law ( gravitation1 ,m w attract ,h m /rongly ?an x does ,o1 by :i*1 ! di/ance betwe5 ,h & ,o w be increas$3 & a spectator on ,o w p]ceive ,h ris+ high] t[>d ,z4 ,9 l mann]1 ,o be+ m /rongly attract$ ?an ,d1 x w move f>!r t[>ds ,m ?an ,d does3 consequ5tly1 ! di/ance betwe5 ,o & ,d w be increas$2 & a spectator on ,o1 n p]ceiv+ 8 own motion1 w see ,d rec$+ f>!r f him t[>ds n3 all effects & appe>ances be+ ! same :e!r ,d rec$es f ,o or ,o f ,d4 ,sid5ote3 ,,plate ,,ix4 #big4 ,suppose n[ !re is a numb] ( bodies1 z ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 ,h plac$ r\nd ,o1 s z to =m a flexible or fluid r+3 !n1 z ! :ole is attract$ t[>ds ,m1 ! p>ts at ,h & ,d w h _! di/ance f ,o increas$2 :il/ ! p>ts at ,b & ,f1 be+ ne>ly at ! same di/ance f ,m z ,o is1 ^! p>ts w n rec$e f "o ano!r2 b r1 by ! oblique attraction ( ,m1 !y w approa* ne>] to ,o4 ,h5ce1 ! fluid r+ w =m itself into an ellipse ,z,i,b,ln,k,f,n,z1 ^: long] ,axis n,o,z produc$ w pass ?r\gh ,m1 & x's %ort] ,axis ,,b( w t]m9ate 9 ,b & ,f4 ,let ! r+ be fill$ ) bodies1 s z to =m a flexible or fluid sph]e r\nd ,o2 !n1 z ! :ole moves t[>d ,m1 ! fluid sph]e be+ l5g?n$ at ,z & n1 w assume an oblong or oval =m4 ,if ,m is ! ,moon1 ,o ! ,e>?'s c5t]1 ,,abcdefgh ! ,sea cov]+ ! ,e>?'s surface1 'tis evid5t by ! above reason+1 t :il/ ! ,e>? by x's gravity falls t[>d ! ,moon1 ! ,wat] directly bel[ h] at ,b w swell & rise gradually t[>ds h]3 also1 ! ,wat] at ,d w rec$e f ! c5t] /rictly speak+1 ! c5t] rec$es f ,d & rise on ! opposite side ( ! ,e>?3 :il/ ! ,wat] at ,b & ,f is depress$1 & falls bel[ ! =m] level4 ,h5ce1 z ! ,e>? turns r\nd x's ,axis f ! ,moon to ! ,moon aga9 9 #bd-c_/d h\rs1 !re w be two tides ( flood & two ( ebb 9 t "t1 z we f9d by exp]i5ce4 ,sid5ote3 ,fig4 ,,ii4 #bih4 ,z ?is explanation ( ! ebb+ & fl[+ ( ! ,sea is d$uc$ f ! ,e>?'s con/antly fall+ t[>d ! ,moon by ! p[] ( gravity1 "s may f9d a difficulty 9 conceiv+ h[ ?is is possible :5 ! ,moon is ,full1 or 9 opposition to ! ,sun2 s9ce ! ,e>? revolves ab\t ! ,sun1 & mu/ cont9ually fall t[>ds x1 & !re=e _c fall contr>y ways at ! same "t3 or if ! ,e>? is con/antly fall+ t[>ds ! ,moon1 !y mu/ come toge!r at la/4 ,to remove ?is difficulty1 let x be consid]$1 t x is n ! c5t] ( ! ,e>? t describes ! annual orbit r\nd ! ,sun2 b ! #fc;common c5t] ( gravity ( ! ,e>? & ,moon toge!r3 & t :il/ ! ,e>? is mov+ r\nd ! ,sun1 x also describes a ,circle r\nd t c5tre ( gravity2 go+ z _m times r\nd x 9 "o revolution ab\t ! ,sun z !re are ,lunations or c\rses ( ! ,moon r\nd ! ,e>? 9 a ye>3 & !re=e1 ! ,e>? is con/antly fall+ t[>ds ! ,moon f a tang5t to ! ,circle x describes r\nd ! said common c5t] ( gravity4 ,let ,m be ! ,moon1 ,,tw "p ( ! ,moon's ,orbit1 & ,c ! c5t] ( gravity ( ! ,e>? & ,moon3 :il/ ! ,moon goes r\nd h] ,orbit1 ! c5t] ( ! ,e>? describes ! ,circle g$ r\nd ,c1 to :i* ,circle gak is a tang5t3 & !re=e1 :5 ! ,moon has gone f ,m to a little pa/ ,w1 ! ,e>? has mov$ f g to e2 & 9 t "t has fall5 t[>ds ! ,moon1 f ! tang5t at a to e2 & s r\nd ! :ole ,circle4 ,sid5ote3 ,,plate ,,ix4 #bii4 ,! ,sun's influ5ce 9 rais+ ! ,tides is b small 9 comp>ison ( ! ,moon's3 ,= ?\gh ! ,e>?'s diamet] be>s a consid]able proportion to x's di/ance f ! ,moon1 x is next to no?+ :5 comp>$ ) ! di/ance ( ! ,sun4 ,& !re=e1 ! diff]5ce ( ! ,sun's attraction on ! sides ( ! ,e>? "u & opposite to him1 is mu* less ?an ! diff]5ce ( ! ,moon's attraction on ! sides ( ! ,e>? "u & opposite to h]3 & !re=e ! ,moon mu/ raise ! ,tides mu* high] ?an !y c be rais$ by ! ,sun4 ,sid5ote3 ,:y ! ,tides are n highe/ :5 ! ,moon is on ! ,m]idian4 ,fig4 ,i4 #cjj4 ,on ?is ,!ory s f> z we h expla9$ x1 ! ,tides ought to be highe/ directly "u & opposite to ! ,moon2 t is1 :5 ! ,moon is due nor? & s\?4 ,b we f9d1 t 9 op5 ,seas1 :]e ! wat] fl[s freely1 ! ,moon ,m is g5]ally pa/ ! nor? & s\? ,m]idian z at p :5 x is high wat] at ,z & at n4 ,! reason is obvi\s2 = ?\gh ! ,moon's attraction 0 to cease altoge!r :5 %e 0 pa/ ! ,m]idian1 yet ! motion ( asc5t communicat$ to ! wat] be=e t "t w\ld make x cont9ue to rise = "s "t aft]2 mu* m mu/ x d s :5 ! attraction is only dim9i%$3 z a little impulse giv5 to a mov+ ball w cause x /ill move f>!r ?an o!rwise x c\ld h done4 ,& z exp]i5ce %ews1 t ! day is hott] ab\t ?ree 9 ! aft]noon1 ?an :5 ! ,sun is on ! ,m]idian1 because ( ! increm5t made to ! heat already imp>t$4 ,sid5ote3 ,nor always answ] to h] be+ at ! same di/ance f x4 #cja4 ,! ,tides answ] n always to ! same di/ance ( ! ,moon f ! ,m]idian at ! same places2 b are v>i\sly affect$ by ! action ( ! ,sun1 :i* br+s !m on soon] :5 ! ,moon is 9 h] fir/ & ?ird ,qu>t]s1 & keeps !m back lat] :5 %e is 9 h] second & f\r?3 because1 9 ! =m] case1 ! ,tide rais$ by ! ,sun alone w\ld be e>li] ?an ! ,tide rais$ by ! ,moon2 & 9 ! latt] case lat]4 ,sid5ote3 ,spr+ & neap ,tides4 ,,plate ,,ix4 ,fig4 ,,vi4 #cjb4 ,! ,moon goes r\nd ! ,e>? 9 an elliptic ,orbit1 & !re=e %e approa*es ne>] to ! ,e>? ?an h] mean di/ance1 & rec$es f>!r f x1 9 e ,lun> ,mon?4 ,:5 %e is ne>e/3 %e attracts /ronge/1 & s rises ! ,tides mo/2 ! contr>y happ5s :5 %e is f>!/1 because ( h] weak] attraction4 ,:5 bo? ,lum9>ies are 9 ! ,equator1 & ! ,moon 9 ,p]igeo1 or at h] lea/ di/ance f ! ,e>?1 %e raises ! ,tides highe/ ( all1 especially at h] ,conjunction & opposition2 bo? because ! equatoreal p>ts h ! greate/ c5trifugal =ce f _! describ+ ! l>ge/ ,circle1 & f ! concurr+ actions ( ! ,sun & ,moon4 ,at ! ,*ange1 ! attractive =ces ( ! ,sun & ,moon be+ unit$1 !y dim9i% ! gravity ( ! wat]s "u ! ,moon1 :i* is also dim9i%$ on ! o!r side1 by means ( a great] c5trifugal =ce4 ,at ! full1 :il/ ! ,moon raises ! ,tide "u & opposite to h]1 ! ,sun act+ 9 ! same l9e1 raises ! ,tide "u & opposite to him2 :5ce _! conjo9t effect is ! same z at ! ,*ange2 & 9 bo? cases1 occasion :at we call ! ,spr+ ,tides4 ,b at ! ,qu>t]s ! ,sun's action on ! wat]s at ,o & ,h dim9i%es ! ,moon's action on ! wat]s at ,z & ,n2 s t !y rise a little "u & opposite to ! ,sun at ,o & ,h1 & fall z mu* "u & opposite to ! ,moon at ,z & ,n2 mak+ :at we call ! ,neap ,tides1 because ! ,sun & ,moon !n act cross-wise to ea* o!r4 ,b1 /rictly speak+1 ^! ,tides happ5 n till "s "t aft]2 because 9 ?is1 z 9 o!r cases1 #cjj1 ! actions d n produce ! greate/ effect :5 !y are at ! /ronge/1 b "s "t aft]w>d4 ,sid5ote3 ,n greate/ at ! ,equ9oxes1 & :y4 #cjc4 ,! ,sun be+ ne>] ! ,e>? 9 ,w9t] ?an 9 ,summ]1 #bje1 is ( c\rse ne>] to x 9 ,febru>y & ,octob] ?an 9 ,m>* & ,septemb]3 & !re=e ! greate/ ,tides happ5 n till "s "t aft] ! autumnal ,equ9ox1 & return a little be=e ! v]nal4 ,sid5ote3 ,! ,tides w\ld n imm$iately cease ^u ! annihilation ( ! ,sun & ,moon4 ,! ,sea be+ ?us put 9 motion1 w\ld cont9ue to ebb & fl[ = sev]al times1 ev5 ?\gh ! ,sun & ,moon 7 annihilat$1 or _! influ5ce %\ld cease3 z if a bason ( wat] 7 agitat$1 ! wat] w\ld cont9ue to move = "s "t aft] ! bason 0 left to /& /ill4 ,or l a ,p5dulum1 :i* hav+ be5 put 9 motion by ! h&1 cont9ues to make sev]al vibrations )\t any new impulse4 ,sid5ote3 ,! lun> day1 :at4 ,! ,tides rise to unequal heights 9 ! same day1 & :y4 ,,plate ,,ix4 ,fig4 ,,iii1 ,,iv1 ,v4 ,fig4 ,,iii4 ,fig4 ,,iv4 ,fig4 ,v4 #cjd4 ,:5 ! ,moon is 9 ! ,equator1 ! ,tides are equally high 9 bo? p>ts ( ! lun> day1 or "t ( ! ,moon's revolv+ f ! ,m]idian to ! ,m]idian aga91 :i* is #bd h\rs #dh m9utes4 ,b z ! ,moon decl9es f ! ,equator t[>ds ei!r ,pole1 ! ,tides are alt]nately high] & l[] at places hav+ nor? or s\? ,latitude4 ,= "o ( ! highe/ elevations1 :i* is t "u ! ,moon1 foll[s h] t[>ds ! same ,pole1 & ! o!r decl9es t[>ds ! opposite2 ea* describ+ p>allels z f> di/ant f ! ,equator1 on opposite sides1 z ! ,moon decl9es f x to ei!r side2 & consequ5tly1 ! p>allels describ$ by ^! elevations ( ! wat] are twice z _m degrees f "o ano!r1 z ! ,moon is f ! ,equator2 increas+ _! di/ance z ! ,moon increases h] decl9ation1 till x be at ! greate/1 :5 ! said p>allels are1 at a mean /ate1 #dg degrees f "o ano!r3 & on t day1 ! ,tides are mo/ unequal 9 _! heights4 ,z ! ,moon returns t[>d ! ,equator1 ! p>allels describ$ by ! opposite elevations approa* t[>ds ea* o!r1 until ! ,moon comes to ! ,equator1 & !n !y co9cide4 ,z ! ,moon decl9es t[>d ! opposite ,pole1 at equal di/ances1 ea* elevation describes ! same p>allel 9 ! o!r "p ( ! lun> day1 :i* x's opposite elevation describ$ be=e4 ,:il/ ! ,moon has nor? decl9ation1 ! greate/ ,tides 9 ! nor!rn ,hemisph]e are :5 %e is above ! ,horizon2 & ! rev]se :il/ h] decl9ation is s\?4 ,let ,,nesq be ! ,e>?1 ,,ncs x's ,axis1 ,,eq ! ,equator1 ,t ! ,tropic ( ,canc]1 t ! ,tropic ( ,capricorn1 ab ! arctic ,circle1 cd ! ,ant>ctic1 ,n ! nor? ,pole1 ,s ! s\? ,pole1 ,m ! ,moon1 ,f & ,g ! two em95ces ( wat]1 ^: l[e/ p>ts are at a & d 7,fig4 ,,iii47 at ,n & ,s 7,fig4 ,,iv47 & at b & c 7,fig4 ,v47 always #ij degrees f ! highe/4 ,n[ :5 ! ,moon is 9 h] greate/ nor? decl9ation at ,m1 ! highe/ elevation ,g "u h]1 is on ! ,tropic ( ,canc] ,t1 & ! opposite elevation ,f on ! ,tropic ( ,capricorn t2 & ^! two elevations describe ! ,tropics by ! ,e>?'s diurnal rotation4 ,all places 9 ! nor!rn ,hemisph]e ,,enq h ! highe/ ,tides :5 !y come into ! position b,q1 "u ! ,moon2 & ! l[e/ ,tides :5 ! ,e>?'s diurnal rotation c>ries !m into ! position a,t,e1 on ! side opposite to ! ,moon2 ! rev]se happ5s at ! same "t 9 ! s\!rn ,hemisph]e ,,esq1 z is evid5t to sight4 ,! ,axis ( ! ,tides a,cd has n[ x's ,poles a & d 7be+ always #ij degrees f ! highe/ elevations7 9 ! arctic & ant>ctic ,circles2 & !re=e 'tis pla91 t at ^! ,circles !re is b "o ,tide ( ,flood1 & "o ( ,ebb1 9 ! lun> day4 ,=1 :5 ! po9t a revolves half r\nd to b1 9 #ab lun> h\rs1 x has a ,tide ( ,flood2 b :5 x comes to ! same po9t a aga9 9 #ab h\rs m1 x has ! l[e/ ebb4 ,9 sev5 days aft]w>d1 ! ,moon ,m comes to ! equ9octial ,circle1 & is ov] ! ,equator ,,eq1 :5 bo? ,elevations describe ! ,equator2 & 9 bo? ,hemisph]es1 at equal di/ances f ! ,equator1 ! ,tides are equally high 9 bo? p>ts ( ! lun> day4 ,! :ole ,ph5om5a be+ rev]s$ :5 ! ,moon has s\? decl9ation to :at !y 7 :5 h] decl9ation 0 nor?1 require no f>!r description4 ,sid5ote3 ,fig4 ,,vi4 ,:5 bo? ,tides are equally high 9 ! same day1 !y arrive at unequal int]vals ( ,"t2 & vice v]sa4 #cje4 ,9 ! ?ree la/-m5tion$ ,figures1 ! ,e>? is or?ographically project$ on ! plane ( ! ,m]idian2 b 9 ord] to describe a p>ticul> ,ph5om5on we n[ project x on ! plane ( ! ,ecliptic4 ,let ,,hzon be ! ,e>? & ,sea1 ,,f$ ! ,equator1 ,t ! ,tropic ( ,canc]1 ,c ! arctic ,circle1 ,p ! nor? ,pole1 & ! ,curves #a1 #b1 #c1 c4 #bd ,m]idians1 or h\r ,circles1 int]sect+ ea* o!r 9 ! ,poles2 ,,agm is ! ,moon's orbit1 ,s ! ,sun1 ,m ! ,moon1 ,z ! ,wat] elevat$ "u ! ,moon1 & ,n ! opposite equal ,elevation4 ,z ! l[e/ p>ts ( ! ,wat] are always #ij degrees f ! highe/1 :5 ! ,moon is 9 ei!r ( ! ,tropics 7z at ,m7 ! ,elevation ,z is on ! ,tropic ( ,capricorn1 & ! opposite ,elevation ,n on ! ,tropic ( ,canc]1 ! l[-wat] ,circle ,,hco t\*es ! pol> ,circles at ,c2 & ! high-wat] ,circle ,,etp#f goes ov] ! ,poles at ,p1 & divides e p>allel ( ,latitude into two equal segm5ts4 ,9 ?is case ! ,tides ^u e p>allel are alt]nately high] & l[]2 b !y return 9 equal times3 ! po9t ,t1 = example1 on ! ,tropic ( ,canc] 7:]e ! dep? ( ! ,tide is repres5t$ by ! bread? ( ! d>k %ade7 has a %all[] ,tide ( ,flood at ,t ?an :5 x revolves half r\nd f !nce to #f1 accord+ to ! ord] ( ! num]al ,figures2 b x revolves z soon f #f to ,t z x did f ,t to #f4 ,:5 ! ,moon is 9 ! ,equ9octial1 ! ,elevations ,z & ,n are transf]r$ to ! ,equator at ,o & ,h1 & ! high & l[-wat] ,circles are got into ea* o!r's =m] places2 9 :i* case ! ,tides return 9 unequal times1 b are equally high 9 bo? p>ts ( ! lun> day3 = a place at #a 7"u ,d7 revolv+ z =m]ly1 goes soon] f #a to #aa 7"u ,f7 ?an f #aa to #a1 because ! p>allel x describes is cut into unequal segm5ts by ! high-wat] ,circle ,,hco3 b ! po9ts #a & #aa be+ equidi/ant f ! ,pole ( ! ,tides at ,c1 :i* is directly "u ! ,pole ( ! ,moon's orbit ,,mga1 ! ,elevations are equally high 9 bo? p>ts ( ! day4 #cjf4 ,& ?us x appe>s1 t z ! ,tides are gov]n$ by ! ,moon1 !y mu/ turn on ! ,axis ( ! ,moon's orbit1 :i* is incl9$ #bc-a_/b degrees to ! ,e>?'s ,axis at a mean /ate3 & !re=e ! ,poles ( ! ,tides mu/ be s _m degrees f ! ,poles ( ! ,e>?1 or 9 opposite po9ts ( ! pol> ,circles1 go+ r\nd ^! ,circles 9 e lun> day4 ',tis true t accord+ to ,fig4 ,,iv4 :5 ! ,moon is v]tical to ! ,equator ,,ecq1 ! ,poles ( ! ,tides seem to fall 9 ) ! ,poles ( ! ,_w ,n & ,s3 b :5 we consid] t ,,fhg is "u ! ,moon's orbit1 x w appe>1 t :5 ! ,moon is ov] ,h1 9 ! ,tropic ( ,capricorn1 ! nor? ,pole ( ! ,tides1 7:i* c be no m ?an #ij degrees f "u ! ,moon7 mu/ be at c 9 ! arctic ,circle1 n at ,n2 ! nor? ,pole ( ! ,e>?2 & z ! ,moon asc5ds f ,h to ,g 9 h] orbit1 ! nor? ,pole ( ! ,tides mu/ %ift f c to a 9 ! arctic ,circle2 & ! ,s\? ,pole z mu* 9 ! ant>ctic4 ,x is n to be d\bt$1 b t ! ,e>?'s quick rotation br+s ! poles ( ! ,tides ne>] to ! ,poles ( ! ,_w1 ?an !y w\ld be if ! ,e>? 7 at re/1 & ! ,moon revolv$ ab\t x only once a mon?2 = o!rwise ! ,tides w\ld be m unequal 9 _! heights1 & times ( _! returns1 ?an we f9d !y are4 ,b h[ ne> ! ,e>?'s rotation may br+ ! ,poles ( x's ,axis & ^? ( ! ,tides toge!r1 or h[ f> ! prec$+ ,tides may affect ^? :i* foll[1 s z to make !m keep up ne>ly to ! same heights1 & times ( ebb+ & fl[+1 is a problem m fit to be solv$ by obs]vation ?an by !ory4 ,sid5ote3 ,to "k at :at times we may expect ! greate/ & lea/ ,tides4 #cjg4 ,^? :o h opportunity to make obs]vations1 & *oose to satisfy !mselves :e!r ! ,tides are really affect$ 9 ! above mann] by ! diff]5t positions ( ! ,moon2 especially z to ! unequal times ( _! returns1 may take ?is g5]al rule = kn[+1 :5 !y ought to be s affect$4 ,:5 ! ,e>?'s ,axis incl9es to ! ,moon1 ! nor!rn ,tides1 if n ret>d$ 9 _! passage ?r\gh ,%oals & ,*annels1 nor affect$ by ! ,w9ds1 ought to be greate/ :5 ! ,moon is above ! ,horizon1 lea/ :5 %e is bel[ x2 & q ! rev]se :5 ! ,e>?'s ,axis decl9es f h]3 b 9 bo? cases1 at equal int]vals ( "t4 ,:5 ! ,e>?'s ,axis incl9es sidewise to ! ,moon1 bo? ,tides are equally high1 b !y happ5 at unequal int]vals ( "t4 ,9 e ,lunation ! ,e>?'s ,axis incl9es once to ! ,moon1 once f h]1 & twice sidewise to h]1 z x does to ! ,sun e ye>2 because ! ,moon goes r\nd ! ,ecliptic e mon?1 & ! ,sun b once 9 a ye>4 ,9 ,summ]1 ! ,e>?'s ,axis incl9es t[>ds ! ,moon :5 ,new2 & !re=e ! day-tides 9 ! nor? ought to be highe/1 & night-tides l[e/ ab\t ! ,*ange3 at ! ,full ! rev]se4 ,at ! ,qu>t]s !y ought to be equally high1 b unequal 9 _! returns2 because ! ,e>?'s ,axis !n incl9es sidewise to ! ,moon4 ,9 w9t] ! ,ph5om5a are ! same at ,full-,moon z 9 ,summ] at ,new4 ,9 ,autumn ! ,e>?'s ,axis incl9es sidewise to ! ,moon :5 ,new & ,full2 !re=e ! ,tides ought to be equally high1 & unequal 9 _! returns at ^! times4 ,at ! fir/ ,qu>t] ! ,tides ( ,flood %\ld be lea/ :5 ! ,moon is above ! ,horizon1 greate/ :5 %e is bel[ x2 & ! rev]se at h] ?ird ,qu>t]4 ,9 ,spr+1 ,ph5om5a ( ! fir/ ,qu>t] answ] to ^? ( ! ?ird ,qu>t] 9 ,autumn2 & vice v]sa4 ,! ne>] any "t is to ei!r ( ^! seasons1 ! m ! ,tides p>take ( ! ,ph5om5a ( ^! seasons2 & 9 ! middle betwe5 any two ( !m ! ,tides are at a mean /ate betwe5 ^? ( bo?4 ,sid5ote3 ,:y ! ,tides rise high] 9 ,riv]s ?an 9 ! ,sea4 #cjh4 ,9 op5 ,seas1 ! ,tides rise b to v small heights 9 proportion to :at !y d 9 wide-m\!d riv]s1 op5+ 9 ! ,direction ( ! ,/ream ( ,tide4 ,=1 9 ,*annels gr[+ n>r[] gradually1 ! wat] is accumulat$ by ! opposition ( ! contract+ ,bank4 ,l a g5tle w9d1 little felt on an op5 pla91 b /rong & brisk 9 a /reet2 especially if ! wid] end ( ! /reet be next ! pla91 & 9 ! way ( ! w9d4 ,sid5ote3 ,! ,tides happ5 at all di/ances ( ! ,moon f ! ,m]idian at diff]5t places1 & :y4 #cji4 ,! ,tides are s ret>d$ 9 _! passage ?r\gh diff]5t ,%oals & ,*annels1 & o!rwise s v>i\sly affect$ by /rik+ aga9/ ,capes & ,headl&s1 t to diff]5t places !y happ5 at all di/ances ( ! ,moon f ! ,m]idian2 consequ5tly at all h\rs ( ! lun> day4 ,! ,tide propagat$ by ! ,moon 9 ! ,g]man ocean1 :5 %e is ?ree h\rs pa/ ! ,m]idian1 takes #ab h\rs to come f !nce to ,london bridge2 :]e x arrives by ! "t t a new ,tide is rais$ 9 ! ocean4 ,& !re=e :5 ! ,moon has nor? decl9ation1 & we %\ld expect ! ,tide at ,london to be greate/ :5 ! ,moon is above ! ,horizon1 we f9d x is lea/2 & ! contr>y :5 %e has s\? decl9ation4 ,at sev]al places 'tis high wat] ?ree h\rs be=e ! ,moon comes to ! ,m]idian2 b t ,tide :i* ! ,moon pu%es z x 7 be=e h]1 is only ! ,tide opposite to t :i* 0 rais$ by h] :5 %e 0 n9e h\rs pa/ ! opposite ,m]idian4 ,sid5ote3 ,! ,wat] nev] rises 9 ,lakes4 #caj4 ,!re are no ,tides 9 ,lakes1 because !y are g5]ally s small t :5 ! ,moon is v]tical %e attracts e "p ( !m alike1 & !re=e by r5d]+ all ! wat] equally light1 no "p ( x c be rais$ high] ?an ano!r4 ,! ,m$it]ranean & ,baltic ,seas suff] v small elevations1 because ! ,inlets by :i* !y communicate ) ! ocean are s n>r[1 t !y _c1 9 s %ort a "t1 receive or dis*>ge en\gh to raise or s9k _! surfaces s5sibly4 ,sid5ote3 ,! ,moon raises ,tides 9 ! ,air4 ,:y ! ,m]cury 9 ! ,b>omet] is n affect$ by ! a]ial ,tides4 #caa4 ,air be+ light] ?an ,wat]1 & ! surface ( ! ,atmosph]e be+ ne>] to ! ,moon ?an ! surface ( ! ,sea1 x _c be d\bt$ t ! ,moon raises mu* high] ,tides 9 ! ,air ?an 9 ! ,sea4 ,& !re=e _m h wond]$ :y ! ,m]cury does n s9k 9 ! ,b>omet] :5 ! ,moon's action on ! p>ticles ( ,air makes !m light] z %e passes ov] ! ,m]idian4 ,b we mu/ consid]1 t z ^! p>ticles are r5d]$ light]1 a great] numb] ( !m is accumulat$1 until ! defici5cy ( gravity be made up by ! height ( ! column2 & !n !re is an equilibrium1 & consequ5tly an equal pressure ^u ! ,m]cury z be=e2 s t x _c be affect$ by ! a]ial ,tides4 ,,*ap4 ,,xviii4 ,( ,eclipses3 ,_! ,numb] & ,p]iods4 ,a l>ge ,catalogue ( ,anci5t & ,mod]n ,eclipses4 ,sid5ote3 ,a %ad[1 :at4 #cab4 ,e ,planet & ,satellite is illum9at$ by ! ,sun2 & ca/s a %ad[ t[>ds t po9t ( ! ,heav5s :i* is opposite to ! ,sun4 ,?is %ad[ is no?+ b a privation ( light 9 ! space hid f ! ,sun by ! opake body t int]cepts 8 rays4 ,sid5ote3 ,eclipses ( ! ,sun & ,moon1 :at4 #cac4 ,:5 ! ,sun's light is s int]cept$ by ! ,moon1 t to any place ( ! ,e>? ! ,sun appe>s p>tly or :olly cov]$1 he is said to und]go an ,eclipse2 ?\gh prop]ly speak+1 'tis only an ,eclipse ( t "p ( ! ,e>? :]e ! ,moon's %ad[ or #fd,p5umbra falls4 ,:5 ! ,e>? comes betwe5 ! ,sun & ,moon1 ! ,moon falls into ! ,e>?'s %ad[2 & hav+ no light ( h] own1 %e suff]s a real ,eclipse f ! int]ception ( ! ,sun's rays4 ,:5 ! ,sun is eclips$ to u1 ! ,moon's ,inhabitants on ! side next ! ,e>? 7if any su* !re be7 see h] %ad[ l a d>k spot travell+ ov] ! ,e>?1 ab\t twice z fa/ z its equatoreal p>ts move1 & ! same way z !y move4 ,:5 ! ,moon is 9 an ,eclipse1 ! ,sun appe>s eclips$ to h]1 total to all ^? p>ts on :i* ! ,e>?'s %ad[ falls1 & ( z long cont9uance z !y are 9 ! %ad[4 ,illu/ration3 ,plate ,x4 ,j4 ,f]guson del94 ,j4 ,mynde ,sculp4 ,sid5ote3 ,a pro( t ! ,e>? & ,moon are globul> bodies4 #cad4 ,t ! ,e>? is sph]ical 7= ! hills take (f no m f ! r\ndness ( ! ,e>?1 ?an gra9s ( du/ d f ! r\ndness ( a common ,globe7 is evid5t f ! figure ( its %ad[ on ! ,moon2 :i* is always b\nd$ by a circul> l9e1 al?\gh ! ,e>? is incessantly turn+ its diff]5t sides to ! ,moon1 & v seldom %ews ! same side to h] 9 diff]5t ,eclipses1 because !y seldom happ5 at ! same h\rs4 ,7 ! ,e>? %ap$ l a r\nd flat plate1 its %ad[ w\ld only be circul> :5 ei!r ( its sides directly fac$ ! ,moon2 & m or less elliptical z ! ,e>? happ5$ to be turn$ m or less obliquely t[>ds ! ,moon :5 %e is eclips$4 ,! ,moon's diff]5t ,phases prove h] to be r\nd #bed2 =1 z %e keeps /ill ! same side t[>ds ! e>?1 if t side 7 flat1 z x appe>s to be1 %e w\ld nev] be visible f ! ?ird ,qu>t] to ! fir/2 & f ! fir/ ,qu>t] to ! ?ird1 %e w\ld appe> z r\nd z :5 we say %e is ,full3 because at ! end ( h] fir/ ,qu>t] ! ,sun's light w\ld come z sudd5ly on all h] side next ! ,e>?1 z x does on a flat wall1 & g (f z abruptly at ! end ( h] ?ird ,qu>t]4 ,sid5ote3 ,& t ! ,sun is mu* bigg] ?an ! ,e>?1 & ! ,moon mu* less4 #cae4 ,if ! ,e>? & ,sun 7 equally big1 ! ,e>?'s %ad[ w\ld be inf9itely ext5d$1 & all ( ! same bread?2 & ! ,planet ,m>s1 9 ei!r ( its nodes & opposite to ! ,sun1 w\ld be eclips$ 9 ! ,e>?'s %ad[4 ,7 ! ,e>? bigg] ?an ! ,sun1 x's %ad[ w\ld increase 9 bread? ! f>!r x 0 ext5d$1 & w\ld eclipse ! great ,planets ,jupit] & ,saturn1 ) all _! ,moons1 :5 !y 7 opposite to ! ,sun4 ,b z ,m>s 9 opposition nev] falls into ! ,e>?'s %ad[1 al?\gh he is n !n above #db millions ( miles f ! ,e>?1 'tis pla9 t ! ,e>? is mu* less ?an ! ,sun2 = o!rwise x's %ad[ c\ld n end 9 a po9t at s small a di/ance4 ,if ! ,sun & ,moon 7 equally big1 ! ,moon's %ad[ w\ld g on to ! ,e>? ) an equal bread?1 & cov] a portion ( ! ,e>?'s surface m ?an #bjjj miles broad1 ev5 if x fell directly aga9/ ! ,e>?'s c5t]1 z se5 f ! ,moon3 & mu* m if x fell obliquely on ! ,e>?3 b ! ,moon's %ad[ is seldom #aej miles broad at ! ,e>?1 unless :5 x falls v obliquely on ! ,e>?1 9 total ,eclipses ( ! ,sun4 ,9 annul> ,eclipses1 ! ,moon's real %ad[ ends 9 a po9t at "s di/ance f ! ,e>?4 ,! ,moon's small di/ance f ! ,e>?1 & ! %ortness ( h] %ad[1 prove h] to be less ?an ! ,sun4 ,&1 z ! ,e>?'s %ad[ is l>ge en\gh to cov] ! ,moon1 if h] diamet] 0 ?ree times z l>ge z x is 7:i* is evid5t f h] long cont9uance 9 ! %ad[ :5 %e goes ?r\gh x's c5t]7 'tis pla91 t ! ,e>? is mu* bigg] ?an ! ,moon4 ,sid5ote3 ,! prim>y ,planets nev] eclipse "o ano!r4 ,,plate ,x4 #caf4 ,?\gh all opake bodies on :i* ! ,sun %9es h _! %ad[s1 yet su* is ! bulk ( ! ,sun1 & ! di/ances ( ! ,planets1 t ! prim>y ,planets c nev] eclipse "o ano!r4 ,a ,prim>y c eclipse only x's second>y1 or be eclips$ by x2 & nev] b :5 9 opposition or conjunction ) ! ,sun4 ,! prim>y ,planets are v seldom 9 ^! positions1 b ! ,sun & ,moon are s e mon?3 :5ce "o may imag9e t ^! two ,lum9>ies %\ld be eclips$ e mon?4 ,b !re are few ,eclipses 9 respect ( ! numb] ( ,new & ,full ,moons2 ! reason ( :i* we %all n[ expla94 ,sid5ote3 ,:y !re are s few ,eclipses4 ,! ,moon's ,nodes4 ,limits ( ,eclipses4 #cag4 ,if ! ,moon's ,orbit 7 co9cid5t ) ! ,plane ( ! ,ecliptic1 9 :i* ! ,e>? always moves & ! ,sun appe>s to move1 ! ,moon's %ad[ w\ld fall ^u ! ,e>? at e ,*ange1 & eclipse ! ,sun to "s p>ts ( ! ,e>?4 ,9 l mann] ! ,moon w\ld g ?r\gh ! middle ( ! ,e>?'s %ad[1 & be eclips$ at e ,full2 b ) ?is diff]5ce1 t %e w\ld be totally d>k5$ = above an h\r & half2 :]eas ! ,sun nev] 0 above f\r m9utes totally eclips$ by ! int]position ( ! ,moon4 ,b "o half ( ! ,moon's ,orbit1 is elevat$ #e-a_/c degrees above ! ,ecliptic1 & ! o!r half z mu* depress$ bel[ x3 consequ5tly1 ! ,moon's ,orbit int]sects ! ,ecliptic 9 two opposite po9ts call$ ! ,moon's ,nodes1 z has be5 already tak5 notice ( #bhh4 ,:5 ^! po9ts are 9 a "r l9e ) ! c5t] ( ! ,sun at ,new or ,full ,moon1 ! ,sun1 ,moon1 & ,e>? are all 9 a "r l9e2 & if ! ,moon be !n ,new1 h] %ad[ falls ^u ! ,e>?2 if ,full ! ,e>?'s %ad[ falls ^u h]4 ,:5 ! ,sun & ,moon are m ?an #ag degrees f ei!r ( ! ,nodes at ! "t ( ,conjunction1 ! ,moon is !n too high or too l[ 9 h] ,orbit to ca/ any "p ( h] %ad[ ^u ! ,e>?4 ,& :5 ! ,sun is m ?an #ab degrees f ei!r ( ! ,nodes at ! "t ( ,full ,moon1 ! ,moon is too high or too l[ 9 h] ,orbit to g ?r\gh any "p ( ! ,e>?'s %ad[3 & 9 bo? ^! cases !re w be no ,eclipse4 ,b :5 ! ,moon is less ?an #ag degrees f ei!r ,node at ! "t ( ,conjunction1 h] %ad[ or ,p5umbra falls m or less ^u ! ,e>?1 z %e is m or less )9 ?is limit4 ,& :5 %e is less ?an #ab degrees f ei!r ,node at ! "t ( opposition1 %e goes ?r\gh a great] or less portion ( ! ,e>?'s %ad[1 z %e is m or less )9 ?is limit4 ,h] ,orbit conta9s #cfj degrees2 ( :i* #ag1 ! limit ( sol> ,eclipses on ei!r side ( ! ,nodes1 & #ab ! limit ( lun> ,eclipses1 are b small portions3 & z ! ,sun commonly passes by ! ,nodes b twice 9 a ye>1 x is no wond] t we h s _m ,new & ,full ,moons )\t ,eclipses4 ,sid5ote3 ,fig4 ,i4 ,,plate ,x4 ,l9e ( ! ,nodes4 ,to illu/rate ?is1 let ,,abcd be ! ,ecliptic1 ,,r/u a ,circle ly+ 9 ! same ,plane ) ! ,ecliptic1 & ,,vwxy ! ,moon's ,orbit1 all ?r[n into an oblique view1 :i* gives !m an elliptical %ape to ! eye4 ,"o half ( ! ,moon's ,orbit1 z ,,vwx1 is always bel[ ! ,ecliptic1 & ! o!r half ,,xyv above x4 ,! po9ts ,v & ,x1 :]e ! ,moon's ,orbit int]sects ! ,circle ,,r/u1 :i* lies ev5 ) ! ,ecliptic1 are ! ,moon's ,nodes2 & a "r l9e z ,,xev drawn f "o to ! o!r1 ?r\gh ! ,e>?'s c5t]1 is ! ,l9e ( ! ,nodes1 :i* is c>ri$ almo/ p>allel to itself r\nd ! ,sun 9 a ye>4 ,if ! ,moon mov$ r\nd ! ,e>? 9 ! ,orbit ,,r/u1 :i* is co9cid5t ) ! ,plane ( ! ,ecliptic1 h] %ad[ w\ld fall ^u ! ,e>? e "t %e is 9 conjunction ) ! ,sun2 & at e opposition %e w\ld g ?r\gh ! ,e>?'s %ad[4 ,7 ?is ! case1 ! ,sun w\ld be eclips$ at e ,*ange1 & ! ,moon at e ,full1 z already m5tion$4 ,b al?\gh ! ,moon's %ad[ ,n mu/ fall ^u ! ,e>? at a1 :5 ! ,e>? is at ,e1 & ! ,moon 9 conjunction ) ! ,sun at i1 because %e is !n v ne> "o ( h] ,nodes2 & at h] opposition n %e mu/ g ?r\gh ! ,e>?'s %ad[ ,i1 because %e is !n ne> ! o!r ,node2 yet1 9 ! "t t %e goes r\nd ! ,e>? to h] next ,*ange1 accord+ to ! ord] ( ! lett]s ,,xyvw1 ! ,e>? advances f ,e to e1 accord+ to ! ord] ( ! lett]s ,,efgh1 & ! l9e ( ! ,nodes ,,vex be+ c>ri$ ne>ly p>allel to itself1 br+s ! po9t f ( ! ,moon's ,orbit 9 conjunction ) ! ,sun at t next ,*ange2 & !n ! ,moon be+ at f is too high above ! ,ecliptic to ca/ h] %ad[ on ! ,e>?3 & z ! ,e>? is /ill mov+ =w>d1 ! ,moon at h] next opposition w be at g1 too f> bel[ ! ,ecliptic to g ?r\gh any "p ( ! ,e>?'s %ad[2 = by t "t ! po9t g w be at a consid]able di/ance f ! ,e>? z se5 f ! ,sun4 ,sid5ote3 ,fig4 ,i & ,,ii4 ,:5 ! ,e>? comes to ,f1 ! ,moon 9 conjunction ) ! ,sun ,z is n at k1 9 a ,plane co9cid5t ) ! ,ecliptic1 b above x at ,y 9 ! highe/ "p ( h] ,orbit3 & !n ! po9t b ( h] %ad[ ,o goes f> above ! ,e>? 7z 9 ,fig4 ,,ii1 :i* is an edge view ( ,fig4 ,i47 ,! ,moon at h] next opposition is n at o 7,fig ,i7 b at ,w :]e ! ,e>?'s %ad[ goes f> above h]1 7z 9 ,fig4 ,,ii47 ,9 bo? ^! cases ! l9e ( ! ,nodes ,,vfx 7,fig4 ,i47 is ab\t #ij degrees f ! ,sun1 & bo? ,lum9>ies z f> z possible f ! limits ( ,eclipses4 ,sid5ote3 ,,plate ,x4 ,:5 ! ,e>? has gone half r\nd ! ,ecliptic f ,e to ,g1 ! l9e ( ! ,nodes ,,vgx is ne>ly1 if n exactly1 direct$ t[>ds ! ,sun at ,z2 & !n ! ,new ,moon l ca/s h] %ad[ ,p on ! ,e>? ,g2 & ! ,full ,moon p goes ?r\gh ! ,e>?'s %ad[ ,l2 :i* br+s on ,eclipses aga91 z :5 ! ,e>? 0 at ,e4 ,:5 ! ,e>? comes to ,h ! ,new ,moon falls n at m 9 a plane co9cid5t ) ! ,ecliptic ,,cd1 b at ,w 9 h] ,orbit bel[ x3 & !n h] %ad[ ,q 7see ,fig4 ,,ii7 goes f> bel[ ! ,e>?4 ,at ! next ,full %e is n at q 7,fig4 ,i7 b at ,y 9 h] orbit #e-a_/c degrees above q1 & at h] greate/ height above ! ,ecliptic ,,cd2 be+ !n z f> z possible1 at any opposition1 f ! ,e>?'s %ad[ ,m 7z 9 ,fig4 ,,ii47 ,s1 :5 ! ,e>? is at ,e & ,g1 ! ,moon is ab\t h] ,nodes at ,new & ,full2 & 9 h] greate/ ,nor? & ,s\? ,decl9ation1 7or ,latitude z x is g5]ally call$7 f ! ,ecliptic at h] ,qu>t]s3 b :5 ! ,e>? is at ,f or ,h1 ! ,moon is 9 h] greate/ ,nor? & ,s\? ,decl9ation f ! ,ecliptic at ,new & ,full1 & 9 ! ,nodes ab\t h] ,qu>t]s4 ,sid5ote3 ,! ,moon's asc5d+ & desc5d+ ,node4 ,h] ,nor? & ,s\? ,latitude4 #cah4 ,! po9t ,x :]e ! ,moon's ,orbit crosses ! ,ecliptic is call$ ! ,asc5d+ ,node1 because ! ,moon asc5ds f x above ! ,ecliptic3 & ! opposite po9t ( int]section ,v is call$ ! ,desc5d+ ,node1 because ! ,moon desc5ds f x bel[ ! ,ecliptic4 ,:5 ! ,moon is at ,y 9 ! highe/ po9t ( h] ,orbit1 %e is 9 h] greate/ ,nor? ,latitude2 & :5 %e is at ,w 9 ! l[e/ po9t ( h] ,orbit1 %e is 9 h] greate/ ,s\? ,latitude4 ,sid5ote3 ,! ,nodes h a retrograde motion4 ,fig4 ,i4 ,:i* br+s on ! ,eclipses soon] e ye> ?an !y w\ld be if ! ,nodes _h n su* a motion4 #cai4 ,if ! l9e ( ! ,nodes1 l ! ,e>?'s ,axis1 0 c>ri$ p>allel to itself r\nd ! ,sun1 !re w\ld be j half a ye> betwe5 ! conjunctions ( ! ,sun & ,nodes4 ,b ! ,nodes %ift backw>d1 or contr>y to ! ,e>?'s annual motion1 #ai-a_/c degrees e ye>2 & !re=e ! same ,node comes r\nd to ! ,sun #ai days soon] e ye> ?an on ! ye> be=e4 ,consequ5tly1 f ! "t t ! asc5d+ ,node ,x 7:5 ! ,e>? is at ,e7 passes by ! ,sun z se5 f ! ,e>?1 x is only #agc days 7n half a ye>7 till ! desc5d+ ,node ,v passes by him4 ,!re=e1 9 :atev] "t ( ! ye> we h ,eclipses ( ! ,lum9>ies ab\t ei!r ,node1 we may be sure t 9 #agc days aft]w>d we %all h ,eclipses ab\t ! o!r ,node4 ,& :5 at any "t ( ! ye> ! l9e ( ! ,nodes is 9 ! situation ,,vgx1 at ! same "t next ye> x w be 9 ! situation r,gs2 ! asc5d+ ,node hav+ gone backw>d1 t is1 contr>y to ! ord] ( ,signs f ,x to s1 & ! desc5d+ ,node f ,v to r2 ea* #ai-a_/c degrees4 ,at ?is rate ! ,nodes %ift ?r\gh all ! ,signs & degrees ( ! ,ecliptic 9 #ah ye>s & #bbe days2 9 :i* "t !re w\ld always be a regul> p]iod ( ,eclipses1 if any compleat numb] ( ,lunations 7 f9i%$ )\t a fraction4 ,b ?is nev] happ5s1 = if ! ,sun & ,moon %\ld />t f a conjunction ) ei!r ( ! ,nodes 9 any po9t ( ! ,ecliptic1 :il/ ! same ,node is go+ r\nd to t po9t aga9 ! ,e>? p]=ms #ah annual revolutions ab\t ! ,sun & #bbb ,degrees 7or #g ,signs #ab ,degrees7 ov]2 & ! ,moon #bcj ,lunations or ,c\rses f ,*ange to ,*ange & #he ,degrees 7or #b ,signs #be ,degrees7 ov]2 s t ! ,sun w be #ach ,degrees f ! same ,node :5 x comes r\nd1 & ! ,moon #he ,degrees f ! ,sun4 ,h5ce1 ! p]iod ( ,eclipses & revolution ( ! ,nodes are complet$ 9 diff]5t times4 ,sid5ote3 ,a p]iod ( ,eclipses4 ,! defects ( x4 #cbj4 ,9 #ah ye>s #aj days #g h\rs #dc m9utes aft] ! ,sun ,moon & ,nodes h be5 9 a l9e ( conjunction1 !y come v ne> to a conjunction aga93 only1 if ! conjunction f :i* y reckon falls 9 a leap-ye>1 ! return ( ! conjunction w be "o day lat]4 ,!re=e1 if to ! #femean "t ( any ,eclipse ( ! ,sun or ,moon 9 leap-ye>1 y add #ah ye>s #aa days #g h\rs #dc m9utes2 or 9 a common ye> a day less1 y w h ! mean "t ( t ,eclipse return$ aga9 = "s ages2 ?\gh n always visible1 because ! #g h\rs #dc m9utes may %ift a sol> ,eclipse into ! night1 & a lun> ,eclipse into ! day4 ,9 ?is p]iod !re are j #bbc ,lunations1 & ! ,sun is aga9 )9 half a degree ( ! same ,node1 b %ort ( x4 ,!re=e1 al?\gh ?is p]iod w s]ve tol]ably well = "s ages to exam9e ,eclipses by1 x _c hold long2 because half a degree f ! ,node sets ! ,moon #b-a_/b m9utes ( a degree f ! ,ecliptic4 ,& z ! ,moon's mean di/ance f ! ,e>? is equal to #fj ,semidiamet]s ( ! ,e>?1 e m9ute ( a degree at t di/ance is equal to #fj geographical miles1 or "o degree on ! ,e>?2 consequ5tly #b-a_/b m9utes ( decl9ation f ! ,ecliptic 9 ! ,moon's ,orbit1 is equal to #aej su* miles1 or #b-a_/b degrees on ! ,e>?4 ,consequ5tly1 if ! ,moon be pass+ by h] asc5d+ ,node at ! end ( ?is p]iod1 h] %ad[ w g #aej miles m s\?w>d on ! ,e>? ?an x did at ! beg9n+ !re(4 ,if ! ,moon be pass+ by h] desc5d+ ,node1 h] %ad[ w g #aej miles m nor?w>d3 & 9 ei!r case1 9 #ejj ye>s ! %ad[ w h too great a ,latitude to t\* ! ,e>?4 ,s t any ,eclipse ( ! ,sun1 :i* beg9s 7= example7 to t\* ! ,e>? at ! s\? ,pole 7& t mu/ be :5 ! ,moon is #ag degrees pa/ h] desc5d+ ,node7 w advance gradually nor?w>d 9 e return = ab\t a ?\s& ye>s1 & !n g (f at ! nor? ,pole2 & _c take su* ano!r c\rse aga9 9 less ?an #aa1fhc ye>s4 ,?is fall+ back ( ! ,sun & ,moon 9 e p]iod1 ) respect to ! ,nodes1 w occasion ^? ,eclipses :i* happ5 ab\t ! asc5d+ ,node to g m s\!rly 9 ea* return2 & ^? :i* happ5 ab\t ! desc5d+ ,node to g m nor!rly3 = ! f>!r ! ,moon is %ort ( ! asc5d+ ,node1 )9 ! limits ( ,eclipses1 ! f>!r %e is s\? ( ! ,ecliptic2 & on ! contr>y1 ! m %e is %ort ( ! desc5d+ ,node1 ! f>!r %e is nor?w>d ( ! ,ecliptic4 ,sid5ote3 ,f ,mr4 ,g4 ,,smi?'s diss]tation on ,eclipses1 pr9t$ at ,london1 by ,e4 ,,cave1 9 ! ye> #agdh4 #cba4 8,to illu/rate ?is a little f>!r1 we %all exam9e "s ( ! mo/ rem>kable circum/ances ( ! returns ( ! ,eclipse :i* happ5$ ,july #ad1 #agdh1 ab\t noon3 ,?is ,eclipse1 aft] trav]s+ ! voids ( space f ! ,creation1 at la/ began to ent] ! ,t]ra ,au/ralis ,incognita1 ab\t #hh ye>s aft] ! ,conque/1 :i* 0 ! la/ ( ,k+ ,,/eph5's reign2 e #ff;,*aldean p]iod x has crept m nor!rly1 b 0 /ill invisible 9 ,brita9 be=e ! ye> #afbb2 :5 on ! #cj? ( ,april x began to t\* ! s\? p>ts ( ,engl& ab\t #b 9 ! aft]noon2 its c5tral appe>ance ris+ 9 ! ,am]ican ,s\? ,seas1 & trav]s+ ,p]u & ! ,amazon's c\ntry1 ?r\gh ! ,atlantic ocean into ,africa1 & sett+ 9 ! ?iopian cont95t1 n f> f ! beg9n+ ( ! ,r$ ,sea4 8,its next visible p]iod 0 aft] ?ree ,*aldean revolutions 9 #afgf1 on ! fir/ ( ,june1 ris+ c5tral 9 ! ,atlantic ocean1 pass+ u ab\t #i 9 ! morn+1 ) f\r #fg;,digits eclips$ on ! "u limb2 & sett+ 9 ! gulf ( ,co*9*9a 9 ! ,ea/-,indies4 8,x be+ n[ ne> ! ,sol/ice1 ?is ,eclipse 0 visible ! v next return 9 #afid1 9 ! ev5+2 & 9 two p]iods m1 :i* 0 9 #agcj1 on ! #d? ( ,july1 0 se5 above half eclips$ j aft] ,sun-rise1 & obs]v$ bo? at ,wirtemb]g 9 ,g]many1 & ,pek9 9 ,*9a1 soon aft] :i* x w5t (f4 8,eighte5 ye>s m af=d$ u ! ,eclipse :i* fell on ! #ad? ( ,july #agdh4 8,! next visible return w happ5 on ,july #be1 #agff1 9 ! ev5+1 ab\t f\r ,digits eclips$2 & aft] two p]iods m1 on ,augu/ #af?1 #ahjb1 e>ly 9 ! morn+1 ab\t five ,digits1 ! c5t] com+ f ! nor? froz5 cont95t1 by ! capes ( ,norway1 ?r\gh ,t>t>y1 ,*9a1 & ,japan1 to ! ,ladrone isl&s1 :]e x goes (f4 8,aga91 9 #ahbj1 ,augu/ #bf1 betwixt "o & two1 !re w be ano!r great ,eclipse at ,london1 ab\t #aj ,digits2 b happ5+ s ne> ! ,equ9ox1 ! c5t] w leave e "p ( ,brita9 to ! ,we/1 & ent] ,g]many at ,embd51 pass+ by ,v5ice1 ,naples1 ,gr& ,cairo1 & set 9 ! gulf ( ,bassora ne> t city4 8,x w be no m visible till #ahgd1 :5 five ,digits w be obscur$1 ! c5t] be+ n[ ab\t to leave ! ,e>? on ,septemb] #bh4 ,9 #ahib ! ,sun w g d[n eclips$ at ,london1 & aga9 9 #aibh ! passage ( ! c5t] w be 9 ! expansum1 ?\gh !re w be two ,digits eclips$ at ,london1 ,octob] ! #ca/ ( t ye>2 & ab\t ! ye> #bjij ! :ole ,p5umbra w be wore (f2 :5ce no m returns ( ?is ,eclipse c happ5 till aft] a revolution ( #aj ?\s& ye>s4 8,f ^! rem>ks on ! intire revolution ( ?is ,eclipse1 we may ga!r1 t a ?\s& ye>s1 m or less 7= !re are "s irregul>ities t may protract or l5g!n ?is p]iod #ajj ye>s7 complete ! :ole t]re/rial ,ph5om5a ( any s+le ,eclipse3 & s9ce #bj p]iods ( #ed ye>s ea*1 & ab\t #cc days1 compreh5d ! intire ext5t ( _! revolution1 'tis evid5t t ! times ( ! returns w pass ?r\gh a circuit ( "o ye> & t5 mon?s1 e ,*aldean p]iod be+ t5 or elev5 days lat]1 & ( ! equable appe>ances ab\t #cb or #cc days4 ,?us1 ?\gh ?is ,eclipse happ5s ab\t ! middle ( ,july1 no o!r subsequ5t ,eclipse ( ?is p]iod w return to ! middle ( ! same mon? aga92 b we> con/antly ea* p]iod #aj or #aa days =w>d1 & at la/ appe> 9 ,w9t]1 b !n x beg9s to cease f affect+ u4 8,ano!r conclusion f ?is revolution may be drawn1 t !re w seldom be any m ?an two great ,eclipses ( ! ,sun 9 ! int]val ( ?is p]iod1 & ^! foll[ sometimes next return1 & (t5 at great] di/ances4 ,t ( #agae return$ aga9 9 #agcc v great2 b ?is pres5t ,eclipse w n be great till ! arrival ( #ahbj1 :i* is a revolution ( f\r ,*aldean p]iods3 s t ! irregul>ities ( _! circuits mu/ und]go new computations to assign !m exactly4 8,nor d all ,eclipses come 9 at ! s\? ,pole3 t dep5ds altoge!r on ! position ( ! lun> ,nodes1 :i* w br+ 9 z _m f ! expansum "o way z ! o!r2 & su* ,eclipses w we> m s\!rly by degrees1 contr>y to :at happ5s 9 ! pres5t case4 8,! ,eclipse1 = example1 ( #agcf1 9 ,septemb]1 _h its c5t] 9 ! expansum1 & set ab\t ! middle ( its obscurity 9 ,brita92 x w we> 9 at ! nor? ,pole1 & 9 ! ye> #bfjj1 or !reab\ts1 g (f into ! expansum on ! s\? side ( ! ,e>?4 8,! ,eclipses !re=e :i* happ5$ ab\t ! ,creation are little m ?an half way yet ( _! e!rial circuit2 & w be #djjj ye>s be=e !y ent] ! ,e>? any m4 ,?is gr& revolution seems to h be5 entirely unkn[n to ! anti5ts4 ,sid5ote3 ,:y our pres5t ,tables agree n ) anti5t obs]vations4 8#cbb4 ,x is p>ticul>ly to be not$1 t ,eclipses :i* h happ5$ _m c5turies ago1 w n be f\nd by our pres5t ,tables to agree exactly ) anti5t obs]vations1 by reason ( ! great ,anomalies 9 ! lun> motions2 :i* appe>s an inconte/able demon/ration ( ! non-et]nity ( ! ,univ]se4 ,= x seems confirm$ by und5iable pro(s1 t ! ,moon n[ f9i%es h] p]iod 9 less "t ?an =m]ly1 & w cont9ue by ! c5tripetal law to approa* ne>] & ne>] ! ,e>?1 & to g soon] & soon] r\nd x3 nor w ! c5trifugal p[] be suffici5t to comp5sate ! diff]5t gravitations ( su* an assemblage ( bodies z con/itute ! sol> sy/em1 :i* w\ld come to ru9 ( itself1 )\t "s new regulation & adju/m5t ( _! orig9al motions#fh4 ,sid5ote3 ,,?ales's ,eclipse4 8#cbc4 ,we are cr$ibly in=m$ f ! te/imony ( ! anti5ts1 t !re 0 a total ,eclipse ( ! ,sun pr$ict$ by ,,?ales to happ5 9 ! f\r? ye> ( ! #dh? #fi,olympiad1 ei!r at ,s>dis or ,miletus 9 ,asia1 :]e ,,?ales !n resid$4 ,t ye> corresponds to ! #ehe? ye> be=e ,,*ri/2 :5 accord+ly !re happ5$ a v signal ,eclipse ( ! ,sun1 on ! #bh? ( ,may1 answ]+ to ! pres5t #aj? ( t mon?#gj1 c5tral ?r\gh ,nor? ,am]ica1 ! s\? p>ts ( ,france1 ,italy1 c4 z f> z ,a!ns1 or ! ,isles 9 ! gean ,sea2 :i* is ! f>!/ t ev5 ! ,c>ol9e ,tables c>ry x2 & consequ5tly make x invisible to any "p ( ,asia1 9 ! total "*2 ?\gh ,i h good reasons to believe t x ext5d$ to ,babylon1 & w5t d[n c5tral ov] t city4 ,we are n h[ev] to imag9e1 t x 0 set be=e x pa/ ,s>dis & ! ,asiatic t[ns1 :]e ! pr$ictor liv$2 because an invisible ,eclipse c\ld h be5 ( no s]vice to demon/rate 8 ability 9 ,a/ronomical ,sci5ces to 8 c\ntrym51 z x c\ld give no pro( ( its reality4 ,sid5ote3 ,,?ucydides's ,eclipse4 8#cbd4 ,= a f>!r illu/ration1 ,,?ucydides relates1 t a sol> ,eclipse happ5$ on a ,summ]'s day 9 ! aft]noon1 9 ! fir/ ye> ( ! ,peloponnesian w>1 s great t ! ,/>s appe>$4 ,rhodius 0 victor 9 ! ,olympic games ! f\r? ye> ( ! said w>1 be+ also ! f\r? ( ! #hg? ,olympiad1 on ! #dbh? ye> be=e ,,*ri/4 ,s t ! ,eclipse mu/ h happ5$ 9 ! #dca/ ye> be=e ,,*ri/2 & by computation x appe>s1 t on ! #c;d ( ,augu/ !re 0 a signal ,eclipse :i* w\ld h pa/ ov] ,a!ns1 c5tral ab\t #f 9 ! ev5+1 b :i* our pres5t ,tables br+ no f>!r ?an ! anti5t ,syrtes on ! ,african coa/1 above #djj miles f ,a!ns2 :i* suff]+ 9 t case b #i ,digits1 c\ld by no means exhibit ! rem>kable d>kness recit$ by ?is hi/orian2 ! c5t] !re=e seems to h pa/ ,a!ns ab\t #f 9 ! ev5+1 & probably might g d[n ab\t ,j]usalem1 or ne> x1 contr>y to ! con/ruction ( ! pres5t ,tables4 ,i h only obviat$ ^! ?+s by way ( caution to ! pres5t ,a/ronom]s1 9 re-comput+ anti5t ,eclipses2 & ref] !m to exam9e ! ,eclipse ( ,nicias1 s fatal to ! ,a!nian fleet#ga2 t :i* ov]?rew ! ,mac$onian ,army#gb c40 ,s f> ,mr4 ,,smi?4 ,sid5ote3 ,! numb] ( ,eclipses4 #cbe4 ,9 any ye>1 ! numb] ( ,eclipses ( bo? ,lum9>ies _c be less ?an two1 nor m ?an sev52 ! mo/ usual numb] is f\r1 & x is v r>e to h m ?an six4 ,= ! ,sun passes by bo? ! ,nodes b once a ye>1 unless he passes by "o ( !m 9 ! beg9n+ ( ! ye>2 & if he does1 he w pass by ! same ,node aga9 a little be=e ! ye> be f9i%$2 because1 z ^! po9ts move #ai degrees backw>d e ye>1 ! ,sun w come to ei!r ( !m #agc days aft] ! o!r #cai4 ,& :5 ei!r ,node is )9 #ag degrees ( ! ,sun at ! "t ( ,new ,moon1 ! ,sun w be eclips$4 ,at ! subsequ5t opposition ! ,moon w be eclips$ 9 ! o!r ,node2 & come r\nd to ! next conjunction aga9 ere ! =m] ,node be #ag degrees pa/ ! ,sun1 & w !re=e eclipse him aga94 ,:5 ?ree ,eclipses fall ab\t ei!r ,node1 ! l numb] g5]ally falls ab\t ! opposite2 z ! ,sun comes to x 9 #agc days aft]w>d3 & six ,lunations conta9 b f\r days m4 ,?us1 !re may be two ,eclipses ( ! ,sun & "o ( ! ,moon ab\t ea* ( h] ,nodes4 ,b :5 ! ,moon *anges 9 ei!r ( ! ,nodes1 %e _c be ne> en\gh ! o!r ,node at ! next ,full to be eclips$2 & 9 six lun> mon?s aft]w>d %e w *ange ne> ! o!r ,node3 9 ^! cases !re c be b two ,eclipses 9 a ye>1 & !y are bo? ( ! ,sun4 ,sid5ote3 ,two p]iods ( ,eclipses4 #cbf4 ,a long]1 & consequ5tly m exact p]iod ?an ! above-m5tion$ #cbj1 = comp>+ & exam9+ ,eclipses :i* happ5 at long int]vals ( "t1 is #eg ,julian ye>s #cbd days #ba h\rs #da m9utes & #ce seconds2 9 :i* "t !re are j #gaf mean ,lunations1 & ! ,sun is aga9 )9 #e m9utes ( ! same ,node z be=e4 ,b a /ill bett] p]iod is #eeg ye>s #ba days #ah h\rs #cj m9utes #ab seconds2 9 :i* "t !re are #fhij mean ,lunations2 & ! ,sun & ,node meet aga9 s ne>ly z to be b #aa seconds di/ant4 ,sid5ote3 ,an acc\nt ( ! foll[+ catalogue ( ,eclipses4 #cbg4 ,we %all subjo9 a catalogue ( ,eclipses record$ 9 hi/ory1 f #gba ye>s be=e ,,*ri/ to ,a4 ,d4 #adhe2 ( comput$ ,eclipses f #adhe to #agjj2 & ( all ! ,eclipses visible 9 ,europe f #agjj to #ahjj4 ,f ! beg9n+ ( ! catalogue to ,a4,d4 #adhe ! ,eclipses are tak5 f ,,/ruyk's ,introduction to univ]sal ,geography1 z t indefatigable au?or has1 ) mu* lab\r1 collect$ !m f ,ptolemy1 ,?ucydides1 ,plut>*1 ,calvisius1 ,x5ophon1 ,diodorus ,siculus1 ,ju/91 ,polybius1 ,titus ,livius1 ,cic]o1 ,lucanus1 ,!ophanes1 ,dion ,cassius1 & _m o!rs4 ,f #adhe to #agjj ! ,eclipses are tak5 f ,ricciolus's ,almage/3 & f #agjj to #ahjj f ,l'art de v]ifi] les ,dates#gc4 ,^? f ,/ruyk h all ! places m5tion$ :]e !y 7 obs]v$3 ,^? f ! ,fr5* au?ors1 viz4 ! religi\s ,b5$ict9es ( ! ,congregation ( ,/4 ,maur1 are fitt$ to ! ,m]idian ( ,p>is3 ,& conc]n+ ^? f ,ricciolus1 t au?or gives ! foll[+ acc\nt4 ,because x is ( great use = fix+ ! ,cycles or ,revolutions ( ,eclipses1 to h at h&1 )\t ! tr\ble ( calculation1 a li/ ( successive ,eclipses = _m ye>s1 comput$ by au?ors ( ,ephem]ides1 al?\gh f ,tables n p]fect 9 all respects1 ,i %all = ! b5efit ( ,a/ronom]s give a summ>y collection ( su*4 ,! au?ors ,i extract f are1 an anonym\s "o :o publi%$ ,ephem]ides f #adhd to #aejf inclusive2 ,jacobus ,pflaum5 & ,jo4 ,/fl]9us1 to ! ,m]idian ( ,ulm1 f #aejg to #aecd3 ,lucas ,gauricus1 to ! ,latitude ( #de degrees1 f #aecd to #aeea3 ,pet] ,appian1 to ! ,m]idian ( ,leys+1 f #aech to #aegh3 ,jo4 ,/fl]us to ! ,m]idian ( ,tub+1 f #aedc to #aeed3 ,petrus ,pitatus1 to ! ,m]idian ( ,v5ice f #aedd to #aeef3 ,georgius-,joa*imus ,rheticus1 = ! ye> #aeea3 ,ni*olaus ,simus1 to ! ,m]idian ( ,bologna1 f #aeeb to #aefh3 ,mi*ael ,m/l91 to ! ,m]idian ( ,tub+1 f #aeeg to #aeij3 ,jo4 ,/adius1 to ! ,m]idian ( ,antw]p1 f #aeed to #aegd3 ,jo4 ,anton9us ,mag9us1 to ! ,m]idian ( ,v5ice1 f #aeha to #afcj3 ,david ,origan1 to ! ,m]idian ( ,franck=t on ! ,od]1 f #aeie to #affd3 ,&rew ,argol1 to ! ,m]idian ( ,rome1 f #afcj to #agjj3 ,franciscus ,montebrunus1 to ! ,m]idian ( ,bologna1 f #adfa to #affj3 ,among :i*1 ,/adius1 ,m/l91 & ,mag9us1 us$ ! ,prut5ic ,tables2 ,origan ! ,prut5ic & ,ty*onic2 ,montebrunus ! ,lansb]gian1 z likewise ^? ( ,duret4 ,almo/ all ! re/ ! ,alphons9e4 ,b1 t ! places may readily be kn[n = :i* ^! ,eclipses 7 comput$1 & f :at ,tables1 consult ! foll[+ li/1 9 :i* ! ye>s inclusive are also set d[n4 ,f #adhe to #aejf ,! place & au?or unkn[n4 #aejg #aeec ,ulm 9 ,suabia1 f ! ,alphons9e4 #aeed #aegf ,antw]p1 f ! ,prut5ic4 #aegg #aehe ,tub+1 f ! ,prut5ic4 #aehf #aeid ,v5ice1 f ! ,prut5ic4 #aeie #afjj ,franck=t on ,od]1 f ! ,prut5ic4 #afja #afdj ,franck=t on ,od]1 f ! ,ty*onic4 #afda #affj ,bologna1 f ! ,lansb]gian4 #affa #agjj ,rome1 f ! ,ty*onic4 ,s f> ,,ricciolus4 ,n4 ,b4 ,! ,eclipses m>k$ ) an ,a/]isk are n 9 ,,ricciolus's catalogue2 b are suppli$ f ,l'art de v]ifi] les ,dates4 ,f ! beg9n+ ( ! catalogue to ,a4 ,d4 #agjj1 ! "t is reckon$ f ! noon ( ! day m5tion$ to ! noon ( ! foll[+ day2 b f #agjj to #ahjj ! "t is set d[n accord+ to our common way ( reckon+4 ,^? m>k$ ,pek9 & ,canton are ,eclipses f ! ,*9ese *ronology accord+ to ,,/ruyk2 & ?r\gh\t ! ,table ?is m>k signifies ,sun1 & ?is ,moon4 ,,/ruyk's ,catalogue ( ,,eclipses4 ---------------------------------------- -------------------- ,bef4 ,eclipses ( ! ,sun ,m4 ,d4 ,middle ,digits ,*r4 & ,moon se5 at ,h4 ,m4 eclips$ ---------------------------------------- -------------------- #gba ,babylon ,m>4 #ai #aj #cd ,total #gbj ,babylon ,m>4 #h #aa #ef #a #e #gbj ,babylon ,sept4 #a #aj #ah #e #d #fba ,babylon ,apr4 #ba #ah #bb #b #cf #ebc ,babylon ,july #af #ab #dg #g #bd #ejb ,babylon ,nov4 #ai #ab #ba #a #eb #dia ,babylon ,apr4 #be #ab #ab #a #dd #dca ,a!ns ,aug4 #c #f #ce #aa #j #dbe ,a!ns ,oct4 #i #f #de ,total #dbd ,a!ns ,m>4 #bj #bj #ag #i #j #dac ,a!ns ,aug4 #bg #aj #ae ,total #djf ,a!ns ,apr4 #ae #h #ej ,total #djd ,a!ns ,sept4 #b #ba #ab #h #dj #djc ,pek9 ,aug4 #bh #e #ec #aj #dj #cid ,gnide ,aug4 #ac #bb #ag #aa #j #chc ,a!ns ,dec4 #bb #ai #f #b #a #chb ,a!ns ,june #ah #h #ed #f #ae #chb ,a!ns ,dec4 #ab #aj #ba ,total #cfd ,!bes ,july #ab #bc #ea #f #aj #ceg ,syracuse ,feb4 #bh #bb -- #c #cc #ceg ,zant ,aug4 #bi #g #bi #d #ba #cdj ,zant ,sept4 #ad #ah -- #i #j #cca ,arbela ,sept4 #bj #aj #i ,total #caj ,sicily ,isl& ,aug4 #ad #bj #e #aj #bb #bai ,mysia ,m>4 #ai #ad #e ,total #bah ,p]gamos ,sept4 #a ris+ ,total #bag ,s>d9ia ,feb4 #aa #a #eg #i #f #bjc ,frus9i ,may #f #b #eb #e #dj #bjb ,cumis ,oct4 #ah #bb #bd #a #j #bja ,a!ns ,sept4 #bb #g #ad #h #eh #bjj ,a!ns ,m>4 #ai #ac #i ,total #bjj ,a!ns ,sept4 #aa #ad #dh ,total #aih ,rome ,aug4 #f ---- ---- #aij ,rome ,m>4 #ac #ah -- #aa #j #ahh ,rome ,july #af #bj #ch #aj #dh #agd ,a!ns ,apr4 #cj #ad #cc #g #a #afh ,mac$onia ,june #ba #h #b ,total #ada ,rhodes ,jan4 #bg #aj #h #c #bf #ajd ,rome ,july #ah #bb #j #aa #eb #fc ,rome ,oct4 #bg #f #bb ,total #fj ,gibralt] ,m>4 #af sett+ ,c5tral #ed ,canton ,may #i #c #da ,total #ea ,rome ,m>4 #g #b #ab #i #j #dh ,rome ,jan4 #ah #aj #j ,total #de ,rome ,nov4 #f #ad -- ,total #cf ,rome ,may #ai #c #eb #f #dg #ca ,rome ,aug4 #bj sett+ ,gr4 ,ecl4 #bi ,canton ,jan4 #e #d #b #aa #j #bh ,pek9 ,june #ah #bc #dh ,total #bf ,canton ,oct4 #bc #d #af #aa #ae #bd ,pek9 ,april #g #d #aa #b #j #af ,pek9 ,nov4 #a #e #ac #b #h #b ,canton ,feb4 #a #bj #h #aa #db ---------------------------------------- -------------------- ---------------------------------------- -------------------- ,aft4 ,eclipses ( ! ,sun ,m4 ,d4 ,middle ,digits ,*r4 & ,moon se5 at ,h4 ,m4 eclips$ ---------------------------------------- -------------------- #a ,pek9 ,june #aj #a #aj #aa #dc #e ,rome ,m>4 #bh #d #ac #d #de #ad ,panonia ,sept4 #bf #ag #ae ,total #bg ,canton ,july #bb #h #ef ,total #cj ,canton ,nov4 #ac #ai #bj #aj #cj #dj ,pek9 ,apr4 #cj #e #ej #g #cd #de ,rome ,july #ca #bb #a #e #ag #df ,pek9 ,july #ba #bb #be #b #aj #df ,rome ,dec4 #ca #i #eb ,total #di ,pek9 ,may #bj #g #af #aj #h #ec ,canton ,m>4 #h #bj #db #aa #f #ee ,pek9 ,july #ab #ba #ej #f #dj #ef ,canton ,dec4 #be #j #bh #i #bj #ei ,rome ,apr4 #cj #c #h #aj #ch #fj ,canton ,oct4 #ac #c #ca #aj #cj #fe ,canton ,dec4 #ae #ba #ej #aj #bc #fi ,rome ,oct4 #ah #aj #dc #aj #di #gj ,canton ,sept4 #bb #ba #ac #h #bf #ga ,rome ,m>4 #d #h #cb #f #j #ie ,ephesus ,may #ba ---- #a #j #abe ,alex&ria ,april #e #i #af #a #dd #acc ,alex&ria ,may #f #aa #dd ,total #acd ,alex&ria ,oct4 #bj #aa #e #aj #ai #acf ,alex&ria ,m>4 #e #ae #ef #e #ag #bcg ,bologna ,apr4 #ab ---- ,total #bch ,rome ,april #a #bj #bj #h #de #bij ,c>?age ,may #ae #c #bj #aa #bj #cjd ,rome ,aug4 #ca #i #cf ,total #caf ,con/ant9ople ,dec4 #cj #ai #ec #b #ah #ccd ,tol$o ,july #ag at noon ,c5tral #cdh ,con/ant9ople ,oct4 #h #ai #bd #h #j #cfj ,ispahan ,aug4 #bg #ah #j ,c5tral #cfd ,alex&ria ,nov4 #be #ae #bd ,total #dja ,rome ,june #aa ---- ,total #dja ,rome ,dec4 #f #ab #ae ,total #djb ,rome ,june #a #h #dc #aj #b #djb ,rome ,nov4 #aj #bj #cc #aj #cj #ddg ,compo/ello ,dec4 #bc #j #df #a -- #dea ,compo/ello ,april #a #af #cd #ai #eb #dea ,compo/ello ,sept4 #bf #f #cj #j #b #deh ,*aves ,may #bg #bc #af #ah #ec #dfb ,compo/ello ,m>4 #a #ac #b #aa #aa #dfd ,*aves ,july #ai #ai #a #aj #ae #dhd ,con/ant9ople ,jan4 #ac #ai #ec #j #j #dhf ,con/ant9ople ,may #ai #a #aj #e #ae #dig ,con/ant9ople ,apr4 #ah #f #e #ag #eg #eab ,con/ant9ople ,june #bh #bc #h #a #ej #ech ,engl& ,feb4 #ad #ai -- #h #bc #edj ,london ,june #ai #bj #ae #h -- #egg ,t\rs ,dec4 #aj #ag #bh #f #df #eha ,p>is ,april #d #ac #cc #f #db #ehb ,p>is ,sept4 #ag #ab #da ,total #eij ,p>is ,oct4 #ah #f #cj #i #be #eib ,con/ant9ople ,m>4 #ah #bb #f #aj #j #fjc ,p>is ,aug4 #ab #c #c #aa #bj #fbb ,con/ant9ople ,febr4 #a #aa #bh ,total #fdd ,p>is ,nov4 #e #j #cj #i #ec #fhj ,p>is ,june #ag #ab #cj ,total #fhc ,p>is ,april #af #aa #cj ,total #fic ,con/ant9ople ,oct4 #d #bc #ed #aa #ed #gaf ,con/ant9ople ,jan4 #ac #g -- ,total #gah ,con/ant9ople ,june #c #a #ae ,total #gcc ,engl& ,aug4 #ac #bj -- #aa #a #gcd ,engl& ,jan4 #bc #ad -- ,total #geb ,engl& ,july #cj #ac -- ,total #gec ,engl& ,june #h #bb -- #aj #ce #gec ,engl& ,jan4 #bc #ac -- ,total #gfj ,engl& ,aug4 #ae #d -- #h #ae #gfj ,london ,aug4 #cj #e #ej #aj #dj #gfd ,engl& ,june #d at noon #g #ae #ggj ,london ,feb4 #ad #g #ab ,total #ggd ,rome ,nov4 #bb #ad #cg #aa #eh #ghd ,london ,nov4 #a #ad #b ,total #ghg ,con/ant9ople ,sept4 #ad #bj #dc #i #dg #gif ,con/ant9ople ,m>4 #bg #af #bb ,total #hjj ,rome ,jan4 #ae #i #j #aj #ag #hjg ,ang\lesme ,feb4 #aj #ba #bd #i #db #hjg ,p>is ,feb4 #be #ac #dc ,total #hjg ,p>is ,aug4 #ba #aj #bj ,total #hji ,p>is ,july #ae #ba #cc #h #h #hji ,p>is ,dec4 #be #h -- ,total #haj ,p>is ,june #bj #h -- ,total #haj ,p>is ,nov4 #cj #j #ab ,total #haj ,p>is ,dec4 #ad #h -- ,total #hab ,con/ant9ople ,may #ad #b #ac #i -- #hac ,cappadocia ,may #c #ag #e #aj #ce #hag ,p>is ,feb4 #e #e #db ,total #hah ,p>is ,july #f #ah -- #f #ee #hbj ,p>is ,nov4 #bc #f #bf ,total #hbd ,p>is ,m>4 #ah #g #ee ,total #hbh ,p>is ,june #cj #ae -- ,total #hbh ,p>is ,dec4 #bd #ac #de ,total #hca ,p>is ,april #cj #f #ai #aa #h #hca ,p>is ,may #ae #bc -- #d #bd #hca ,p>is ,oct4 #bd #aa #ah ,total #hcb ,fulda ,apr4 #ah #i #j ,total #hdj ,p>is ,may #d #bc #bb #i #bj #hda ,p>is ,oct4 #ag #ah #eh #e #bd #hdb ,p>is ,m>4 #bi #ad #ch ,total #hdc ,p>is ,m>4 #ai #g #a ,total #hfa ,p>is ,m>4 #bi #ae #g ,total #hgh ,p>is ,oct4 #ad #af -- ,total #hgh ,p>is ,oct4 #bi #a -- #aa #ad #hhc ,arracta ,july #bc #g #dd #aa -- #hhi ,con/ant9ople ,april #c #ag #eb #i #bc #hia ,con/ant9ople ,aug4 #g #bc #dh #aj #cj #ija ,arracta ,aug4 #b #ae #g ,total #ijd ,london ,may #ca #aa #dg ,total #ijd ,london ,nov4 #be #i #j ,total #iab ,london ,jan4 #f #ae #ab ,total #ibf ,p>is ,m>4 #ca #ae #ag ,total #icd ,p>is ,apr4 #af #d #cj #aa #cf #ici ,p>is ,july #ah #ai #de #aj #g #iee ,p>is ,sept4 #d #aa #ah ,total #ifa ,rhemes ,may #af #bj #ac #i #ah #igj ,con/ant9ople ,may #g #ah #ch #aa #bb #igf ,london ,july #ac #ae #g ,total #ihe ,mess9a ,july #bj #c #eb #d #aj #ihi ,con/ant9ople ,may #bh #f #ed #h #dj #iij ,fulda ,apr4 #ab #aj #bb #i #e #iij ,fulda ,oct4 #f #ae #d #aa #aj #iij ,con/ant9ople ,oct4 #ba #j #de #aj #e #iie ,augsburgh ,july #ad #aa #bg ,total #ajji ,f]r>a ,oct4 #f #aa #ch ,total #ajaj ,mess9a ,m>4 #ah #e #da #i #ab #ajaf ,nimegu5 ,nov4 #af #af #ci ,total #ajag ,nimegu5 ,oct4 #bb #b #h #f -- #ajbj ,cologne ,sept4 #d #aa #ch ,total #ajbc ,london ,jan4 #bc #bc #bi #aa -- #ajcj ,rome ,feb4 #bj #aa #dc ,total #ajca ,p>is ,feb4 #i #aa #ea ,total #ajcc ,p>is ,dec4 #h #aa #aa #i #ag #ajcd ,milan ,june #d #i #h ,total #ajcg ,p>is ,apr4 #ag #bj #de #aj #de #ajci ,aux]re ,aug4 #ba #bc #dj #aa #e #ajdb ,rome ,jan4 #h #af #ci ,total #ajdd ,aux]re ,nov4 #g #af #ab #aj #a #ajdd ,cluny ,nov4 #ba #bb #ab #aa -- #ajef ,nuremburg ,april #b #ab #i ,total #ajfc ,rome ,nov4 #h #ab #af ,total #ajgd ,augsburgh ,oct4 #g #aj #ac ,total #ajhj ,con/ant9ople ,nov4 #bi #aa #ab #i #cf #ajhb ,london ,may #ad #aj #cb #aj #b #ajhf ,con/ant9ople ,feb4 #af #d #g ,total #ajhi ,naples ,june #be #f #f ,total #ajic ,augsburgh ,sept4 #bb #bb #ce #aj #ab #ajif ,gembl\rs ,feb4 #aj #af #d ,total #ajif ,augsburgh ,aug4 #f #h #ba ,total #ajih ,augsburgh ,dec4 #be #a #be #aj #ab #ajii ,naples ,nov4 #cj #d #eh ,total #aajc ,rome ,sept4 #ag #aj #ah ,total #aajf ,erfurd ,july #ag #aa #bh #aa #ed #aajg ,naples ,jan4 #aj #ac #af ,total #aaji ,erfurd ,may #ca #a #cj #aj #bj #aaaj ,london ,may #e #aj #ea ,total #aaac ,j]usalem ,m>4 #ah #ai #j #i #ab #aaad ,london ,aug4 #ag #ae #e ,total #aaag ,tri] ,june #ae #ac #bf ,total #aaag ,tri] ,dec4 #aj #ab #ea ,total #aaah ,naples ,nov4 #bi #ae #df #d #aa #aaba ,tri] ,sept4 #bg #af #dg ,total #aabb ,prague ,m>4 #bd #aa #bj #c #di #aabd ,erfurd ,feb4 #a #f #dc #h #ci #aabd ,london ,aug4 #aj #bc #bi #i #eh #aacb ,erfurd ,m>* #c #h #ad ,total #aacc ,prague ,feb4 #bj #af #da #c #bc #aace ,london ,dec4 #bb #bj #aa ,total #aadb ,rome ,feb4 #aa #ad #ag #h #cj #aadc ,rome ,feb4 #a #f #cf ,total #aadg ,auran*es ,oct4 #be #bb #ch #g #bj #aadi ,b>y ,m>4 #be #ac #ed #e #bi #aaea ,eimbeck ,aug4 #bh #ab #d #d #bi #aaec ,augsburgh ,jan4 #bf #j #db #aa -- #aaed ,p>is ,june #bf #af #a ,total #aaed ,p>is ,dec4 #ba #h #cj #d #db #aaee ,auran*es ,june #aj #h #de #j #ec #aafj ,rome ,aug4 #ah #g #ec #f #di #aafa ,rome ,aug4 #g #h #ae ,total #aafb ,erfurd ,feb4 #a #f #dj #e #ef #aafb ,erfurd ,july #bg #ab #cj #d #aa #aafc ,mont ,cass94 ,july #c #g #dj #b #j #aafd ,milan ,june #f #aj #j ,total #aafh ,london ,sept4 #ah #ad #j ,total #aagb ,cologne ,jan4 #aa #ac #ca ,total #aagf ,auran*es ,april #be #g #b #h #f #aagf ,auran*es ,oct4 #ai #aa #bj #h #ec #aagh ,cologne ,m>* #e sett+ #g #eb #aagh ,auran*es ,aug4 #bi #ac #eb #e #ca #aagh ,cologne ,sept4 #ab -- -- #aj #ea #aagi ,cologne ,aug4 #ah #ad #bh ,total #aahj ,auran*es ,jan4 #bh #d #ad #aj #cd #aaha ,auran*es ,july #ac #c #ae #c #dh #aaha ,auran*es ,dec4 #bb #h #eh #d #dj #aahe ,rhemes ,may #a #a #ec #i #j #aahf ,cologne ,april #e #f -- ,total #aahf ,franck=t ,april #bj #g #ai #d #j #aahg ,p>is ,m>4 #be #af #ag #h #db #aahg ,engl& ,sept4 #c #ba #ed #h #f #aahi ,engl& ,feb4 #b #aj -- #i -- #aaia ,engl& ,june #bc #j #bj #aa #cb #aaib ,france ,nov4 #bj #ad -- #f -- #aaic ,france ,nov4 #aj #e #bg ,total #aaid ,london ,april #bb #b #ae #f #di #abjj ,london ,jan4 #b #ag #b #d #ce #abja ,london ,june #ag #ae #d ,total #abjd ,engl& ,april #ae #ab #ci ,total #abjd ,saltzburg ,oct4 #aj #f #cb ,total #abjg ,rhemes ,feb4 #bg #aj #ej #aj #bj #abjh ,rhemes ,feb4 #b #e #aj ,total #abaa ,vi5na ,nov4 #ba #ac #eg ,total #abae ,cologne ,m>4 #af #ae #ce ,total #abaf ,acre ,feb4 #ah #ba #ae #aa #cf #abaf ,acre ,m>* #e #i #ch #g #d #abah ,damietta ,july #i #i #df #aa #ca #abbb ,rome ,oct4 #bb #ad #bh ,total #abbc ,colm> ,april #af #h #ac #aa #j #abbh ,naples ,dec4 #bg #i #ee #i #ai #abcj ,naples ,may #ac #ag -- ,total #abcj ,london ,nov4 #ba #ac #ba #i #cd #abcb ,rhemes ,oct4 #ae #d #bi #d #be #abde ,rhemes ,july #bd #ag #dg #f -- #abdh ,london ,june #g #h #di ,total #abee ,london ,july #bj #i #dg ,total #abee ,con/ant9ople ,dec4 #cj #b #eb ,annul4 #abeh ,augsburgh ,may #ah #aa #ag ,total #abfa ,vi5na ,m>4 #ca #bb #dj #i #h #abfb ,vi5na ,m>* #g #e #ej ,total #abfb ,vi5na ,aug4 #cj #ad #ci ,total #abfc ,vi5na ,feb4 #bd #f #eb #f #bi #abfc ,augsburgh ,aug4 #e #c #bd #aa #ag #abfc ,vi5na ,aug4 #bj #g #ce #i #g #abfe ,vi5na ,dec4 #bc #af #be ,total #abfg ,con/ant9ople ,may #bd #bc #aa #aa #dj #abgj ,vi5na ,m>4 #bb #ah #dg #aj #dj #abgb ,vi5na ,aug4 #aj #g #bg #h #ec #abgd ,vi5na ,jan4 #bc #aj #ci #i #be #abge ,laub5 ,dec4 #d #f #bj #d #bi #abgf ,vi5na ,nov4 #bb #ae -- ,total #abgg ,vi5na ,may #ah -- -- ,total #abgi ,franck=t ,apr4 #ab #f #ee #aj #f #abhj ,london ,m>4 #ag #ab #ab ,total #abhd ,reggio ,dec4 #bc #af #aa #i #ac #abij ,wittemburg ,sept4 #d #ai #cg #aj #cj #abia ,london ,feb4 #ad #aj #b ,total #acjb ,con/ant9ople ,jan4 #ad #aj #be ,total #acjg ,f]r>a ,april #b #bb #ah #j #ed #acji ,london ,feb4 #bd #ag #dd ,total #acji ,lucca ,aug4 #ba #aj #cb ,total #acaj ,wittemburg ,jan4 #ca #b #b #aj #aj #acaj ,torcello ,feb4 #ad #d #h #aj #bj #acaj ,torcello ,aug4 #aj #ae #cc #g #af #acab ,wittemburg ,july #d #ai #di #c #bc #acab ,plaisance ,dec4 #ad #g #ai ,total #acac ,torcello ,dec4 #c #h #eh #i #cd #acaf ,mod5a ,oct4 #a #ad #ee ,total #acba ,wittemburg ,june #be #ah #a #aa #ag #acbc ,flor5ce ,may #bj #ae #bd ,total #acbd ,flor5ce ,may #i #f #c ,total #acbd ,wittemburg ,apr4 #bc #f #ce #h #h #acbg ,con/ant9ople ,aug4 #ca #ah #bf ,total #acbh ,con/ant9ople ,feb4 #be #ac #dg #aa -- #accj ,flor5ce ,june #cj #ae #aj #g #cd #accj ,con/ant9ople ,july #af #d #e #aj #dc #accj ,prague ,dec4 #be #ae #di ,total #acca ,prague ,nov4 #bi #bj #bf #g #da #acca ,prague ,dec4 #ad #ah -- #aa -- #accc ,wittemburg ,may #ad #c -- #aj #ah #accd ,ces5a ,apr4 #ai #aj #cc ,total #acda ,con/ant9ople ,nov4 #bc #ab #bc ,total #acda ,con/ant9ople ,dec4 #h #bb #ae #f #cj #acdb ,con/ant9ople ,may #bj #ad #bg ,total #acdd ,alex&ria ,oct4 #f #ah #dj #h #ee #acdi ,wittemburg ,june #cj #ab #bj ,total #aced ,wittemburg ,sept4 #af #bj #de #h #dc #acef ,flor5ce ,feb4 #af #aa #dc ,total #acfa ,con/ant9ople ,may #d #bb #ae #h #ed #acfg ,9 ,*9a ,jan4 #af #h #bg ,total #achi ,eugib9 ,nov4 #c #ag #e ,total #acif ,augsburg ,jan4 #aa #j #af #f #bb #acif ,augsburg ,june #ba #aa #aj ,total #acii ,=li ,oct4 #bi #j #dc #i -- #adjf ,con/ant9ople ,june #a #ac -- #aj #ca #adjf ,con/ant9ople ,june #ae #ah #a #aa #ch #adjh ,=li ,oct4 #ah #ba #dg #i #cb #adji ,con/ant9ople ,apr4 #ae #c #a #aj #dh #adaj ,vi5na ,m>4 #bj #ac #ac ,total #adae ,wittemburg ,june #f #f #dc ,total #adai ,franck=t ,m>4 #be #bb #e #a #de #adba ,=li ,feb4 #ag #h #b ,total #adbb ,=li ,feb4 #f #h #bf #aa #g #adbd ,wittemburg ,june #bf #c #eg #aa #bj #adca ,=li ,feb4 #ab #b #d #a #ci #adcc ,wittemburg ,june #ag #e -- ,total #adch ,wittemburg ,sept4 #ah #bj #ei #h #g #addb ,rome ,dec4 #ag #c #ef ,total #addh ,tub+ ,aug4 #bh #bb #bc #h #ec #adej ,con/ant9ople ,july #bd #g #ai ,total #adeg ,vi5na ,sept4 #c #aa #ag ,total #adfj ,au/ria ,july #c #g #ca #e #bc #adfj ,au/ria ,july #ag #ag #cb #aa #ai #adfj ,vi5na ,dec4 #bg #ac #cj ,total #adfa ,vi5na ,june #bb #aa #ej ,total #adfa ,rome ,dec4 #ag -- -- ,total #adfb ,vit]bo ,june #aa #ae -- #g #ch #adfb ,vit]bo ,nov4 #ba #j #aj #b #f #adfd ,padua ,apr4 #ba #ab #dc ,total #adfe ,rome ,sept4 #bj #e #ae #h #df #adfe ,rome ,oct4 #d #e #ab ,total #adfi ,rome ,jan4 #bg #g #i ,total #adhe ,norimburg ,m>4 #af #c #ec #aa -- ---------------------------------------- -------------------- ,! foll[+ ,,eclipses are all tak5 f ,,ricciolus1 except ^? m>k$ ) an ,a/]isk1 :i* are f ,l',art de v]ifi] les ,dates4 ---------------------------------------- - ,aft4 ,m4 ,d4 ,middle ,digits ,*r4 ,h4 ,m4 eclips$ ---------------------------------------- - #adhf ,feb4 #ah #e #da ,total #adhf ,m>4 #e #ag #dc #i #j #adhg ,feb4 #g #ae #di ,total #adhg ,july #bj #b #f #g #j #adhh ,jan4 #bh #f -- 99 #adhh ,july #h #ag #cj #d #j #adhi ,dec4 #g #ag #da ,total #adij ,may #ai ,noon 99 #adij ,june #b #aj #f ,total #adij ,nov4 #bf #ah #be ,total #adia ,may #h #b #ai #i #j #adia ,nov4 #ae #ah -- 99 #adib ,apr4 #bf #g -- 99 #adib ,oct4 #bj #bc -- 99 #adic ,april #a #ad #j ,total #adic ,oct4 #aj #b #dj #h #j #adid ,m>4 #g #d #ab #d #j #adid ,m>4 #ba #ad #ch ,total #adid ,sept4 #ad #ai #de ,total #adie ,m>4 #aj #af -- 99 #adie ,aug4 #ai #ag -- 99 #adif ,jan4 #bi #ad -- 99 #adig ,jan4 #ah #f #ch ,total #adig ,july #bi #c #b #c #j #adii ,june #bb #ag -- 99 #adii ,aug4 #bc #ah -- 99 #adii ,nov4 #ag #aj -- 99 #aejj ,m>4 #bg ,9 ! ,night #aejj ,apr4 #aa ,at ,noon #aejj ,oct4 #e #ad #b #aj #j #aeja ,may #b #ag #di ,total #aejb ,sept4 #cj #ai #de #aj #j #aejb ,oct4 #ae #ab #bj #b #j #aejc ,m>4 #ab #i -- 99 #aejc ,sept4 #ai #bb -- 99 #aejd ,feb4 #bi #ac #cf ,total #aejd ,m>4 #af #c -- 99 #aeje ,aug4 #ad #h #ah ,total #aejf ,feb4 #g #ae -- 99 #aejf ,july #bj #c #aa #b #j #aejf ,aug4 #c #aj -- 99 #aejg ,jan4 #ab #ai -- 99 #aejh ,jan4 #b #d -- 99 #aejh ,may #bi #f -- 99 #aejh ,june #ab #ag #dj ,total #aeji ,june #b #aa #aa #g #j #aeji ,nov4 #aa #bb -- 99 #aeaj ,oct4 #af #ai -- 99 #aeaa ,oct4 #f #aa #ej ,total #aeab ,sept4 #be #c #ef ,total #aeac ,m>4 #g #j #cj #f #j #aeac ,aug4 #cj #a -- 99 #aeae ,jan4 #bi #ae #ah ,total #aeaf ,jan4 #ai #f #j ,total #aeaf ,july #ac #aa #cg ,total #aeaf ,dec4 #bc #c #dg #c #j #aeag ,june #ah #af -- 99 #aeag ,nov4 #bg #ai -- 99 #aeah ,may #bd #aa #ai #i #aa #aeah ,june #g #ag #ef #aa #j #aeai ,may #bh #a -- 99 #aeai ,oct4 #bc #d #cc #f #j #aeai ,nov4 #f #f #bd ,total #aebj ,may #b #g -- 99 #aebj ,oct4 #aa #e #bb #c #aebj ,oct4 #be #ai -- 99 #aebj ,m>4 #ba #ag -- 99 #aeba ,april #f #ai -- 99 #aeba ,sept4 #cj #c -- 99 #aebb ,sept4 #e #ab #ag ,total #aebc ,m>4 #a #h #bf ,total #aebc ,aug4 #be #ae #bd ,total #aebd ,feb4 #d #a -- 99 #aebd ,aug4 #af #af -- 99 #aebe ,jan4 #bc #d -- 99 #aebe ,july #d #aj #aj ,total #aebe ,dec4 #bi #aj #df ,total #aebf ,dec4 #ah #aj #cj ,total #aebg ,jan4 #b #c -- 99 #aebg ,dec4 #g #aj -- 99 #aebh ,may #ag #bj -- 99 #aebi ,oct4 #af #bj #bc #aa #ee #aecj ,m>4 #bh #ah #bc #h #bd #aecj ,oct4 #f #ab #aa ,total #aeca ,april #a #g -- 99 #aecb ,aug4 #cj #j #di #c #ce #aecc ,aug4 #d #aa #ej ,total #aecc ,aug4 #ai #ag -- 99 #aecd ,jan4 #ad #a #db #e #de #aecd ,jan4 #bi #ad #be ,total #aece ,june #cj ,noon 99 #aece ,july #ad #h -- 99 #aece ,dec4 #bd #b -- 99 #aecf ,june #ah #b #b #h #j #aecf ,nov4 #bg #f #ba #aj #ae #aecg ,may #bd #h #c ,total #aecg ,june #g #g -- 99 #aecg ,nov4 #af #ad #ef ,total #aech ,may #ac #ad #bd #c #j #aech ,nov4 #f #e #ca #c #cg #aeci ,apr4 #ah #d #cc #i #j #aedj ,april #f #ag #ae ,total #aeda ,m>4 #aa #af #cd ,total #aeda ,aug4 #ba #j #ef #c #j #aedb ,m>4 #a #h #df #a #ch #aedb ,aug4 #aj #ag -- 99 #aedc ,july #ae #af -- 99 #aedd ,jan4 #i #ah #ac ,total #aedd ,jan4 #bc #ba #af #aa #ag #aedd ,july #d #h #ca ,total #aedd ,dec4 #bh #ah #bg ,total #aede ,june #h #bj #dh #c #de #aede ,dec4 #ag #ah -- 99 #aedf ,may #cj #e -- 99 #aedf ,nov4 #bb #bc -- 99 #aedg ,may #d #aj #bg #h #j #aedg ,oct4 #bh #d #ef #aa #cd #aedg ,nov4 #ab #b #i #i #cj #aedh ,april #h #c -- 99 #aedh ,apr4 #bb #aa #bd ,total #aedi ,apr4 #aa #ae #ai #b #j #aedi ,oct4 #f #f -- 99 #aeej ,m>4 #af #bj -- 99 #aeea ,feb4 #bj #h #ba ,total #aeea ,aug4 #ca #b #j #a #eb #aeec ,jan4 #ab #bb #ed #a #bb #aeec ,july #aj #g -- 99 #aeec ,july #bd #af #j #j #ca #aeed ,june #bi #f -- 99 #aeed ,dec4 #h #ac #g #aj #ab #aeee ,june #d #ae #j ,total #aeee ,nov4 #ac #ai -- 99 #aeef ,nov4 #a #ah #j #i #da #aeef ,nov4 #af #ab #dd #f #ee #aeeg ,oct4 #bj #bj -- 99 #aeeh ,april #b #aa #j #i #ej #aeeh ,apr4 #ah #a -- 99 #aeei ,apr4 #af #d #ej ,total #aefj ,m>4 #aa #ae #dj #d #ac #aefj ,aug4 #ba #a #j #f #bb #aefj ,sept4 #d #g -- 99 #aefa ,feb4 #ac #ai -- 99 #aefb ,feb4 #c #e -- 99 #aefb ,july #ae #ae #ej ,total #aefc ,jan4 #bb #ai -- 99 #aefc ,june #bj #d #ej #h #ch #aefc ,july #e #h #d #aa #cd #aefe ,m>4 #g #ab #ec ------ #aefe ,may #ad #af -- 99 #aefe ,nov4 #g #ab #df #aa #df #aeff ,oct4 #bh #e #ch ,total #aefg ,april #h #bc #d #i #cd #aefg ,oct4 #ag #ac #dc #b #dj #aefh ,m>4 #bh #e -- 99 #aefi ,m>4 #b #ae #ah ,total #aegj ,feb4 #bj #e #df ,total #aegj ,aug4 #ae #i #ag ,total #aega ,jan4 #be #d -- 99 #aegb ,jan4 #ad #ai -- 99 #aegb ,june #be #i #j #e #bf #aegc ,june #bh #ah -- 99 #aegc ,nov4 #bd #d -- 99 #aegc ,dec4 #h #f #ea ,total #aegd ,nov4 #ac #c #ej #e #ba #aege ,may #ai #h -- 99 #aege ,nov4 #b #e -- 99 #aegf ,oct4 #g #i #de ------ #aegg ,april #b #h #cc ,total #aegg ,sept4 #bf #ac #d ,total #aegh ,sept4 #ae #ac #d #b #bj #aegi ,feb4 #ae #e #da #h #cf #aegi ,aug4 #bj #ai #j 99 #aehj ,jan4 #ca #aj #g ,total #aeha ,jan4 #ai #i #bb ,total #aeha ,july #ae #ag #ea ,total #aehb ,jan4 #h #aj #bi #j #ec #aehb ,june #ai #ag #e #g #e #aehc ,nov4 #bh #ba #ea ,total #aehd ,may #i #ah #bj #c #cf #aehd ,nov4 #ag #ad #ae ,total #aehe ,apr4 #bi #g #ec #aa #g #aehe ,may #ac #e #b #f #ed #aehf ,sept4 #bg #h -- 99 #aehf ,oct4 #ab ,noon 99 #aehg ,sept4 #af #i #bh #aj #b #aehh ,feb4 #bf #a #bc #a #c #aehh ,m>4 #ab #ad #ad ,total #aehh ,sept4 #d #ag #cj ,total #aehi ,aug4 #aj #ah -- 99 #aehi ,aug4 #be #h #a #c #ed #aeij ,feb4 #d #e -- 99 #aeij ,july #af #ag #d #c #ed #aeij ,july #cj #ai #eg #aj #bg #aeia ,jan4 #i #f #ba #i #dj #aeia ,july #f #e #h ,total #aeia ,july #bj #d #b #a #j #aeia ,dec4 #bi #af #aa ,total #aeib ,june #bd #aj #ac #h #eh #aeib ,dec4 #ah #g #bd #e #ed #aeic ,may #cj #b #cj #b #ch #aeid ,may #ai #ad #eh #aj #bc #aeid ,oct4 #bh #ai #ae #i #dj #aeie ,april #i ,t]4 de ,fuego #aeie ,apr4 #bd #d #ab ,total #aeie ,may #g #bb -- 99 #aeie ,oct4 #c #b #d #e #ah #aeie ,oct4 #ah #bj #dg ,total #aeif ,m>4 #bh ,9 ,*ili #aeif ,apr4 #ab #h #eb #f #d #aeif ,sept4 #ba ,9 ,*9a #aeif ,oct4 #f #ba #ae #c #cc #aeig ,m>4 #ag ,/4 ,pet4 ,isle #aeig ,sept4 #aa ,picora #i #di #aeih ,feb4 #bj #ah #ab #aj #ee #aeih ,m>4 #f #bb #ab #aa #eg #aeih ,aug4 #af #h #ae ,total #aeih ,aug4 #ca ,magel4 #h #cd #aeii ,feb4 #aj #ag #ba ,total #aeii ,july #bb #d #ca #d #ah #aeii ,aug4 #f ------ ,total #afjj ,jan4 #ae ,java #aa #dh #afjj ,jan4 #cj #f #dj #b #eh #afjj ,july #aj #b #aj #e #ci #afja ,jan4 #d ,e?iop4 #i #dj #afja ,june #ae #f #ah #d #eb #afja ,june #bi ,*9a #d #bi #afja ,dec4 #i #g #f #aj #ec #afja ,dec4 #bd #b #df #i #eb #afjb ,may #ba ,gre5l4 #b #da #afjb ,june #d #g #ah ,total #afjb ,june #ai ,n4 ,gra4 #e #dc #afjb ,nov4 #ac ,magel4 #c -- #afjb ,nov4 #bh #aj #b ,total #afjc ,may #aj ,*9a #aa #ba #afjc ,may #bd #aa #da #g #ei #afjc ,nov4 #c ,rom4 ,i4 #aa #ag #afjc ,nov4 #ah #g #ca #c #bf #afjd ,apr4 #bi ,arabia #i #cb #afjd ,oct4 #bb ,p]u #f #di #afje ,april #c #i #ai #aa #di #afje ,apr4 #ah ,madag4 #e #ca #afje ,sept4 #bg #d #bg #i #bf #afje ,oct4 #ab #b #cb #i #bd #afjf ,m>4 #h ,mexico #f #j #afjf ,m>4 #bd #aa #ag ,total #afjf ,sept4 #b ,magel4 #f #dj #afjf ,sept4 #af #ae #f ,total #afjg ,feb4 #be #ba #dh #a #ac #afjg ,m>4 #ac #f #cf #a #bb #afjg ,sept4 #e #ae #dj #d #g #afjh ,feb4 #ae at ! ,antipo4 #afjh ,july #bg #j #cj #a #ec #afjh ,aug4 #i #d #ci #j #dj #afji ,jan4 #ai #ae #ba #aj #cb #afji ,feb4 #d ,fuego #e #bb #afji ,july #af #ab #h ,total #afji ,july #cj ,canada #d #aj #afji ,dec4 #bf #ai -- #e #ej #afaj ,jan4 #i #a #ca ,total #afaj ,june #bj ,java #aj #df #afaj ,july #e #af #eh #aa #ac #afaj ,dec4 #ae ,cyprus #d #ej #afaj ,dec4 #bi #af #dg #d #bc #afaa ,june #aj ,cali=4 #aa #cj #afab ,may #ad #aj #ch #g #bb #afab ,may #bi #bc #ch #g #ad #afab ,nov4 #h #c #bb #i #di #afab ,nov4 #bb ,magel4 #i #j #afac ,apr4 #bj ,magel lanica #afac ,may #d #j #ce ,total #afac ,may #ai ,ea/ ,t>t>y #afac ,oct4 #ac ,s\? ,am]4 #afac ,oct4 #bh #d #ai ,total #afad ,april #h ,n4 ,gui4 #h #dd #afad ,apr4 #bc #ag #cf #e #be #afad ,oct4 #c #j #eg #e #b #afad ,oct4 #ag #d #ch #d #ef #afae ,m>4 #bi ,goa #aj #ch #afae ,sept4 #bb ,salom ,isle #afaf ,m>4 #c #a #eh ,total #afaf ,m>4 #ag ,mexico #f #dg #afaf ,aug4 #bf #ae #cc ,total #afaf ,sept4 #aj ,magel4 #aj #cc #afag ,feb4 #e ,magel lanica #afag ,feb4 #bj #a #di ,total #afag ,m> #f #bb -- 99 #afag ,aug4 #a ,bi>mia #afag ,aug4 #af #h #bb ,total #afah ,jan4 #bf ,magel lanica #afah ,feb4 #i #c #bi #b #eg #afah ,july #ba ,mexico ------ #afai ,jan4 #ae ,cali= nia #afai ,june #bf #ab #dj #c #aj #afai ,july #aa ,africa #aa #ci #afai ,dec4 #bj #ae #ec #aj #dg #afbj ,may #ca ,arctic ,circle #afbj ,june #ad #ac #dg ,total #afbj ,june #bi ,magel4 #g #bj #afbj ,dec4 #i #f #ci ,total #afbj ,dec4 #bc ,magel lanica #afba ,may #bj #ad #ed #aj #dd #afba ,june #c #ai #db #i #ec #afba ,nov4 #ac ,magel lanica #afba ,nov4 #bh #ae #dc #c #ch #afbb ,may #aj ,c4 ,v]d #aa #eb #afbb ,nov4 #b ,malac ca ,94 #afbc ,apr4 #ad #g #ai #aj #ed #afbc ,apr4 #bi ------ ------ #afbc ,oct4 #h #j #bb #h #ce #afbc ,oct4 #bc ,cali=4 #aj #df #afbd ,may #ah ,n4 ,zem4 #f #j #afbd ,apr4 #c #g #i ,total #afbd ,apr4 #ag ,ant>4 ,circle #afbd ,sept4 #ab ,magel lanica #afbd ,sept4 #bf #h #ee ,total #afbe ,m>4 #h ,florida #afbe ,m>4 #bc #ad #aa #b #aa #afbe ,sept4 #a ,/4 ,pete r's ,isl4 #afbe ,sept4 #af #aa #da #e #f #afbf ,feb4 #be ,madag4 #h #bg #afbf ,aug4 #g #g #dh #j #be #afbf ,aug4 #ba ,9 ,mexico #afbg ,jan4 #cj #aa #ch #aj #ba #afbg ,feb4 #ae ,magel lanica #afbg ,july #bg #i #d ,total #afbg ,aug4 #aa ,t5duc #aj #j #afbh ,jan4 #f ,t5duc #e #dj #afbh ,jan4 #bj #aj #aa ,total #afbh ,july #a ,c ,good ,hope #afbh ,july #af #aa #bf ,total #afbh ,dec4 #be ,9 ,engl& #afbi ,jan4 #i #a #cf #d #bg #afbi ,june #ba ,ganges #aa #be #afbi ,dec4 #ad ,p]u #aj #ad #afcj ,may #be #ag #ef #f #j #afcj ,june #aj #g #dg #i #h #afcj ,nov4 #ai #aa #bd #i #bg #afcj ,dec4 #c ,n4 ,gui4 #aj #aj #afca ,apr4 #cj ,ant>4 ,circle #afca ,may #ae #h #ae ,total #afca ,oct4 #bd ,c ,good ,hope #afca ,nov4 #h #ab #j ,total #afcb ,apr4 #ai ,c ,good ,hope #afcb ,may #d #a #bd #f #ce #afcb ,oct4 #ac ,mexico #h #cg #afcb ,oct4 #bg #ab #bc #e #ca #afcc ,april #h #e #ad #d #cj #afcc ,oct4 #c ,maldiv4 ,total #afcd ,m>4 #ad #i #ce #aa #ah #afcd ,m>4 #bh ,japan #aj #ai #afcd ,sept4 #g #e #j ,total #afcd ,sept4 #bb ,c4,g4,h4 #i #ed #afce ,feb4 #ag ,ant>4 ,circle #afce ,m>4 #c #i #bf ,total #afce ,m>4 #ah ,mexico #j #af #afce ,aug4 #ab ,icel& #e #j #afce ,aug4 #bg #af #d ,total #afcf ,feb4 #f ,9 ,p]u #afcf ,feb4 #bj #aa #cd #c #bc #afcf ,aug4 #a ,t>t>y #aa #bj #afcf ,aug4 #af #d #cd #a #be #afcg ,jan4 #bf ,camboya #afcg ,july #ba ,jucutan #afcg ,dec4 #ca #j #dd #aj #de #afch ,jan4 #ad ,p]sia #i #de #afch ,june #be #bj #ag ,total #afch ,july #aa ,magellan #i #e #afch ,dec4 #e ,magellan #b #aj #afch ,dec4 #bj #ae #af ,total #afci ,jan4 #d ,t>t>y #j #cj #afci ,june #a #e #ei #aj #dj #afci ,june #ae #b #da #aa #i #afci ,nov4 #bd ,magel4 #aa #j #afci ,dec4 #i #aa #eg #c #df #afdj ,may #bj ,n4 ,spa4 #aj #cj #afdj ,nov4 #ac ,p]u #aj #cf #afda ,apr4 #be #a #b #i #di #afda ,may #i ,p]u #aj #af #afda ,oct4 #ah #h #ai #f #ca #afda ,nov4 #b #ah #df ------ #afdb ,m>4 #cj ,e/otl4 #d #j #afdb ,apr4 #ad #ad #ca ,total #afdb ,sept4 #be ,magel lan #afdb ,oct4 #g #af #de ,total #afdc ,m>4 #ai #ac #ec ------ #afdc ,april #c #ba #aj #c #i #afdc ,sept4 #ab #ag #j ------ #afdc ,sept4 #bg #g #ch #f #j #afdd ,m>4 #h #f #bj ------ #afdd ,aug4 #ca #ah #aj ------ #afde ,feb4 #aj #g #de #h #eb #afde ,feb4 #bf ,rom4 ,i4 #aj #df #afde ,aug4 #g #b #d ,total #afde ,aug4 #ba #j #ce #d #dj #afdf ,jan4 #af ,/r4 ( ,anian4 #afdf ,jan4 #cj #ah #aa ,total #afdf ,july #ab #f #eg ------ #afdf ,july #bg #f #b ,total #afdg ,jan4 #e #ab #aj ------ #afdg ,jan4 #bj #i #dc #d #dg #afdg ,july #b #j #i ------ #afdg ,dec4 #be #ac #ch ------ #afdh ,june #e #j #ee #d #bh #afdh ,june #bj #ac #bh ------ #afdh ,nov4 #bi #ai #ag #g #dj #afdh ,dec4 #ac #ba #dh ------ #afdi ,may #be #ae #bj ,total #afdi ,june #i ,arct4 ,c4 #d #j #afdi ,nov4 #d #b #aj #e #ai #afdi ,nov4 #ah #ai #ef ,total #afej ,apr4 #cj #e #ed ------ #afej ,may #ae #h #cg #g #eg #afej ,oct4 #bd #ag #ag ------ #afej ,nov4 #g #bj #bi #e #c #afea ,apr4 #ai ,tub]4 ------ #afea ,oct4 #ad #b #ae ------ #afeb ,m>4 #bd #af #eb #h #ej #afeb ,april #g #bb #dj #i #ei #afeb ,sept4 #ag #g #bg #i #di #afeb ,oct4 #b #e #b ------ #afec ,feb4 #bg -- -- ------ #afec ,m>4 #ac #ag #i ,total #afec ,aug4 #bb -- -- ------ #afec ,sept4 #f #bc #de ,total #afed ,feb4 #af #i #aj ------ #afed ,m>4 #b #ai #be #c #ad #afed ,aug4 #aa #bb #bd #b #bh #afed ,aug4 #bg #aa #di #a #ec #afee ,feb4 #f #b #cg #d #bj #afee ,aug4 #a #ad #ai ------ #afee ,aug4 #af #af -- 99 #afef ,jan4 #aa #i #d #aj #j #afef ,july #f #c #ag ,total #afef ,july #ba #aa #dh ------ #afef ,dec4 #cj #bc #cj ,total #afeg ,june #aa #aa #bj ------ #afeg ,june #be #i #ce ,total #afeg ,dec4 #d #bj #j ------ #afeg ,dec4 #bj #g #dg #c #i #afeh ,may #ca #af #j ------ #afeh ,june #ad #bb #eh ------ #afeh ,nov4 #i #ac #ef #j #aj #afeh ,nov4 #bd #aa #cf ------ #afei ,may #f #h #cd #h #e #afei ,may #bj #ag #d ------ #afei ,oct4 #bi #af #af #e #eb #afei ,nov4 #ad #d #be #i #ea #affj ,apr4 #bd #ba #eh ,total #affj ,oct4 #c #bb #cd ------ #affj ,oct4 #ah #j #cb ,total #affj ,nov4 #b #ac #dh ------ #affa ,m>4 #bi #bb #cb ------ #affa ,apr4 #ad #d #bh ------ #affa ,sept4 #bc #a #cf #aa #ai #affa ,oct4 #g #ad #ea #g #d #affb ,m>4 #ai #ae #h ------ #affb ,apr4 #ab #a #h ------ #affc ,feb4 #ba #af #aa #c #ad #affc ,m>4 #i #e #dg ------ #affc ,aug4 #ah #h #de ,total #affc ,sept4 #a #h #h ------ #affd ,jan4 #bg #bj #dj ------ #affd ,feb4 #aa #c #af ------ #affd ,july #bb #ad #dh ------ #affd ,aug4 #bj #bb #aj ------ #affe ,jan4 #cj #ah #dg #d #cd #affe ,july #ab #g #dh ------ #affe ,july #bf #ac #ca #j #aj #afff ,jan4 #d #ba #cc ------ #afff ,july #a #ai #j #aa #aj #affg ,june #e ,noon ------ #affg ,july #ba #b #cb ------ #affg ,nov4 #ae #aa #cj ------ #affh ,may #aj ,sett+ ------ #affh ,may #be #af #bf #i #cb #affh ,nov4 #d #b #ec #i #ej #affh ,nov4 #ah #c #ed #f #de #affi ,apr4 #bi #ah #ah ------ #affi ,oct4 #bd #aj #ac ------ #afgj ,apr4 #ai #g #j ------ #afgj ,sept4 #aj #ai #j ------ #afgj ,sept4 #bh #ae #dc #i #g #afgj ,oct4 #ac #ab #e ------ #afga ,april #h #bc #bi ------ #afga ,sept4 #b #ba #be ------ #afga ,sept4 #ah #g #dd ,total #afgb ,feb4 #bh #c #ch ------ #afgb ,m>4 #ac #c #ag ------ #afgb ,aug4 #bb #f #dc ------ #afgb ,sept4 #f #ah #ed ------ #afgc ,feb4 #af #g #bi ------ #afgc ,aug4 #aa #ba #dd ------ #afgd ,jan4 #ba #ah #bb #aa #ba #afgd ,feb4 #e #i #d ------ #afgd ,july #ag #i #dj ,total #afge ,jan4 #aa #h #bi ,total #afge ,jan4 #be #aj #cf ------ #afge ,july #f #af #ca ,total #afgf ,june #aj #ba #bf #d #cd #afgf ,june #be #f #bf ------ #afgf ,dec4 #d #bj #eb ------ #afgg ,nov4 #bd #ab #e ------ #afgg ,may #af #af #be #h #ae #afgh ,may #f #e #cj ------ #afgh ,oct4 #bi #i #ag ,total #afgi ,apr4 #aj #ba #j ------ #afgi ,apr4 #be #aa #ec #e #dg #afhj ,m>4 #bi #bc #bb ------ #afhj ,sept4 #bb #g #eg ------ #afha ,m>4 #d ,noon ------ #afha ,m>4 #aj #ac #dc ------ #afha ,aug4 #bh #ae #bb #aj #ce #afha ,sept4 #aa #ae #dc ------ #afhb ,feb4 #ba #ab #bh ,total #afhb ,aug4 #ag #ah #ef ,total #afhc ,jan4 #bg #a #ce #aj #cj #afhc ,feb4 #i #c #ci ------ #afhc ,aug4 #f #bj #cf ------ #afhd ,jan4 #af #f #cd ------ #afhd ,june #bf #ae #ah #a #ce #afhd ,july #ab #c #bf ,total #afhd ,dec4 #ba #aa #ah #i #de #afhe ,jan4 #d #af #j ------ #afhe ,june #af #f #j ------ #afhe ,dec4 #aj #aa #bf ,total #afhf ,may #ba #ag #i ------ #afhf ,june #f ,noon ------ #afhf ,nov4 #bi #ab #bb ,total #afhg ,may #aa #a -- 99 #afhg ,may #bf #ad -- 99 #afhg ,apr4 #ae #g #d #f #di #afhh ,apr4 #bi #af #bg ------ #afhh ,oct4 #i ,noon ------ #afhh ,oct4 #be #ai #dj ------ #afhi ,april #d #g #db ,total #afhi ,sept4 #bh #ae #df ,total #afij ,m>4 #aj -- -- ------ #afij ,m>4 #bd #aa #ad #e #dc #afij ,sept4 #c -- -- ------ #afij ,sept4 #ah #b #db ------ #afia ,feb4 #bg #ag #cj ------ #afia ,aug4 #bc #e #ea ------ #afib ,feb4 #b #c #bj ------ #afib ,feb4 #af #ag #ca ------ #afib ,july #bg #af #i ,total #afic ,jan4 #ba #ag #be ,total #afic ,july #ag ,noon ------ #afid ,jan4 #aa ,noon ------ #afid ,june #bb #d #bb #f #bb #afid ,july #f #ac #ea #j #dg #afie ,may #aa #f #c ------ #afie ,may #bh ,noon ------ #afie ,nov4 #bj #h #j #f #ee #afie ,dec4 #e #ag #g ------ #afif ,may #af #ab #de ,total #afif ,may #cj #ab #ef ------ #afif ,nov4 #h #ag #cj ,total #afif ,nov4 #bc #ag #cb ------ #afig ,apr4 #bj #ad #cb ------ #afig ,may #e #ah #bg ------ #afig ,oct4 #bi #h #dd #h #ed #afih ,apr4 #aj #i #ac ------ #afih ,oct4 #c #ae #bi ------ #afii ,m>4 #ae #h #ad #i #g #afii ,m>4 #cj #bb #j ------ #afii ,sept4 #h #bc #bb ------ #afii ,sept4 #bc #bb #ch #i #eh #agjj ,m>4 #d #bj #aa ------ #agjj ,aug4 #bi #a #db ------ ---------------------------------------- - ,! ,eclipses f ,,/ruyk 7 obs]v$3 ^? f ,,ricciolus calculat$3 ! foll[+ f ,l',art de v]ifi] les ,dates1 are only ^? :i* are visible 9 ,europe = ! pres5t c5tury3 ^? :i* are total are m>k$ ) a ,t2 & ,m signifies ,morn+1 ,a ,aft]noon4 ,visible ,,eclipses f #agjj to #ahjj4 --------------------------------- ,aft4 ,mon?s ,"t ( ,*r4 & ! ,day ,days4 or ,night4 --------------------------------- #agja ,feb4 #bb #aa ,a4 #agjc ,jan4 #c #g ,m4 #agjc ,june #bi #a ,m4 ,t4 #agjc ,dec4 #bc #g ,m4 ,t4 #agjd ,dec4 #aa #g ,m4 #agjf ,apr4 #bh #b ,m4 #agjf ,may #ab #aj ,m4 #agjf ,oct4 #ba #g ,a4 #agjg ,apr4 #ag #b ,m4 ,t4 #agjh ,april #e #f ,m4 #agjh ,dec4 #ad #h ,m4 #agjh ,sept4 #bi #i ,a4 #agji ,m>4 #aa #b ,a4 #agaj ,feb4 #ac #aa ,a4 #agaj ,feb4 #bh #a ,a4 #agaa ,july #ae #h ,a4 #agaa ,july #bi #f ,a4 ,t4 #agab ,jan4 #bc #h ,a4 #agac ,june #h #f ,a4 #agac ,dec4 #b #d ,m4 #agae ,may #c #i ,m4 ,t4 #agae ,nov4 #aa #e ,m4 #agag ,m>4 #bg #c ,m4 #agag ,may #bj #f ,a4 #agah ,sept4 #i #h ,a4 ,t4 #agai ,aug4 #bi #i ,a4 #agba ,jan4 #ac #c ,a4 #agbb ,june #bi #c ,m4 #agbb ,dec4 #h #c ,a4 #agbb ,dec4 #bb #d ,a4 #agbd ,may #bb #g ,a4 ,t4 #agbd ,nov4 #a #d ,m4 #agbe ,oct4 #ba #g ,a4 #agbf ,sept4 #be #f ,a4 #agbf ,oct4 #aa #e ,m4 #agbg ,sept4 #ae #g ,m4 #agbi ,feb4 #ac #i ,a4 ,t4 #agbi ,aug4 #i #a ,m4 #agcj ,feb4 #d #d ,m4 #agca ,june #bj #b ,m4 #agcb ,dec4 #a #aj ,a4 ,t4 #agcc ,may #ac #g ,a4 #agcc ,may #bh #g ,a4 #agce ,oct4 #b #a ,m4 #agcf ,m>4 #bf #ab ,a4 ,t4 #agcf ,sept4 #bj #c ,m4 ,t4 #agcf ,oct4 #d #f ,a4 #agcg ,m>4 #a #d ,a4 #agcg ,sept4 #i #d ,m4 #agch ,aug4 #ae #aa ,m4 #agci ,jan4 #bd #aa ,a4 #agci ,aug4 #d #e ,a4 #agci ,dec4 #cj #i ,m4 #agdj ,jan4 #ac #aa ,a4 ,t4 #agda ,jan4 #a #ab ,a4 #agdc ,nov4 #b #c ,m4 ,t4 #agdd ,aug4 #bf #i ,a4 #agdf ,aug4 #cj #ab ,a4 #agdg ,feb4 #ad #e ,m4 ,t4 #agdh ,july #be #aa ,m4 #agdh ,aug4 #h #ab ,a4 #agdi ,dec4 #bc #h ,a4 #agej ,jan4 #h #i ,m4 #agej ,june #ai #i ,a4 ,t4 #agej ,dec4 #ac #g ,m4 #agea ,june #i #b ,m4 #agea ,dec4 #b #aj ,a4 #ageb ,may #ac #h ,a4 #agec ,apr4 #ag #g ,a4 #agec ,oct4 #bf #aj ,m4 #agee ,m>4 #bh #a ,m4 #ageg ,feb4 #d #f ,m4 #ageg ,july #cj #ab ,a4 #ageh ,jan4 #bd #g ,m4 ,t4 #ageh ,dec4 #cj #g ,m4 #agei ,june #bd #g ,a4 #agei ,dec4 #ai #b ,a4 #agfj ,may #bi #i ,a4 #agfj ,june #ac #g ,m4 #agfj ,nov4 #bb #i ,a4 #agfa ,may #ah #aa ,a4 ,t4 #agfb ,may #h #d ,m4 #agfb ,oct4 #ag #h ,m4 #agfb ,nov4 #a #h ,a4 #agfc ,apr4 #ac #h ,m4 #agfd ,apr4 #a #aj ,m4 #agfd ,apr4 #af #a ,m4 #agfe ,m>4 #ba #b ,a4 #agfe ,aug4 #af #e ,a4 #agff ,feb4 #bd #g ,a4 #agff ,aug4 #e #g ,a4 #agfh ,jan4 #d #e ,m4 #agfh ,june #cj #d ,m4 ,t4 #agfh ,dec4 #bc #d ,a4 ,t4 #agfi ,june #d #h ,m4 #agfi ,dec4 #ac #g ,m4 #aggj ,nov4 #ag #aj ,m4 #agga ,apr4 #bh #b ,m4 #agga ,oct4 #bc #e ,a4 #aggb ,oct4 #aa #f ,a4 ,t4 #aggb ,oct4 #bf #aj ,m4 #aggc ,m>4 #bc #e ,m4 #aggc ,sept4 #cj #g ,a4 #aggd ,m>4 #ab #aj ,m4 #aggf ,july #ca #a ,m4 ,t4 #aggf ,aug4 #ad #e ,m4 #aggg ,jan4 #i #e ,a4 #aggh ,june #bd #d ,a4 #aggh ,dec4 #d #f ,m4 #aggi ,may #cj #e ,m4 ,t4 #aggi ,june #ad #h ,m4 #aggi ,nov4 #bc #h ,a4 #aghj ,oct4 #bg #f ,a4 #aghj ,nov4 #ab #d ,m4 #agha ,apr4 #bc #f ,a4 #agha ,oct4 #ag #h ,m4 #aghb ,apr4 #ab #g ,a4 #aghc ,m>4 #ah #i ,a4 ,t4 #aghc ,sept4 #aj #aa ,a4 ,t4 #aghd ,m>4 #g #c ,m4 #aghe ,feb4 #i #a ,a4 #aghg ,jan4 #c #ab ,a4 ,t4 #aghg ,jan4 #ai #aj ,m4 #aghg ,june #ae #e ,a4 #aghg ,dec4 #bd #c ,a4 #aghh ,june #d #i ,m4 #aghi ,nov4 #b #ab ,a4 #agij ,apr4 #bh #ab ,a4 ,t4 #agij ,oct4 #bc #a ,m4 ,t4 #agia ,april #c #a ,a4 #agia ,oct4 #ab #c ,m4 #agib ,sept4 #af #aa ,m4 #agic ,feb4 #be #aj ,a4 #agic ,sept4 #e #c ,a4 #agid ,jan4 #ca #d ,a4 #agid ,feb4 #ad #aa ,a4 ,t4 #agid ,aug4 #be #e ,a4 #agie ,feb4 #d #a ,m4 #agie ,july #af #i ,m4 #agie ,july #ca #h ,a4 #agig ,june #be #h ,a4 #agig ,dec4 #d #f ,m4 #agih ,may #bg #g ,a4 ,t4 #ahjj ,oct4 #b #aa ,a4 --------------------------------- #cbh4 ,a ,li/ ( ,eclipses1 & hi/orical ,ev5ts1 :i* happ5$ ab\t ! same ,times1 f ,,ricciolus4 ,sid5ote3 ,hi/orical ,eclipses4 ,be=e ,,*ri/4 #ged ,july #e ,b accord+ to an old ,cal5d> ?is ,eclipse ( ! ,sun 0 on ! #ba/ ( ,april1 on :i* day ! ,f\ndations ( ,rome 7 laid if we may believe ,t>untius ,firmanus4 #gba ,m>* #ai ,a total ,eclipse ( ! ,moon4 ,! ,assyrian ,empire at an end2 ! ,babylonian e/abli%$4 #ehe ,may #bh ,an ,eclipse ( ! ,sun =etold by ,,?ales1 by :i* a peace 0 br\ght ab\t betwe5 ! ,m$es & ,lydians4 #ebc ,july #af ,an ,eclipse ( ! ,moon1 :i* 0 foll[$ by ! dea? ( ,,cambyses4 #ejb ,nov4 #ai ,an ,eclipse ( ! ,moon1 :i* 0 foll[$ by ! slaught] ( ! ,sab9es1 & dea? ( ,val]ius ,publicola4 #dfc ,april #cj ,an ,eclipse ( ! ,sun4 ,! ,p]sian w>1 & ! fall+ (f ( ! ,p]sians f ! ,egyptians4 #dca ,april #be ,an ,eclipse ( ! ,moon1 :i* 0 foll[$ by a great fam9e at ,rome2 & ! beg9n+ ( ! ,peloponnesian w>4 #dca ,augu/ #c ,a total ,eclipse ( ! ,sun4 ,a ,comet & ,plague at ,a!ns#gd4 #dac ,aug4 #bg ,a total ,eclipse ( ! ,moon4 ,nicias ) 8 %ip de/roy$ at ,syracuse4 #cid ,aug4 #ad ,an ,eclipse ( ! ,sun4 ,! ,p]sians beat by ,conon 9 a sea engagem5t4 #afh ,june #ba ,a total ,eclipse ( ! ,moon4 ,! next day ,p]seus ,k+ ( ,mac$onia 0 conqu]$ by ,paulus ,emilius4 ,aft] ,,*ri/4 #ei ,april #cj ,an ,eclipse ( ! ,sun4 ,?is is reckon$ among ! prodigies1 on acc\nt ( ! mur!r ( ,agripp9us by ,n]o4 #bcg ,april #ab ,a total ,eclipse ( ! ,sun4 ,a sign t ! reign ( ! ,gordiani w\ld n cont9ue long4 ,a six? p]secution ( ! ,*ri/ians4 #cjf ,july #bg ,an ,eclipse ( ! ,sun4 ,! ,/>s 7 se51 & ! ,emp]or ,con/antius di$4 #hdj ,may #d ,a dreadful ,eclipse ( ! ,sun4 ,& ,lewis ! ,pi\s di$ )9 six mon?s aft] x4 #ajji ---- ,an ,eclipse ( ! ,sun4 ,& ,j]usalem tak5 by ! ,s>ac5s4 #aacc ,aug4 #b ,a t]rible ,eclipse ( ! ,sun4 ,! ,/>s 7 se54 ,a s*ism 9 ! *ur*1 occasion$ by !re be+ ?ree ,popes at once4 ,illu/ration3 ,plate ,,xi4 ,j4 ,f]guson del94 ,j4 ,mynde ,sculp4 ,sid5ote3 ,! sup]/iti\s notions ( ! anti5ts ) reg>d to ,eclipses4 ,,plate ,,xi4 #cbi4 ,i h n cit$ "o half ( ,,ricciolus's li/ ( pot5t\s ,eclipses2 & = ! same reason t he decl9es giv+ any m ( !m ?an :at t li/ conta9s3 namely1 t 'tis mo/ disagreeable to dwell any long] on su* nons5se1 & z mu* z possible to avoid tir+ ! read]3 ! sup]/ition ( ! anti5ts may be se5 by ! few "h copi$4 ,my au?or f>!r says1 t !re 7 treatises writt5 to %ew aga9/ :at regions ! malevol5t effects ( any p>ticul> ,eclipse 0 aim$3 & ! writ]s affirm$1 t ! effects ( an ,eclipse ( ! ,sun cont9u$ z _m ye>s z ! ,eclipse la/$ h\rs2 & t ( ! ,moon z _m mon?s4 ,sid5ote3 ,v =tunate once = ,,*ri/oph] ,,columbus4 #ccj4 ,yet su* idle notions 7 once ( no small advantage to ,,*ri/oph] ,,columbus2 :o1 9 ! ye> #adic1 0 driv5 on ! isl& ( ,jamaica1 :]e he 0 9 ! greate/ di/ress = want ( provisions1 & 0 moreov] refus$ any assi/ance f ! inhabitants2 on :i* he ?reat5$ !m ) a plague1 & t 9 tok5 ( x !re %\ld be an ,eclipse3 :i* accord+ly fell on ! day he _h =etold1 & s t]rifi$ ! ,b>b>ians1 t !y /rove :o %\ld be fir/ 9 br++ him all sorts ( provisions2 ?r[+ !m at 8 feet1 & implor+ 8 =giv5ess4 ,,ricciolus's ,almage/1 ,vol4 ,i4 #a4 v4 c4 ii4 ,sid5ote3 ,:y !re are m visible ,eclipses ( ! ,moon ?an ( ! ,sun4 #cca4 ,eclipses ( ! ,sun are m frequ5t ?an ( ! ,moon1 because ! ,sun's ecliptic limits are great] ?an ! ,moon's #cag3 yet we h m visible ,eclipses ( ! ,moon ?an ( ! ,sun1 because ,eclipses ( ! ,moon are se5 f all p>ts ( t ,hemisph]e ( ! ,e>? :i* is next h]1 & equally great to ea* ( ^! p>ts2 b ! ,sun's ,eclipses are visible only to t small portion ( ! ,hemisph]e next him :]eon ! ,moon's %ad[ falls2 z %all be expla9$ by & by at l>ge4 ,sid5ote3 ,fig4 ,i4 ,total & annul> ,eclipses ( ! ,sun4 ,,plate ,,xi4 #ccb4 ,! ,moon's ,orbit be+ elliptical1 & ! ,e>? 9 "o ( its focuses1 %e is once at h] lea/ di/ance f ! ,e>?1 & once at h] greate/ 9 e ,lunation4 ,:5 ! ,moon *anges at h] lea/ di/ance f ! ,e>?1 & s ne> ! ,node t h] d>k %ad[ falls on ! ,e>?1 %e appe>s big en\gh to cov] ! :ole #ge;,disc ( ! ,sun f t "p on :i* h] %ad[ falls2 & ! ,sun appe>s totally eclips$ !re1 z at ,a1 = "s m9utes3 ,b :5 ! ,moon *anges at h] greate/ di/ance f ! ,e>?1 & s ne> ! ,node t h] d>k %ad[ is direct$ t[>ds ! ,e>?1 h] diamet] subt5ds a less angle ?an ! ,sun's2 & !re=e %e _c hide 8 :ole ,disc f any "p ( ! ,e>?1 nor does h] %ad[ rea* x at t "t2 & to ! place ov] :i* ! po9t ( h] %ad[ hangs1 ! ,eclipse is annul> z at ,b2 ! ,sun's edge appe>+ l a lum9\s r+ all ar\nd ! body ( ! ,moon4 ,:5 ! ,*ange happ5s )9 #ag degrees ( ! ,node1 & ! ,moon at h] mean di/ance f ! ,e>?1 ! po9t ( h] %ad[ j t\*es ! ,e>?1 & %e eclipse? ! ,sun totally to t small spot :]eon h] %ad[ falls2 b ! d>kness is n ( a mom5t's cont9uance4 ,sid5ote3 ,! longe/ duration ( total ,eclipses ( ! ,sun4 #ccc4 ,! ,moon's app>5t diamet] :5 l>ge/ exce$s ! ,sun's :5 lea/ only #a m9ute #ch seconds ( a degree3 ,& 9 ! greate/ ,eclipse ( ! ,sun t c happ5 at any "t & place1 ! total d>kness cont9ues no long] ?an :il/ ! ,moon is go+ #a m9ute #ch seconds f ! ,sun 9 h] ,orbit2 :i* is ab\t #c m9utes & #ac seconds ( an h\r4 ,sid5ote3 ,to h[ mu* ( ! ,e>? ! ,sun may be totally or p>tially eclips$ at once4 #ccd4 ,! ,moon's d>k %ad[ cov]s only a spot on ! ,e>?'s surface1 ab\t #ahj ,engli% miles broad1 :5 ! ,moon's diamet] appe>s l>ge/ & ! ,sun's lea/2 & ! total d>kness c ext5d no f>!r ?an ! d>k %ad[ cov]s4 ,yet ! ,moon's p>tial ,%ad[ or ,p5umbra may !n cov] a circul> space #dijj miles 9 diamet]1 )9 all :i* ! ,sun is m or less eclips$ z ! places are less or m di/ant f ! ,c5t] ( ! ,p5umbra4 ,:5 ! ,moon *anges exactly 9 ! ,node1 ! ,p5umbra is circul> on ! ,e>? at ! middle ( ! g5]al ,eclipse2 because at t "t x falls p]p5dicul>ly on ! ,e>?'s surface3 ,b at e o!r mom5t x falls obliquely1 & w !re=e be elliptical2 & ! m s1 z ! "t is long] be=e or aft] ! middle ( ! g5]al ,eclipse2 & !n1 mu* great] portions ( ! ,e>?'s surface are involv$ 9 ! ,p5umbra4 ,sid5ote3 ,duration ( g5]al & p>ticul> ,eclipses4 ,! ,moon's d>k %ad[4 ,& ,p5umbra4 #cce4 ,:5 ! ,p5umbra fir/ t\*es ! ,e>? ! g5]al ,eclipse beg9s3 :5 x leaves ! ,e>? ! g5]al ,eclipse ends3 f ! beg9n+ to ! end ! ,sun appe>s eclips$ 9 "s "p ( ! ,e>? or o!r4 ,:5 ! ,p5umbra t\*es any place ! ,eclipse beg9s at t place1 & ends :5 ! ,p5umbra leaves x4 ,:5 ! ,moon *anges 9 ! ,node1 ! ,p5umbra goes ov] ! c5t] ( ! ,e>?'s ,disc z se5 f ! ,moon2 & consequ5tly1 by describ+ ! longe/ l9e possible on ! ,e>?1 cont9ues ! longe/ ^u x2 namely1 at a mean rate1 #e h\rs #ej m9utes3 m1 if ! ,moon be at h] greate/ di/ance f ! ,e>?1 because %e !n moves sl[e/2 less1 if %e be at h] lea/ di/ance1 because ( h] quick] motion4 ,sid5ote3 ,fig4 ,,ii4 #ccf4 ,to make ! la/ five articles & sev]al o!r ,ph5om5a pla9]1 let ,s be ! ,sun1 ,e ! ,e>?1 ,m ! ,moon1 & ,,amp ! ,moon's ,orbit4 ,draw ! "r l9e ,wc #ab f ! we/]n edge ( ! ,sun at ,w1 t\*+ ! we/]n edge ( ! ,moon at c & ! ,e>? at #ab3 draw also ! "r l9e ,vd #ab f ! ea/]n edge ( ! ,sun at ,v1 t\*+ ! ea/]n edge ( ! ,moon at d & ! ,e>? at #ab3 ! d>k space ce #ab d includ$ betwe5 ^? l9es is ! ,moon's %ad[1 end+ 9 a po9t at #ab :]e x t\*es ! ,e>?2 because 9 ?is case ! ,moon is suppos$ to *ange at ,m 9 ! middle betwe5 ,a ! ,apogee1 or f>!/ po9t ( h] ,orbit f ! ,e>?1 & ,p ! ,p]igee1 or ne>e/ po9t to x4 ,=1 _h ! po9t ,p be5 at ,m1 ! ,moon _h be5 ne>] ! ,e>?2 & h] d>k %ad[ at e w\ld h cov]$ a space ^u x ab\t #ahj miles broad1 & ! ,sun w\ld h be5 totally d>k5$ z at ,a 7,fig ,i7 ) "s cont9uance3 b _h ! po9t ,a 7,fig4 ,,ii7 be5 at ,m1 ! ,moon w\ld h be5 f>!r f ! ,e>?1 & h] %ad[ w\ld h end$ 9 a po9t ab\t e1 & !re=e ! ,sun w\ld h appe>$ z at ,b 7,fig4 ,i7 l a lum9\s r+ all ar\nd ! ,moon4 ,draw ! "r l9es ,w,xdh & ,v,xcg1 t\*+ ! contr>y sides ( ! ,sun & ,moon1 & end+ on ! ,e>? at a & b3 draw also ! "r l9e ,,sxm #ab1 f ! c5t] ( ! ,sun's ,disc1 ?r\gh ! ,moon's c5t]1 to ! ,e>? at #ab2 & suppose ! two =m] l9es ,w,xdh & ,v,xcg to revolve on ! l9e ,,sxm #ab z an ,axis1 & _! po9ts a & b w describe ! limits ( ! ,p5umbra ,,tt on ! ,e>?'s surface1 includ+ ! l>ge space a#j;b#ab;a2 )9 :i* ! ,sun appe>s m or less eclips$ z ! places are m or less di/ant f ! v]ge ( ! ,p5umbra a#j;b4 ,sid5ote3 ,digits1 :at4 ,draw ! "r l9e y #ab across ! ,sun's ,disc1 & p>allel to ! plane ( ! ,moon's ,orbit2 divide ?is l9e into twelve equal p>ts1 z 9 ! ,figure1 = ! twelve #gf;,digits ( ! ,sun's diamet]3 & at equal di/ances f ! c5t] ( ! ,p5umbra ,,tt to its edge on ! ,e>?1 or f #ab to #j1 draw twelve conc5tric ,circles1 z m>k$ ) ! num]al ,figures #a #b #c #d c4 & rememb] t ! ,moon's motion 9 h] ,orbit ,,amp is f we/ to ea/1 z f s to t4 ,!n1 ,sid5ote3 ,! diff]5t phases ( a sol> ,eclipse4 ,,plate ,,xi4 ,fig4 ,,iii4 ,to an obs]v] on ! ,e>? at b1 ! ea/]n limb ( ! ,moon at d seems to t\* ! we/]n limb ( ! ,sun at ,w1 :5 ! ,moon is at ,m2 & ! ,sun's ,eclipse beg9s at b2 appe>+ z at ,a 9 ,fig4 ,,iii at ! left h&2 b at ! same mom5t ( absolute "t to an obs]v] at a 9 ,fig4 ,,ii ! we/]n edge ( ! ,moon at c leaves ! ea/]n edge ( ! ,sun at ,v1 & ! ,eclipse ends1 z at ! "r h& ,c ( ,fig4 ,,iii4 ,at ! v same in/ant1 to all ^? :o live on ! ,circle m>k$ #a on ! ,e>? ,e 9 ,fig4 ,,ii1 ! ,moon ,m cuts (f or d>k5s a twelf? "p ( ! ,sun ,s1 & eclipses him "o ,digit1 z at #a 9 ,fig4 ,,iii3 to ^? :o live on ! ,circle m>k$ #b 9 ,fig4 ,,ii ! ,moon cuts (f two twelf? p>ts ( ! ,sun1 z at #b 9 ,fig4 ,,iii3 to ^? on ! ,circle #c1 ?ree p>ts2 & s on to ! c5t] at #ab 9 ,fig4 ,,ii1 :]e ! ,sun is c5trally eclips$ z at ,b 9 ! middle ( ,fig4 ,,iii3 "u :i* ,figure !re is a scale ( h\rs & m9utes1 to %ew at a mean /ate h[ long x is f ! beg9n+ to ! end ( a c5tral ,eclipse ( ! ,sun on ! p>allel ( ,london2 & h[ _m ,digits are eclips$ at any p>ticul> "t f ! beg9n+ at ,a to ! middle at ,b1 or ! end at ,c4 ,?us 9 #af m9utes f ! beg9n+1 ! ,sun is two ,digits eclips$2 9 an h\r & five m9utes1 #h ,digits2 & 9 an h\r & ?irty-sev5 m9utes1 #ab ,digits4 ,sid5ote3 ,fig4 ,,ii4 ,! ,velocity ( ! ,moon's %ad[ on ! ,e>?4 ,fig4 ,,iv4 #ccg4 ,by ,fig4 ,,ii x is pla91 t ! ,sun is totally or c5trally eclips$ b to a small "p ( ! ,e>? at any "t2 because ! d>k conical %ad[ e ( ! ,moon ,m falls b on a small "p ( ! ,e>?3 & t ! p>tial ,eclipse is conf9$ at t "t to ! space includ$ by ! ,circle a #j b1 ( :i* only "o half c be project$ 9 ! ,figure1 ! o!r half be+ suppos$ to be hid by ! convexity ( ! ,e>? ,e3 & likewise1 t no "p ( ! ,sun is eclips$ to ! l>ge space ,,yy ( ! ,e>?1 because ! ,moon is n betwe5 ! ,sun & t "p ( ! ,e>?3 & !re=e to all t "p ! ,eclipse is invisible4 ,! ,e>? turns ea/w>d on its ,axis1 z f g to h1 :i* is ! same way t ! ,moon's %ad[ moves2 b ! ,moon's motion is mu* swift] 9 h] ,orbit f s to t3 & !re=e1 al?o' ,eclipses ( ! ,sun are ( long] duration on acc\nt ( ! ,e>?'s motion on its ,axis1 ?an !y w\ld be if t motion 0 /opt1 yet 9 #c m9utes & #ac seconds ( "t1 ! ,moon's swift] motion c>ries h] d>k %ad[ q ov] any place t its c5t] t\*es at ! "t ( greate/ obscuration4 ,! motion ( ! %ad[ on ! ,e>?'s ,disc is equal to ! ,moon's motion f ! ,sun1 :i* is ab\t #cj-a_/b m9utes ( a degree e h\r at a mean rate2 b s mu* ( ! ,moon's ,orbit is equal to #cj-a_/b degrees ( a great ,circle on ! ,e>?1 #cbj2 & !re=e ! ,moon's %ad[ goes #cj-a_/b degrees or #ahcj geographical miles on ! ,e>? 9 an h\r1 or #cj-a_/b miles 9 a m9ute1 :i* is almo/ f\r times z swift z ! motion ( a cannon-ball4 ,sid5ote3 ,,plate ,,xi4 ,fig4 ,,iv4 ,ph5om5a ( ! ,e>? z se5 f ! ,sun or ,new ,moon at diff]5t times ( ! ye>4 #cch4 ,z se5 f ! ,sun or ,moon1 ! ,e>?'s ,axis appe>s diff]5tly incl9$ e day ( ! ye>1 on acc\nt ( keep+ its p>allelism ?r\gh\t its annual c\rse4 ,let ,e1 ,d1 ,o1 ,n1 be ! ,e>? at ! two ,equ9oxes & ! two ,sol/ices2 ,n ,s its ,axis1 ,n ! ,nor? ,pole1 ,s ! ,s\? ,pole1 ,q ! ,equator1 ,t ! ,tropic ( ,canc]1 t ! ,tropick ( ,capricorn1 & ,,abc ! ,circumf]5ce ( ! ,e>?'s enlight5$ ,disc z se5 f ! ,sun or ,new ,moon at ^! times4 ,! ,e>?'s ,axis has ! position ,,nes at ! v]nal ,equ9ox1 ly+ t[>ds ! "r h&1 z se5 f ! ,sun or ,new ,moon2 its ,poles ,n & ,s be+ !n 9 ! ,circumf]5ce ( ! ,disc2 & ! ,equator & all its p>allels seem to be /raight l9es1 because _! planes pass ?r\gh ! obs]v]'s eye look+ d[n ^u ! ,e>? f ! ,sun or ,moon directly ov] ,e1 :]e ! ,ecliptic ,,fg int]sects ! ,equator 4 ,at ! ,summ] ,sol/ice1 ! ,e>?'s ,axis has ! position ,,nds2 & t "p ( ! ,ecliptic ,,fg 9 :i* ! ,moon is !n ,new1 t\*es ! ,tropic ( ,canc] ,t at ,d4 ,! ,nor? ,pole ,n at t "t incl9+ #bc-a_/b degrees t[>ds ! ,sun1 falls s _m degrees )9 ! ,e>?'s enlight5$ ,disc1 because ! ,sun is !n v]tical to ,d1 #bc-a_/b degrees nor? ( ! ,equator ,q2 & ! ,equator ) all its p>allels seem elliptic curves b5d+ d[nw>d1 or t[>ds ! ,s\? ,pole z se5 f ! ,sun3 :i* ,pole1 toge!r ) #bc-a_/b degrees all r\nd x1 is hid beh9d ! ,disc 9 ! d>k ,hemisph]e ( ! ,e>?4 ,at ! autumnal ,equ9ox ! ,e>?'s ,axis has ! position ,,nos1 ly+ to ! left h& z se5 f ! ,sun or ,new ,moon1 :i* are !n v]tical to ,o1 :]e ! ,ecliptic cuts ! ,equator ,q4 ,bo? ,poles n[ lie 9 ! circumf]5ce ( ! ,disc1 ! ,nor? ,pole j go+ to disappe> beh9d x1 & ! ,s\? ,pole j ent]+ into x2 & ! ,equator ) all its p>allels seem to be /raight l9es1 because _! planes pass ?r\gh ! obs]v]'s eye1 z se5 f ! ,sun1 & v ne>ly s z se5 f ! ,moon4 ,at ! ,w9t] ,sol/ice ! ,e>?'s ,axis has ! position ,,nns2 :5 its ,s\? ,pole ,s incl9+ #bc-a_/b degrees t[>d ! ,sun falls #bc-a_/b degrees )9 ! enlight5$ ,disc1 z se5 f ! ,sun or ,new ,moon :i* are !n v]tical to ! ,tropic ( ,capricorn t1 #bc-a_/b degrees s\? ( ! ,equator ,q2 & ! ,equator ) all its p>allels seem elliptic curves b5d+ upw>d2 ! ,nor? ,pole be+ z f> hid beh9d ! ,disc 9 ! d>k ,hemisph]e1 z ! ,s\? ,pole is come into ! light4 ,! ne>] t any "t ( ! ye> is to ! ,equ9oxes or ,sol/ices1 ! m x p>takes ( ! ,ph5om5a relat+ to !m4 ,sid5ote3 ,,plate ,,xi4 ,v>i\s positions ( ! ,e>?'s ,axis1 z se5 f ! ,sun at diff]5t times ( ! ye>4 #cci4 ,?us x appe>s1 t f ! v]nal equ9ox to ! autumnal1 ! ,nor? ,pole is enlight5$2 & ! ,equator & all its p>allels appe> ,semi-ellipses z se5 f ! ,sun1 m or less curv$ z ! "t is ne>] to or f>!r f ! ,summ] ,sol/ice2 & b5d+ d[nw>ds or t[>ds ! ,s\? ,pole2 ! rev]se ( :i* happ5s f ! autumnal ,equ9ox to ! v]nal4 ,a little consid]ation w be suffici5t to conv9ce ! read]1 t ! ,e>?'s ,axis incl9es t[>ds ! ,sun at ! ,summ] ,sol/ice2 f ! ,sun at ! ,w9t] ,sol/ice2 & sidewise to ! ,sun at ! ,equ9oxes2 b t[>ds ! "r h&1 z se5 f ! ,sun at ! v]nal ,equ9ox2 & t[>ds ! left h& at ! autumnal4 ,f ! ,w9t] to ! ,summ] ,sol/ice1 ! ,e>?'s ,axis incl9es m or less to ! "r h&1 z se5 f ! ,sun2 & ! contr>y f ! ,summ] to ! ,w9t] ,sol/ice4 ,sid5ote3 ,h[ ^! positions affect sol> ,eclipses4 #cdj4 ,! diff]5t positions ( ! ,e>?'s ,axis1 z se5 f ! ,sun at diff]5t times ( ! ye>1 affect sol> ,eclipses greatly ) reg>d to p>ticul> places2 yea s f> z w\ld make c5tral ,eclipses :i* fall at "o "t ( ! ye> invisible if !y fell at ano!r1 ev5 ?\gh ! ,moon %\ld always *ange 9 ! ,nodes & at ! same h\r ( ! day3 ( :i* indef9itely v>i\s affections1 we %all only give ,examples = ! times ( ! ,equ9oxes & ,sol/ices4 ,sid5ote3 ,fig4 ,,iv4 ,9 ! same ,diagram1 let ,,fg be "p ( ! ,ecliptic1 & ,,ik ik ik ik "p ( ! ,moon's ,orbit2 bo? se5 edgewise1 & !re=e project$ into "r l9es2 & let ! int]sections ,n1 ,o1 ,d1 ,e be "o & ! same ,node at ! above times1 :5 ! ,e>? has ! =em5tion$ diff]5t positions2 & let ! spaces includ$ by ! ,circles ,p1 p1 p1 p be ! ,p5umbra at ^! times1 z its c5t] is pass+ ov] ! c5t] ( ! ,e>?'s ,disc4 ,at ! ,w9t] ,sol/ice1 :5 ! ,e>?'s ,axis has ! position ,,nns1 ! c5t] ( ! ,p5umbra ,p t\*es ! ,tropic ( ,capricorn t 9 ,n at ! middle ( ! g5]al ,eclipse2 b no "p ( ! ,p5umbra t\*es ! ,tropic ( ,canc] ,t4 ,at ! ,summ] ,sol/ice1 :5 ! ,e>?'s ,axis has ! position ,,nds 7i,dk be+ !n "p ( ! ,moon's ,orbit ^: ,node is at ,d7 ! ,p5umbra p has its c5t] on ! ,tropic ( ,canc] ,t at ! middle ( ! g5]al ,eclipse1 & !n no "p ( x t\*es ! ,tropic ( ,capricorn t4 ,at ! autumnal ,equ9ox ! ,e>?'s ,axis has ! position ,,nos 7i,ok be+ !n "p ( ! ,moon's ,orbit7 & ! ,p5umbra equally includes "p ( bo? ,tropics ,t & t at ! middle ( ! g5]al ,eclipse3 at ! v]nal ,equ9ox x does ! same1 because ! ,e>?'s ,axis has ! position ,,nes3 ,b1 9 ! =m] ( ^! two la/ cases1 ! ,p5umbra ent]s ! ,e>? at ,a1 nor? ( ! ,tropic ( ,canc] ,t1 & leaves x at m1 s\? ( ! ,tropic ( ,capricorn t2 hav+ gone ov] ! ,e>? obliquely s\?w>d1 z its c5t] describ$ ! l9e ,a,om3 :]eas 9 ! latt] case ! ,p5umbra t\*es ! ,e>? at n1 s\? ( ! ,equator ,q1 & describ+ ! l9e n,eq 7simil> to ! =m] l9e ,a,om 9 op5 space7 goes obliquely nor?w>d ov] ! ,e>?1 & leaves x at q1 nor? ( ! ,equator4 ,9 all ^! circum/ances1 ! ,moon has be5 suppos$ to *ange at noon 9 h] desc5d+ ,node3 _h %e *ang$ 9 h] asc5d+ ,node1 ! ,ph5om5a w\ld h be5 z v>i\s ! contr>y way1 ) respect to ! ,p5umbra's go+ nor?w>d or s\?w>d ov] ! ,e>?4 ,b because ! ,moon *anges at all h\rs1 z (t5 9 "o ,node z ! o!r1 & at all di/ances f !m bo? at diff]5t times z x happ5s1 ! v>iety ( ! ,phases ( ,eclipses are almo/ innum]able1 ev5 at ! same places1 consid]+ also h[ v>i\sly ! same places are situat$ on ! enlight5$ ,disc ( ! ,e>?1 ) respect to ! ,p5umbra's motion1 at ! diff]5t h\rs t ,eclipses happ54 ,sid5ote3 ,h[ mu* ( ! ,p5umbra falls on ! ,e>? at diff]5t di/ances f ! ,nodes4 #cda4 ,:5 ! ,moon *anges #ag degrees %ort ( h] desc5d+ ,node1 ! ,p5umbra ,p #ah j t\*es ! nor!rn "p ( ! ,e>?'s ,disc1 ne> ! ,nor? ,pole ,n2 &1 z se5 f t place ! ,moon appe>s to t\* ! ,sun1 b hides no "p ( him f sight4 ,_h ! ,*ange be5 z f> %ort ( ! asc5d+ ,node1 ! ,p5umbra w\ld h t\*$ ! s\!rn "p ( ! ,disc ne> ! ,s\? ,pole ,s4 ,:5 ! ,moon *anges #ab degrees %ort ( ! desc5d+ ,node1 m ?an a ?ird "p ( ! ,p5umbra ,p #ab falls on ! nor!rn p>ts ( ! ,e>? at ! middle ( ! g5]al ,eclipse3 _h %e *ang$ z f> pa/ ! same ,node1 z mu* ( ! o!r side ( ! ,p5umbra ab\t ,p w\ld h fall5 on ! s\!rn "p ( ! ,e>?2 all ! re/ 9 ! expansum1 or op5 space4 ,:5 ! ,moon *anges #f degrees f ! ,node1 almo/ ! :ole ,p5umbra ,p#f falls on ! ,e>? at ! middle ( ! g5]al ,eclipse4 ,& la/ly1 :5 ! ,moon *anges 9 ! ,node1 ! ,p5umbra ,,pn takes ! longe/ c\rse possible on ! ,e>?'s ,disc2 its c5t] fall+ on ! middle !re(1 at ! middle ( ! g5]al ,eclipse4 ,! f>!r ! ,moon *anges f ei!r ,node )9 #ag degrees ( x1 ! %ort] is ! ,p5umbra's cont9uance on ! ,e>?1 because x goes ov] a less portion ( ! ,disc1 z is evid5t by ! ,figure4 ,sid5ote3 ,! ,e>?'s diurnal motion l5g!ns ! duration ( sol> ,eclipses1 :i* fall )\t ! pol> ,circles4 #cdb4 ,! ne>] t ! ,p5umbra's c5t] is to ! ,equator at ! middle ( ! g5]al ,eclipse1 ! long] is ! duration ( ! ,eclipse at all ^? places :]e x is c5tral2 because1 ! ne>] t any place is to ! ,equator1 ! great] is ! ,circle x describes by ! ,e>?'s motion on its ,axis3 & s1 ! place mov+ quick] keeps long] 9 ! ,p5umbra ^: motion is ! same way ) t ( ! place1 ?o' fa/] z has be5 already m5tion$ #ccg4 ,?us1 7see ! ,e>? at ,d & ! ,p5umbra at #ab7 :il/ ! po9t b 9 ! pol> ,circle abcd is c>ri$ f b to c by ! ,e>?'s diurnal motion1 ! po9t d on ! ,tropick ( ,canc] ,t is c>ri$ a mu* great] l5g? f d to ,d3 & !re=e1 if ! ,p5umbra's c5t] goes "o "t ov] c & ano!r "t ov] ,d1 ! ,p5umbra w be long] 9 pass+ ov] ! mov+ place d ?an x 0 9 pass+ ov] ! mov+ place b4 ,consequ5tly1 c5tral ,eclipses ab\t ! ,poles are ( ! %orte/ duration2 & ab\t ! ,equator ( ! longe/4 ,sid5ote3 ,& %ort5s ! duration ( "s :i* fall )9 ^! ,circles4 #cdc4 ,9 ! middle ( ,summ] ! :ole frigid ,zone includ$ by ! pol> ,circle abcd is enlight5$2 & if x !n happ5s t ! ,p5umbra's c5t] goes ov] ! nor? ,pole1 ! ,sun w be eclips$ mu* ! same numb] ( ,digits at a z at c2 b :il/ ! ,p5umbra moves ea/w>d ov] c x moves we/w>d ov] a1 because ) respect to ! ,p5umbra1 ! motions ( a & c are contr>y3 = c moves ! same way ) ! ,p5umbra t[>ds d1 b a moves ! contr>y way t[>ds b2 & !re=e ! ,eclipse w be ( long] duration at c ?an at a4 ,at a ! ,eclipse beg9s on ! ,sun's ea/]n limb1 b at c on 8 we/]n3 at all places ly+ )\t ! pol> ,circles1 ! ,sun's ,eclipses beg9 on 8 we/]n limb1 or ne> x1 & end on or ne> 8 ea/]n4 ,at ^? places :]e ! ,p5umbra t\*es ! ,e>?1 ! ,eclipse beg9s ) ! ris+ ,sun1 on ! top ( 8 we/]n or upp]mo/ edge2 & at ^? places :]e ! ,p5umbra leaves ! ,e>?1 ! ,eclipse ends ) ! sett+ ,sun1 on ! top ( 8 ea/]n edge :i* is !n ! upp]mo/1 j at its disappe>+ 9 ! ,horizon4 ,sid5ote3 ,! ,moon has no ,atmosph]e4 #cdd4 ,if ! ,moon 7 surr\nd$ by an ,atmosph]e ( any consid]able ,d5sity1 x w\ld seem to t\* ! ,sun a little be=e ! ,moon made h] appulse to 8 edge1 & we %\ld see a little fa9tness on t edge be=e x 7 eclips$ by ! ,moon3 ,b z no su* fa9tness has be5 obs]v$1 at lea/ s f> z ,i ev] he>d1 x seems pla91 t ! ,moon has no su* ,atmosph]e z t ( ! ,e>?4 ,! fa9t r+ ( light surr\nd+ ! ,sun 9 total ,eclipses1 call$ by ,,cass9i la ,*evelure du ,soleil1 seems to be ! ,atmosph]e ( ! ,sun2 because x has be5 obs]v$ to move equally ) ! ,sun1 n ) ! ,moon4 ,sid5ote3 ,,plate ,,xi4 #cde4 ,hav+ be5 s prolix conc]n+ ,eclipses ( ! ,sun1 we %all drop t subject at pres5t1 & proce$ to ! doctr9e ( lun> ,eclipses2 :i*1 be+ m simple1 may be expla9$ 9 less "t4 ,sid5ote3 ,eclipses ( ! ,moon4 ,fig4 ,,ii4 ,t ! ,moon c nev] be eclips$ b at ! "t ( h] be+ ,full1 & ! reason :y %e is n eclips$ at e ,full1 h be5 %ewn already #caf1 #cag4 ,let ,s be ! ,sun1 ,e ! ,e>?1 ,,rr ! ,e>?'s %ad[1 & ,b ! ,moon 9 opposition to ! ,sun3 9 ?is situation ! ,e>? int]cepts ! ,sun's light 9 its way to ! ,moon2 & :5 ! ,moon t\*es ! ,e>?'s %ad[ at v %e beg9s to be eclips$ on h] ea/]n limb x1 & cont9ues eclips$ until h] we/]n limb y leaves ! %ad[ at w3 at ,b %e is 9 ! middle ( ! %ad[1 & consequ5tly 9 ! middle ( ! ,eclipse4 ,sid5ote3 ,:y ! ,moon is visible 9 a total ,eclipse4 #cdf4 ,! ,moon :5 totally eclips$1 is n invisible if %e be above ! ,horizon & ! ,sky be cle>2 b appe>s g5]ally ( a dusky col\r l t>ni%$ copp]1 :i* "s h ?\ght to be ! ,moon's native light4 ,b ! true cause ( h] be+ visible is ! scatt]$ beams ( ! ,sun1 b5t into ! ,e>?'s %ad[ by go+ ?r\gh ! ,atmosph]e2 :i*1 be+ m d5se ne> ! ,e>? ?an at consid]able heights above x1 refracts or b5ds ! ,sun's rays m inw>d #agi1 ! ne>] !y are pass+ by ! ,e>?'s surface1 ?an ^? rays :i* g ?r\gh high] p>ts ( ! ,atmosph]e1 :]e x is less d5se accord+ to its height1 until x be s ?9 or r>e z to lose its refractive p[]4 ,let ! ,circle fghi1 conc5tric to ! ,e>?1 include ! ,atmosph]e ^: refractive p[] vani%es at ! heights f & i2 s t ! rays ,wfw & ,viv g on /raight )\t suff]+ ! lea/ refraction3 ,b all ^? rays :i* ent] ! ,atmosph]e betwe5 f & k1 & betwe5 i & l1 on opposite sides ( ! ,e>?1 are gradually m b5t inw>d z !y g ?r\gh a great] portion ( ! ,atmosph]e1 until ! rays ,wk & ,vl1 t\*+ ! ,e>? at m & n1 are b5t s z to meet at q1 a little %ort ( ! ,moon2 & !re=e ! d>k %ad[ ( ! ,e>? is conta9$ 9 ! space moqpn :]e none ( ! ,sun's rays c ent]3 all ! re/ ,,rr1 be+ mix$ by ! scatt]$ rays :i* are refract$ z above1 is 9 "s measure enlight5$ by !m2 & "s ( ^? rays fall+ on ! ,moon give h] ! col\r ( t>ni%$ copp]1 or ( iron almo/ r$ hot4 ,s t if ! ,e>? _h no ,atmosph]e1 ! ,moon w\ld be z invisible 9 total ,eclipses z %e is :5 ,new4 ,if ! ,moon 7 s ne> ! ,e>? z to g into its d>k %ad[1 suppose ab\t po1 %e w\ld be invisible dur+ h] /ay 9 x2 b visible be=e & aft] 9 ! fa9t] %ad[ ,,rr4 ,sid5ote3 ,,plate ,,xi4 ,:y ! ,sun & ,moon are sometimes visible :5 ! ,moon is totally eclips$4 #cdg4 ,:5 ! ,moon goes ?r\gh ! c5t] ( ! ,e>?'s %ad[ %e is directly opposite to ! ,sun3 yet ! ,moon has be5 (t5 se5 totally eclips$ 9 ! ,horizon :5 ! ,sun 0 also visible 9 ! opposite "p ( x3 =1 ! horizontal refraction be+ almo/ #cd m9utes ( a degree #aha1 & ! diamet] ( ! ,sun & ,moon be+ ea* at a mean /ate b #cb m9utes1 ! refraction causes bo? ,lum9>ies to appe> above ! ,horizon :5 !y are really bel[ x #agi4 ,sid5ote3 ,fig4 ,v4 ,duration ( c5tral ,eclipses ( ! ,moon4 #cdh4 ,:5 ! ,moon is ,full at #ab degrees f ei!r ( h] ,nodes1 %e j t\*es ! ,e>?'s %ad[ b ent]s n into x4 ,let ,,gh be ! ,ecliptic1 ef ! ,moon's ,orbit :]e %e is #ab degrees f ! ,node at h] ,full2 cd h] ,orbit :]e %e is #f degrees f ! ,node1 ab h] ,orbit :]e %e is ,full 9 ! ,node1 ,,ab ! ,e>?'s %ad[1 & ,m ! ,moon4 ,:5 ! ,moon describes ! l9e ef %e j t\*es ! %ad[ b does n ent] into x2 :5 %e describes ! l9e cd %e is totally ?\gh n c5trally imm]s$ 9 ! %ad[2 & :5 %e describes ! l9e ab %e passes by ! ,node at ,m 9 ! c5t] ( ! %ad[1 & takes ! longe/ l9e possible1 :i* is a diamet]1 ?r\gh x3 & su* an ,eclipse be+ bo? total & c5tral is ( ! longe/ duration1 namely1 #c h\rs #eg m9utes #f seconds f ! beg9n+ to ! end1 if ! ,moon be at h] greate/ di/ance f ! ,e>?3 & #c h\rs #cg m9utes #bf seconds1 if %e be at h] lea/ di/ance4 ,! reason ( ?is diff]5ce is1 t :5 ! ,moon is f>!/ f ! ,e>? %e moves sl[e/2 & :5 ne>e/ to x1 quicke/4 ,sid5ote3 ,digits4 #cdi4 ,! ,moon's diamet]1 z well z ! ,sun's1 is suppos$ to be divid$ into twelve equal p>ts call$ ,digits2 & s _m ( ^! p>ts z are d>k5$ by ! ,e>?'s %ad[1 s _m ,digits is ! ,moon eclips$4 ,all t ! ,moon is eclips$ above #ab ,digits1 %ew h[ f> ! %ad[ ( ! ,e>? is ov] ! body ( ! ,moon1 on t edge to :i* %e is ne>e/ at ! middle ( ! ,eclipse4 ,sid5ote3 ,:y ! beg9n+ & end ( a lun> ,eclipse is s difficult to be det]m9$ by obs]vation4 #cej4 ,x is difficult to obs]ve exactly ei!r ! beg9n+ or end+ ( a lun> ,eclipse1 ev5 ) a good ,telescope2 because ! ,e>?'s %ad[ is s fa9t1 & ill def9$ ab\t ! edges1 t :5 ! ,moon is ei!r j t\*+ or leav+ x1 ! obscuration ( h] limb is sc>ce s5sible2 & !re=e ! nice/ obs]v]s c h>dly be c]ta9 to f\r or five seconds ( "t4 ,b bo? ! beg9n+ & end+ ( sol> ,eclipses are visibly in/antane\s2 = ! mom5t t ! edge ( ! ,moon's ,disc t\*es ! ,sun's1 8 r\ndness seems a little broke on t "p2 & ! mom5t %e leaves x he appe>s p]fectly r\nd aga94 ,sid5ote3 ,! use ( ,eclipses 9 ,a/ronomy1 ,geography1 & ,*ronology4 #cea4 ,9 ,a/ronomy1 ,eclipses ( ! ,moon are ( great use = asc]ta9+ ! p]iods ( h] motions2 especially su* ,eclipses z are obs]v$ to be alike 9 all circum/ances1 & h long int]vals ( "t betwe5 !m4 ,9 ,geography1 ! ,longitudes ( places are f\nd by ,eclipses1 z already %ewn 9 ! elev5? *apt]3 b = ?is purpose ,eclipses ( ! ,moon are m useful ?an ^? ( ! ,sun1 because !y are m frequ5tly visible1 & ! same lun> ,eclipse is ( equal l>g5ess & duration at all places :]e x is se54 ,9 ,*ronology1 bo? sol> & lun> ,eclipses s]ve to det]m9e exactly ! "t ( any pa/ ev5t3 = !re are s _m p>ticul>s obs]vable 9 e ,eclipse1 ) respect to its quantity1 ! places :]e x is visible 7if ( ! ,sun7 & ! "t ( ! day or night2 t 'tis impossible !re c be two ,eclipses 9 ! c\rse ( _m ages :i* are alike 9 all circum/ances4 ,sid5ote3 ,! d>kness at our ,,savi\r's crucifixion sup]natural4 #ceb4 ,f ! above explanation ( ! doctr9e ( ,eclipses x is evid5t1 t ! d>kness at our ,,savi\r's crucifixion 0 sup]natural4 ,= he suff]$ on ! next day aft] eat+ 8 la/ ,passov]-,supp]1 on :i* day x 0 impossible t ! ,moon's %ad[ c\ld fall on ! ,e>?1 = ! ,jews kept ! ,passov] at ! "t ( ,full ,moon3 nor does ! d>kness 9 total ,eclipses ( ! ,sun la/ f\r m9utes 9 any place #ccc1 :]eas ! d>kness at ! crucifixion la/$ ?ree h\rs1 ,matt4 xxviii4 #ae4 & ov]spread at lea/ all ! l& ( ,judea4 ,,*ap4 ,,xix4 ,! ,calculation ( ,new & ,full ,moons & ,eclipses4 ,! geometrical ,con/ruction ( ,sol> & ,lun> ,eclipses4 ,! exam9ation ( anti5t ,eclipses4 #cec4 ,to con/ruct an ,eclipse ( ! ,sun1 we mu/ collect ^! t5 ,elem5ts or ,requisites f ! foll[+ ,a/ronomical ,tables4 ,sid5ote3 ,requisites = a sol> ,eclipse4 ,i4 ,! true "t ( conjunction ( ! ,sun & ,moon3 to "k at :at conjunctions ! ,sun mu/ be eclips$2 & to ! times ( ^? conjunctions1 ,,ii4 ,! ,moon's horizontal p>allax1 or angle :i* ! semi-diamet] ( ! ,e>? subt5ds z se5 f ! ,moon4 ,,iii4 ,! ,sun's true place1 & di/ance f ! sol/itial colure to :i* he is !n ne>e/1 ei!r 9 com+ to x or go+ f x4 ,,iv4 ,! ,sun's decl9ation4 ,v4 ,! angle ( ! ,moon's visible pa? ) ! ,ecliptic4 ,,vi4 ,! ,moon's ,latitude or ,decl9ation f ! ,ecliptic4 ,,vii4 ,! ,moon's true h\rly motion f ! ,sun4 ,,viii4 ,! ,angle ( ! ,sun's semi-diamet] z se5 f ! ,e>?4 ,,ix4 ,! ,angle ( ! ,moon's semi-diamet] z se5 f ! ,e>?4 ,x4 ,! semi-diamet] ( ! ,p5umbra4 ,& = an ,eclipse ( ! ,moon1 ! foll[+ ,elem5ts4 ,sid5ote3 ,requisites = a lun> ,eclipse4 ,i4 ,! true "t ( opposition ( ! ,sun & ,moon2 & = t "t1 ,,ii4 ,! ,moon's horizontal p>allax4 ,,iii4 ,! ,sun's semi-diamet]4 ,,iv4 ,! semi-diamet] ( ! ,e>?'s %ad[4 ,v4 ,! ,moon's semi-diamet]4 ,,vi4 ,! ,moon's ,latitude4 ,,vii4 ,! ,moon's true h\rly motion f ! ,sun4 ,,viii4 ,! ,angle ( ! ,moon's visible pa? ) ! ,ecliptic4 ,^! ,elem5ts are easily f\nd f ! foll[+ ,tables & ,precepts1 by ! common ,rules ( ,ari?metic4 ,note1 #fj m9utes make a ,degree1 #cj degrees a ,sign1 & #ab ,signs a ,circle4 ,a ,sign is m>k$ ?us s1 a ,degree ?us 1 & a ,m9ute ?us 4 ,:5 y exce$ #ab ,signs1 always reject !m & set d[n ! rema9d]4 ,:5 ! numb] ( ,signs to be subtract$ is great] ?an ! numb] y subtract f1 add #ab ,signs to t :i* y subtract f2 & !n y w h a rema9d] to set d[n4 ,sid5ote3 ,h[ ! ,signs are reckon$4 #ced4 ,z we fix arbitr>ily ^u ! beg9n+ ( ! ,sign ,aries to reckon f1 :5 we speak ( ! places ( ! ,sun1 ,moon1 & ,nodes2 we call ,aries #j ,signs1 ,taurus #a ,sign1 ,gem9i #b ,signs1 ,canc] #c ,signs1 c4 ,s1 :5 ! ,sun is 9 ! #aj? degree ( ,aries1 we say 8 ,place or ,longitude is #j ,signs #aj ,degrees1 because he is only #aj ,degrees f ! beg9n+ ( ,aries3 if he is 9 ! #e?1 #aj?1 c4 ,degree ( ,taurus1 we say 8 ,place or ,longitude is #a ,sign1 #e1 #aj1 c4 ,degrees3 & s on1 till he comes q r\nd aga94 ,b 9 reckon+ ! ,anomalies ( ! ,sun & ,moon1 & _! di/ance f ! ,nodes1 we only consid] ! numb] ( ,signs & ,degrees ! ,lum9>ies are gone pa/ _! ,apogee or ,nodes2 n h[ f> !y h to g to ^! po9ts1 7 ! di/ance ev] s little4 ,! ,sun1 ,moon1 & ,apogee move accord+ to ! ord] ( ,signs1 b ! ,nodes contr>y4 ,we %all n[ give ! ,precepts & ,examples = ! above ,requisites 9 _! due ord]4 ,to calculate ! "t ( ,new & ,full ,moon4 ,sid5ote3 ,fir/ ,elem5t or ,requisite4 #cee4 ,,precept ,i4 ,= any propos$ ye> 9 ! #ah? ,c5tury1 take out ! mean "t ( ! ,new ,moon 9 ,m>* f ,table ,i41 & ! mean "t ( ,full ,moon f ,table ,,iii41 = ! ,old ,/ile2 or f ,tables ,,ii & ,,iv = ,new ,/ile2 ) ! mean ,anomalies ( ! ,sun & ,moon = ^! times1 & set !m by !mselves4 ,!n1 f ,table ,,vi1 take out z _m ,lunations z ! propos$ ,mon? is aft] ,m>*1 ) ! days1 h\rs1 & m9utes belong+ to !m2 & also ! mean ,anomalies ( ! ,sun & ,moon = ^! ,lunations4 ,,ii4 ,add ! days1 h\rs1 & m9utes ( ^! ,lunations to ! "t ( ,new or ,full ,moon 9 ,m>*1 & ! ,anomalies = ! ,lunations to ! ,anomalies = ,m>*3 ! sums give ! h\rs & m9utes ( ! mean ,new or ,full ,moon requir$1 & ! mean ,anomalies ( ! ,sun & ,moon = t "t4 ,,iii4 ,!n1 ) ! numb] ( days ent] ,table ,,vii1 "u ! giv5 ,mon?1 & "r aga9/ ?is numb]1 9 ! left h& column y h ! day ( ,new or ,full ,moon2 :i* set be=e ! h\rs & m9utes above-m5tion$4 ,,iv4 ,b1 7z x w sometimes happ57 if ! numb] ( days fall %ort ( all ^? "u ! giv5 ,mon?1 add "o ,lunation ) its ,anomalies f ,table ,,vi to ! =esaid sums2 s y w h a new sum ( days :]e) to ent] ! #g? ,table "u ! giv5 ,mon?1 :]e y are sure to f9d t sum ! second "t1 if ! fir/ falls %ort4 ,v4 ,) ! ,signs & ,degrees ( ! ,sun's ,anomaly ent] ,table ,,viii1 ,! ,moon's annual ,equation1 & take out ! m9utes ( "t ( t ,equation by ! ,anomaly2 remembr+1 t if ! ,signs are at ! head ( ! ,table1 ! degrees are at ! left h&1 9 :i* case ! ,equation f\nd 9 ! ,angle ( meet+ mu/ be subtract$ f ! mean "t ( ,new or ,full ,moon1 z ! title ,subtract1 at ! head ( ! ,table directs3 b if ! ,signs are at ! foot ( ! ,table _! degrees are 9 ! "r-h& column1 & ! ,equation :]e ! ,signs & ,degrees meet 9 ! ,table is to be add$ to ! mean "t1 z ! title ,add1 at ! foot ( ! ,table directs2 :i* ,equation1 s appli$1 gives ! mean "t ( ,new or ,full ,moon correct$4 ,,vi4 ,) ! ,signs & ,degrees ( ! ,sun's ,anomaly ent] ,table ,,ix1 ,equation ( ! ,moon's mean ,anomaly1 & take out ! ,equation !re(2 add+ x to ! mean ,anomaly or subtract+ x !refrom1 z ! titles at ! head or foot ( ! ,table direct2 & x gives ! mean ,anomaly correct$4 ,!n1 ) ! ,sun's ,anomaly ent] ,table ,,xii1 ,equation ( ! ,sun's mean ,place1 & take out t ,equation1 apply+ x to ! ,moon's correct$ ,anomaly z ! titles direct2 & x w give ! ,moon's ,anomaly equat$#gg4 ,n4 ,b4 ,9 all ^! ,equations1 c>e mu/ be tak5 to make prop] all[ance = ! odd m9utes ( ,anomaly2 ! ,tables hav+ ! ,equations only = compleat ,degrees4 ,,vii4 ,) ! ,moon's equat$ ,anomaly ent] ,table ,x1 ,! ,moon's elliptic ,equation1 & take out t ,equation 9 ! same mann] z ! prec$+3 add+ x to ! =m] correct$ "t if ! ,signs be at ! head ( ! ,table1 or subtract+ x if !y be at ! foot1 z ! ,table directs2 & ?is gives ! mean "t equat$4 ,,viii4 ,la/ly1 ent] ,table ,,xi1 ,! ,sun's ,equation at ,new & ,full ,moon1 ) ! ,sun's ,anomaly1 & take out ! ,sun's ,equation 9 ! same mann] z ! o!rs2 add+ x to1 or subtract+ x f ! =m] equat$ "t1 z ! titles direct3 & by ?is la/ ,equation y h ! true "t ( ,new or ,full ,moon1 agree+ ) well regulat$ ,clocks & ,wat*es4 ,b to make x agree ) true ,sun-,dials1 ! ,equation ( "t mu/ be appli$ z taught #bbe4 ,,example ,i4 ,to f9d ! "t ( ,new ,moon 9 ,april #agfd1 ,n4 ,s4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,tab4 ,,ii4 ,mean "t ( ,new ,moon 9 ,m>* #b #h #eg #h #b #bc #aj #ac #cb ,add1 = ,lunation1 f ,tab4 ,,vi4 #bi #ab #dd #j #bi #f #j #be #di -------- ---------- ---------- ,mean ,new ,moon & ,anomaly #ca #ba #da #j #a #bi #aa #i #ba ,to :i* ,"t add ! ,moon's ------------- ,ann4 ,equ4 ,tab4 ,,viii4 #j #bb ,equ4 ,moon's ,anom4 - #bj ,& x gives ! ,mean "t -------- ---------- correct$ #ca #bb #c ,anom4 cor4 #aa #i #a ,f :i* subtract ! ,moon's ,sun's ,equat4 #a #ef elliptic ,equ4 ,tab4 ,x4 - #c #aj ---------- -------- ,moon's ,ano4 #aa #aj #eg ,& x gives ! ,mean "t equat$ #ca #ah #ec --------------------------- ,to :i* add ! ,sun's ,equation1 h4 m4 ,tab4 ,,xi4 #c #cb ,moon's ann4 ,equ4 #j #bb add ,& x gives ! true "t -------- ,h] ellipt4 ,equ4 #c #aj sub4 ( ,conjunction #ca #bb #be ,sun's ,equation #c #cb add ------------------------------------- ,:i* true "t answ]s to ! fir/ ( ,april1 at #be m9utes pa/ #aj 9 ! =5oon3 =1 z ! ,a/ronomical ,day beg9s at ,noon1 !n #bb h\rs #be m94 aft] ! ,noon ( ,m>* #ca1 is ,april #a1 at #aj h\rs #be m94 9 ! ,=5oon4 ---------------------------------------- ----------------------------------- ,,example ,,ii4 ,to f9d ! "t ( ,full ,moon 9 ,may #agfa1 ,n4 ,s4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,mean "t ( ,full ,moon 9 ,m>* #bj #ab #i #h #bj #b #i #a #ac ,add1 = two ,lunations #ei #a #bh #a #bh #ac #a #ba #ch -------- ---------- ---------- ,! sev]al sums are #gi #ac #cg #aj #ah #ae #aj #bb #ea ----------------------- ,! days1 9 ,tab4 ,,vii1 answ] to ,equ4 ,moon's ,anom4 - #ac ,may #ah #ah #ac #cg ---------- ,moon's annual ,equation add #ad ,anom4 cor4 #aj #bb #ch -------- ,sun's ,equat4 #a #ae ,mean "t correct$ #ah #ac #ea ---------- ,moon's elliptic ,equation subtract - #e #ch ,moon's ,ano4 #aj #bc #ec -------- --------------------------- ,mean "t equat$ #ah #h #ac h4 m4 ,sun's ,equation add #b #ai ,moon's ann4 ,equ4 #j #ad add -------- ,h] ellipt4 ,equ4 #e #ch sub4 ,true "t ( ,opposition1 ,may #ah #aj #cb ,sun's ,equation #b #ai add ------------------------------------- ,namely1 ! #ah? day1 at #cb m9utes pa/ #aj at night4 ---------------------------------------- ----------------------------------- ,! ,leap-ye>s are all[$ = 9 ! ,tables1 s z to give no ,tr\ble 9 ^! ,calculations4 ,to compute ! "t ( ,new & ,full ,moon 9 a giv5 ye> & mon?1 ( any p>ticul> ,c5tury1 betwe5 ! ,*ri/ian ra#gh & #ah? ,c5tury4 ,,precept ,i4 ,f9d ! l ye> ( ! #ah? ,c5tury 9 ,table ,i41 = ,new ,moon1 or ,table ,,iii41 = ,full ,moon2 & take out ! ,new or ,full ,moon 9 ,m>* = t ye>1 ) ! ,anomalies ( ! ,sun & ,moon4 ,,ii4 ,f ,table ,v1 take z _m compleat ,c5turies1 z :5 subtract$ f ! above ye> ( ! #ah? ,c5tury1 w answ] to ! giv5 ye>2 & take out ! ,conjunctions & ,anomalies ( ^! ,c5turies4 ,,iii4 ,subtract ! ,conjunctions & ,anomalies ( ^! ,c5turies f ^? ( ! ,new or ,full ,moon 9 ,m>* above tak5 out1 & ! rema9d]s w %ew ! mean "t ( ,new or ,full ,moon 9 ,m>* ! giv5 ye>1 ) ! ,anomalies ( ! ,sun & ,moon at t "t4 ,!n1 "w 9 all respects = ! true "t ( ! propos$ ,new or ,full ,moon1 z taught by ! ,precepts already giv5 #cee4 ,,example ,i4 ,to f9d ! "t ( ,new ,moon 9 ,july #aeha1 ,o4 ,s4 ,f #agha subtract #bjj ye>s1 & !re rema9s #aeha4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------- ,table ,i4 ,mean "t ( ,new ,moon 9 ,m>* #agha #ac #g #eb #h #bc #cg #j #j #ec ,tab4 ,v4 ,conj4 & ,anom4 = #bjj ye>s subtract #h #af #bb #j #f #db #e #j #dd --------- ---------- ---------- ,rema9 ! ,conj4 & ,anom4 = ,m>* #aeha #d #ae #cj #h #af #ee #g #j #i ,tab4 ,,vi4 ,add1 = five ,lunations1 to br+ x to ,july #adg #ae #dj #d #be #cb #d #i #e --------- ---------- ---------- ,! sums are #aeb #g #aj #a #ab #bg #aa #i #ad ------------------------ ,! ,days 9 ,tab4 ,,vii4 answ] ,equ4 ,moon's ,anom4 #ac to ,july #cj? #cj #g #aj ----------- ,sum ( ! ?ree ,equations ,anom4 cor4 #aa #i #bg subtract - #g #i ,sun's ,equat4 - #a #af --------- ----------- ,true "t ( ,conjunction1 ,july #cj #j #a ,moon's ,ano4 #aa #h #aa ------------------------------------- ,:i* is ! #cj? day1 at "o m9ute ,moon's ann4 ,eq4 #j;h #adm sub4 pa/ noon1 z %ewn by well ,h] ellipt4 ,equ4 #c #ce sub4 regulat$ ,clocks or ,wat*es ,sun's ,equation #c #bj sub4 ------------- ,sum #g #i sub4 ---------------------------------------- ---------------------------------- ,,example ,,ii4 ,to f9d ! "t ( ,full ,moon 9 ,april ,a4 ,d4 #cj1 ,o4 ,s4 ,f #agcj subtract #agjj1 & !re rema9s #cj4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,tab4 ,,iii4 ,mean "t ( ,full ,moon 9 ,m>* #agcj #bb #f #eh #i #b #dj #c #ac #bc ,tab4 ,v4 ,conj4 & ,anom4 = #agjj ye>s subtract #ad #ag #cg #aa #bh #df #aj #bi #cf -------- ---------- ---------- ,rem4 ! ,opposition & ,anom4 9 ,m>* ,a4 ,d4 #cj #g #ac #ba #i #c #ed #d #ac #dg ,tab4 ,v4 ,add1 = "o ,lunation1 to br+ x into ,april #bi #ab #dd #j #bi #f #j #be #di -------- ---------- ---------- ,! sums are #cg #b #e #aj #c #j #e #i #cf ----------------------- ,! ,days 9 ,tab4 ,,vii4 answ] to ,equ4 ,moon's ,anom4 - #ag ,april #f #f #b #e ---------- ,to :i* add ! sum ( ! ?ree ,anom4 cor4 #e #i #ai ,equations #f #a ,sun's ,equat4 #a #ce -------- ---------- ,true "t ( ,opposition ,moon's ,ano4 #e #aj #ed ,april ,a4 ,d4 #cj #f #h #f ------------------------------------ ,:i* is ! #f? day1 at #f m9utes pa/ ,moon's ann4 ,eq4 #j;h #ahm add #h 9 ! ,ev5+4 ,& ?us1 ! "t ,h] ellipt4 ,equ4 #b #df add ( ,new or ,full ,moon may be f\nd = ,sun's ,equat4 #b #eg add any giv5 ye> & mon? aft] ! ------------- ,*ri/ian ra4 ,sum #f #a add ---------------------------------------- ---------------------------------- ,sid5ote3 ,rem>k4 ,n4 ,b4 ,sometimes x happ5s t ! days annex$ to ! ,c5turies 9 ,table ,v are m 9 numb] ?an ! days on :i* ! ,new or ,full ,moon happ5s 9 ,m>* ! ye> ( ! #ah? ,c5tury1 ) :i* ! computation beg9s2 z 9 ! ?ird foll[+ ,example1 viz4 = ! ,full ,moon 9 ,m>* ! ye> be=e ,,*ri/ #gba3 9 :i* case1 a ,lunation & x's ,anomalies mu/ be add$1 f ,table ,,vi1 to ! days & ,anomalies ( ! ,new or ,full ,moon 9 ,m>*2 & !n1 subtraction c be made3 & hav+ ga9$ a rema9d]1 "w 9 all respects z taught 9 #cee4 ,to f9d ! "t ( ,new or ,full ,moon 9 any giv5 ye> & mon? be=e ! ,*ri/ian ra4 #cef4 ,,precept ,i4 ,f9d a ye> ( ! #ah? ,c5tury1 :i* add$ to ! giv5 numb] ( ye>s be=e ,,*ri/1 dim9i%$ by "o1 %all make a numb] ( :ole ,c5turies4 ,,ii4 ,f9d ?is numb] ( ,c5turies 9 ,table ,v1 & subtract ! ,"t & ,anomalies answ]+ to x f ! ,"t & ,anomalies answ]+ to ! mean ,new or ,full ,moon 9 ,m>* ! ye> ( ! #ah? ,c5tury ?us f\nd2 & !y w give ! mean "t ( ,new or ,full ,moon 9 ,m>* ! giv5 ye> be=e ,,*ri/1 ) ! ,anomalies answ]+ !reto4 ,:5ce ! true "t ( t ,new or ,full ,moon may be _h by ! ,precepts already deliv]$ #cee4 ,,iii4 ,! ,tables are calculat$ = ! ,m]idian ( ,london3 !re=e1 9 comput+ = any place we/w>d ( ,london1 f\r m9utes ( "t mu/ be subtract$ f ! "t %ewn by ! ,tables1 = e degree ! place is we/w>d2 & add$ = e degree x is ea/w>d4 ,see #baj4 ,,example ,i4 ,to f9d ! "t ( ,new ,moon at ,london & ,a!ns 9 ,m>*1 ! ye> be=e ,*ri/ #dbd4 ,! ye>s #dbc add$ to #aggg make #bbjj1 or #bb ,c5turies4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,tab4 ,i4 ,mean ,new ,moon 9 ,m>* ,a4 ,d4 #aggg #bg #g #ec #i #g #bg #e #be #ea ,f :i* subtract #bbjj ye>s 9 ,tab4 ,v4 #f #ba #dg #aa #af #bf #d #bj #cg -------- ---------- ---------- ,mean ,conj4 & ,anom4 9 ,m>* be=e ,*r4 #dbd #bj #aj #f #i #ba #a #a #e #ad ,:i* )1 ! total ( ! ?ree ------------- ,equations add$ #i #bj ,equ4 ,moon's ,anom4 - #ai -------- ---------- ,gives ! true "t ( ,conjunction #bj #ai #bf ,anom4 cor4 #a #d #ee ---------- ,sun's ,equat4 #a #dh ,:i* 0 ! #ba/ day ( ,m>*1 at --------- #bf m9utes pa/ #g 9 ! morn+ at ,moon's ,ano4 #a #f #dc ,london3 & if #a h\r #ce m9utes ------------------------------ be add$ = ,a!ns1 :i* is #bc #eb ,moon's ann4 ,eq4 #j;h #bjm add ea/ ( ! m]idian ( ,london1 we ,h] ellipt4 ,equ4 #e #dc add h ! "t at ,a!ns2 namely1 ,sun's ,equation #c #ag add #a m9ute pa/ #i 9 ! morn+4 ,total #i #bj add ---------------------------------------- ---------------------------------- ,,example ,,ii4 ,to f9d ! "t ( ,full ,moon 9 ,octob]1 ! ye> be=e ,*ri/ #djcj4 ,! ye>s #agga add$ to #djbi make #ehjj1 or #eh ,c5turies4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------- ,tab4 ,,iii4 ,f ! mean ,full ,moon 9 ,m>* #agga #ai #g #aa #h #bi #f #g #bb #cj ------------------------------------- ,tab4 ,v4 ,subtr4 ! numb]s = #ehjj ye>s #ejjj #aj #g #ef #aj #bc #ef #j #ag #cf #hjj #e #d #dc #aa #bg #dc #g #g #g --------- ---------- ---------- ,:i* collect$ make #ae #ab #ci #aj #ba #ci #g #bd #dc --------- ---------- ---------- ,rem4 ! mean ,full ,moon c4 ,m>* be=e ,*r4 #djcj #c #ah #cb #aj #g #bg #aa #bg #dg ,to :i* add eight ,lunations to c>ry x to ,octob] #bcf #e #eb #g #bb #ej #f #bf #cb --------- ---------- ---------- ,& ! sev]al sums w be #bdj #j #bd #f #j #ag #f #bd #ai ------------------------------------- ,:i*1 = ,full ,moon day1 ,tab4 ,,vii1 is ,octob] #bf #bf #j #bd h4 m4 ,moon's ellipt4 ,equation subtr4 !re be+ none besides #c #bh ,moon's ,ann4 ,eq4 #j #j add --------- ,moon's ellipt4 ,rem4 ! true "t ( ,full ,moon1 ,eq4 #c #bh sub4 ,octob] #be #bj #ef ,sun's ,equation #j #j add ----------- --------- ,:i* is ! #bf? day1 at #h h\rs ,total #c #bh sub4 #bf m9utes 9 ! =5oon#gi4 ---------------------------------------- ---------------------------------- ,sid5ote3 ,age ( ! _w unc]ta94 ,by ! me?od prescrib$ #bdh x w be f\nd1 t ! ,autumnal ,equ9ox 9 ! ye> be=e ,,*ri/ #djcj1 fell on ! #bf? ( ,octob]2 z ?is ,example %ews ! ,full ,moon to h be5 on ! same day3 & by work+ z h]eaft] taught1 x w appe> t ! ,dom9ical ,lett] 0 !n ,g1 :i* %ews ! #bf? ( t ,octob] to h be5 on a ,friday2 namely our six? day ( ! week1 b ! ,ante-,mosaic fif? day4 ,& z1 accord+ to ,g5esis1 *ap4 i4 v]4 #ad4 ! ,sun & ,moon 7 creat$ on ! f\r? day ( ! week1 ^? :o are ( op9ion t ! _w 0 made at ! "t ( ! ,autumnal ,equ9ox1 & t ! ,moon at h] fir/ appe>ance 0 9 full lu/re1 opposite to ! ,sun1 or ne>ly s1 may p]haps look ^u ?is z a ,crit]ion = asc]ta9+ ! ye> ( ! creation2 s9ce x %ews ! ,moon to h be5 ,full ! next day aft] %e 0 made3 & ?is is only #i ye>s soon] ?an ,rhe9holt makes x1 & #aa ye>s lat] ?an accord+ to ,lange4 ,:]eas1 !y :o ma9ta9 t ! _w 0 creat$ 9 ! #djjg? ye> be=e ,,*ri/1 ) ! ,sun on ! ,autumnal ,equ9octial ,po9t1 ,octob] #bf1 & ! ,moon !n ,full2 w f9d1 if !y compute by ! be/ ,tables extant1 t ! ,moon 0 ,new1 in/ead ( be+ ,full1 on t day4 ,if x c\ld be prov$ f ! writ+s ( ,moses t ! ,sun 0 creat$ on ! po9t ( ! ,autumnal ,equ9ox1 & ! ,moon 9 opposition2 z well z x c be prov$ t ^! ,lum9>ies 7 made 7or accord+ to "s1 did n %9e out till7 on ! f\r? day ( ! creation-week1 !re w\ld be ,data en\gh = asc]ta9+ ! age ( ! _w3 = suppos+ ! ,moon to h be5 ,full on an ,equ9octial ,day1 :i* 0 ! f\r? day ( ! week1 x w\ld require _m ?\s&s ( ye>s to br+ ^! ?ree *>act]s toge!r aga94 ,=1 ! soone/ 9 :i* ! ,moon returns to be ,new or ,full on ! same days ( ! ,mon?s z be=e1 is #ai ye>s want+ an h\r & half1 b !n ! days ( ! week return n to ! same days ( ! mon?s 9 less ?an #bh ye>s1 9 :i* "t ! ,moon has gone ?r\gh "o ,c\rse ( ,lunations1 & #i ye>s ov]2 !re=e a co-incid5ce ( ! ,full ,moon & day ( ! ,week & ,mon? _c happ5 9 t "t1 & if we multiply #ai by #bh1 :i* is ! ne>e/ co-incid5ce ( ^! ?ree *>act]s1 namely #ecb ye>s2 ! ,moon's fall+ back an h\r & half e #ai ye>s w am\nt to #db h\rs 9 s _m ye>s2 & ! ,equ9ox w h anticipat$ five days4 ,f all :i* we may v5ture to say1 t #bjjjjj ye>s w\ld n be suffici5t to br+ all ^! circum/ances toge!r aga94 ,,example ,,iii4 ,to f9d ! "t ( ,full ,moon at ,babylon 9 ,m>*1 ! ye> be=e ,*ri/ #gba4 ,! ye>s #gbj add$ to #aghj make #bejj1 or #be ,c5turies4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,tab4 ,i4 ,to ! mean ,f4 ,moon & ,anom4 9 ,m>4 #aghj #i #d #da #h #ai #dh #g #h #aj ,add "o ,lunation & x's ,anomalies f ,tab4 ,,vi#hj #bi #ab #dd #j #bi #f #j #be #di -------- ---------- ---------- ,! sev]al sums are #ch #ag #be #i #ah #ed #h #c #ei ,fr4 :i* subt4 ! ,days ,anom4 ( #bejj ye>s1 ,tab4 ,v #ai #bb #bj #aa #bf #ai #f #f #dc -------- --------- ---------- ,rem4 ! mean "t & ,anom4 ( ,f4,m4 9 ,m>4 b4,c4 #gba #ah #ai #e #i #bb #be #a #bg #af ,to :i* add ! sum ( ! ------------- ?ree ,equations #aa #cf ,equ4 ,moon's ,anom4 - #ah -------- ,anom4 cor4 #a #bf #dh ,& x gives ! true "t ( ,sun's ,equat4 #a #dg ,full ,moon1 ,m>4 b4,c4 #gba #ah #f #da ---------- --------- ,moon's ,anom4 #a #bh #ce ,:i* 0 ! #ai? day1 at #da m9utes ------------------------------- pa/ #f 9 ! ev5+1 at ,london2 ,moon's ann4 ,eq4 #j;h #bjm add to :i* "t1 if#ha #b h\rs #ea ,h] ellipt4 ,equ4 #h #a add m9utes be add$1 we %all h ,sun's ,equation #c #ae add ! "t at ,babylon1 namely1 ,sum #aa #cf add #i h\rs #ea m9utes4 ---------------------------------------- ---------------------------------- #ceg4 ,to "k :e!r ! ,sun w be eclips$ or no1 at ! "t ( any giv5 ,new ,moon2 collect ! ,sun's di/ance f ! ,node at t "t1 & if x be less ?an #ag degrees he w be eclips$1 o!rwise n4 ,,example4 ,= ! "t ( ,new ,moon 9 ,april #agfd4 ,sun f ,node s ,table ,,ii1 mean ,new ,moon 9 ,m>* #agfd1 ,new ,/ile1 #aa #d #eg ,table ,,vi1 add = #a ,lunation to c>ry x to ,april #a #j #dj -------- ,sun's di/ance f ! ,node at ,new ,moon 9 ,april #j #e #cg -------- ,:i*1 be+ )9 ! above limit1 ! ,sun mu/ be eclips$3 & !re=e1 we proce$ to f9d ! re/ ( ! ,elem5ts = comput+ ?is ,eclipse4 ,to f9d ! ,moons ,horizontal ,p>allax1 or ! ,angle ( ! ,e>?'s semi-diamet] z se5 f ! ,moon4 ,sid5ote3 ,second ,elem5t4 #ceh4 ,,precept4 ,hav+ f\nd ! ,moon's mean ,anomaly = ! above "t1 by ! fir/ & second ,precepts ( #cee1 ent] ! ,x,vth ,table ) ! signs & degrees ( t ,anomaly1 & !reby take out ! ,moon's ,horizontal ,p>allax3 only note1 t ?is is giv5 b to e #f? degree ( ,anomaly 9 ! ,table1 because x is v easy to make prop] all[ance by sight4 ,s ! ,moon's ,horizontal ,p>allax ,april ! #a/ #agfd1 at #aj h\rs #be m9utes 9 ! ,=5oon1 answ]+ to h] mean ,anomaly at t "t 7namely #aas #i #ba7 is #ee #g2 :i*1 dim9i%$ by #aj1 ! ,sun's con/ant ,horizontal ,p>allax1 gives = ! semi-diamet] ( ! ,e>?'s ,disc #ed #eg4 ,to f9d ! ,sun's true ,place1 & 8 di/ance f ! ne>e/ ,sol/ice4 ,sid5ote3 ,?ird ,elem5t4 #cei4 ,,precept ,i4 ,we are to consid]1 t ! beg9n+ ( ,aries & ( ,libra1 :i* are ! ,equ9octial ,po9ts1 are equidi/ant f ! beg9n+ ( ,canc] & ( ,capricorn1 :i* are ! ,sol/itial ,po9ts4 ,h5ce1 :5 we "k 9 :at ,sign & ,degree ! ,sun is1 we c easily f9d 8 di/ance f ! ne>e/ ,sol/ice4 ,n[1 to f9d ! ,sun's ,place1 or ,longitude f ,aries1 ,april ! #a/1 #agfd1 at #aj h\rs #ba m9utes 9 ! ,=5oon2 be+ ! equat$ "t ( ,new ,moon4 ,,precept ,,ii4 ,?is be+ to ! "t ( ,new ,moon1 take out ! ,sun's mean ,place & ,anomaly f ,table ,,ii4 = t "t1 & ! ,equation ( 8 mean ,place f ,table ,,xii by 8 ,anomaly2 add+ ! ,equation to 8 mean ,place or subtract+ x f ! same1 z ! ,table directs1 w give 8 true ,place4 ,,example4 ---------------------------------------- ------------------------------- ,sun's ,long4 ,sun's mean f ,aries4 ,anomaly4 ------------------------- s s ,table ,i4 ,to ! ,sun's mean ,place & ------------------------- ,anomaly at ! mean "t ( ,new ,moon 9 ,m>* #agfd1 ,n4 ,s4 #aa #ag #g #h #b #bc ,add ! same f ,tab4 ,,vi4 = "o ,lunation1 to c>ry x to ,april #j #bi #f #j #bi #f --------- ---------- ,mean ,place & ,anomaly at ! "t ( ,new ,moon 9 ,april #j #aj #ac #i #a #bi ,to :i* place add ! ,sun's ,equation ------------ f ,tab4 ,,xii4 #a #ef ,equal --------- #a #ef ,& x gives ! ,sun's true place #j #ab #i ,additive4 ------------------------- ,:i* is ,aries #ab #i2 & ?is1 :5 tak5 f ?ree ,signs1 or ! beg9n+ ( ,canc]1 leaves #b signs #ag deg4 #ea m941 or #gg #ea = ! ,sun's di/ance f ! !n ne>e/ ,sol/ice4 ---------------------------------------- --------------------------------- #cfj4 ,b because ! ,sun's true ,place is (t5 want$ :5 ! ,moon is nei!r ,new nor ,full1 we %all next %ew h[ x may be f\nd = any giv5 mom5t ( "t3 ?\gh ?is be digress+ f our pres5t purpose4 ,9 ,table ,,xvi f9d ! ne>e/ less] ye> to t 9 :i* ! ,sun's ,place is s\ght2 & take out ! ,sun's mean ,longitude & ,anomaly answ]+ !reto2 to :i* add 8 mean motion & ,anomaly = ! compleat residue ( ! ye>s1 ) ! mon?1 day1 h\r1 & m9ute1 all tak5 f ! same ,table1 & y h ! ,sun's mean ,longitude & ,anomaly = ! giv5 "t4 ,!n1 f ,table ,,xii take out ! ,sun's ,equation by means ( 8 ,anomaly 7mak+ proportions = ! odd m9utes ( ,anomaly7 :i* ,equation be+ add$ to or subtract$ f ! ,sun's mean ,longitude f ,aries1 z ! titles 9 ! ,table direct1 gives 8 true ,place1 or ,longitude f ! beg9n+ ( ,aries1 reckon$ accord+ to ! ord] ( ! ,signs #ced4 ,,example4 ,to f9d ! ,sun's true ,place ,april #cj?1 ,a4 ,d4 #ageg1 at #ah m9utes #dj seconds pa/ #aj 9 ! morn+4 ---------------------------------------- ------------------------------- ,sun's ,long4 ,sun's ,anom4 ,! ye> next less ?an #ageg 9 ! ,table -------------------------- is #agec1 at ! beg9n+ ( :i*1 ! s s ,sun's mean ,longitude f ! beg9n+ -------------------------- ( ,aries1 & 8 mean ,anomaly1 is #i #aj #af #eb #f #a #ch ,to :i* add 8 mean ,mot4 & ,anom4 = f\r ye>s to make #ageg #j #j #a #di #aa #bi #eh ,april #b #bh #db #cj #b #bh #db days #bi #j #bh #ce #b #j #bh #ce ,& likewise 8 mean ,mot4 & h\rs #bb #j #ed #ac #j #ed ,anom4 = m94 #ah #j #dd #a sec4 #di #b #j ----------- ------------- ,sun's mean ,longitude & ,anomaly = ! giv5 "t is #a #h #ca #ab #i #bi #dh ,to :i* add ! ,equation ( ! ,sun's mean ,place #a #dj #ad ------------- ----------- ,sun's ,eq4 ,& x gives 8 true ,place1 viz4 #a #dj #ad ,taurus #aj #aa #bf #a #aj #aa #bf ---------------------------------------- ------------------------------- ,n4 ,b4 ,9 leap-ye>s aft] ,febru>y1 ! ,sun's mean ,motion & ,anomaly mu/ be tak5 out = ! day next aft] ! giv5 "o4 #cfa4 ,to calculate ! ,sun's true ,place = any "t 9 a giv5 ye> be=e ! fir/ ye> ( ,,*ri/3 subtract ! mean ,motions & ,anomalies = ! compleat hundr$s next above ! giv5 ye>2 to ! rema9d] add ^? = ! residue ( ye>s1 mon?s1 c4 & !n "w 9 all respects z above taught4 ,,example4 ,to f9d ! ,suns true ,place ,may ! #bh? at #d h\rs #c m94 #db sec4 9 ! aft]noon1 ! ye> be=e ,*ri/ #ehe1 :i* 0 a ,leap ye>#hb4 ---------------------------------------- ------------------------------- ,sun's ,long4 ,sun's ,anom4 -------------------------- s s ,f ! ,sun's mean ,longitude & ,anomaly -------------------------- at ! beg9n+ ( ! ye> ,*ri/ #a #i #g #ec #aj #f #bi #ed ,subtract 8 mean ,motion & ,anomaly = #fjj ye>s #j #d #cb #j #aa #bd #b ----------- ---------- ,& ! rema9d]1 or radix1 is #i #c #ba #aj #g #e #eb ,to :i* add :at #ehe wants ( #fjj1 viz4 #ae ye>s #aa #bi #bb #bg #aa #bi #g ,may #c #bh #af #dj #c #bh #ag days #bh ,bissextile #j #bh #ce #b #j #bh #ce ,& also ^? ( h\rs #d #j #i #ea #j #aj m94 #c #j #g ---------- sec4 #db #b #j #b #a ----------- ,sun's ,anom4 ,sun's mean ,long4 ,may #bh?1 at #d h\r ------------- #c m94 #bd sec4 aft]noon #a #bi #de #ai ,equation ( ! ,sun's mean ,place subtract #b #b #b #bb ----------- ,sun's ,equat4 ,rem4 8 true ,place = ! same "t1 subtract4 viz4 ,taurus #bi #dc #ag #a #bi #dc #ag ---------------------------------------- ------------------------------- ,n4 ,b4 ,z ! ,longitudes or ,places ( all ! visible ,/>s 9 ! ,heav5s are well kn[n1 we h an easy me?od ( f9d+ ! ,sun's true ,place 9 ! ,ecliptic3 = ! ,sun is directly opposite to t ,po9t ( ! ,ecliptic :i* comes to ! ,m]idian at mid-night4 ,to f9d ! ,sun's ,decl9ation4 ,sid5ote3 ,f\r? ,elem5t4 #cfb4 ,,precept4 ,ent] ,table ,,xvii ) ! ,signs & ,degrees ( ! ,sun's ,place2 & mak+ proportions1 take out 8 ,decl9ation answ]+ !reto4 ,if ! ,signs are at ! head ( ! ,table1 ! ,degrees are at ! left h&2 b if ! ,signs are at ! foot ( ! ,table1 ! ,degrees are at ! "r h&4 ,s1 ! ,sun's ,decl9ation answ]+ to 8 true ,place 7f\nd by #cei to be #js #ab #i7 is #d degrees #dh m9utes #ed seconds1 mak+ all[ance = ! #i t 8 ,place exce$s #ab4 ,to f9d ! ,angle ( ! ,moon's visible ,pa? ) ! ,ecliptic4 ,sid5ote3 ,fif? ,elem5t4 ,,precept4 ,?is we may /ate at #e degrees #ch m9utes1 z ne> en\gh = ! purpose2 s9ce x is nev] above #h m9utes ( a degree m or less4 ,to f9d ! ,moon's ,latitude4 ,sid5ote3 ,six? ,elem5t4 #cfc4 ,,precept4 ,hav+ f\nd ! ,sun's di/ance f ! ,asc5d+ ,node by #ceg1 at ! mean "t ( ,new ,moon1 & 8 ,anomaly = t "t by #cei1 f9d ! ,equation ( ! ,node 9 ,table ,,xiii1 by ! ,sun's ,anomaly1 & ! ,equation ( ! ,sun's mean ,place 9 ,table ,,xii by 8 ,anomaly3 ^! two ,equations appli$ 7z ! titles direct7 to ! ,sun's mean di/ance f ! ,asc5d+ ,node1 give 8 true di/ance f x1 & also ! ,moon's true di/ance at ! "t ( ,*ange3 b :5 ! ,moon is ,full1 ?is di/ance mu/ be increas$ by ! addition ( #f ,signs1 :i* w !n be ! ,moon's true di/ance f ! same ,node4 ,! ,moon's true di/ance f ! ,asc5d+ ,node is call$ ! ,argum5t ( ! ,moon's ,latitude2 ) ! ,signs ( :i*1 at ! head ( ,table ,,xiv1 & ,degrees at ! left h&1 or ) ! ,signs at ! foot ( ! ,table & ,degrees at ! "r h&1 take out ! ,moon's ,latitude3 :i* is ,nor? ,asc5d+1 ,nor? ,desc5d+1 ,s\? ,asc5d+1 or ,s\? ,desc5d+1 accord+ to ! lett]s ,,na1 ,,nd1 ,,sa or ,,sd1 annex$ to ! ,signs ( ! said ,argum5t4 ,illu/ration3 ,plate ,,xii4 ,! ,geometrical ,con/ruction ( ,sol> & ,lun> ,eclipses4 ,j4 ,f]guson del94 ,j4 ,mynde ,sculp4 ,,example4 s ,sun's mean ,di/4 f ! #hc,node at ,new ,moon 9 ,april #agfd #j #e #cg ,to :i* add ! ,equation ( ! ,node #aj ---------- ,& x gives ! ,sun's correct$ ,di/ance f ! ,node #j #e #dg ,to :i* cor4 ,di/4 add ! ,eq4 ( ! ,sun's mean ,place #a #ef ---------- ,& x gives ! ,sun's true ,di/ance f ! ,node #j #g #dc ,:i*1 be+ at ! "t ( ,new ,moon1 is ! ,argum5t ( ,latitude2 & 9 ,table ,,xiv1 7mak+ proportions = ! #dc7 %ews ! ,moon's ,latitude to be #dj #i ,nor? ,asc5d+#hd4 ,to f9d ! ,moon's true h\rly ,motion f ! ,sun4 ,sid5ote3 ,sev5? ,elem5t4 #cfd4 ,,precept4 ,) ! ,moon's ,anomaly ent] ,table ,,xv1 & !reby take out h] true h\rly ,motion3 !n ) ! ,sun's ,anomaly take out 8 true h\rly ,motion f ! same ,table3 :i* done1 subtract ! ,sun's h\rly ,motion f ! ,moon's1 & ! rema9d] w be ! ,moon's true h\rly ,motion f ! ,sun2 :i*1 = ! above "t #cei1 is #bg #ej4 ,to f9d ! ,semi-diamet]s ( ! ,sun & ,moon z se5 f ! ,e>? at ! above-m5tion$ "t4 ,sid5ote3 ,eigh? & ,n9? ,elem5ts4 #cfe4 ,,precept4 ,ent] ! ,x,vth ,table ) ! ,sun's ,anomaly1 & !reby take out 8 ,semi-diamet]2 & 9 ! same mann] take out ! ,moon's ,semi-diamet] by h] ,anomaly4 ,! =m] ( :i* = ! above "t w be f\nd to be #af #f2 ! latt] #ad #eh4 ,to f9d ! ,semi-diamet] ( ! ,p5umbra4 ,sid5ote3 ,t5? ,elem5t4 #cff4 ,,precept4 ,add ! ,sun's semi-diamet] to ! ,moon's1 & _! ,sum w be ! ,semi-diamet] ( ! ,p5umbra2 namely1 at ! above "t #ca #d4 ,sid5ote3 ,pl4 ,,xii4 #cff4 ,hav+ f\nd ! prop] ,elem5ts or ,requisites = ! ,sun's ,eclipse ,april #a1 #agfd1 & int5d+ to project ?is ,eclipse ,geometrically1 we %all n[ collect !m "u ! eye1 t !y may be ! m readily f\nd z !y are want$ 9 ord] = ! ,projection4 ,sid5ote3 ,! prop] ,elem5ts collect$4 ,d ,h ,m #cfg4 ,i4 ,! true "t ( ,conj4 or ,new ,moon ,april #a #aj #be ,,ii4 ,! ,e>?'s ,semi-,disc1 :i* is equal to ! ,moon's ,horizontal ,p>allax #ee #g dim9i%$ by ! ,sun's ,horizontal ,p>allax :i* is always #aj #j #ed #eg ,,iii4 ,! ,sun's di/ance f ! ne>e/ ,sol/ice1 viz4 #gg #ea #j ,,iv4 ,! ,sun's ,decl9ation1 ,nor? #d #dh #ed ,v4 ,! ,angle ( ! ,moon's vis4 pa? ) ! ,eclipt4 #e #ch #j ,,vi4 ,! ,moon's true ,latitude1 ,nor? ,asc5d+ #dj #i ,,vii4 ,! ,moon's true ,hor>y ,motion f ! ,sun #bg #ej ,,viii4 ,! ,sun's ,semi-diamet] #af #f ,,ix4 ,! ,moon's ,semi-diamet] #ad #eh ,x4 ,! ,semi-diamet] ( ! ,p5umbra #ca #d #cfh4 ,hav+ collect$ ^! ,elem5ts or ,requisites1 ! foll[+ "p ( ! "w may be v mu* facilitat$ by means ( a good ,sector1 ) ! use ( :i* ! read] %\ld be s well acqua9t$1 z to "k h[ to op5 x to any giv5 ,radius1 z f> z x w g2 & to take (f ! ,*ord or ,s9e ( any ,arc ( t ,radius4 ,?is is done by fir/ tak+ ! ext5t ( ! giv5 ,radius 9 y\r ,compasses1 & !n op5+ ! ,sector s z ! di/ance cross-wise betwe5 ! ends ( ! l9es ( ,s9es or ,*ords at ,s or ,c1 f ,leg to ,leg ( ! ,sector1 may be equal to t ext5t2 !n1 )\t alt]+ ! ,sector1 take ! ,s9e or ,*ord ( ! giv5 ,arc ) y\r ,compasses ext5d$ cross-wise f ,leg to ,leg ( ! ,sector 9 ^! l9es4 ,b if ! op]ator has n a ,sector1 he mu/ con/ruct ^! l9es to su* diff]5t l5g?s z he wants !m 9 ! projection4 ,& le/ ?is ,treatise %\ld fall into ! h&s ( any p]son :o w\ld wi% to project ! ,figure ( a sol> or lun> ,eclipse1 & has n a ,sector to d x by1 we %all %ew h[ he may make a l9e ( ,s9es or ,*ords to any ,radius4 ,sid5ote3 ,fig4 ,,ii4 ,h[ to make a l9e ( ,*ords4 ,pl4 ,,xii4 #cfi4 ,draw ! "r l9e ,,bca at pleasure2 & ^u ,c z a ,c5t]1 ) ! di/ance ,,ca or ,,cb z a ,radius1 describe ! ,semi-circle ,,bda2 & f ! ,c5t] ,c draw ,,ac p]p5dicul> to ,,bca4 ,!n divide ! ,quadrants ,,ad & ,,bd ea* into #ij equal p>ts or degrees1 & jo9 ! "r l9e ,,ad = ! ,*ord ( ! ,quadrant ,,ad4 ,?is done1 sett+ "o foot ( ! ,compasses 9 ,a1 ext5d ! o!r to ! diff]5t divisions ( ! ,quadrant ,,ad2 & s transf] !m to ! "r l9e ,,ad z 9 ! ,figure1 & y h a l9e ( ,*ords ,,ad to ! ,radius ,,ca4 ,n4 ,b4 #fj ,degrees on ! ,l9e ( ,*ords is always equal to ! ,radius ( ! ,circle x is made f2 z is evid5t by ! ,figure1 :]e ! ,ar* ,e1 ^: ,c5t] is ,a1 drawn f #fj on ! ,quadrant ,,ad1 cuts ! ,*ord l9e 9 #fj degrees1 & t]m9ates 9 ! ,c5t] ,c4 ,sid5ote3 ,& ( ,s9es4 ,!n1 f ! divisions or degrees ( ! ,quadrant ,,bd1 draw l9es p>allel to ,,cd1 :i* w fall p]p5dicul>ly on ! ,radius ,,bc1 divid+ x into a l9e ( ,s9es2 & x w be ne> en\gh = ! pres5t purpose1 to h !m to e fif? ,degree1 z 9 ! ,figure4 ,& ?us ! "y ,tyro may supply himself ) ,*ords & ,s9es1 if he has n a ,sector4 ,b z ! ,sector greatly %ort5s ! "w1 we %all describe ! projection z done by x1 s f> z ,signs & ,*ords are requir$4 ,sid5ote3 ,fig4 ,,ii4 ,e>?'s ,semi-,disc4 #cgj4 ,make a ,scale ( any conv5i5t l5g? 7six in*es at lea/7 z ,,ac1 & divide x into z _m equal p>ts z ! semi-diamet] ( ! ,e>?'s ,disc conta9s m9utes1 :i* 9 ?is con/ruction ( ! ,eclipse = ,london 9 ,april #agfd1 is #ed m9utes & #eg seconds2 b z x wants only #c ( #ee ! ,scale may be divid$ into #ee equal p>ts1 z 9 ! ,figure4 ,!n1 ) ! :ole l5g? ( ! ,scale z a ,radius1 sett+ "o foot ( y\r ,compasses 9 ,c z a c5t]1 describe ! ,semi-circle ,,amb = ! nor!rn ,hemisph]e or ,semi-disc ( ! ,e>?1 z se5 f ! ,sun at t "t4 ,_h ! ,place = :i* ! ,con/ruction is made be5 9 ,s\? ,latitude1 ?is ,semi-circle w\ld h be5 ! ,s\!rn ,hemisph]e ( ! ,e>?'s ,disc4 ,sid5ote3 ,axis ( ! ,ecliptic4 #cga4 ,^u ! c5t] ,c raise ! /raight l9e ,,* = ! ,axis ( ! ,ecliptic1 p]p5dicul> to ,,acb4 ,sid5ote3 ,nor? ,pole ( ! ,e>?4 #cgb4 ,make a l9e ( ,*ords to ! ,radius ,,ac1 & tak+ f !nce ! ,*ord ( #bc-a_/b ,degrees1 set x (f f ,h to g & to h1 on ! p]iph]y ( ! ,semi-disc2 & draw ! /raight l9e g,nh1 9 :i* ! ,nor? ,pole ( ! ,disc is always f\nd4 #cgc4 ,:ile ! ,sun is 9 ,aries1 ,taurus1 ,gem9i1 ,canc]1 ,leo1 & ,virgo1 ! ,nor? ,pole ( ! ,disc is illum9at$2 b :ile ! ,sun is 9 ,libra1 ,scorpio1 ,sagitt>y1 ,capricorn1 & ,aqu>ius1 ! ,nor? ,pole is hid 9 ! obscure "p beh9d ! ,disc4 #cgd4 ,&1 :il/ ! ,sun is 9 ,capricorn1 ,aqu>ius1 ,pisces1 ,aries1 ,taurus1 & ,gem9i1 ! ,e>?'s ,axis ,,cp lies to ! "r h& ( ! ,axis ( ! ,ecliptic ,,* z se5 f ! ,sun1 & to ! left h& :ile ! ,sun is 9 ! o!r six ,signs4 ,sid5ote3 ,e>?'s ,axis4 ,univ]sal ,m]idian4 #cge4 ,make a l9e ( ,s9es equal 9 l5g? to ,ng or ,nh1 & take (f ) y\r ,compasses f x ! ,s9e ( ! ,sun's di/ance f ! ne>e/ ,sol/ice1 :i* 9 ! pres5t case is #gg #ea #cfg1 & set t di/ance to ! "r h&1 f ,n to ,p1 on ! l9e g,nh1 because ! ,sun be+ 9 ,aries #cei1 ! ,e>?'s ,axis lies to ! "r h& ( ! ,axis ( ! ,ecliptic #cgd3 !n draw ! /raight l9e ,c,,xii,p1 = ! ,e>?'s ,axis & ! ,univ]sal ,m]idian2 ( bo? :i* ,p is ! ,nor? ,pole4 ,sid5ote3 ,pa? ( a giv5 ,place on ! ,disc z se5 f ! ,sun4 #cgf4 ,to draw ! p>allel ( ,latitude ( any giv5 ,place 7suppose ,london7 :i* p>allel is ! visible ,pa? ( ! ,place ,on ! ,disc1 z se5 f ! ,sun1 f ! "t t ! ,sun rises till x sets2 subtract ! ,latitude ( ! ,place 7,london7 #ea-a_/b degrees f #ij degrees1 & !re rema9s #ch-a_/b2 :i* take f ! ,l9e ( ,*ords 9 y\r ,compasses1 & set x f h 7:]e ! ,univ]sal ,m]idian ,,cp cuts ! p]iph]y ( ! ,semi-disc7 to ,,vi & ,,vi2 & draw ! occult ,l9e ,,vi,l,,vi4 ,!n1 on ! left h& ( ! ,e>?'s ,axis1 set (f ! ,*ord ( ! ,sun's ,decl9ation #d #dh #e #cfg1 f ,,vi to ,d & to ,f2 set (f ! same on ! "r h& f ,,vi to ,e & to ,g2 & draw ! occult ,l9es ,ds,e & ,f,,xii,g p>allel to ,,vi ,l ,,vi4 ,sid5ote3 ,situation ( ! ,place on ! ,disk f ,sun-rise to ,sun-set4 #cgg4 ,bisect s ,,xii 9 ,k1 & ?r\gh ! po9t ,k draw ! black ,l9e ,,vi,k,v#a p>allel to ! occult or dott$ ,l9e ,,vi,l,,vi4 ,!n1 mak+ ,,ac ! ,radius or l5g? ( a ,l9e ( ,l9es1 set (f ! ,s9e ( #ch-a_/b degrees1 ! ,co-,latitude ( ,london1 f ,k to ,,vi & ,,vi2 & ) t ext5t z a ,radius1 describe ! ,semi-,circle ,,vi #g #h #i c4 & divide x into #ab equal p>ts1 beg9n+ at ,,vi4 ,f ^! divisions1 draw ! occult ,l9es #gm1 #hl1 #ik1 c4 all to ! ,l9e ,,vi,k,,vi1 & p>allel to ,c,,xii,p4 ,!n1 ) ,k,,xii z a ,radius1 describe ! ,circle abcdef1 r\nd ! ,c5t] ,k1 & divide ! ,quadrant a,,xii into six equal p>ts1 z ab1 bc1 cd1 de1 c4 ,!n1 ?r\gh ^! po9ts ( division b1 c1 d1 e1 & f1 draw ! occult ,l9es ,,viib,v1 ,,viiic,,iiii1 ,,ixd,,iii1 c4 int]sect+ ! =m] ,l9es #gm1 #hl1 #ik1 #aj;i1 c4 9 ! po9ts ,,vii1 ,,viii1 ,,ix1 ,x1 ,,xi1 c4 :i* po9ts m>k ! situation ( ,london on ! ,e>?'s ,disc z se5 f ! ,sun at ^! h\rs respectively1 f six 9 ! morn+ till six at night3 & if ! elliptic ,curve ,,vi1 ,,vii1 ,,viii1 c4 be drawn ?r\gh ^! po9ts1 x w repres5t ! p>allel ( ,london1 or ! pa? x seems to describe z view$ f ! ,sun1 f ,sun-rise to ,sun-set4 ,n4,b4 ,:5 ! ,sun's ,decl9ation is ,nor?1 ! said ,curve is ! diurnal ,pa? ( ,london2 & ! opposite "p ,,vis,,vi is x's nocturnal ,pa? beh9d ! ,disc1 or 9 ! obscure "p !re(1 #cch1 #cci4 ,b if ! ,sun's ,decl9ation _h be5 ,s\?1 ! ,curve ,,vis,,vi w\ld h be5 ! diurnal pa? ( ,london2 9 :i* case ! ,l9es #gm1 #hl1 c4 mu/ h be5 cont9u$ ?ro' ! "r ,l9e ,,vi,k,,vi1 & _! l5g?s beyond t l9e det]m9$ by divid+ ! ,quadrant s a ( ! little ,circle abcd into six equal p>ts1 & draw+ ! p>allels ,,viib1 ,,viiic c4 ?r\gh t division1 9 ! same mann] z done on ! side ,k ,,xii2 & ! ,curve ,,vii1 ,,viii1 ,,ix1 c4 w\ld h be5 ! nocturnal ,pa?4 ,x is requisite to divide ! h\rs ( ! diurnal ,pa? into qu>t]s1 z 9 ! ,diagram2 & if possible into m9utes also4 ,sid5ote3 ,axis ( ! ,moon's ,orbit4 #cgh4 ,f ! ,l9e ( ,*ords #cgb take ! ,angle ( ! ,moon's visible ,pa? ) ! ,ecliptic1 viz4 #e #ch #cfg3 & note1 t :5 ! ,moon's ,latitude is ,nor? ,asc5d+1 z 9 ! pres5t case1 ! ,*ord ( ?is ,angle mu/ be set (f to ! left h& ( ! ,axis ( ! ,ecliptic ,,*1 z f ,h to ,m1 & ! "r l9e ,,cm drawn = ! ,axis ( ! ,moon's ,orbit3 b :5 ! ,moon's ,latitude is ,nor? ,desc5d+1 ?is ,angle & ,axis mu/ be set to ! "r h&1 or f ,h t[>d h4 ,:5 ! ,moon's ,latitude ,s\? ,asc5d+1 ! ,axis ( h] ,orbit lies ! same way z :5 h] ,latitude is ,nor? ,asc5d+2 & :5 ,s\? ,desc5d+1 ! same way z :5 ,nor? ,desc5d+4 ,sid5ote3 ,pa? ( ! ,p5umbra's c5t] ov] ! ,e>?4 #cgi4 ,take ! ,moon's ,latitude1 #dj #i #cfg1 f ! ,scale ,,ca1 & set x f ,c to ,t on ! ,axis ( ! ,ecliptic2 & ?r\gh ,t1 at "r ,angles to ! ,axis ( ! ,moon's ,orbit ,,cm1 draw ! /raight ,l9e ,,rts2 :i* is ! ,moon's ,pa?1 or ,l9e t ! c5t] ( h] %ad[ & ,p5umbra describes 9 go+ ov] ! ,e>?'s ,disc4 ,! ,po9t ,t 9 ! ,axis ( ! ,ecliptic is ! ,place :]e ! true ,conjunction ( ! ,sun & ,moon falls1 accord+ to ! ,tables2 & ! ,po9t ,w1 9 ! ,axis ( ! ,moon's ,orbit1 is t :]e ! c5t] ( ! ,p5umbra approa*es ne>e/ to ! c5t] ( ! ,e>?'s ,disc1 & consequ5tly ! middle ( ! g5]al ,eclipse4 ,sid5ote3 ,x's ,place on ! ,e>?'s ,disc %ewn = e m9ute ( x's ,transit4 #chj4 ,take ! ,moon's true ,hor>y ,motion f ! ,sun #bg #ej #cfg1 f ! ,scale ,,ca ) y\r ,compasses 7e division ( ! ,scale be+ a m9ute ( a ,degree7 & ) t ext5t make m>ks 9 ! ,l9e ( ! ,moon's ,pa? ,,rts3 !n divide ea* ( ^! equal spaces by dots into #fj equal p>ts or hor>y m9utes1 & set ! h\rs to e #fj? m9ute1 9 su* a mann] t ! dot2 signify+ ! precise m9ute ( ,new ,moon by ! ,tables1 may fall 9 ! ,po9t ,t :]e ! ,axis ( ! ,ecliptic cuts ! ,l9e ( ! ,moon's ,pa?2 :i*1 9 ?is ,eclipse1 is ! #be? m9ute pa/ t5 9 ! ,=5oon3 & !n ! o!r m>ks w %ew ! places on ! ,e>?'s ,disc :]e ! c5t] ( ! ,p5umbra is1 at ! h\rs & m9utes d5ot$ by !m1 dur+ its transit ov] ! ,e>?4 ,sid5ote3 ,middle ( ! ,eclipse4 ,x's ,phases4 #cha4 ,apply "o side ( a ,squ>e to ! ,l9e ( ! ,moon's ,pa?1 & move ! ,squ>e backw>d or =w>d until ! o!r side cuts ! same h\r & m9ute bo? 9 ! ,pa? ( ! ,place 7,london1 9 ?is ,con/ruction7 & ,pa? ( ! ,moon2 & t m9ute1 cut at ! same "t 9 bo? ,pa?s1 w be ! precise m9ute ( visible ,conjunction ( ! ,sun & ,moon at ,london1 & !re=e ! "t ( greate/ obscuration1 or middle ( ! ,eclipse at ,london2 :i* "t1 9 ?is ,projection1 falls at t1 #cd m9utes pa/ #aj 9 ! ,moon's ,pa?2 & at u1 #cd m9utes pa/ #aj 9 ! ,pa? ( ,london4 ,!n1 ^u ! ,po9t u z a c5t]1 describe ! ,circle z,yy ^: ,radius uy is equal to ! ,sun's semi-diamet] #af #f #cfg1 tak5 f ! ,scale ,,ca3 ,& ^u ! ,po9t t z a c5t]1 describe ! ,circle ,hy ^: ,radius is equal to ! ,moon's semi-diamet] #ad #eh #cfg1 tak5 f ! same ,scale4 ,! ,circle z,yy repres5ts ! ,disc ( ! ,sun z se5 f ! ,e>?1 & ! ,circle ,hy ! ,disc ( ! ,moon4 ,! portion ( ! ,sun's ,disc cut (f by ! ,moon's %ews ! ,quantity ( ! ,eclipse at ! "t ( greate/ obscuration3 & if a "r ,l9e z yz be drawn across ! ,sun's ,disc ?r\gh t & u1 ! m9ute ( greate/ obscuration 9 bo? ,pa?s1 & divid$ into #ab equal p>ts1 x w %ew :at numb] ( ,digits are !n eclips$4 ,if ^! two ,circles d n t\* "o ano!r1 ! ,eclipse w n be visible at ! giv5 ,place4 ,sid5ote3 ,x's beg9n+ & end+4 #chb4 ,la/ly1 take ! ,semi-diamet] ( ! ,p5umbra #ca #d #cfg1 f ! ,scale ,,ca ) y\r ,compasses2 & sett+ "o foot 9 ! ,moon's ,pa?1 to ! left h& ( ! ,axis ( ! ,ecliptic1 direct ! o!r t[>d ! ,pa? ( ,london2 & c>ry ?is ext5t backw>ds or =w>ds until bo? ,po9ts ( ! ,compasses fall into ! same in/ants ( "t 9 bo? ,pa?s3 :i* w d5ote ! "t ( ! beg9n+ ( ! ,eclipse3 !n1 d ! same on ! "r h& ( ! ,axis ( ! ,ecliptic1 & :]e bo? ,po9ts m>k ! same in/ants 9 bo? ,pa?s1 !y w %ew at :at "t ! ,eclipse ends4 ,^! trials give ! ,po9ts ,r 9 ! ,moon's ,pa? & r 9 ! ,pa? ( ,london1 namely #i m9utes pa/ #i 9 ! ,morn+ = ! beg9n+ ( ! ,eclipse at ,london1 ,april #a1 #agfd3 t & u = ! middle or greate/ obscuration1 at #ce m9utes pa/ #aj2 :5 ! ,eclipse w be b>ely annul> on ! ,sun's l[]-mo/ edge1 & only two ?irds ( a ,digit left free on 8 upp]-mo/ edge3 & = ! end ( ! ,eclipse1 ,s 9 ! ,moon's ,pa? & x 9 ! ,pa? ( ,london1 at #d m9utes pa/ #ab at ,noon4 ,9 ?is ,con/ruction x is suppos$ t ! ,equator1 ,tropics1 ,p>allel ( ,london1 & ,m]idians ?r\gh e #ae? degree ( ,longitude are project$ 9 visible ,l9es on ! ,e>?'s ,disc1 z se5 f ! ,sun at almo/ an inf9ite di/ance2 t ! ,angle "u :i* ! ,moon's diamet] is se51 dur+ ! "t ( ! ,eclipse1 cont9ues inv>iably ! same2 t ! ,moon's motion is uni=m1 & h] ,pa? rectil9eal1 = t "t4 ,b all ^! suppositions d n exactly agree ) ! tru?2 & !re=e1 suppos+ ! ,elem5ts #cfg1 giv5 by ! ,tables to be p]fectly accurate1 yet ! "t & phases ( ! ,eclipse d$uc$ f x's ,con/ruction w n answ] exactly to :at passe? 9 ! ,heav5s2 b may be two or ?ree m9utes wrong ?\gh done ) ! utmo/ c>e4 ,moreov]1 ! ,pa?s ( all ,places ( consid]able ,latitude g ne>] ! c5t] ( ! ,disc z se5 f ! ,moon ?an ^! ,con/ructions make !m2 because ! ,e>?'s ,disc is project$ z if ! ,e>? 7 a p]fect sph]e1 al?\gh x is kn[n to be a sph]oid4 ,consequ5tly1 ! ,moon's %ad[ w g f>!r ,nor? 9 places ( nor!rn ,latitude1 & f>!r ,s\? 9 places ( s\!rn ,latitude ?an ^! projections answ] to4 ,h5ce we may v5ture to pr$ict t ?is ,eclipse w be m annul> at ,london 7t is1 ! annulus w be some:at broad] on ! s\!rn ,limb ( ! ,sun7 ?an ! ,diagram %ews x4 #chc4 ,hav+ %ewn h[ to compute ! times & project ! phases ( a ,sol> ,eclipse1 we n[ proce$ to ^? ( ! ,lun>4 ,& x has be5 already m5tion$ #cag1 t :5 ! ,full ,moon is )9 #ab degrees ( ei!r ( h] ,nodes1 %e mu/ be eclips$4 ,we %all n[ enquire :e!r or no ! ,moon w be eclips$ ,may #ah1 #agfa1 ,n4 ,s4 at #cb m9utes pa/ #aj at ,night4 ,see page #aic4 ,sid5ote3 ,table ,,iv4 ,table ,,vi4 s ,sun f ,node at ,full ,moon 9 ,m>* #agfa #i #be #bg ,add 8 di/ance = two ,lunations1 to br+ x into ,may #b #a #bj --------- ,& 8 di/ance at ,full ,moon 9 t mon? is #aa #bf #dg ,subtract ?is f a ,circle1 or #ab ,signs1 & !re w rema9 #c #ac2 :i* is all t ! ,sun wants ( com+ r\nd to ! ,asc5d+ ,node2 & ! ,moon be+ !n opposite to ! ,sun1 mu/ be j z ne> ! ,desc5d+ ,node3 consequ5tly1 f> )9 ! limit ( an ,eclipse4 #chd4 ,kn[+ !n t ! ,moon w be eclips$ 9 ,may #agfa1 we mu/ f9d h] true di/ance f ! ,node at t "t1 by apply+ ! prop] ,equations z taught #cfc1 & !n f9d h] true ,latitude z taught 9 t article4 ,sid5ote3 ,table ,,iv4 ,table ,,xiii4 ,table ,,xii4 s ,sun's mean di/ance f ! ,node at ,f4 ,moon 9 ,may #agfa #aa #bf #dg ,add ! ,equation ( ! ,node1 = ! ,sun's ,anomaly #ajs #ah #aehe #f -------- ,sun's mean di/ance f ! ,node correct$ #aa #bf #ec ,add ! ,equation ( ! ,sun's mean ,place #a #ae -------- ,sun's true di/ance f ! ,asc5d+ ,node #aa #bh #h ,to :i* add #f ,signs1 ,see #cfc #f -------- ,! sum is ! ,moon's true di/ance f ! same ,node #e #bh #h ,sid5ote3 ,pl4 ,,xii4 ,or ! ,argum5t ( h] ,latitude2 :i* 9 ,table ,,xiv1 gives ! ,moon's true ,latitude1 viz4 #i #ef ,nor? ,desc5d+4 #che4 ,hav+ by ! =ego+ precepts #cee f\nd ! true "t ( ,opposition ( ! ,sun & ,moon 9 a lun> ,eclipse1 ) ! ,moon's ,anomaly ent] ,table ,,xv & take out h] horizontal ,p>allax1 also h] true hor>y ,motion & ,semi-diamet]3 & likewise ^? ( ! ,sun by 8 ,anomaly1 z already taught #cfd seq4 ,!n add ! ,sun's horizontal ,p>allax1 :i* is always #aj ,seconds1 to ! ,moon's horizontal ,p>allax1 & f _! sum subtract ! ,sun's ,semi-diamet]2 ! rema9d] w be ! ,semi-diamet] ( t "p ( ! ,e>?'s %ad[ :i* ! ,moon goes ?r\gh4 #chf4 ,f ! ,sum ( ! ,semi-diamet]s ( ! ,moon & ,e>?'s ,%ad[1 subtract ! ,moon's ,latitude2 ! rema9d] is ! p>ts defici5t4 ,!n1 z ! ,semi-diamet] ( ! ,moon is to #f ,digits1 s are ! p>ts defici5t to ! ,digits eclips$4 #chg4 ,if ! p>ts defici5t be m ?an ! ,moon's ,diamet]1 ! ,eclipse w be total ) cont9uance2 if less1 x w n be total2 if equal1 x w be total1 b )\t cont9uance4 #chh4 ,n[ collect ! ,elem5ts = project+ ?is ,eclipse4 ,moon's horizontal ,p>allax #ee #cb ,sun's horizontal ,p>allax 7always7 #aj ,! ,sum ( bo? ,p>allaxes #ee #db ,f :i* subtract ! ,sun's ,semi-diamet] #ae #ed ,rema9s ! ,semi-diamet] ( ! ,e>?'s ,%ad[ #ci #dh ,semidiamet] ( ! ,moon #ae #b ,sum ( ! two la/ #ed #ej ,moon's ,latitude subtract #i #ef ,rema9s ! p>ts defici5t #de #j ,moon's hor>y motion #cj #df ,sun's hor>y motion subtract #b #bd ,rema9s ! ,moon's hor>y motion f ! ,sun #bh #bb ,sid5ote3 ,to project a lun> ,eclipse4 ,fig4 ,,iii4 #chi4 ,?is done1 make a ,scale ( any conv5i5t l5g? z ,w1 :]e( ea* division is a m9ute ( a degree2 & take f x 9 y\r ,compasses #ed ,m9utes #ej ,seconds1 ! ,sum ( ,semi-diamet]s ( ! ,moon & ,e>?'s %ad[2 & ) t ext5t z a ,radius1 describe t ,circle ,,ovlg r\nd ,c z a ,c5t]4 ,f ! same ,scale take #ci ,m9utes #dh ,seconds1 ! ,semi-diamet] ( ! ,e>?'s %ad[1 & !re) z a ,radius1 describe ! ,circle ,,uuuu = ! ,e>?'s %ad[1 r\nd ,c z a ,c5t]4 ,subtract ! ,moon's ,semi-diamet] f ! ,semi-diamet] ( ! ,%ad[1 & ) ! diff]5ce #bd ,m9utes #df seconds z a ,radius1 tak5 f ! ,scale ,w1 describe ! ,circle ,,yz r\nd ! ,c5t] ,c4 ,draw ! "r l9e ,,ab ?r\gh ! ,c5t] ,c = ! ,ecliptic1 & cross x at "r ,angles ) ! l9e ,,eg = ! ,axis ( ! ,ecliptic4 ,because ! ,moon's ,latitude 9 ?is ,eclipse is ,nor? ,desc5d+1 #chd1 set (f ! ,angle ( h] visible ,pa? ) ! ,ecliptic #e ,degrees #ch ,m9utes 7,page #bjb47 f ,e to ,v2 & draw ,v,cv = ! ,axis ( ! ,moon's ,orbit4 ,_h ! ,moon's ,latitude be5 ,nor? ,asc5d+1 ?is ,angle mu/ h be5 set (f f ,e to f4 ,n4 ,b4 ,:5 ! ,moon's ,latitude is ,s\? ,asc5d+1 ! ,axis ( h] ,orbit lies ! same way z :5 %e has ,nor? ,asc5d+ ,latitude2 & :5 h] ,latitude is ,nor? ,desc5d+1 ! ,axis ( h] ,orbit lies ! same way z :5 h] ,latitude is ,s\? ,desc5d+4 ,take ! ,moon's true ,latitude #i #ef 9 y\r ,compasses f ! ,scale ,w1 & set x (f f ,c to ,f on ! ,axis ( ! ,ecliptic because ! ,moon is nor? ( ! ,ecliptic2 7_h %e be5 to ! ,s\? ( x1 h] ,latitude mu/ h be5 set (f ! contr>y way1 z f ,c t[>ds v37 & ?r\gh ,f1 at "r ,angles to ! ,axis ( ! ,moon's ,orbit ,v,cv1 draw ! "r l9e ,,lmhno = ! ,moon's ,orbit1 or h] ,pa? ?r\gh ! ,e>?'s %ad[4 ,n4 ,b4 ,:5 ! ,moon's ,latitude is ,nor? ,asc5d+1 or ,nor? ,desc5d+1 %e is above ! ,ecliptic3 b :5 h] ,latitude is ,s\? ,asc5d+1 or ,s\? ,desc5d+1 %e is bel[ x4 ,take ! ,moon's true hor>y motion f ! ,sun1 viz4 #bh ,m9utes #bb ,seconds1 f ! ,scale ,w 9 y\r ,compasses2 & ) t ext5t make m>ks 9 ! l9e ( ! ,moon's ,pa? ,,lmhno3 !n divide ea* ( ^! equal spaces into #fj equal p>ts or m9utes ( "t3 & set ! h\rs to !m z 9 ! ,figure1 9 su* a mann] t ! precise "t ( ,full ,moon1 z %ewn by ! ,tables1 may fall 9 ! ,axis ( ! ,ecliptic at ,f1 :]e ! l9e ( ! ,moon ,pa? cuts x4 ,la/ly1 ,take ! ,moon's ,semi-diamet] #ae ,m9utes #b ,seconds f ! ,scale ,w 9 y\r ,compasses1 & !re) z a ,radius describe ! ,circles ,p1 ,q1 ,r1 ,s1 & ,t on ! ,c5t]s ,l1 ,m1 ,h1 ,n1 & ,o2 ! ,circles ,p & ,t j t\*+ ! ,e>?'s ,%ad[ ,,uu1 b no "p ( !m )9 x2 ! ,circles ,q & ,s all )9 x1 b t\*+ at its edges2 & ! ,circle ,r 9 ! middle ( ! ,moon's ,pa? ?r\gh ! %ad[4 ,s ! ,circle ,p %all be ! ,moon t\*+ ! %ad[ at ! mom5t ! ,eclipse beg9s2 ! ,circle ,q ! ,moon j imm]s$ into ! %ad[ at ! mom5t %e is totally eclips$2 ! ,circle ,r ! ,moon at ! greate/ obscuration1 9 ! middle ( ! ,eclipse2 ! ,circle ,s ! ,moon j beg9n+ to be enlight5$ on h] we/]n limb at ! end ( total d>kness2 & ! ,circle ,t ! ,moon q cle> ( ! ,e>?'s %ad[ at ! mom5t ! ,eclipse ends4 ,! mom5ts ( "t m>k$ at ! po9ts ,l1 ,m1 ,h1 ,n & ,o answ] to ^! ,ph5om5a3 & accord+ to ?is small projection are z foll[4 ,! beg9n+ ( ! ,eclipse at #h ,h\rs #cf ,m9utes ,p4 ,m4 ,! total imm]sion at #i ,h\rs #db ,m9utes4 ,! middle ( ! ,eclipse at #aj ,h\rs #bf ,m9utes4 ,! end ( total d>kness at #aa ,h\rs #ab ,m9utes4 ,& ! end ( ! ,eclipse at #ab ,h\rs #ah ,m9utes2 b ! ,figure is too small to admit ( precision4 ,sid5ote3 ,! exam9ation ( anti5t ,eclipses4 #cij4 ,by comput+ ! times ( ,new & ,full ,moons1 toge!r ) ! di/ance ( ! ,sun & ,moon f ! ,nodes2 & kn[+ t :5 ! ,sun is )9 #ag ,degrees ( ei!r ,node at ,new ,moon he mu/ be eclips$2 & :5 ! ,moon is )9 #ab ,degrees ( ei!r ,node at ,full %e _c escape an ,eclipse2 & t !re c be no ,eclipses )\t ^! limits2 'tis easy to exam9e :e!r ! acc\nts ( anti5t ,eclipses record$ 9 hi/ory be true4 ,i %all take ! lib]ty to exam9e two ( ^? m5tion$ 9 ! =ego+ catalogue1 namely1 t ( ! ,moon at ,babylon on ! #ai? ( ,m>* 9 ! #gba/ ye> be=e ,,*ri/2 & t ( ! ,sun at ,a!ns1 on ! #bj? ( ,m>*1 9 ! #dbd? ye> be=e ,,*ri/4 ,! "t ( ,full ,moon = ! =m] ( ^! ,eclipses is already calculat$1 ,page #aih1 & ! "t ( ,new ,moon = ! latt]1 ,page #aif1 bo? to ! ,old ,/yle2 s t we h no?+ n[ to d b f9d ! ,sun's di/ance f ! ,nodes ! same way z we did ! ,anomalies2 & if ! ,full ,moon 9 ,m>* #gba ye>s be=e ,,*ri/ 0 )9 #ab degrees ( ei!r ,node1 %e 0 !n eclips$2 & if ! ,sun1 at ! "t ( ,new ,moon 9 ,m>* #dbd ye>s be=e ,,*ri/ 0 )9 #ag degrees ( ei!r ,node1 he mu/ h be5 eclips$ at t "t4 ,,example ,i4 ,to f9d ! di/ance ( ! ,sun & ,moon f ! ,nodes1 at ! "t ( ,full ,moon 9 ,m>*1 ! ye> be=e ,,*ri/ #gba1 ,o4 ,s4 ,! ye>s #gbj add$ to #aghj make #bejj1 or #be ,c5turies4 ,sun f ,node s ,to ! mean "t ( ,full ,moon 9 ,m>* #aghj1 ,table ,,iii4 #aj #c #a ,add ! di/ance = #a ,lunation ,see ,n4 ,b4 ,page #aie1 & ,example ,,iii1 ,page #aih #a #j #dj -------- ,sum #aa #c #da ,f :i* subtract ! ,sun's di/ance f ! ,node = #bejj ye>s1 ,table ,v #e #d #aa -------- ,rema9s ! ,sun's di/ance f ! ,node1 ,m>* #ai1 #gba ye>s be=e ,,*ri/ #e #bi #cj ,to :i* add #f ,signs = ! ,moon's di/ance1 because %e 0 !n 9 opposition to ! ,sun #f #j #j -------- ,! ,sum is ! ,moon's di/4 f ! ,asc5d4 ,node #aa #bi #cj ,t is1 %e 0 )9 half a degree ( com+ r\nd to x aga92 & !re=e1 be+ s ne>1 %e mu/ h be5 totally1 & almo/ c5trally eclips$4 ,,example ,,ii ,to f9d ! ,suns di/ance f ! ,node at ! ,"t ( ,new ,moon 9 ,m>*1 ! ye> be=e ,,*ri/ #dbd1 ,o4 ,s4 ,! ye>s #dbc add$ to #aggg make #bbjj1 or #bb ,c5turies4 ,sun f ,node s ,at ! mean "t ( ,new ,moon 9 ,m>* #aggg1 ,tab4 ,i4 #h #bc #cc ,f :i* subtract ! ,sun's di/ance f ! ,node = #bbjj ye>s1 ,table ,v #c #f #j -------- ,rema9s ! ,sun's di/ance f ! ,asc5d+ ,node1 ,m>* #ba1 #dbd ye>s be=e ,,*ri/ #e #ag #cc ,:i*1 tak5 f #f ,signs1 ! di/ance ( ! ,nodes f ea* o!r #f #j #j -------- ,leaves ! ,sun's di/ance at t "t f ! ,desc5d+ ,node1 ,desc5d+ viz4 #j #ab #bg ,:i* be+ less ?an #ag degrees1 %ews t ! ,sun 0 !n eclips$4 ,& z f ^! %ort ,calculations we f9d ^? two anti5t ,eclipses tak5 at a v5ture1 to be truly record$2 x is natural to imag9e t s are all ! re/ 9 ! catalogue4 ,"h foll[ ,,a/ronomical ,,tables1 = calculat+ ! ,times ( ,,new & ,,full ,,moons & ,,eclipses4 ---------------------------------------- --------------------------------- ,,table ,i4 ,! mean "t ( ,new ,moon 9 ,m>*1 ! mean ,anomaly ( ! ,sun & ,moon1 ! ,sun's mean ,di/ance f ! ,asc5d+ ,node2 ) ! mean ,longitude ( ! ,sun & ,node f ! beg9n+ ( ! ,sign ,aries1 at ! times ( all ! ,new ,moons 9 ,m>* = #ajj ye>s1 ,old ,/yle4 ---------------------------------------- --------------------------- ,ye>s ,mean "t ,! ,sun's ,! ,moon's,! ,sun's ,! ,sun's ,! ,node's ( ( ,new mean mean di/ance ,longitude ,longitude ,,*ri/4,moon 9 ,anomaly4 ,anomaly4 f ! f f ,m>*4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- --------------------------- #agja #bg #ac #de #i #h #bc #j #bh #e #g #bc #ae #j #af #c #d #bb #dh #agjb #af #bb #cd #h #bg #ci #aa #g #ec #h #a #ag #j #e #bj #d #d #c #agjc #f #g #bc #h #af #ee #i #ag #da #h #i #bj #aa #bd #cg #c #ae #ag #agjd #bd #d #ee #i #d #cj #h #bc #ah #i #ah #c #j #ac #j #b #bd #eg #agje #ac #ac #dd #h #bc #ed #g #c #f #i #bf #f #j #b #ag #b #f #aa ---------------------------------------- --------------------------- #agjf #b #bb #cb #h #ac #dh #e #ab #ed #aj #d #i #aa #ba #cd #a #ag #be #agjg #ba #bj #e #i #b #ag #d #ah #ca #aa #ab #eb #j #i #eg #j #bg #e #agjh #aj #d #ed #h #ba #aj #b #bh #ai #aa #bj #ee #aa #bi #ad #j #h #ai #agji #bi #b #bf #i #i #dh #b #c #ef #j #bi #ch #j #ag #cg #aa #ag #ei #agaj #ah #aa #af #h #bh #cb #j #ac #dd #a #g #dj #j #f #ed #aj #bi #ad ---------------------------------------- --------------------------- #agaa #g #bj #e #h #ag #bg #aj #bc #cc #a #ae #dc #aa #bf #aa #aj #aj #bh #agab #be #ag #cf #i #e #h #i #bi #aj #b #bd #bf #j #ad #cd #i #bj #h #agac #ae #b #be #h #be #dh #h #h #eh #c #b #bi #j #c #ej #i #a #ba #agad #d #aa #ad #h #ad #eb #f #af #df #c #aj #cb #aa #bc #g #h #ab #ce #agae #bc #h #df #i #c #cg #e #bd #bb #d #ai #ae #j #aa #cj #g #bb #ae ---------------------------------------- --------------------------- #agaf #aa #ag #ce #h #ba #bf #d #d #aa #d #bg #ah #j #j #dg #g #c #bi #agag #a #b #bc #h #aa #eh #b #ac #ei #e #e #bj #aa #bj #d #f #ad #dd #agah #ai #bc #ef #i #j #ca #a #ai #cf #f #ad #c #j #h #bg #e #bd #bd #agai #i #h #de #h #ai #dg #aa #bi #bd #f #bb #f #aa #bg #dc #e #e #cg #agbj #bg #f #ag #i #h #i #aa #e #a #h #j #di #j #af #f #d #ae #ag ---------------------------------------- --------------------------- #agba #af #ae #f #h #bg #be #i #ad #di #h #h #eb #j #e #bc #c #bf #ca #agbb #e #bc #ee #h #af #da #g #bd #ch #h #af #ee #aa #bd #dj #c #g #de #agbc #bd #ba #bg #i #e #c #g #j #ae #i #be #ch #j #ac #d #b #ag #bf #agbd #ac #f #af #h #bd #ai #e #aj #c #aj #c #da #j #b #bb #a #bh #da #agbe #b #ae #d #h #ac #de #c #ai #ea #aj #aa #dc #aa #ba #ci #a #i #ef ---------------------------------------- --------------------------- #agbf #ba #ab #cg #i #a #eg #b #be #bh #aa #bj #bf #j #aj #c #j #ai #cg #agbg #aj #ba #bf #h #ba #ac #a #e #af #aa #bh #bi #aa #bi #bj #j #j #ea #agbh #bh #ah #eh #i #i #ce #j #aj #ec #a #g #ac #j #ag #dc #aa #aj #cj #agbi #ah #c #dg #h #bh #ea #aj #bj #da #a #ae #ae #j #g #j #aj #ba #de #agcj #g #ab #cf #h #ah #g #i #j #bi #a #bc #ah #aa #bf #ag #aj #b #ei ---------------------------------------- --------------------------- #agca #bf #aj #h #i #f #bi #h #f #f #c #b #a #j #ad #dj #i #ab #ci #agcb #ad #ah #eg #h #be #de #f #ae #ed #c #aj #c #j #c #eg #h #bc #ed #agcc #d #c #de #h #ad #di #d #be #dc #c #ah #f #aa #bc #ad #h #e #g #agcd #bc #a #ah #i #c #be #d #a #bj #d #bf #di #j #aa #cg #g #ad #dh #agce #ab #aj #g #h #bb #ci #b #aa #h #e #d #eb #j #j #ed #f #bf #a ---------------------------------------- --------------------------- #agcf #cj #g #ci #j #aa #a #a #af #de #f #ac #ce #j #ai #ag #f #e #db #agcg #ai #af #bh #i #j #a #aa #bf #cc #f #ba #ch #j #h #cd #e #af #ef #agch #i #a #ag #h #ai #cc #aj #f #ba #f #bi #db #aa #bg #ea #d #bh #i #agci #bg #bb #di #i #g #ee #i #aa #eh #h #h #bd #j #af #ad #d #g #ej #agdj #af #g #ch #h #bg #aa #g #ba #df #h #af #bg #j #e #cj #c #ai #c ---------------------------------------- --------------------------- #agda #e #af #bf #h #af #bg #f #a #cd #h #bd #cj #aa #bd #dg #c #j #af #agdb #bd #ac #ei #i #d #di #e #g #aa #aj #c #ab #j #ac #aj #b #i #eh #agdc #ac #bb #dh #h #bd #e #c #af #ei #aj #aa #ae #j #b #bg #a #ba #ab #agdd #b #g #cf #h #ac #ba #a #bf #dh #aj #ai #ah #aa #ba #dd #a #b #be #agde #ba #e #i #i #a #dc #a #b #be #aa #bh #j #j #aj #g #j #ab #g ---------------------------------------- --------------------------- #agdf #aj #ac #eh #h #bj #ei #aa #ab #ac #j #f #c #aa #bi #dd #aa #bc #bj #agdg #bi #aa #cj #i #i #ba #aj #ag #ej #a #ad #de #j #ag #dg #aa #c #b #agdh #ag #bj #ai #h #bh #cg #h #bg #ch #a #bb #di #j #g #d #aj #ad #ae #agdi #g #e #h #h #ag #ec #g #g #bf #b #j #ec #aa #bf #ba #i #be #bh #agej #bf #b #dj #i #f #ae #f #ac #c #c #i #ce #j #ad #dd #i #e #i ---------------------------------------- --------------------------- #agea #ae #aa #bi #h #be #cb #d #bb #ea #c #ag #ch #j #d #a #h #af #bc #ageb #c #bj #ag #h #ad #dg #c #b #ci #c #be #da #aa #bc #ah #g #bg #cg #agec #bb #ag #ej #i #c #aj #b #h #af #e #d #bd #j #aa #da #g #g #ag #aged #ab #b #ci #h #bb #bf #j #ah #d #e #ab #bg #j #j #ei #f #ah #cb #agee #a #aa #bg #h #aa #da #aj #bg #eb #e #bj #cj #aa #bj #af #e #bi #de ---------------------------------------- --------------------------- #agef #ai #i #j #i #j #d #aj #c #cj #f #bi #ac #j #h #ci #e #i #bg #ageg #h #ag #di #h #ai #bj #h #ac #ah #g #aj #ae #aa #bg #ef #d #bj #da #ageh #bg #ae #ba #i #g #db #g #ah #ee #h #ae #eh #j #af #ai #d #j #ba #agei #ag #j #aj #h #bf #eh #e #bh #dc #h #bd #a #j #e #cf #c #aa #cf #agfj #e #h #eh #h #af #ac #d #h #ca #i #b #d #aa #bd #ec #b #bb #di ---------------------------------------- --------------------------- #agfa #bd #f #ca #i #d #ce #c #ad #h #aj #aj #dg #j #ac #af #b #b #bi #agfb #ac #ae #ai #h #bc #eb #a #bc #ef #aj #ah #ea #j #b #cc #a #ac #dd #agfc #c #j #h #h #ac #g #j #c #dd #aj #bf #ec #aa #ba #ej #j #bd #eg #agfd #bj #ba #da #i #a #bi #aa #i #ba #j #e #cf #j #aj #ac #j #d #cg #agfe #aj #f #cj #h #bj #df #i #ai #i #j #ac #ch #aa #bi #cj #aa #ae #eb ---------------------------------------- --------------------------- #agff #bi #d #b #i #i #h #h #bd #df #a #bb #ba #j #ag #ec #aj #be #cb #agfg #ah #ab #ea #h #bh #bd #g #d #ce #b #j #bd #j #g #aj #aj #f #dg #agfh #f #ba #ci #h #ag #ci #e #ad #bc #b #h #bg #aa #bf #bg #i #ah #a #agfi #be #ai #ab #i #f #b #d #bj #j #c #ag #j #j #ad #ej #h #bg #da #aggj #ae #d #a #h #be #ag #b #bi #dh #c #be #ab #j #d #g #h #h #ef ---------------------------------------- --------------------------- #agga #d #ab #di #h #ad #cc #a #i #cf #d #c #af #aa #bc #bd #g #bj #h #aggb #bb #aj #bb #i #b #ef #j #ae #ac #e #aa #di #j #aa #dg #f #bi #dh #aggc #aa #ai #aj #h #bb #aa #aj #be #a #e #bj #a #j #a #d #f #aa #c #aggd #a #c #ei #h #aa #bg #i #d #di #e #bh #d #aa #bj #ba #e #bb #ag #agge #bj #a #cb #h #bi #ej #h #aj #bf #g #f #d #j #h #dd #e #a #eg ---------------------------------------- --------------------------- #aggf #h #aj #bj #h #ai #e #f #bj #ad #g #ad #ej #aa #bh #a #d #ac #ab #aggg #bg #g #ec #i #g #bg #e #be #ea #h #bc #bc #j #af #bd #c #bb #eb #aggh #af #af #db #h #bf #dc #d #e #dj #i #a #cf #j #e #da #c #d #f #aggi #f #a #cj #h #ae #ei #b #ae #bh #i #i #ci #aa #bd #eh #b #ae #ai #aghj #bc #bc #c #i #d #ba #a #ba #e #aj #ah #bb #j #ac #ba #a #bd #ei ---------------------------------------- -------------------------- #agha #ac #g #eb #h #bc #cg #j #j #ec #aj #bf #bd #j #b #ch #a #f #ad #aghb #b #af #dj #h #ab #ec #aj #aj #da #aa #d #bg #aa #ba #ed #j #ag #bg #aghc #ba #ad #ac #i #a #ae #i #af #ah #j #ac #aj #j #aj #ag #aa #bg #g #aghd #i #bc #b #h #bj #cb #g #bf #f #j #ba #ac #aa #bi #cd #aa #h #bb #aghe #bh #bj #ce #i #h #ed #g #a #dc #a #bi #ef #j #ag #eg #aj #ah #b ---------------------------------------- -------------------------- #aghf #ah #e #bc #h #bh #i #e #aa #ca #b #g #ei #j #g #ad #i #bi #af #aghg #g #ad #aa #h #ag #be #c #ba #ai #b #af #b #aa #bf #ca #i #aj #bi #aghh #be #aa #dd #i #e #dg #b #bf #ef #c #bd #de #j #ad #ed #h #bj #i #aghi #ad #bj #cc #h #be #c #a #f #de #d #b #dg #j #d #aa #h #a #be #agij #d #e #ba #h #ad #ai #aa #af #cc #d #aj #ej #aa #bc #bh #g #ab #ch ---------------------------------------- -------------------------- #agia #bc #b #ed #i #b #da #aj #bb #aj #e #ai #cc #j #aa #ea #f #bb #ah #agib #aa #aa #dc #h #ba #eg #i #a #eh #e #bg #ef #j #a #g #f #c #cb #agic #j #bj #ca #h #aa #ab #g #aa #de #f #e #ci #aa #bj #bd #e #ad #de #agid #ai #ah #d #h #bi #ce #f #ag #bc #g #ad #bb #j #h #dh #d #bd #bg #agie #i #b #eb #h #ah #ea #d #bg #aa #g #bb #be #aa #bh #f #d #e #da ---------------------------------------- -------------------------- #agif #bg #j #be #i #g #ac #d #b #dh #i #a #h #j #af #bi #c #ae #ba #agig #af #i #ad #h #bf #bi #b #ab #cf #i #i #aj #j #e #df #b #bf #cf #agih #e #ah #b #h #ae #dd #j #bb #bd #i #ag #ac #aa #be #c #b #g #ej #agii #bd #ae #ce #i #d #f #aa #bh #a #aj #be #ef #j #ac #bf #a #ag #cj #ahjj #ac #j #bd #h #bc #bc #aj #g #di #aa #c #ei #j #b #dc #j #bh #dd ---------------------------------------- -------------------------- ---------------------------------------- --------------------------------- ,,table ,,ii4 ,! mean ,new ,moons1 c4 9 ,m>* to ! ,new ,/yle4 ---------------------------------------- --------------------------- ,ye>s ,mean "t ,! ,sun's ,! ,moon's,! ,sun's ,! ,sun's ,! ,node's ( ( ,new mean mean di/ance ,longitude ,longitude ,,*ri/4,moon 9 ,anomaly4 ,anomaly4 f ! f f ,m>*4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- --------------------------- #agec #d #e #f #g #d #b #a #ab #bg #d #c #dd #aa #ab #ce #g #h #ej #aged #bc #b #ci #h #bb #bf #j #ah #d #e #ab #bg #j #j #ei #f #ah #cb #agee #ab #aa #bg #h #aa #da #aj #bg #eb #e #bj #bi #aa #bj #af #e #bi #de ---------------------------------------- --------------------------- #agef #cj #i #j #i #j #c #aj #c #bi #f #bi #ab #j #h #ci #e #i #bg #ageg #ai #ag #di #h #ai #ai #h #ac #ag #g #g #ae #aa #bg #ef #d #bj #da #ageh #i #b #cg #h #h #ce #f #bc #e #g #ae #ah #aa #ag #ac #d #a #ed #agei #bh #j #i #h #bf #eh #e #bh #dc #h #bd #a #j #e #cf #c #aa #cf #agfj #af #h #eh #h #af #ad #d #h #ca #i #b #d #aa #bd #ec #b #bb #di ---------------------------------------- --------------------------- #agfa #e #g #dg #h #e #bi #b #ah #ai #i #aj #i #aa #ad #aj #b #d #a #agfb #bd #ae #ai #h #bc #eb #a #bc #ef #aj #ah #ea #j #b #cc #a #ac #dd #agfc #ad #j #h #h #ac #g #j #c #dd #aj #bf #ec #aa #ba #ej #j #bd #eg #agfd #b #h #eg #h #b #bc #aj #ac #cb #aa #d #eg #aa #aa #g #j #f #aj #agfe #ba #f #cj #h #bj #df #i #ai #i #j #ac #ch #aa #bi #cj #aa #ae #eb ---------------------------------------- --------------------------- #agff #aj #ae #ah #h #aj #a #g #bh #eh #j #ba #da #aa #ah #dg #aj #bg #e #agfg #bi #ab #ea #h #bh #bc #g #d #ce #b #j #bc #j #g #aj #aj #f #dg #agfh #ag #ba #ci #h #ag #ci #e #ad #bc #b #h #bf #aa #bf #bg #i #ah #a #agfi #g #f #bh #h #f #ee #c #bd #aa #b #af #bi #aa #ae #dd #h #bi #ae #aggj #bf #d #a #h #be #ah #b #bi #dh #c #be #aa #j #d #g #h #h #ef ---------------------------------------- --------------------------- #agga #ae #ab #di #h #ad #cc #a #i #cf #d #c #af #aa #bc #bd #g #bj #h #aggb #c #ba #ch #h #c #di #aa #ai #bd #d #aa #ai #aa #ab #da #g #a #bb #aggc #bb #ai #aj #h #bb #aa #aj #be #a #e #bj #a #j #a #d #f #aa #c #aggd #ab #c #ei #h #aa #bg #i #d #di #e #bh #d #aa #bj #ba #e #bb #ag #agge #a #ab #dh #h #j #dc #g #ad #cg #f #f #g #aa #i #ch #e #c #cj ---------------------------------------- --------------------------- #aggf #ai #aj #bj #h #ai #e #f #bj #ad #g #ad #ej #aa #bh #a #d #ac #ab #aggg #h #ai #i #h #h #ba #e #j #b #g #bb #ec #aa #ag #ah #c #bd #be #aggh #bg #af #db #h #bf #dc #d #e #dj #i #a #cf #j #e #da #c #d #f #aggi #ag #a #cj #h #ae #ei #b #ae #bh #i #i #ci #aa #bd #eh #b #ae #ai #aghj #e #aj #ai #h #e #ae #j #be #af #i #ag #db #aa #ad #ae #a #bf #cb ---------------------------------------- --------------------------- #agha #bd #g #eb #h #bc #cg #j #j #ec #aj #bf #bd #j #b #ch #a #f #ad #aghb #ac #af #dj #h #ab #ec #aj #aj #da #aa #d #bg #aa #ba #ed #j #ag #bg #aghc #c #a #bi #h #b #h #h #bj #bi #aa #ab #cj #aa #aa #aa #aa #bh #dj #aghd #bj #bc #b #h #bj #cb #g #bf #f #j #ba #ac #aa #bi #cd #aa #h #bb #aghe #aj #g #ej #h #i #dg #f #e #ed #j #bi #af #aa #ah #ea #aj #ai #ce ---------------------------------------- --------------------------- #aghf #bi #e #bc #h #bh #i #e #aa #ca #b #g #ei #j #g #ad #i #bi #af #aghg #ah #ad #aa #h #ag #be #c #ba #ai #b #af #b #aa #bf #ca #i #aj #bi #aghh #f #bc #j #h #f #da #b #a #g #b #bd #e #aa #ae #dh #h #ba #dc #aghi #be #bj #cc #h #be #c #a #f #de #d #b #dg #j #d #aa #h #a #be #agij #ae #e #ba #h #ad #ai #aa #af #cc #d #aj #ej #aa #bc #bh #g #ab #ch ---------------------------------------- --------------------------- #agia #d #ad #aj #h #c #cd #i #bf #ba #d #ah #ec #aa #ab #dd #f #bc #ea #agib #bb #aa #dc #h #ba #eg #i #a #eh #e #bg #cf #j #a #g #f #c #cb #agic #aa #bj #ca #h #aa #ab #g #aa #de #f #e #ci #aa #bj #bd #e #ad #de #agid #a #f #bj #h #j #bi #e #ba #cd #f #ac #db #aa #i #bb #d #g #ae #agie #bj #b #eb #h #ah #ea #d #bg #aa #g #bb #be #aa #bh #f #d #e #da ---------------------------------------- --------------------------- #agif #h #aa #da #h #h #f #c #f #ei #h #j #bh #aa #ag #bc #c #af #ed #agig #bg #i #ad #h #bf #bi #b #ab #cf #i #i #aj #j #e #df #b #bf #cf #agih #af #ah #b #h #ae #dd #j #bb #bd #i #ag #ac #aa #be #c #b #g #ej #agii #f #b #ea #h #e #j #aa #b #ab #i #be #af #aa #ad #bj #a #ai #c #ahjj #be #j #bd #h #bc #bc #aj #g #di #aa #c #ei #j #b #dc #j #bh #dd ---------------------------------------- --------------------------- ---------------------------------------- --------------------------------- ,,table ,,iii4 ,! mean "t ( ,full ,moon 9 ,m>*1 ! mean ,anomaly ( ! ,sun & ,moon1 ! ,sun's mean ,di/ance f ! ,asc5d+ ,node2 ) ! mean ,longitude ( ! ,sun & ,node f ! beg9n+ ( ! ,sign ,aries1 at ! "t ( all ! ,full ,moons 9 ,m>* = #ajj ye>s1 ,old ,/yle4 ---------------------------------------- --------------------------- ,ye>s ,mean "t ,! ,sun's ,! ,moon's,! ,sun's ,! ,sun's ,! ,node's ( ( ,full mean mean di/ance ,longitude ,longitude ,,*ri/4,moon 9 ,anomaly4 ,anomaly4 f ! f f ,m>*4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- --------------------------- #agja #ab #ai #bc #h #bc #ef #f #ae #aa #g #g #ee #j #a #cj #d #bc #ce #agjb #b #d #ab #h #ac #f #d #bd #ei #g #ae #eg #aa #bj #dg #d #d #dh #agjc #ba #a #de #i #a #bh #d #j #ce #h #bd #dj #j #i #aj #c #ad #cj #agjd #i #aj #cc #h #ai #eg #b #aj #bd #i #b #dc #aa #bh #bg #b #be #dc #agje #bh #h #f #i #h #bg #a #af #j #aj #aa #bf #j #af #ej #b #e #be ---------------------------------------- --------------------------- #agjf #ag #af #ed #h #bh #aa #aa #be #dh #aj #ai #bi #j #f #g #a #af #ch #agjg #g #a #dc #h #ag #dd #aj #e #cg #aj #bg #cb #aa #be #bd #j #bg #ea #agjh #bd #bc #af #i #e #dc #i #aa #ad #j #f #ae #j #ac #dg #j #g #cc #agji #ad #h #d #h #be #ae #g #ba #b #j #ad #ah #j #c #d #aa #ah #df #agaj #c #af #ed #h #ac #ei #f #j #ej #j #bb #ba #aa #bb #ba #aa #j #j ---------------------------------------- --------------------------- #agaa #bb #ad #bg #i #b #j #e #f #bg #b #a #c #j #aj #dd #aj #i #db #agab #aj #bc #ad #h #bj #ce #c #af #af #b #i #f #j #j #a #i #bj #ee #agac #bi #bj #dg #i #aj #ba #b #ba #eb #c #ag #dh #j #ah #bc #i #j #ce #agad #ai #e #cf #h #bi #be #a #a #dj #c #be #ec #j #g #dj #h #aa #dh #agae #h #ad #bd #h #ai #d #aa #aa #bh #d #c #ef #aa #bf #eg #g #bc #a ---------------------------------------- --------------------------- #agaf #bf #aa #eg #i #e #ei #j #ag #e #e #ab #ch #j #ae #bj #g #b #dc #agag #ae #bj #de #h #bf #ca #ah #bf #ec #e #bj #da #j #d #cg #f #ac #ef #agah #e #e #cd #h #ae #eh #g #f #db #e #bh #dd #aa #bc #ed #e #be #aj #agai #bd #c #g #i #d #bj #f #ab #ah #g #g #bf #j #ab #ag #e #d #eb #agbj #ab #aa #ee #h #bc #cf #d #bb #g #g #ae #bi #j #a #cd #d #af #e ---------------------------------------- --------------------------- #agba #a #bj #dd #h #ab #eb #c #a #ee #g #bc #cb #aa #bj #ea #c #bg #ah #agbb #bj #ah #ag #i #a #ad #b #g #cb #i #b #ae #j #i #ad #c #f #ei #agbc #aj #c #e #h #bj #cj #j #ag #ba #i #aj #ah #aa #bh #ca #b #ah #ab #agbd #bh #j #ch #i #h #eb #aa #bb #eg #aj #ai #j #j #af #ee #a #bg #ee #agbe #ag #i #bf #h #bh #ah #aj #b #de #aj #bg #c #j #f #ab #a #i #i ---------------------------------------- --------------------------- #agbf #f #ah #ae #h #ag #bd #h #ab #cd #aa #e #f #aa #be #cj #j #bj #bc #agbg #be #ae #dh #i #e #df #g #ah #aj #j #ac #di #j #ac #ec #j #j #e #agbh #ad #j #cf #h #be #b #e #bg #ei #j #ba #eb #j #c #aj #aa #aa #ah #agbi #c #i #be #h #ad #ah #d #g #dg #j #bi #ee #aa #bb #bg #aj #bb #cb #agcj #bb #f #eh #i #b #dj #c #ac #bc #b #h #ch #j #aj #ej #aj #b #ac ---------------------------------------- --------------------------- #agca #aa #ae #df #h #ba #ef #a #bc #ab #b #af #da #j #j #g #i #ac #bf #agcb #bi #ac #ai #i #aj #ah #j #bh #dh #c #be #bc #j #ah #cj #h #bc #h #agcc #ah #bb #g #h #bi #bb #aa #h #cg #d #c #bf #j #g #dg #h #d #ba #agcd #h #f #ef #h #ah #ej #i #ah #bf #d #aa #bi #aa #bg #d #g #ae #cd #agce #bg #d #bi #i #g #ab #h #bd #b #e #bj #ab #j #ae #bg #f #be #ae ---------------------------------------- --------------------------- #agcf #ae #ac #ag #h #bf #bi #g #c #ea #e #bh #ae #j #d #dd #f #f #bi #agcg #d #bb #f #h #ae #dd #e #ac #ci #f #f #ah #aa #bd #a #e #ag #db #agch #bc #ai #ci #i #d #f #d #ai #ae #g #ae #a #j #ab #bd #d #bg #bd #agci #ac #d #bg #h #bc #bb #b #bi #d #g #bc #d #j #a #da #d #h #cg #agdj #a #ac #af #h #ab #ch #a #h #eb #h #a #g #aa #bj #eg #c #ai #ej ---------------------------------------- --------------------------- #agda #bj #aj #dh #i #a #j #j #ad #bh #i #i #di #j #i #bj #b #bi #cj #agdb #i #ai #cg #h #bj #af #aj #bd #ag #i #ag #eb #aa #bh #cg #b #aj #dd #agdc #bh #ag #aj #i #h #ch #i #bi #ec #aj #bf #ce #j #ag #j #a #bj #bf #agdd #ag #a #eh #h #bg #ed #h #i #db #aa #d #ch #j #f #ag #a #a #ci #agde #f #aj #dg #h #ag #aj #f #ai #ca #aa #ab #da #aa #be #cd #j #ab #eb ---------------------------------------- --------------------------- #agdf #be #h #ai #i #e #cb #e #be #g #j #ba #bd #j #ac #eg #aa #bb #cd #agdg #ad #ag #h #h #bd #dh #d #d #ef #j #bi #bg #j #c #ad #aa #c #dg #agdh #c #a #eg #h #ad #d #b #ad #dd #a #g #cj #aa #bb #ca #aj #ae #j #agdi #ba #bc #cj #i #b #bf #a #bj #bj #b #af #ab #j #aj #ed #i #bd #db #agej #aa #h #ah #h #ba #db #j #j #i #b #bd #ae #j #j #aa #i #e #ei ---------------------------------------- --------------------------- #agea #cj #e #ea #i #aj #e #aa #e #de #d #b #eh #j #ah #cd #h #ae #cg #ageb #ah #ad #ci #h #bi #bj #i #ae #cc #d #aa #a #j #g #ea #g #bf #ej #agec #g #bc #ah #g #ah #ce #g #be #ba #d #ai #d #aa #bg #h #g #h #d #aged #bf #ba #a #i #f #ei #g #j #eh #g #bg #dg #j #ae #cb #f #ag #de #agee #af #e #di #h #bf #ad #e #aj #df #f #e #di #j #d #di #e #bi #j ---------------------------------------- --------------------------- #agef #d #ad #ch #h #ae #cj #c #bj #ce #f #ac #eb #aa #bd #f #e #aj #ad #ageg #bc #ab #aa #i #c #ec #b #bf #ab #g #be #ce #j #ab #bi #d #ai #ed #ageh #ab #bj #ei #h #bc #h #a #e #ei #h #j #ch #j #a #df #d #a #i #agei #b #e #dg #h #ab #be #aa #ae #dh #h #h #da #aa #ba #c #c #ab #bb #agfj #bj #c #bj #i #j #df #aj #ba #be #i #ag #bd #j #i #bf #b #bb #b ---------------------------------------- --------------------------- #agfa #i #ab #i #h #bj #b #i #a #ac #i #be #bg #aa #bh #dc #b #c #af #agfb #bh #i #da #i #h #be #h #f #ej #aa #d #aa #j #ag #f #a #ab #eg #agfc #ag #ah #cj #h #bg #dj #f #af #ch #aa #ab #ac #j #f #bc #j #bd #aa #agfd #f #c #ai #h #af #ef #d #bf #bf #aa #bj #af #aa #be #dj #j #e #bd #agfe #be #j #eb #i #e #ai #d #b #c #j #bh #eh #j #ad #c #aa #ae #e ---------------------------------------- --------------------------- #agff #ad #i #dj #h #bd #cd #b #aa #eb #a #g #a #j #c #bj #aj #bf #bj #agfg #g #ah #bi #h #ac #ej #j #ba #da #a #ae #d #aa #bb #cg #aj #g #cd #agfh #ba #af #a #i #b #ab #aa #bg #ag #b #bc #dg #j #aa #j #i #ag #ad #agfi #aa #j #ej #h #ba #bh #aj #g #i #c #a #di #j #j #ag #h #bh #bh #aggj #j #i #ci #h #aj #dd #h #af #eg #c #i #eb #aa #ai #ed #h #i #db ---------------------------------------- --------------------------- #agga #ai #g #aa #h #bi #f #g #bb #cj #d #ah #cf #j #g #eg #g #ai #ba #aggb #g #af #j #h #ah #bb #f #b #ah #d #bf #ci #aa #bg #ad #g #j #ce #aggc #bf #ac #cb #i #f #dd #e #g #ee #f #e #ba #j #ae #cg #f #aj #af #aggd #ae #bb #ba #h #bf #j #c #ag #dc #f #ac #bd #j #d #ed #e #ba #ca #agge #e #g #aj #h #ae #af #a #bg #ca #f #ba #bg #aa #bd #aa #e #b #dd ---------------------------------------- --------------------------- #aggf #bc #d #db #i #c #ch #a #c #h #h #j #aj #j #ab #cd #d #ab #be #aggg #ab #ac #ca #h #bb #ed #aa #ab #ef #h #h #ac #j #a #ea #h #bc #cj #aggh #a #bb #bj #h #ab #aj #i #bb #de #h #af #af #aa #ba #h #c #d #eb #aggi #bj #ai #eb #i #j #cb #h #bh #bb #i #bd #ei #j #i #ca #b #ad #cb #aghj #i #d #da #h #ai #dh #g #h #aj #aj #c #a #aa #bh #dh #a #be #dg ---------------------------------------- --------------------------- #agha #bh #b #ad #i #h #i #f #ac #dg #aa #aa #dd #j #ag #aa #a #e #bg #aghb #ai #aa #b #h #bg #bh #d #bc #cd #aa #ai #dg #j #f #bg #j #f #da #aghc #f #ai #ea #h #af #dd #c #c #bc #aa #bg #ej #aa #be #dd #aa #bg #ed #aghd #bd #ag #bd #i #e #d #b #i #j #a #f #ce #j #ad #g #aa #g #ce #aghe #ad #b #ab #h #bd #bj #j #ah #dh #a #ad #cf #j #c #bd #aj #ah #dh ---------------------------------------- --------------------------- #aghf #c #aa #a #h #ac #cf #aj #bh #cg #a #bb #ci #aa #bb #da #aj #j #b #aghg #bb #h #cc #i #a #eg #aj #d #ac #c #a #bb #j #aa #d #i #i #db #aghh #aj #ag #bb #h #ba #ad #h #ad #b #c #i #be #j #j #ba #h #bj #eg #aghi #bi #ad #ee #i #i #cf #g #ai #ci #d #ah #g #j #ah #dd #h #j #ch #agij #ah #bc #dc #h #bh #eb #e #bi #bg #d #bf #aj #j #h #a #g #aa #ea ---------------------------------------- --------------------------- #agia #h #h #cb #h #ah #h #d #i #ae #e #d #ac #aa #bg #ag #f #bc #d #agib #bf #f #e #i #f #bj #c #ad #eb #f #ab #ef #j #ae #dj #f #b #de #agic #ae #ad #ec #h #be #df #a #bd #dj #f #bj #ei #j #d #eh #e #ac #ei #agid #d #bc #db #h #ae #b #j #d #bi #f #bi #b #aa #bd #ae #d #be #ac #agie #bc #ba #ad #i #c #ad #aa #aj #e #h #g #de #j #ab #ci #d #d #ed ---------------------------------------- --------------------------- #agif #ab #f #c #h #bb #ci #i #ai #ec #h #ae #dh #j #a #ef #c #af #h #agig #a #ad #eb #h #aa #ee #g #bi #db #h #bc #ej #aa #ba #ac #b #bg #bc #agih #bj #ab #bd #i #j #g #g #e #ah #aj #b #cc #j #i #cf #b #g #c #agii #i #ba #ac #h #ai #cc #e #ae #f #aj #aj #cf #aa #bh #ec #a #ah #ah #ahjj #bg #ah #df #i #g #df #d #bj #dc #aa #ai #ai #j #ag #af #j #bg #eg ---------------------------------------- --------------------------- ---------------------------------------- --------------------------------- ,,table ,,iv4 ,! mean ,full ,moons1 c4 9 ,m>* to ! ,new ,/yle4 ---------------------------------------- --------------------------- ,ye>s ,mean "t ,! ,sun's ,! ,moon's,! ,sun's ,! ,sun's ,! ,node's ( ( ,full mean mean di/ance ,longitude ,longitude ,,*ri/4,moon 9 ,anomaly4 ,anomaly4 f ! f f ,m>*4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- --------------------------- #agec #ah #bc #ah #g #ah #ce #g #be #ba #d #ai #d #aa #bg #h #g #h #d #aged #h #h #ag #g #g #ec #f #e #aj #d #bg #g #aa #af #bf #f #ai #ah #agee #bg #e #di #h #bf #ad #e #aj #df #f #e #di #j #d #di #e #bi #j ---------------------------------------- --------------------------- #agef #ae #ad #ch #h #ae #cj #c #bj #ce #f #ac #eb #aa #bd #f #e #aj #ad #ageg #d #bc #bg #h #d #cf #b #j #bc #f #ba #ee #aa #ac #bc #d #ba #bg #ageh #bc #bj #ei #h #bc #h #a #e #ei #h #j #ch #j #a #df #d #a #i #agei #ac #e #dg #h #ab #be #aa #ae #dh #h #h #da #aa #ba #c #c #ab #bb #agfj #a #ad #cf #h #a #da #i #be #cg #h #af #dd #aa #aj #bj #b #bc #ce ---------------------------------------- --------------------------- #agfa #bj #ab #i #h #bj #b #i #a #ac #i #be #bg #aa #bh #dc #b #c #af #agfb #i #bj #eg #h #i #ai #g #aa #b #aj #c #ca #aa #ah #j #a #ad #bi #agfc #bh #ah #cj #h #bg #dj #f #af #ch #aa #ab #ac #j #f #bc #j #bd #aa #agfd #ag #c #ai #h #af #ef #d #bf #bf #aa #bj #af #aa #be #dj #j #e #bd #agfe #f #ab #h #h #f #ac #c #f #ae #aa #bh #ai #aa #ad #eg #aa #af #ch ---------------------------------------- --------------------------- #agff #be #i #dj #h #bd #cd #b #aa #eb #a #g #a #j #c #bj #aj #bf #bj #agfg #ah #ah #bi #h #ac #ej #j #ba #da #a #ae #d #aa #bb #cg #aj #g #cc #agfh #c #c #ag #h #c #f #aa #a #bi #a #bc #g #aa #aa #ed #i #ah #df #agfi #bb #j #ej #h #ba #bh #aj #g #e #c #a #di #j #j #ag #h #bh #bh #aggj #aa #i #ci #h #ae #de #h #af #ed #c #i #eb #aa #ai #cd #h #i #db ---------------------------------------- --------------------------- #agga #cj #g #aa #h #bi #f #g #bb #cj #d #ah #cf #j #g #eg #g #ai #ba #aggb #ah #af #j #h #ah #bb #f #b #ah #d #bf #ci #aa #bg #ad #g #j #ce #aggc #h #j #dh #h #g #ch #d #ab #g #e #d #db #aa #af #ca #f #aa #di #aggd #bf #bb #ba #h #bf #j #c #ag #dc #f #ac #bd #j #d #ed #e #ba #ca #agge #af #g #aj #h #ae #af #a #bg #ca #f #ba #bg #aa #bd #aa #e #b #dd ---------------------------------------- --------------------------- #aggf #d #ae #eh #h #d #cb #j #g #bj #f #bi #cj #aa #ac #bh #d #ac #eh #aggg #bc #ac #ca #h #bb #ed #aa #ab #ef #h #h #ac #j #a #ea #c #bc #ci #aggh #ab #bb #bj #h #ab #aj #i #bb #de #h #af #af #aa #ba #h #c #d #eb #aggi #b #g #h #h #a #bf #h #b #cd #h #bd #ai #aa #aj #be #b #af #e #aghj #bj #d #da #h #ai #dh #g #h #aj #aj #c #a #aa #bh #dh #a #be #dg ---------------------------------------- --------------------------- #agha #i #ac #cj #h #i #d #e #ag #ei #aj #aa #d #aa #ah #e #a #g #j #aghb #bh #aa #b #h #bg #bh #d #bc #cd #aa #ai #dg #j #f #bg #j #af #da #aghc #ag #ai #ea #h #af #dd #c #c #bc #aa #bg #ej #aa #be #dd #aa #bg #ed #aghd #f #d #dj #h #e #ei #a #ac #ab #j #e #ec #aa #ae #a #aa #i #g #aghe #be #b #ab #h #bd #bj #j #ah #dh #a #ad #cf #j #c #bd #aj #ah #dh ---------------------------------------- --------------------------- #aghf #ad #aa #a #h #ac #cf #aj #bh #cg #a #bb #ci #aa #bb #da #aj #j #b #aghg #c #ai #di #h #b #eb #i #h #be #b #j #db #aa #aa #eh #i #aa #ae #aghh #ba #ag #bb #h #ba #ad #h #ad #b #c #i #be #j #j #ba #h #bj #eg #aghi #aa #b #aa #h #aj #cj #f #bc #ea #c #ag #bh #aa #ai #ch #h #b #aj #agij #bi #bc #dc #h #bh #eb #e #bi #bg #d #bf #aj #j #h #a #g #aa #ea ---------------------------------------- --------------------------- #agia #ai #h #cb #h #ah #h #d #i #ae #e #d #ac #aa #bg #ag #f #bc #d #agib #g #ag #ba #h #g #bd #b #ai #d #e #ab #af #aa #af #cd #f #d #ag #agic #bf #ad #ec #h #be #df #a #bd #dj #f #bj #ei #j #d #eh #e #ac #ei #agid #ae #bc #db #h #ae #b #j #d #bi #f #bi #b #aa #bd #ae #d #be #ac #agie #e #h #cj #h #d #ah #aj #ad #ag #g #g #e #j #ac #cb #d #f #bf ---------------------------------------- --------------------------- #agif #bc #f #c #h #bb #ci #i #ai #ec #h #ae #dh #j #a #ef #c #af #h #agig #ab #ad #eb #h #aa #ee #g #bi #db #h #bc #ej #aa #ba #ac #b #bg #bc #agih #a #bc #dj #h #a #aa #f #i #cj #i #a #ec #aa #aj #cj #b #h #cf #agii #bj #ba #ac #h #ai #cc #e #ae #f #aj #aj #cf #aa #bh #ec #a #ah #ah #ahjj #aj #f #b #h #h #ej #c #bd #ee #aj #ah #ci #aa #ah #aj #j #bi #ca ---------------------------------------- --------------------------- ---------------------------------------- ------------------------------------ ,,tab4 ,v4 ,! fir/ mean ,conjunction ( ! ,sun & ,moon aft] a compleat ,c5tury1 beg9n+ ) ,m>*1 = #ejjj ye>s #aj days #g h\rs #ef m9utes 79 :i* "t !re are j #fahdc mean ,lunations7 ) ! mean ,anomaly ( ! ,sun & ,moon1 ! ,sun's mean di/ance f ! ,asc5d+ ,node1 & ! mean ,long4 ( ! ,sun & ,node f ! beg9n+ ( ! sign ,aries1 at ! times ( all ^? mean ,conjunctions4 ---------------------------------------- ------------------------------ ,c5turies ,fir/ ,! ,sun's ,! ,moon's,! ,sun's ,! ,sun's ,! ,node's ( ,conjunction mean mean di/ance ,longitude ,longitude ,julian aft] a ,anomaly4 ,anomaly4 f ! f f ,ye>s4 ,c5tury4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- ------------------------------ #ajj #d #h #aa #j #c #ba #h #ae #bb #d #ai #bg #j #e #b #d #ad #be #bjj #h #af #bb #j #f #db #e #j #dd #i #h #ee #j #aj #d #h #bh #ea #cjj #ac #j #cc #j #aj #c #a #af #f #a #bh #bb #j #ae #f #a #ac #af #djj #ag #h #dc #j #ac #bd #aj #a #bh #f #ag #di #j #bj #h #e #bg #da #ejj #ba #af #ed #j #af #df #f #af #ej #aa #g #af #j #be #aj #aj #ab #f ---------------------------------------- ------------------------------ #fjj #bf #a #e #j #bj #g #c #b #ab #c #bf #dd #a #j #ab #b #bf #cb #gjj #j #bj #cb #aa #bd #bb #aj #ba #de #g #ae #ca #j #f #g #g #i #bd #hjj #e #d #dc #aa #bg #dc #g #g #g #j #d #eh #j #aa #i #aa #bc #di #ijj #i #ab #ed #j #a #d #c #bb #bi #d #bd #be #j #af #ab #d #h #ac #ajjj #ac #ba #e #j #d #be #j #g #ea #i #ac #ec #j #ba #ad #h #bb #ci ---------------------------------------- ------------------------------ #aajj #ah #e #af #j #g #df #h #bc #ac #b #c #bj #j #bf #af #a #g #d #abjj #bb #ac #bf #j #aa #g #e #h #ce #f #bb #dg #a #a #ah #e #ba #bi #acjj #bf #ba #cg #j #ad #bh #a #bc #eg #aa #ab #ae #a #f #bj #aj #e #ee #adjj #a #ag #d #aa #ah #dc #i #ac #cj #c #a #b #j #ab #ae #b #ah #dg #aejj #f #a #ae #aa #bb #d #e #bh #eb #g #bj #bi #j #ag #ag #g #c #ab ---------------------------------------- ------------------------------ #afjj #aj #i #bf #aa #be #be #b #ad #ad #j #i #ef #j #bb #ai #aa #ag #cg #agjj #ad #ag #cg #aa #bh #df #aj #bi #cf #d #bi #bc #j #bg #bb #d #b #b #ahjj #ai #a #dh #j #b #h #g #ad #eh #i #ah #ea #a #b #bd #h #af #bg #aijj #bc #i #eh #j #e #bi #d #j #bj #b #h #ah #a #g #bf #a #j #eb #bjjj #bg #ah #i #j #h #ej #j #ae #db #f #bg #de #a #ab #bh #e #ae #ag ---------------------------------------- ------------------------------ #bajj #b #ac #cf #aa #ac #e #h #e #ae #aj #af #cb #j #ah #bd #i #bh #h #bbjj #f #ba #dg #aa #af #bf #d #bj #cg #c #f #j #j #bc #bf #b #ab #cd #bcjj #aa #e #eh #aa #ai #dg #a #e #ei #g #be #bg #j #bh #bh #f #bf #ei #bdjj #ae #ad #i #aa #bc #h #i #ba #ba #j #ad #ed #a #c #cj #aa #aa #bd #bejj #ai #bb #bj #aa #bf #bi #f #f #dc #e #d #aa #a #h #cb #c #be #di ---------------------------------------- ------------------------------ #bfjj #bd #f #ca #aa #bi #ej #b #bb #d #i #bc #di #a #ac #ce #h #aj #ad #bgjj #bh #ad #da #j #c #aa #aa #ag #bf #b #ac #af #a #ah #cg #j #bd #ci #bhjj #c #aj #h #aa #g #bf #f #bf #ei #f #b #c #j #bd #ca #e #g #cc #bijj #g #ah #ai #aa #aj #dg #c #ab #ba #aj #ba #cj #j #bi #cc #i #ba #eh #cjjj #ab #b #cj #aa #ad #h #aa #bg #dc #c #aj #eh #a #d #ce #b #f #bc ---------------------------------------- ------------------------------ #cajj #af #aj #da #aa #ag #cj #h #ac #e #h #aj #be #a #i #cg #f #bj #dh #cbjj #bj #ah #eb #aa #bj #ea #d #bh #bg #j #ai #eb #a #ad #ci #aa #e #ac #ccjj #be #c #c #aa #bd #aa #a #ac #di #e #i #bj #a #ai #da #c #ai #ci #cdjj #bi #aa #ad #aa #bg #cb #i #bi #aa #i #bh #dg #a #bd #dc #h #d #d #cejj #d #f #da #aa #a #dg #e #ah #dd #a #ag #cd #a #j #da #j #af #ec ---------------------------------------- ------------------------------ #cfjj #h #ad #eb #aa #d #eh #b #d #f #f #g #a #a #e #db #e #a #ai #cgjj #ab #bc #c #aa #h #i #aj #ai #bh #aj #bf #bh #a #aj #dc #i #ae #de #chjj #ag #g #ad #aa #aa #bj #g #d #ej #c #ae #ee #a #ae #de #b #j #aj #cijj #ba #ae #be #aa #ad #ca #d #bj #ab #h #e #bb #a #bj #dg #f #ad #ce #djjj #be #bc #cf #aa #ag #db #a #e #cd #j #bd #di #a #be #di #aj #bi #j ---------------------------------------- ------------------------------ #dajj #j #ai #c #aj #bb #ef #h #be #g #d #ac #cf #a #j #de #c #ab #ea #dbjj #e #c #ad #aj #bf #ag #e #aj #bi #i #c #c #a #f #dg #g #f #af #dcjj #i #aa #be #aj #bi #cg #a #be #ea #a #ab #cj #a #aa #dh #aa #be #ci #ddjj #ac #ai #cf #aa #b #eh #aj #aa #ac #f #a #eg #a #af #ea #d #aj #d #dejj #ah #c #df #aa #f #ah #f #bf #ce #aj #ba #bd #a #ba #ec #h #bi #ca ---------------------------------------- ------------------------------ #dfjj #bb #aa #eg #aa #i #ci #c #aa #ae #c #aj #ea #a #bf #ee #a #ac #ef #dgjj #bf #bj #g #aa #ab #ei #aa #bg #ai #h #j #af #b #a #eg #e #bh #ai #dhjj #a #ae #cd #aj #ag #ad #g #af #eb #aa #ai #d #a #g #ec #aj #aa #aa #dijj #e #bc #de #aj #bj #ce #d #b #ad #d #h #cj #a #ab #ee #b #be #ce #ejjj #aj #g #ef #aj #bc #ef #j #ag #cf #h #bg #eg #a #ag #eg #g #aj #j ---------------------------------------- ------------------------------ ---------------------------------------- ------------------------------------- ,,table ,,vi4 ,! mean ,anomaly ( ! ,sun & ,moon1 ! ,sun's mean di/ance f ! ,asc5d+ ,node1 ) ! mean ,longitude ( ! ,sun & ,node f ! beg9n+ ( ! ,sign ,aries1 = #ac mean ,lunations4 ---------------------------------------- ------------------------------- ,! ,sun's ,! ,moon's,! ,sun's ,! ,sun's ,! ,node's ,lunations4 ,mean mean mean motion mean retrograde ,lunations4 ,anomaly4 ,anomaly4 f ,motion4 ,motion4 ! ,node4 ---------------------------------------- --------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- ------------------------------- #a #bi #ab #dd #j #bi #f #j #be #di #a #j #dj #j #bi #f #j #a #cd #b #ei #a #bh #a #bh #ac #a #ba #ch #b #a #bj #a #bh #ac #j #c #h #c #hh #ad #ab #b #bg #ai #b #ag #bg #c #b #a #b #bg #ai #j #d #da #d #aah #b #ef #c #bf #bf #c #ac #af #d #b #da #c #bf #bf #j #f #ae #e #adg #ae #d #d #be #cb #d #i #e #e #c #ba #d #be #cb #j #g #di ---------------------------------------- ------------------------------- #f #agg #d #bd #e #bd #ch #e #d #ed #f #d #a #e #bd #ch #j #i #bc #g #bjf #ag #h #f #bc #dd #f #j #dc #g #d #db #f #bc #de #j #aj #eg #h #bcf #e #eb #g #bb #ej #f #bf #cb #h #e #bb #g #bb #ea #j #ab #ca #i #bfe #ah #cf #h #ba #eg #g #bb #ba #i #f #b #h #ba #eh #j #ad #d #aj #bie #g #ba #i #ba #c #h #ah #aj #aj #f #db #i #ba #d #j #ae #ch ---------------------------------------- ------------------------------- #aa #cbd #bj #e #aj #bj #i #i #ac #ei #aa #g #bb #aj #bj #aj #j #ag #ab #ab #ced #h #di #aa #ai #af #aj #i #dh #j #h #c #aa #ai #ag #j #ah #df #ac #chc #ba #cc #j #ah #bb #aa #e #cg #a #h #dc #j #ah #bc #j #bj #bj ---------------------------------------- ------------------------------- ,! fir/1 second1 ?ird1 & f\r? ,tables may be cont9u$1 by means ( ! six?1 to any l5g? ( "t3 =1 by add+ #ab ,lunations to ! mean "t ( ! ,new or ,full ,moon :i* happ5s next aft] ! #aa? day ( ,m>*1 & !n1 ca/+ out #cfe days 9 common ye>s1 & #cff days 9 leap-ye>s1 we h ! mean "t ( ,new or ,full ,moon 9 ,m>* ! foll[+ ye>4 ,b :5 ! mean ,new or ,full ,moon happ5s on or be=e ! #aa? ( ,m>*1 !re mu/ be #ac ,lunations add$ to c>ry x to ,m>* aga94 ,! ,anomalies1 ,sun's di/ance f ! ,node1 & ,longitude ( ! ,sun1 are f\nd ! same way1 by add+ !m = #ab or #ac ,lunations4 ,b ! retrograde ,motion ( ! ,node = ^! ,lunations mu/ be subtract$ f x's longitude f ,aries 9 ,m>*1 to h x's ,longitude or ,place 9 ! ,m>* foll[+4 ---------------------------------------- ------------ ,,table ,,vii4 ,! numb] ( ,days1 reckon$ f ! beg9n+ ( ,m>*1 answ]+ to ! ,days ( all ! mean ,new & ,full ,moons4 ---------------------------------------- ,days,m>,apr,may,jun,jul,aug,sep,oct,nov ,dec,jan,feb ---------------------------------------- #a #a #cb #fb #icabcaedahebaebdfbgfcjgcch #b #b #cc #fc #idabdaeeahfbafbdgbggcjhcci #c #c #cd #fd #ieabeaefahgbagbdhbghcjicdj #d #d #ce #fe #ifabfaegahhbahbdibgicajcda #e #e #cf #ff #igabgaehahibaibejbhjcaacdb ---------------------------------------- #f #f #cg #fg #ihabhaeiaijbbjbeabhacabcdc #g #g #ch #fh #iiabiafjaiabbabebbhbcaccdd #h #h #ci #fiajjacjafaaibbbbbecbhccadcde #i #i #dj #gjajaacaafbaicbbcbedbhdcaecdf #aj #aj #da #gaajbacbafcaidbbdbeebhecafcdg ---------------------------------------- #aa #aa #db #gbajcaccafdaiebbebefbhfcagcdh #ab #ab #dc #gcajdacdafeaifbbfbegbhgcahcdi #ac #ac #dd #gdajeaceaffaigbbgbehbhhcaicej #ad #ad #de #geajfacfafgaihbbhbeibhicbjcea #ae #ae #df #gfajgacgafhaiibbibfjbijcbaceb ---------------------------------------- #af #af #dg #ggajhachafibjjbcjbfabiacbbcec #ag #ag #dh #ghajiaciagjbjabcabfbbibcbcced #ah #ah #di #giaajadjagabjbbcbbfcbiccbdcee #ai #ai #ej #hjaaaadaagbbjcbccbfdbidcbecef #bj #bj #ea #haaabadbagcbjdbcdbfebiecbfceg ---------------------------------------- #ba #ba #eb #hbaacadcagdbjebcebffbifcbgceh #bb #bb #ec #hcaadaddagebjfbcfbfgbigcbhcei #bc #bc #ed #hdaaeadeagfbjgbcgbfhbihcbicfj #bd #bd #ee #heaafadfaggbjhbchbfibiiccjcfa #be #be #ef #hfaagadgaghbjibcibgjcjjccacfb ---------------------------------------- #bf #bf #eg #hgaahadhagibajbdjbgacjaccbcfc #bg #bg #eh #hhaaiadiahjbaabdabgbcjbccccfd #bh #bh #ei #hiabjaejahababbdbbgccjcccdcfe #bi #bi #fj #ijabaaeaahbbacbdcbgdcjdccecff #cj #cj #fa #iaabbaebahcbadbddbgecjeccf--- #ca #ca -- #ib---aecahd---bde---cjfccg--- ---------------------------------------- ---------------------------------------- - ,,table ,,viii4 ,! ,moon's annual ,equation4 --------------------------------------- ,sun's ,subtract ,sun's ,ano4 ------------------------,ano4 #j #a #b #c #d #e ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ---------------------------------- ,d4 ,m4 ,m4 ,m4 ,m4 ,m4 ,m4 ,d4 ---------------------------------- #j #j #aa #ah #bb #ai #aa #cj #a #j #aa #ai #bb #ai #aa #bi #b #a #aa #ai #bb #ah #aj #bh #c #a #aa #ai #bb #ah #aj #bg #d #a #ab #ai #bb #ah #aj #bf #e #b #ab #ai #bb #ah #i #be #f #b #ab #ai #ba #ah #i #bd #g #c #ac #bj #ba #ag #i #bc #h #c #ac #bj #ba #ag #h #bb #i #c #ac #bj #ba #ag #h #ba #aj #d #ad #bj #ba #ag #h #bj #aa #d #ad #bj #ba #af #g #ai #ab #d #ad #bj #ba #af #g #ah #ac #e #ad #bj #ba #af #f #ag #ad #e #ae #bj #ba #af #f #af #ae #e #ae #ba #ba #ae #f #ae #af #f #ae #ba #ba #ae #e #ad #ag #f #ae #ba #ba #ae #e #ac #ah #f #af #ba #ba #ae #e #ab #ai #g #af #ba #bj #ad #d #aa #bj #g #af #ba #bj #ad #d #aj #ba #g #af #ba #bj #ad #c #i #bb #h #ag #ba #bj #ac #c #h #bc #h #ag #ba #bj #ac #c #g #bd #i #ag #ba #bj #ac #b #f #be #i #ag #ba #bj #ac #b #e #bf #i #ah #ba #bj #ab #b #d #bg #aj #ah #ba #ai #ab #a #c #bh #aj #ah #ba #ai #ab #a #b #bi #aj #ah #bb #ai #aa #j #a #cj #aa #ah #bb #ai #aa #j #j ---------------------------------- ,sun's #aa #aj #i #h #g #f ,sun's ,ano4 ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ,ano4 ------------------------ ,add --------------------------------------- ---------------------------------------- - ,,table ,,ix4 ,equation ( ! ,moon's mean ,anomaly4 --------------------------------------- ,sun's ,sun's ,anom4 ,add ,anom4 ---------------------------------- #j #a #b #c #d #e ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ---------------------------------- ---------------------------------- #j #j #aj #ag #bj #ag #aj #cj #a #j #aj #ag #bj #ag #aj #bi #b #a #aa #ag #bj #ag #i #bh #c #a #aa #ah #bj #ag #i #bg #d #a #aa #ah #bj #ag #i #bf #e #b #ab #ah #bj #ag #i #be #f #b #ab #ah #bj #af #h #bd #g #b #ab #ah #bj #af #h #bc #h #c #ab #ah #bj #af #h #bb #i #c #ab #ai #bj #af #g #ba #aj #c #ac #ai #bj #af #g #bj #aa #d #ac #ai #bj #ae #g #ai #ab #d #ac #ai #bj #ae #f #ah #ac #d #ac #ai #ai #ae #f #ag #ad #e #ad #ai #ai #ae #f #af #ae #e #ad #ai #ai #ad #e #ae #af #e #ad #ai #ai #ad #e #ad #ag #f #ad #ai #ai #ad #e #ac #ah #f #ae #ai #ai #ad #d #ab #ai #f #ae #bj #ai #ac #d #aa #bj #g #ae #bj #ai #ac #d #aj #ba #g #ae #bj #ai #ac #c #i #bb #g #af #bj #ai #ac #c #h #bc #h #af #bj #ai #ab #c #g #bd #h #af #bj #ah #ab #b #f #be #h #af #bj #ah #ab #b #e #bf #i #af #bj #ah #aa #a #d #bg #i #ag #bj #ah #aa #a #c #bh #i #ag #bj #ah #aa #a #b #bi #aj #ag #bj #ah #aj #j #a #cj #aj #ag #bj #ag #aj #j #j ---------------------------------- #aa #aj #i #h #g #f ,sun's ,s4 ,s4 ,s4 ,s4 ,s4 ,s4,sun's ,anom4------------------------,anom4 ,subtract --------------------------------------- ---------------------------------------- --------------------- ,,table ,x4 ,! ,moon's elliptic ,equation4 ---------------------------------------- ------------------- ,moon's ,add ,moon's ---------------------------------------- -- ,ano4 #j #a #b #c #d #e ,ano4 ,signs ,signs ,signs ,signs ,signs ,signs ---------------------------------------- -------------- ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ---------------------------------------- -------------- #j #j #j #d #di #h #h #i #b #g #cb #d #ad #cj #a #j #aj #d #eg #h #ab #i #a #g #bg #d #f #bi #b #j #bj #e #e #h #af #i #j #g #bb #c #eh #bh #c #j #cj #e #ac #h #bj #h #ei #g #ag #c #ej #bg #d #j #dj #e #ba #h #bd #h #eh #g #ab #c #db #bf #e #j #ej #e #bi #h #bh #h #eg #g #f #c #cd #be #f #a #j #e #cg #h #ca #h #ee #g #j #c #bf #bd #g #a #aj #e #de #h #cd #h #ec #f #ed #c #ah #bc #h #a #bj #e #ec #h #cg #h #ea #f #dh #c #aj #bb #i #a #cj #f #a #h #dj #h #di #f #db #c #b #ba #aj #a #dj #f #i #h #dc #h #dg #f #cf #b #ec #bj #aa #a #ej #f #af #h #de #h #dd #f #cj #b #de #ai #ab #b #j #f #bc #h #dg #h #da #f #bd #b #cg #ah #ac #b #aj #f #cj #h #di #h #ch #f #ah #b #bi #ag #ad #b #bj #f #cg #h #ea #h #ce #f #aa #b #ba #af #ae #b #cj #f #dd #h #ec #h #cb #f #d #b #ab #ae #af #b #dj #f #ea #h #ee #h #bi #e #eg #b #c #ad #ag #b #ej #f #eh #h #eg #h #bf #e #ej #a #ed #ac #ah #c #j #g #d #h #ei #h #bc #e #dc #a #de #ab #ai #c #aj #g #aj #i #j #h #bj #e #cf #a #cf #aa #bj #c #ai #g #af #i #a #h #af #e #bi #a #bg #aj #ba #c #bh #g #bb #i #b #h #ab #e #bb #a #ai #i #bb #c #cg #g #bh #i #b #h #h #e #ae #a #aa #h #bc #c #df #g #cc #i #c #h #d #e #h #a #c #g #bd #c #ee #g #ch #i #c #h #j #e #a #j #ed #f #be #d #d #g #dc #i #d #g #ef #d #ed #j #de #e #bf #d #ac #g #dh #i #d #g #eb #d #df #j #cf #d #bg #d #bb #g #ec #i #d #g #dg #d #ch #j #bg #c #bh #d #ca #g #eh #i #c #g #db #d #cj #j #ah #b #bi #d #dj #h #c #i #c #g #cg #d #bb #j #i #a #cj #d #di #h #h #i #b #g #cb #d #ad #j #j #j ---------------------------------------- -------------- #aa #aj #i #h #g #f ,moon's ,signs ,signs ,signs ,signs ,signs ,signs ,moon's ---------------------------------------- -- ,ano4 ,subtract ,ano4 ---------------------------------------- ------------------- ---------------------------------------- ----------------------- ,,table ,,xi4 ,! ,sun's ,equation at ! "t ( ,new & ,full ,moon4 ---------------------------------------- --------------------- ,subtract ,sun's ---------------------------------------- -- ,sun's ,anom4 #j #a #b #c #d #e ,anom4 ,signs ,signs ,signs ,signs ,signs ,signs ---------------------------------------- ---------------- ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ---------------------------------------- ---------------- #j #j #j #a #dd #c #b #c #cb #c #e #a #dh #cj #a #j #d #a #dg #c #c #c #cb #c #c #a #de #bi #b #j #g #a #ej #c #e #c #cb #c #b #a #db #bh #c #j #aa #a #ec #c #g #c #cb #c #j #a #ch #bg #d #j #ad #a #eg #c #i #c #cb #b #eh #a #ce #bf #e #j #ah #b #j #c #aj #c #ca #b #ef #a #ca #be #f #j #bb #b #c #c #ab #c #ca #b #ed #a #bh #bd #g #j #be #b #f #c #ad #c #ca #b #eb #a #bd #bc #h #j #bi #b #h #c #af #c #cj #b #ej #a #ba #bb #i #j #cb #b #aa #c #ag #d #cj #b #dh #a #ag #ba #aj #j #cf #b #ad #c #ah #c #cj #b #de #a #ad #bj #aa #j #dj #b #ag #c #ai #c #bi #b #dc #a #aa #ai #ab #j #dc #b #bj #c #bj #c #bi #b #dj #a #g #ah #ac #j #dg #b #bb #c #ba #c #bh #b #cg #a #d #ag #ad #j #ej #b #be #c #bb #c #bg #b #ce #a #j #af #ae #j #ed #b #bh #c #bc #c #bf #b #cb #j #ef #ae #af #j #eg #b #cj #c #bd #c #be #b #bi #j #eb #ad #ag #a #j #b #cb #c #be #c #bd #b #bf #j #di #ac #ah #a #d #b #ce #c #bf #c #bc #b #bc #j #de #ab #ai #a #g #b #ch #c #bg #c #bb #b #ba #j #da #aa #bj #a #aa #b #dj #c #bh #c #ba #b #ah #j #ch #aj #ba #a #ad #b #dc #c #bh #c #bj #b #ae #j #cd #i #bb #a #ag #b #de #c #bi #c #ai #b #ab #j #cj #h #bc #a #ba #b #dg #c #bi #c #ah #b #aj #j #bf #g #bd #a #bd #b #di #c #cj #c #ag #b #g #j #bc #f #be #a #bh #b #ea #c #cj #c #ae #b #d #j #ai #e #bf #a #ca #b #ed #c #ca #c #ac #b #a #j #ae #d #bg #a #cd #b #eg #c #ca #c #aa #a #eh #j #aa #c #bh #a #ch #b #ei #c #ca #c #i #a #ee #j #g #b #bi #a #da #c #a #c #cb #c #g #a #eb #j #d #a #cj #a #dd #c #b #c #cb #c #e #a #dh #j #j #j ---------------------------------------- ---------------- #aa #aj #i #h #g #f ,sun's ,signs ,signs ,signs ,signs ,signs ,signs ,sun's ,anom4 ---------------------------------------- -- ,anom4 ,add ---------------------------------------- --------------------- ---------------------------------------- ----------------------- ,,table ,,xii4 ,equation ( ! ,sun's mean ,place4 ---------------------------------------- --------------------- ,subtract ,sun's ---------------------------------------- -- ,sun's ,anom4 #j #a #b #c #d #e ,anom4 ,signs ,signs ,signs ,signs ,signs ,signs ---------------------------------------- ---------------- ---------------------------------------- ---------------- #j #j #j #j #eg #a #dj #a #ef #a #db #j #ei #cj #a #j #b #j #ei #a #da #a #ef #a #da #j #eg #bi #b #j #d #a #j #a #db #a #ef #a #dj #j #ef #bh #c #j #f #a #a #a #dc #a #ef #a #ci #j #ed #bg #d #j #h #a #b #a #dd #a #ef #a #ch #j #eb #bf #e #j #aj #a #d #a #de #a #ef #a #cf #j #ej #be #f #j #ab #a #f #a #de #a #ef #a #ce #j #dh #bd #g #j #ad #a #g #a #df #a #ee #a #cd #j #df #bc #h #j #af #a #i #a #dg #a #ee #a #cc #j #dd #bb #i #j #ah #a #aj #a #dh #a #ee #a #cb #j #db #ba #aj #j #bj #a #ab #a #dh #a #ed #a #cj #j #da #bj #aa #j #bb #a #ad #a #di #a #ed #a #bi #j #ci #ai #ab #j #bd #a #ae #a #ej #a #ed #a #bh #j #cg #ah #ac #j #bf #a #ag #a #ea #a #ec #a #bf #j #ce #ag #ad #j #bh #a #ah #a #ea #a #ec #a #be #j #cc #af #ae #j #cj #a #bj #a #eb #a #eb #a #bc #j #ca #ae #af #j #ca #a #ba #a #eb #a #eb #a #bb #j #bi #ad #ag #j #cc #a #bb #a #ec #a #ea #a #ba #j #bg #ac #ah #j #ce #a #bd #a #ec #a #ea #a #ai #j #be #ab #ai #j #cg #a #be #a #ed #a #ej #a #ah #j #bc #aa #bj #j #ci #a #bg #a #ed #a #di #a #af #j #ba #aj #ba #j #da #a #bh #a #ee #a #di #a #ad #j #ai #i #bb #j #dc #a #bi #a #ee #a #dh #a #ac #j #ag #h #bc #j #de #a #cj #a #ee #a #dg #a #aa #j #ad #g #bd #j #df #a #cb #a #ef #a #df #a #aj #j #ab #f #be #j #dh #a #cc #a #ef #a #df #a #h #j #aj #e #bf #j #ej #a #cd #a #ef #a #de #a #f #j #h #d #bg #j #eb #a #ce #a #ef #a #de #a #e #j #f #c #bh #j #ed #a #cf #a #ef #a #dd #a #c #j #d #b #bi #j #ee #a #ch #a #ef #a #dc #a #a #j #b #a #cj #j #eg #a #dj #a #ef #a #db #j #ei #j #j #j ---------------------------------------- ---------------- #aa #aj #i #h #g #f ,sun's ,signs ,signs ,signs ,signs ,signs ,signs ,sun's ,anom4 ---------------------------------------- -- ,anom4 ,add ---------------------------------------- --------------------- ---------------------------------------- - ,,table ,,xiii4 ,equation ( ! ,moon's ,nodes4 --------------------------------------- ,subtract ,sun's------------------------,sun's ,ano4 #j #a #b #c #d #e ,ano4 ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ---------------------------------- ---------------------------------- #j #j #e #h #aj #h #e #cj #a #j #e #h #aj #h #e #bi #b #j #e #h #aj #h #e #bh #c #j #e #h #aj #h #d #bg #d #a #e #h #aj #h #d #bf #e #a #e #h #aj #h #d #be #f #a #f #i #aj #h #d #bd #g #a #f #i #i #h #d #bc #h #a #f #i #i #h #d #bb #i #a #f #i #i #g #c #ba #aj #b #f #i #i #g #c #bj #aa #b #f #i #i #g #c #ai #ab #b #f #i #i #g #c #ah #ac #b #f #i #i #g #c #ag #ad #b #g #i #i #g #c #af #ae #b #g #i #i #g #c #ae #af #b #g #i #i #g #b #ad #ag #c #g #i #i #g #b #ac #ah #c #g #i #i #f #b #ab #ai #c #g #i #i #f #b #aa #bj #c #g #i #i #f #b #aj #ba #c #g #i #i #f #b #i #bb #d #g #i #i #f #a #h #bc #d #h #i #i #f #a #g #bd #d #h #i #i #f #a #f #be #d #h #i #i #f #a #e #bf #d #h #aj #i #e #a #d #bg #d #h #aj #i #e #a #c #bh #d #h #aj #h #e #j #b #bi #e #h #aj #h #e #j #a #cj #e #h #aj #h #e #j #j ---------------------------------- #aa #aj #i #h #g #f ,sun's ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ,sun's ,ano4 ------------------------,ano4 ,add ---------------------------------------- ,! above titles1 ,add & ,subtract1 are "r :5 ! ,equation is appli$ to ! ,sun's mean di/ance f ! ,node2 b :5 x is appli$ to ! mean place ( ! ,node1 ! titles mu/ be *ang$4 ---------------------------------------- - ------------------------ ,,tab4 ,,xiv4 ,! ,moon's latitude 9 ,eclipses4 ------------------------ ,argum5t ( ,latit4 ----------------------- ,moon fr4 ,sig4 #j ,n4 ,a4 ! ,sig4 #f ,s4 ,d4 ,node4 ---------------------- ---------------------- #j #j #j #j #cj #a #j #e #ae #bi #b #j #aj #cj #bh #c #j #ae #dd #bg #d #j #bj #ei #bf #e #j #bf #ac #be #f #j #ca #bf #bd #g #j #cf #ci #bc #h #j #da #ea #bb #i #j #dg #b #ba #aj #j #eb #ac #bj #aa #j #eg #bc #ai #ab #a #b #ca #ah #ac #a #g #ch #ag #ad #a #ab #dd #af #ae #a #ag #di #ae #af #a #bb #eb #ad #ag #a #bg #ec #ac #ah #a #cb #ed #ab ---------------------- ,moon ,n4 ,d4 ,sig4 #e fr4 ,s4 ,a4 ,sig4 #aa ! ,node4 ----------------------- ,argum5t ( ,latit4 ------------------------ ,?is ,table ext5ds no f>!r ?an ! limits ( ,eclipses4 ,n4 ,a4 signifies ,nor? ,asc5d+ ,lat4 ,s4 ,a4 ,s\? ,asc5d+2 ,n4 ,d4 ,nor? ,desc5d+2 & ,s4 ,d4 ,s\? ,desc5d+4 ------------------------ ---------------------------------------- ---------------- ,,table ,,xv4 ,! ,moons ,horizontal ,p>allax2 ! ,semidiamet]s & true ,hor>y motions ( ! ,sun & ,moon4 ---------------------------------------- ---------------- ,anomaly ( ! ,sun & ,moon4 ---------------------------------------- -------- ,moon's ,horizontal ,p>allax4 ---------------------------------------- ,sun's ,semidiamet]4 -------------------------------- ,moon's ,semidiamet4 ------------------------ ,moon's hor>y ,mot4 ---------------- ,sun's hor>y ,mot4 --------- ,anomaly ( ! ,sun & ,moon4 ---------------------------------------- ---------- s s ---------------------------------------- ---------- #j #j #ed #ei #ae #ej #ad #ed #cj #aj #b #bc #ab #j #f #ed #ei #ae #ej #ad #ee #cj #ab #b #bc #bd #ab #ee #j #ae #ej #ad #ef #cj #ae #b #bc #ah #ah #ee #d #ae #ea #ad #eg #cj #ah #b #bc #ab #bd #ee #aa #ae #ea #ad #eh #cj #bf #b #bc #f #a #j #ee #bj #ae #eb #ad #ei #cj #cd #b #bc #aa #j #f #ee #cj #ae #ec #ae #a #cj #dd #b #bd #bd #ab #ee #dj #ac #ed #ae #d #cj #ee #b #bd #ah #ah #ee #ea #ae #ee #ae #h #ca #i #b #bd #ab #bd #ef #j #ae #ef #ae #ab #ca #bc #b #be #f #b #j #ef #aa #ae #eh #ae #ag #ca #dj #b #be #aj #j #f #ef #bd #ae #ei #ae #bb #ca #eh #b #bf #bd #ab #ef #da #af #a #ae #bf #cb #ag #b #bg #ah #ah #eg #ab #af #b #ae #cj #cb #ci #b #bg #ab #bd #eg #cj #af #d #ae #cf #cc #aa #b #bh #f #c #j #eg #di #af #f #ae #da #cc #bc #b #bh #i #j #f #eh #aj #af #h #ae #df #cc #dg #b #bi #bd #ab #eh #ca #af #i #ae #eb #cd #aa #b #bi #ah #ah #eh #eb #af #aa #ae #eh #cd #cd #b #bi #ab #bd #ei #aa #af #ac #af #c #cd #eh #b #cj #f #d #j #ei #cj #af #ad #af #i #ce #bb #b #cj #h #j #f #ei #eb #af #ae #af #ad #ce #de #b #ca #bd #ab #fj #i #af #ag #af #ai #cf #j #b #ca #ah #ah #fj #bf #af #ai #af #bd #cf #bj #b #cb #ab #bd #fj #dj #af #bj #af #bh #cf #dj #b #cb #f #e #j #fj #ed #af #ba #af #ca #cg #j #b #cb #g #j #f #fa #d #af #ba #af #cd #cg #aj #b #cc #bd #ab #fa #aa #af #bb #af #cg #cg #ai #b #cc #ah #ah #fa #af #af #bb #af #ch #cg #bh #b #cc #ab #bd #fa #bj #af #bc #af #ci #cg #cf #b #cc #f #f #j #fa #bd #af #bc #af #ci #cg #dj #b #cc #f #j ---------------------------------------- ---------- ,! gradual increase or decrease ( ! above numb]s be+ s small1 x is suffici5t to h !m to e six? degree2 ! proportions = ! int]m$iate degrees be+ easily made by sight4 ---------------------------------------- ---------------- ---------------------------------- ,,table ,,xvi4 ,! ,sun's mean ,motion & ,anomaly4 -------------------------------- ,sun's mean ,sun's ,ye>s ( ,longitude mean ,*ri/ f ,aries4 ,anomaly4 beg9n+----------------------- s s -------------------------------- ,o4,s4 #a #i #g #ec #aj #f #bi #ed #acja #i #ag #db #cj #f #af #eh #adja #i #ah #bg #ej #f #ae #ei #aeja #i #ai #ac #aj #f #ad #ei #afja #i #ai #eh #cj #f #ac #ei #agja #i #bj #dc #ej #f #ab #ei ,n4,s4 #agec #i #aj #af #eb #f #a #ch #ahja #i #i #ci #ci #f #j #aj ,old ,/yle -------------------------------- to ! ,sun's mean ,sun's beg9n+ ,ye>s ( ,motion4 mean ( ,a4 ,d4 ,*ri/ ,anomaly4 #agec2 compleat ----------------------- !n s s ,new ,/yle -------------------------------- #a #aa #bi #de #dj #aa #bi #de #b #aa #bi #ca #bj #aa #bi #bi #c #aa #bi #ag #j #aa #bi #ad #d #j #j #a #di #aa #bi #eh #e #aa #bi #dg #bi #aa #bi #db #f #aa #bi #cc #i #aa #bi #bg #g #aa #bi #ah #di #aa #bi #aa #h #j #j #c #ch #aa #bi #ee #i #aa #bi #di #ah #aa #bi #dj #aj #aa #bi #cd #eh #aa #bi #bd #aa #aa #bi #bj #ch #aa #bi #i #ab #j #j #e #bf #aa #bi #ec #ac #aa #bi #ea #g #aa #bi #cg #ad #aa #bi #cf #dg #aa #bi #bb #ae #aa #bi #bb #bg #aa #bi #g #af #j #j #g #ae #aa #bi #ej #ag #aa #bi #eb #ee #aa #bi #ce #ah #aa #bi #ch #ce #aa #bi #bj #ai #aa #bi #bd #af #aa #bi #d #bj #j #j #i #d #aa #bi #dh #dj #j #j #ah #h #aa #bi #cf #fj #j #j #bg #ab #aa #bi #bd #hj #j #j #cf #af #aa #bi #ab #ajj #j #j #de #bj #aa #bi #j #bjj #j #a #cj #dj #aa #bh #a #cjj #j #b #af #j #aa #bg #a #djj #j #c #a #bj #aa #bf #a #ejj #j #c #df #dj #aa #be #b #fjj #j #d #cb #j #aa #bd #b #gjj #j #e #ag #bj #aa #bc #b #hjj #j #f #b #dj #aa #bb #c #ijj #j #f #dh #j #aa #ba #c #ajjj #j #g #cc #bj #aa #bj #c #bjjj #j #ae #f #dj #aa #aj #g #cjjj #j #bb #dj #j #aa #j #aj #djjj #a #j #ac #bj #aj #bj #ac #ejjj #a #g #df #dj #aj #aj #af #fjjj #a #ae #bj #j #aj #j #ai -------------------------------- ,sun's mean ,sun's ,motion4 mean ,anomaly4 ,mon?s ----------------------- s s -------------------------------- ,jan4 #j #j #j #j #j #j #j ,feb4 #a #j #cc #ah #a #j #cc ,m>4 #a #bh #i #aa #a #bh #i ,apr4 #b #bh #db #cj #b #bh #db ,may4 #c #bh #af #dj #c #bh #ag ,june #d #bh #di #eh #d #bh #ej ,july #e #bh #bd #h #e #bh #bd ,aug4 #f #bh #eg #bf #f #bh #eg ,sep4 #g #bi #cj #dd #g #bi #cj ,oct4 #h #bi #d #ed #h #bi #d ,nov4 #i #bi #ch #ab #i #bi #cg ,dec4 #aj #bi #ab #bb #aj #bi #aa -------------------------------- ------------------ ,sun's mean ,motion & ,anomaly4 ,days4------------- s ------------------ #a #j #j #ei #h #b #j #a #eh #ag #c #j #b #eg #be #d #j #c #ef #cc #e #j #d #ee #db #f #j #e #ed #ej #g #j #e #ec #eh #h #j #g #ec #g #i #j #h #eb #ae #aj #j #i #ea #bc #aa #j #aj #ej #cb #ab #j #aa #di #dj #ac #j #ab #dh #dh #ad #j #ac #dg #eg #ae #j #ad #dg #e #af #j #ae #df #ac #ag #j #af #de #bb #ah #j #ag #dd #cj #ai #j #ah #dc #ch #bj #j #ai #db #dg #ba #j #bj #da #ee #bb #j #ba #da #c #bc #j #bb #dj #ab #bd #j #bc #ci #bj #be #j #bd #ch #bh #bf #j #be #cg #cg #bg #j #bf #cf #de #bh #j #bg #ce #ec #bi #j #bh #ce #b #cj #j #bi #cd #aj #ca #a #j #cc #ah ------------------ ,9 ,leap-ye>s1 aft] ,febru>y1 add "o ,day & "o ,day's motion4 ------------------- ---------------------- ,sun's mean ,motion & ,anomaly4 --------------------- ,h\rs4 ,mot4 ,ano4 --------------- --------------------- #a #j #b #bh #b #j #d #ef #c #j #g #bd #d #j #i #ea #e #j #ab #ai #f #j #ad #dg #g #j #ag #ae #h #j #ai #dc #i #j #bb #aa #aj #j #bd #ch #aa #j #bg #f #ab #j #bi #cd #ac #j #cb #b #ad #j #cd #cj #ae #j #cf #eh #af #j #ci #bf #ag #j #da #ec #ah #j #dd #ba #ai #j #df #di #bj #j #di #ag #ba #j #ea #de #bb #j #ed #ac #bc #j #ef #dj #bd #j #ei #h #be #a #a #cf #bf #a #d #d #bg #a #f #cb #bh #a #i #j #bi #a #aa #bh #cj #a #ac #ee #ca #a #af #bc #cb #a #ah #ea #cc #a #ba #ai #cd #a #bc #dg #ce #a #bf #ae #cf #a #bh #db #cg #a #ca #aj #ch #a #cc #ch #ci #a #cf #f #dj #a #ch #cd #da #a #da #b #db #a #dc #cj #dc #a #de #eg #dd #a #dh #be #de #a #ej #ec #df #a #ec #ba #dg #a #ee #di #dh #a #eh #ag #di #b #j #dd #ej #b #c #ab #ea #b #e #dj #eb #b #h #h #ec #b #aj #cf #ed #b #ac #d #ee #b #ae #cb #ef #b #ag #ei #eg #b #bj #bg #eh #b #bb #ee #ei #b #be #bc #fj #b #bg #ea --------------------- ,9 ,leap-ye>s1 aft] ,febru>y1 add "o ,day & "o ,day's motion4 ---------------------- ---------------------------------------- ------ ,,table ,,xvii4 ,! ,sun's ,decl9ation 9 e ,degree ( ! ,ecliptic4 ---------------------------------------- -- ,signs #j #f #a #g #b #h ,nor4 ,s\4 ,nor4 ,s\4 ,nor4 ,s\4 ---------------------------------------- -- ---------------------------------------- -- #j #j #j #j #aa #bi #cc #bj #aa #af #cj #a #j #bc #ed #aa #ej #ce #bj #bc #di #bi #b #j #dg #dh #ab #aa #bf #bj #cf #j #bh #c #a #aa #db #ab #cb #e #bj #dg #dh #bg #d #a #ce #cd #ab #eb #ca #bj #ei #ac #bf #e #a #ei #be #ac #ab #dd #ba #aj #ae #be #f #b #bc #ad #ac #cb #ed #ba #bj #ec #bd #g #b #dg #a #ac #eb #cb #ba #ca #g #bc #h #c #aj #de #ad #ab #e #ba #dj #eh #bb #i #c #cd #bf #ad #ca #bd #ba #ej #bd #ba #aj #c #eh #d #ad #ej #bh #ba #ei #be #bj #aa #d #ba #ch #ae #i #ag #bb #h #b #ai #ab #d #de #h #ae #bg #ea #bb #af #ad #ah #ac #e #h #cd #ae #df #i #bb #bd #j #ag #ad #e #ca #ee #af #d #aa #bb #ca #ba #af #ae #e #ee #aa #af #ba #eg #bb #ch #af #ae #af #f #ah #ba #af #ci #bf #bb #dd #de #ad #ag #f #da #be #af #ef #cg #bb #ej #di #ac #ah #g #d #bc #ag #ac #ca #bb #ef #bf #ab #ai #g #bg #ae #ag #cj #g #bc #a #cf #aa #bj #g #ej #j #ag #df #ae #bc #f #bj #aj #ba #h #ab #cf #ah #b #bd #bc #aj #ch #i #bb #h #ce #e #ah #ah #c #bc #ad #bi #h #bc #h #eg #bf #ah #cc #bd #bc #ag #eb #g #bd #i #ai #ci #ah #dh #be #bc #bj #di #f #be #i #da #dc #ai #c #e #bc #bc #ai #e #bf #aj #c #cg #ai #ag #bf #bc #be #bb #d #bg #aj #be #ba #ai #ca #be #bc #bf #eg #c #bh #aj #df #ef #ai #de #c #bc #bh #e #b #bi #aa #h #bj #ai #eh #bj #bc #bh #df #a #cj #aa #bi #cc #bj #aa #af #bc #bi #j #j ---------------------------------------- -- ,signs #a #e #aj #d #i #c ,s\4 ,nor4 ,s\4 ,nor4 ,s\4 ,nor4 ---------------------------------------- -- ,if ! ,sun's place be tak5 f ! ,tables on pag4 #aad & #aae1 8 decl9ation may be _h !reby1 ne> en\gh = common use1 f ?is ,table1 by ent]+ x ) ! signs at ! head & degrees at ! left h&2 or ) ! signs at ! foot & degrees at ! "r h&4 ,?us1 ,m>* ! #e?1 ! ,sun's place is #ad #ec 7call x #ae1 be+ s ne>7 to :i* answ]s #e #ee #aa ( ! s\? decl9ation4 ---------------------------------------- ----- --------------------------------- ,,table ,,xviii4 ,lunations f #a to #ajjjjj4 ----------------------------- ,lunat4 ,days4 ,h4 ,m4 ,s4 ----------------------------- ,conta9 #a #bi #ab #dd #c #b #ei #a #bh #f #c #hh #ad #ab #i #d #aah #b #ef #ac #e #adg #ae #dj #af ----------------------------- #f #agg #d #bd #ai #g #bjf #ag #h #bb #h #bcf #e #eb #be #i #bfe #ah #cf #bh #aj #bie #g #bj #ca ----------------------------- #bj #eij #ad #da #c #cj #hhe #bb #a #cd #dj #aaha #e #bb #f #ej #adgf #ab #db #cg #fj #agga #bj #c #i ----------------------------- #gj #bjfg #c #bc #dj #hj #bcfb #aj #dd #ab #ij #bfeg #ah #d #dc #ajj #biec #a #be #ae #bjj #eijf #b #ej #cj ----------------------------- #cjj #hhei #d #ae #de #djj #aahab #e #da #j #ejj #adgfe #g #f #ae #fjj #aggah #h #ca #cj #gjj #bjfga #i #ef #de ----------------------------- #hjj #bcfbd #aa #bb #j #ijj #bfegg #ab #dg #ae #ajjj #biecj #ad #ab #cj #bjjj #eijfa #d #be #j #cjjj #hheia #ah #cg #cj ----------------------------- #djjj #aahabb #h #ej #j #ejjj #adgfeb #bc #b #cj #fjjj #aggahc #ac #ae #j #gjjj #bjfgad #c #bg #cj #hjjj #bcfbdd #ag #dj #j ----------------------------- #ijjj #bfegge #g #eb #cj #ajjjj #biecje #bb #e #bjjjj #eijfaa #bj #aj #cjjjj #hheiag #ah #ae #djjjj #aahabbc #af #bj ----------------------------- #ejjjj #adgfebi #ad #be #fjjjj #aggahce #ab #cj #gjjjj #bjfgada #aj #ce #hjjjj #bcfbddg #h #dj #ijjjj #bfeggec #f #de #ajjjjj #biecjei #d #ej ----------------------------- ,by comp>+ ?is ,table ) ! ,table on page #aac1 x is easy to f9d h[ _m ,lunations are conta9$ 9 any giv5 numb] ( ,sid]eal1 ,julian1 & ,sol> ye>s1 f #a to #hjjj4 --------------------------------- ,,*ap4 ,,xx4 ,( ! fix$ ,/>s4 ,sid5ote3 ,:y ! fix$ ,/>s appe> bigg] :5 view$ by ! b>e eye ?an :5 se5 ?r\gh a telescope4 #cia4 ,! ,/>s are said to be fix$1 because !y h be5 g5]ally obs]v$ to keep at ! same di/ance f ea* o!r3 _! app>5t diurnal revolutions be+ caus$ solely by ! ,e>?'s turn+ on its ,axis4 ,!y appe> ( a s5sible magnitude to ! b>e eye1 because ! ret9a is affect$ n only by ! rays ( light :i* are emitt$ directly f !m1 b by _m ?\s&s m1 :i* fall+ ^u our eye-lids1 & ^u ! a]ial p>ticles ab\t u1 are reflect$ into our eyes s /rongly z to excite vibrations n only 9 ^? po9ts ( ! ret9a :]e ! real images ( ! ,/>s are =m$1 b also 9 o!r po9ts at "s di/ance r\nd ab\t4 ,?is makes u imag9e ! ,/>s to be mu* bigg] ?an !y w\ld appe>1 if we saw !m only by ! few rays :i* come directly f !m1 s z to ent] our eyes )\t be+ int]mix$ ) o!rs4 ,any "o may be s5sible ( ?is1 by look+ at a ,/> ( ! fir/ ,magnitude ?r\gh a long n>r[ tube2 :i*1 ?\gh x takes 9 z mu* ( ! sky z w\ld hold a ?\s& su* ,/>s1 yet sc>ce r5d]s t "o visible4 ,sid5ote3 ,a pro( t !y %9e by _! own light4 ,! m a telescope magnifies1 ! less is ! ap]ture ?r\gh :i* ! ,/> is se52 & consequ5tly ! few] rays x admits into ! eye4 ,n[ s9ce ! ,/>s appe> less 9 a telescope :i* magnifies #bjj times ?an !y d to ! b>e eye1 insomu* t !y seem to be only indivisible po9ts1 x proves at once bo? t ! ,/>s are at imm5se di/ances f u1 & t !y %9e by _! own prop] light4 ,if !y %one by borr[$ light !y w\ld be z invisible )\t telescopes z ! ,satellites ( ,jupit] are3 = ^! ,satellites appe> bigg] :5 view$ ) a good telescope ?an ! l>ge/ fix$ ,/>s d4 ,sid5ote3 ,_! numb] mu* less ?an is g5]ally imag9$4 #cib4 ,! numb] ( ,/>s discov]able1 9 ei!r ,hemisph]e1 by ! nak$ eye1 is n above a ?\s&4 ,?is at fir/ may appe> incr$ible1 because !y seem to be )\t numb]3 ,b ! deception arises f our look+ confus$ly ^u !m1 )\t r$uc+ !m into any ord]4 ,= look b /$fa/ly ^u a pretty l>ge portion ( ! sky1 & c\nt ! numb] ( ,/>s 9 x1 y w be surpris$ to f9d !m s few4 ,or1 if "o consid]s h[ seldom ! ,moon meets ) any ,/>s 9 h] way1 al?\gh !re are z _m ab\t h] ,pa? z 9 o!r p>ts ( ! ,heav5s 7! ,milky way except$7 he w soon be conv9c$ t ! ,/>s are mu* ?9n] s[n ?an he 0 aw>e (4 ,! ,briti% catalogue1 :i*1 besides ! ,/>s visible to ! b>e eye1 includes a great numb] :i* _c be se5 )\t ! assi/ance ( a telescope1 conta9s no m ?an #cjjj1 9 bo? ,hemisph]es4 ,sid5ote3 ,! absurdity ( suppos+ ! ,/>s 7 made only to enlight5 our nights4 #cic4 ,z we h incomp>ably m light f ! ,moon ?an f all ! ,/>s toge!r1 x 7 ! greate/ absurdity to imag9e t ! ,/>s 7 made = no o!r purpose ?an to ca/ a fa9t light ^u ! ,e>?3 especially s9ce _m m require ! assi/ance ( a good telescope to f9d !m out1 ?an are visible )\t t ,in/rum5t4 ,our ,sun is surr\nd$ by a sy/em ( ,planets & ,comets2 all :i* w\ld be invisible f ! ne>e/ fix$ ,/>4 ,& f :at we already "k ( ! imm5se di/ance ( ! ,/>s1 ! ne>e/ may be comput$ at #cb1jjj1jjj1jjj1jjj ( miles f u :i* is m ?an a cannon bullet w\ld fly 9 #g1jjj1jjj ( ye>s4 ,h5ce 'tis easy to prove1 t ! ,sun se5 f su* a di/ance1 w\ld appe> no bigg] ?an a ,/> ( ! fir/ magnitude4 ,f all ?is x is highly probable t ea* ,/> is a ,sun to a sy/em ( worlds mov+ r\nd x ?\gh unse5 by u2 especially1 z ! doctr9e ( a plurality ( worlds is rational1 & greatly manife/s ! ,p[]1 ,wisdom1 & ,goodness ( ! great ,creator4 ,sid5ote3 ,_! diff]5t ,magnitudes4 #cid4 ,! ,/>s1 on acc\nt ( _! app>5tly v>i\s magnitudes1 h be5 di/ribut$ into sev]al classes or ord]s4 ,^? :i* appe> l>ge/ are call$ ,/>s ( ! fir/ magnitude2 ! next to !m 9 lu/re1 ,/>s ( ! second magnitude1 & s on to ! six?1 :i* are ! smalle/ t are visible to ! b>e eye4 ,?is di/ribution hav+ be5 made long be=e ! inv5tion ( telescopes1 ! ,/>s :i* _c be se5 )\t ! assi/ance ( ^! in/rum5ts are di/+ui%$ by ! "n ( ,telescopic ,/>s4 ,sid5ote3 ,& division into ,con/ellations4 #cie4 ,! anti5ts divid$ ! />ry ,sph]e into p>ticul> ,con/ellations1 or ,sy/ems ( ,/>s1 accord+ z !y lay ne> "o ano!r1 s z to occupy ^? spaces :i* ! figures ( diff]5t sorts ( animals or ?+s w\ld take up1 if !y 7 !re del9eat$4 ,& ^? ,/>s :i* c\ld n be br\ght into any p>ticul> ,con/ellation 7 call$ un=m$ ,/>s4 ,sid5ote3 ,! use ( ?is division4 #cif4 ,?is division ( ! ,/>s into diff]5t ,con/ellations or ,a/]isms1 s]ves to di/+ui% !m f "o ano!r1 s t any p>ticul> ,/> may be readily f\nd 9 ! ,heav5s by means ( a ,cele/ial ,globe2 on :i* ! ,con/ellations are s del9eat$ z to put ! mo/ rem>kable ,/>s into su* p>ts ( ! figures z are mo/ easily di/+ui%$4 ,! numb] ( ! anti5t ,con/ellations is #dh1 & ^u our pres5t ,globes ab\t #gj4 ,on ,s5ex's ,globes are ins]t$ ,bay]'s ,lett]s2 ! fir/ 9 ! ,greek ,alphabet be+ put to ! bigge/ ,/> 9 ea* ,con/ellation1 ! second to ! next1 & s on3 by :i* means1 e ,/> is z easily f\nd z if a "n 7 giv5 to x4 ,?us1 if ! ,/> 9 ! ,con/ellation ( ! ,ram be m5tion$1 e ,a/ronom] kn[s z well :at ,/> is meant z if x 7 po9t$ out to him 9 ! ,heav5s4 ,sid5ote3 ,! ,zodiac4 #cig4 ,!re is also a division ( ! ,heav5s into ?ree p>ts4 #a4 ,! ,zodiac1 77 f ,zodion an ,animal1 because mo/ ( ! ,con/ellations 9 x1 :i* are twelve 9 numb]1 are ! figures ( ,animals3 z ,aries ! ,ram1 ,taurus ! ,bull1 ,gem9i ! ,tw9s1 ,canc] ! ,crab1 ,leo ! ,lion1 ,virgo ! ,virg91 ,libra ! ,balance1 ,scorpio ! ,scorpion1 ,sagitt>ius ! ,ar*]1 ,capricornus ! ,goat1 ,aqu>ius ! ,wat]-be>]1 & ,pisces ! ,fi%es4 ,! ,zodiac goes q r\nd ! ,heav5s3 x is ab\t #af degrees broad1 s t x takes 9 ! ,orbits ( all ! ,planets1 & likewise ! ,orbit ( ! ,moon4 ,along ! middle ( ?is ,zone or ,belt is ! ,ecliptic1 or ,circle :i* ! ,e>? describes annually z se5 f ! ,sun2 & :i* ! ,sun appe>s to describe z se5 f ! ,e>?4 #b4 ,all t ,region ( ! ,heav5s1 :i* is on ! nor? side ( ! ,zodiac1 conta9+ #ba ,con/ellations4 ,& #c4 t on ! s\? side1 conta9+ #ae4 ,sid5ote3 ,! mann] ( divid+ x by ! anti5ts4 #cih4 ,! anti5ts divid$ ! ,zodiac into ! above #ab ,con/ellations or ,signs 9 ! foll[+ mann]4 ,!y took a vessel ) a small hole 9 ! bottom1 & hav+ fill$ x ) wat]1 suff]$ ! same to di/il drop by drop into ano!r ,vessel set b5ea? to receive x2 beg9n+ at ! mom5t :5 "s ,/> rose1 & cont9u+ until x rose ! next foll[+ night4 ,! wat] fall5 d[n into ! receiv] !y divid$ into twelve equal p>ts2 & hav+ two o!r small vessels 9 read9ess1 ea* ( !m fit to conta9 "o "p1 !y aga9 p\r$ all ! wat] into ! upp] vessel1 & /rictly obs]v+ ! ris+ ( "s ,/> 9 ! ,zodiac1 !y at ! same "t suff]$ ! wat] to drop into "o ( ! small vessels2 & z soon z x 0 full1 !y %ift$ x & set an empty "o 9 x's place4 ,by ?is means1 :5 ea* vessel 0 full1 !y obs]v$ :at ,/> ( ! ,zodiac rose2 & ?\gh n possible 9 "o night1 yet 9 _m1 !y obs]v$ ! ris+ ( twelve ,/>s1 by :i* !y divid$ ! ,zodiac into twelve p>ts4 #cii4 ,! names ( ! ,con/ellations1 & ! numb] ( ,/>s obs]v$ 9 ea* ( !m by diff]5t ,a/ronom]s1 are z foll[s4 ,key to table ,p ,ptolemy4 ,t ,ty*o4 ,h ,hevelius4 ,f ,flam/e$4 ,! anti5t ,con/ellations4 ,p ,t ,h ,f ,ursa m9or ,! ,little ,be> #h #g #ab #bd ,ursa major ,! ,great ,be> #ce #bi #gc #hg ,draco ,! ,dragon #ca #cb #dj #hj ,cepheus ,cepheus #ac #d #ea #ce ,bootes1 ,arctophilax #bc #ah #eb #ed ,corona ,borealis ,! nor!rn ,cr[n #h #h #h #ba ,h]cules1 ,engonas9 ,h]cules kneel+ #bi #bh #de #aac ,lyra ,! ,h>p #aj #aa #ag #ba ,cygnus1 ,gall9a ,! ,swan #ai #ah #dg #ha ,cassiopea ,! ,lady 9 h] ,*air #ac #bf #cg #ee ,p]seus ,p]seus #bi #bi #df #ei ,auriga ,! ,waggon] #ad #i #dj #ff ,s]p5t>ius1 ,ophiu*us ,s]p5t>ius #bi #ae #dj #gd ,s]p5s ,! ,s]p5t #ah #ac #bb #fd ,sagitta ,! ,arr[ #e #e #e #ah ,aquila1 ,vultur ,! ,eagle #ab #bc #ae #ga ,ant9\s ,ant9\s #c #ai ,delph9us ,! ,dolph9 #aj #aj #ad #ah ,equulus1 ,equi sectio ,! ,horse's ,head #d #d #f #aj ,pegasus1 ,equus ,! ,fly+ ,horse #bj #ai #ch #hi ,&rom$a ,&rom$a #bc #bc #dg #ff ,triangulum ,! ,triangle #d #d #ab #af ,aries ,! ,ram #ah #ba #bg #ff ,taurus ,! ,bull #dd #dc #ea #ada ,gem9i ,! ,tw9s #be #be #ch #he ,canc] ,! ,crab #bc #ae #bi #hc ,leo ,! ,lion #cj #di #ie #ce ,coma ,b]5ices ,b]5ice's ,hair #ad #ba #dc ,virgo ,! ,virg9 #cb #cc #ej #aaj ,libra1 ,*el ,! ,scales #ag #aj #bj #ea ,scorpius ,! ,scorpion #bd #aj #bj #dd ,sagitt>ius ,! ,ar*] #ca #ad #bb #fi ,capricornus ,! ,goat #bh #bh #bi #ea ,aqu>ius ,! ,wat]-be>] #de #da #dg #ajh ,pisces ,! ,fi%es #ch #cf #ci #aac ,cetus ,! ,:ale #bb #ba #de #ig ,orion ,orion #ch #db #fb #gh ,eridanus1 ,fluvius ,eridanus1 ! ,riv] #cd #aj #bg #hd ,lepus ,! ,h>e #ab #ac #af #ai ,canis major ,! ,great ,dog #bi #ac #ba #ca ,canis m9or ,! ,little ,dog #b #b #ac #ad ,argo ,navis ,! ,%ip #de #c #d #fd ,hydra ,! ,hydra #bg #ai #ca #fj ,crat] ,! ,cup #g #c #aj #ca ,corvus ,! ,cr[ #g #d #i ,c5taurus ,! ,c5taur #cg #ce ,lupus ,! ,wolf #ai #bd ,ara ,! ,alt> #g #i ,corona ,au/ralis ,! s\!rn ,cr[n #ac #ab ,pisces ,au/ralis ,! s\!rn ,fi% #ah #bd ,! ,new ,s\!rn ,con/ellations4 ,columba ,noa*i ,noah's ,dove #aj ,robur ,c>ol9um ,! ,royal ,oak #ab ,grus ,! ,crane #ac ,phnix ,! ,ph5ix #ac ,indus ,! ,indian #ab ,pavo ,! ,peacock #ad ,apus1 ,avis ,indica ,! ,bird ( ,p>adise #aa ,apis1 ,musca ,! ,bee or ,fly #d ,*amleon ,! ,*ameleon #aj ,triangulum ,au/ralis ,! ,s\? ,triangle #e ,piscis volans1 ,pass] ,! ,fly+ ,fi% #h ,dorado1 ,xiphias ,! ,sword ,fi% #f ,t\can ,! ,am]ican ,goose #i ,hydrus ,! ,wat] ,snake #aj ,hevelius's ,con/ellations made out ( ! un=m$ ,/>s4 ,hevelius4 ,flam/e$4 ,lynx ,! ,lynx #ai #dd ,leo m9or ,! ,little ,lion #ec ,a/]ion ,*>a ,! ,greyh\nds #bc #be ,c]b]us ,c]b]us #d ,vulpecula ,ans] ,! ,fox & ,goose #bg #ce ,scutum ,sobieski ,sobieski's ,%ield #g ,lac]ta ,! ,liz>d #aj #af ,camelop>dalus ,! ,camelop>d #cb #eh ,monoc]os ,! ,unicorn #ai #ca ,sextans ,! ,sextant #aa #da ,sid5ote3 ,! ,milky ,way4 #djj4 ,!re is a rem>kable track r\nd ! ,heav5s1 call$ ! ,milky ,way f its peculi> :it5ess1 :i* is ow+ to a great numb] ( ,/>s scatt]$ !re92 none ( :i* c be di/9ctly se5 )\t telescopes4 ,?is track appe>s s+le 9 "s p>ts1 9 o!rs d\ble4 ,sid5ote3 ,lucid ,spots4 #dja4 ,!re are sev]al little :iti% spots 9 ! ,heav5s1 :i* appe> magnifi$1 & m lum9\s :5 se5 ?r\gh telescopes2 yet )\t any ,/>s 9 !m4 ,"o ( ^! is 9 ,&rom$a's girdle1 fir/ obs]v$ ,a4 ,d4 #afab1 by ,simon ,m>ius2 & :i* has "s :iti% rays ne> its middle3 x is liable to sev]al *anges1 & is sometimes invisible4 ,ano!r is ne> ! ,ecliptic1 betwe5 ! head & b[ ( ,sagitt>ius3 x is small1 b v lum9\s4 ,a ?ird is on ! back ( ! ,c5taur1 :i* is too f> ,s\? to be se5 9 ,brita94 ,a f\r?1 ( a small] size1 is be=e ,ant9\s's "r foot2 hav+ a ,/> 9 x1 :i* makes x appe> m bright4 ,a fif? is 9 ! ,con/ellation ( ,h]cules1 betwe5 ! ,/>s & 1 :i* spot1 ?\gh b small1 is visible to ! b>e eye if ! sky be cle> & ! ,moon abs5t4 ,sid5ote3 ,cl\dy ,/>s4 ,magellanic ,cl\ds4 #djb4 ,cl\dy ,/>s are s call$ f _! mi/y appe>ance4 ,!y look l dim ,/>s to ! nak$ eye2 b ?r\gh a telescope !y appe> broad illum9at$ p>ts ( ! sky2 9 "s ( :i* is "o ,/>1 9 o!rs m4 ,five ( ^! are m5tion$ by ,ptolemy4 #a4 ,"o at ! extremity ( ! "r h& ( ,p]seus4 #b4 ,"o 9 ! middle ( ! ,crab4 #c4 ,"o un=m$1 ne> ! ,/+ ( ! ,scorpion4 #d4 ,! eye ( ,sagitt>ius4 #e4 ,"o 9 ! head ( ,orion4 ,9 ! fir/ ( ^! appe> m ,/>s ?r\gh ! telescope ?an 9 any ( ! re/1 al?\gh #ba h be5 c\nt$ 9 ! head ( ,orion1 & above #dj 9 t ( ! ,crab4 ,two are visible 9 ! eye ( ,sagitt>ius )\t a telescope1 & sev]al m ) x4 ,flam/e$ obs]v$ a cl\dy ,/> 9 ! b[ ( ,sagitt>ius1 conta9+ _m small ,/>s3 & ! ,/> d above ,sagitt>y's "r %\ld] is encompass$ ) sev]al m4 ,bo? ,cass9i & ,flam/e$ discov]$ "o betwe5 ! ,great & ,little ,dog1 :i* is v full ( ,/>s visible only by ! telescope4 ,! two :iti% spots ne> ! ,s\? ,pole1 call$ ! ,magellanic ,cl\ds by ,sailors1 :i* to ! b>e eye resemble "p ( ! ,milky-,way1 appe> ?r\gh telescopes to be a mixture ( small ,cl\ds & ,/>s4 ,b ! mo/ rem>kable ( all ! cl\dy ,/>s is t 9 ! middle ( ,orion's ,sword1 :]e sev5 ,/>s 7( :i* ?ree are v close toge!r7 seem to %9e ?r\gh a cl\d1 v lucid ne> ! middle1 b fa9t & ill def9$ ab\t ! edges4 ,x looks l a gap 9 ! sky1 ?r\gh :i* "o may see 7z x 77 "p ( a mu* bright] region4 ,al?\gh mo/ ( ^! spaces are b a few m9utes ( a degree 9 bread?1 yet1 s9ce !y are among ! fix$ ,/>s1 !y mu/ be spaces l>g] ?an :at is occupi$ by our sol> ,sy/em2 & 9 :i* !re seems to be a p]petual un9t]rupt$ day among numb]less ,worlds :i* no human art ev] c discov]4 ,sid5ote3 ,*anges 9 ! ,heav5s4 #djc4 ,sev]al ,/>s are m5tion$ by anti5t ,a/ronom]s1 :i* are n n[ to be f\nd2 & o!rs are n[ visible to ! b>e eye :i* are n record$ 9 ! anti5t catalogues4 ,hipp>*us obs]v$ a new ,/> ab\t #abj ye>s be=e ,,*ri/2 b he has n m5tion$ 9 :at "p ( ! ,heav5s x 0 se51 al?\gh x occasion$ 8 mak+ a catalogue ( ! ,/>s2 :i* is ! mo/ anti5t t we h4 ,sid5ote3 ,new ,/>s4 ,! fir/ ,new ,/> t we h any good acc\nt (1 0 discov]$ by ,cornelius ,gemma on ! #h? ( ,novemb] ,a4 ,d4 #aegb1 9 ! ,*air ( ,cassiopea4 ,x surpass$ ,sirius 9 brightness & magnitude2 & 0 se5 = #af mon?s successively4 ,at fir/ x appe>$ bigg] ?an ,jupit] to "s eyes1 by :i* x 0 se5 ev5 at mid-day3 aft]w>ds x decay$ gradually bo? 9 magnitude & lu/re1 until ,m>* #aegc1 :5 x became invisible4 ,on ! #ac? ( ,augu/ #aeif1 ,david ,fabricius obs]v$ ! ,/ella ,mira1 or wond]ful ,/>1 9 ! ,neck ( ! ,:ale2 :i* has be5 s9ce f\nd to appe> & disappe> p]iodically1 sev5 times 9 six ye>s1 cont9u+ 9 its greate/ lu/re = #ae days toge!r2 & is nev] q ext+ui%$4 ,9 ! ye> #afjj1 ,william ,jans5ius discov]$ a *angeable ,/> 9 ! ,neck ( ! ,swan2 :i*1 9 "t became s small z to be ?\ght to disappe> entirely1 till ! ye>s #afeg1 #afeh1 & #afei1 :5 x recov]$ its =m] lu/re & magnitude2 b soon decay$1 & is n[ ( ! smalle/ size4 ,9 ! ye> #afjd ,kepl] & sev]al ( 8 fri5ds saw a new ,/> ne> ! heel ( ! "r foot ( ,s]p5t>ius1 s bright & sp>kl+ t x exce$$ any ?+ !y _h ev] se5 be=e2 & took notice t x 0 e mom5t *ang+ into "s ( ! col\rs ( ! ra9b[1 except :5 x 0 ne> ! horizon1 at :i* "t x 0 g5]ally :ite4 ,x surpass$ ,jupit] 9 magnitude1 :i* 0 ne> x all ! mon? ( ,octob]1 b easily di/+ui%$ f x by a /eady light4 ,x disappe>$ betwe5 ,octob] #afje & ! ,febru>y foll[+1 & has n be5 se5 s9ce t "t4 ,9 ! ye> #afgj1 ,july #ae1 ,hevelius discov]$ a new ,/>1 :i* 9 ,octob] 0 s decay$ z to be sc>ce p]ceptible4 ,9 ,april foll[+ x rega9$ its lu/re1 b :olly disappe>$ 9 ,augu/4 ,9 ,m>* #afgb x 0 se5 aga91 b v small2 & has n be5 visible s9ce4 ,9 ! ye> #afhf a new ,/> 0 discov]$ by ,kir*1 :i* returns p]iodically 9 #djd days4 ,9 ! ye> #afgb1 ,cass9i saw a ,/> 9 ! ,neck ( ! ,bull1 :i* he ?\ght 0 n visible 9 ,ty*o's "t2 nor :5 ,bay] made 8 ,figures4 ,sid5ote3 ,_c be ,comets4 #djd4 ,_m ,/>s1 besides ^? above-m5tion$1 h be5 obs]v$ to *ange _! magnitudes3 & z none ( !m c\ld ev] be p]ceiv$ to h tails1 'tis pla9 !y c\ld n be ,comets2 especially z !y _h no p>allax1 ev5 :5 l>ge/ & brighte/4 ,x w\ld seem t ! p]iodical ,/>s h va/ clu/]s ( d>k spots1 & v sl[ rotations on _! ,axis2 by :i* means1 !y mu/ disappe> :5 ! side cov]$ ) spots is turn$ t[>ds u4 ,& z = ^? :i* break out all ( a sudd5 ) su* lu/re1 'tis by no means improbable t !y are ,suns ^: ,fuel is almo/ sp5t1 & aga9 suppli$ by "s ( _! ,comets fall+ ^u !m1 & occasion+ an uncommon blaze & spl5dor = "s "t3 :i* inde$ appe>s to be ! greate/ use ( ! comet>y "p ( any sy/em#hf4 ,sid5ote3 ,"s ,/>s *ange _! ,places4 ,"s ( ! ,/>s1 p>ticul>ly ,arcturus1 h be5 obs]v$ to *ange _! places above a m9ute ( a degree ) respect to o!rs4 ,b :e!r ?is be ow+ to any real motion 9 ! ,/>s !mselves1 mu/ require ! obs]vations ( _m ages to det]m9e4 ,if our sol> ,sy/em *ange? its ,place1 ) reg>d to absolute space1 ?is mu/ 9 process ( "t occasion an app>5t *ange 9 ! di/ances ( ! ,/>s f ea* o!r3 & 9 su* a case1 ! places ( ! ne>e/ ,/>s to u be+ m affect$ ?an ( ^? :i* are v remote1 _! relative positions mu/ seem to alt]1 ?\gh ! ,/>s !mselves 7 really immoveable4 ,on ! o!r h&1 if our own sy/em be at re/1 & any ( ! ,/>s 9 real motion1 ?is mu/ v>y _! positions2 & ! m s1 ! ne>] !y are to u1 or ! swift] _! motions are2 or ! m prop] ! direction ( _! motion is1 = our p]ception4 ,sid5ote3 ,! ,ecliptic less oblique n[ to ! ,equator ?an =m]ly4 #dje4 ,! obliquity ( ! ,ecliptic to ! ,equ9octial is f\nd at pres5t to be above a ?ird "p ( a degree less ?an ,ptolemy f\nd x4 ,& mo/ ( ! obs]v]s aft] him f\nd x to decrease gradually d[n to ,ty*o's "t4 ,if x be object$1 t we _c dep5d on ! obs]vations ( ! anti5ts1 because ( ! incorrectness ( _! ,in/rum5ts2 we h to answ]1 t bo? ,ty*o & ,flam/e$ are all[$ to h be5 v good obs]v]s3 & yet we f9d t ,flam/e$ makes ?is obliquely #b-a_/b m9utes ( a degree less ?an ,ty*o did1 ab\t #ajj ye>s be=e him3 & z ,ptolemy 0 #acbd ye>s be=e ,ty*o1 s ! gradual decrease answ]s ne>ly to ! diff]5ce ( "t betwe5 ^! ?ree ,a/ronom]s4 ,if we consid]1 t ! ,e>? is n a p]fect sph]e1 b an oblate sph]oid1 hav+ its ,axis %ort] ?an its ,equatoreal diamet]2 & t ! ,sun & ,moon are con/antly act+ obliquely ^u ! great] quantity ( matt] ab\t ! ,equator1 pull+ x1 z x 71 t[>ds a ne>] & ne>] co-incid5ce ) ! ,ecliptic2 x w n appe> improbable t ^! actions %\ld gradually dim9i% ! ,angle betwe5 ^? ,planes4 ,nor is x less probable t ! mutual attractions ( all ! ,planets %\ld h a t5d5cy to br+ ! planes ( all _! ,orbits to a co-incid5ce3 b ?is *ange is too small to become s5sible 9 _m ages4 ,,*ap4 ,,xxi4 ,( ! ,division ( ,"t4 ,a p]petual ,table ( ,new ,moons4 ,! ,times ( ! ,bir? & ,dea? ( ,,*ri/4 ,a ,table ( rem>kable ras or ,ev5ts4 #djf4 ,! p>ts ( "t are ,seconds1 ,m9utes1 ,h\rs1 ,days1 ,ye>s1 ,cycles1 ,ages1 & ,p]iods4 ,sid5ote3 ,a ,ye>4 #djg4 ,! orig9al /&>d1 or integral measure ( ,"t1 is a ye>2 :i* is det]m9$ by ! ,revolution ( "s ,cele/ial ,body 9 its ,orbit1 viz4 ! ,sun or ,moon4 ,sid5ote3 ,tropical ,ye>4 #djh4 ,! "t measur$ by ! ,sun's ,revolution 9 ! ,ecliptic1 f any ,equ9ox or ,sol/ice to ! same aga91 is call$ ! ,sol> or ,tropical ,ye>1 :i* conta9s #cfe days #e h\rs #dh m9utes #eg seconds2 & is ! only prop] or natural ye>1 because x always keeps ! same seasons to ! same mon?s4 ,sid5ote3 ,sid]eal ye>4 #dji4 ,! quantity ( "t1 measur$ by ! ,sun's ,revolution1 z f any fix$ ,/> to ! same ,/> aga91 is call$ ! ,sid]eal ,ye>2 :i* conta9s #cfe days #f h\rs #i m9utes #ad-a_/b seconds2 & is #bj m9utes #ag-a_/b seconds long] ?an ! true ,sol> ,ye>4 ,sid5ote3 ,lun> ,ye>4 #daj4 ,! "t measur$ by twelve ,revolutions ( ! ,moon1 f ! ,sun to ! ,sun aga91 is call$ ! ,lun> ,ye>2 x conta9s #ced days #h h\rs #dh m9utes #cg seconds2 & is !re=e #aj days #ba h\rs #j m9utes #bj seconds %ort] ?an ! ,sol> ,ye>4 ,?is is ! f\ndation ( ! ,epact4 ,sid5ote3 ,civil ,ye>4 #daa4 ,! ,civil ,ye> is t :i* is 9 common use among ! diff]5t nations ( ! _w2 ( :i*1 "s reckon by ! ,lun>1 b mo/ by ! ,sol>4 ,! ,civil ,sol> ,ye> conta9s #cfe days1 = ?ree ye>s runn+1 :i* are call$ ,common ,ye>s2 & !n comes 9 :at is call$ ! ,bissextile or ,leap-,ye>1 :i* conta9s #cff days4 ,?is is also call$ ! ,julian ,ye> on acc\nt ( ,julius ,cs>1 :o appo9t$ ! ,int]cal>y-day e f\r? ye>1 ?9k+ !reby to make ! ,civil & ,sol> ,ye> keep pace toge!r4 ,& ?is day1 be+ add$ to ! #bc;d ( ,febru>y1 :i* 9 ! ,roman ,cal5d>1 0 ! six? ( ! ,cal5ds ( ,m>*1 t six? day 0 twice reckon$1 or ! #bc;d & #bd? 7 reckon$ z "o day2 & 0 call$ ,bis sextus dies1 & !nce came ! "n ,bissextile = t ye>4 ,b 9 our common ,almanacks ?is day is add$ at ! end ( ,febru>y4 ,sid5ote3 ,lun> ,ye>4 #dab4 ,! ,civil ,lun> ,ye> is also common or int]cal>y4 ,! common ,ye> consi/s ( #ab ,lunations1 :i* conta9 #ced days2 at ! end ( :i*1 ! ye> beg9s aga94 ,! ,int]cal>y1 or ,embolimic ,ye> is t :]e9 a mon? 0 add$1 to adju/ ! ,lun> ,ye> to ! ,sol>4 ,?is me?od 0 us$ by ! ,jews1 :o kept _! acc\nt by ! ,lun> ,motions4 ,b by int]calat+ no m ?an a mon? ( #cj days1 :i* !y call$ ,ve-,ad>1 e ?ird ye>1 !y fell #c-c_/d days %ort ( ! ,sol> ,ye> 9 t "t4 ,sid5ote3 ,roman ,ye>4 #dac4 ,! ,romans also us$ ! ,lun> ,embolimic ,ye> at fir/1 z x 0 settl$ by ,romulus _! fir/ ,k+1 :o made x to consi/ only ( t5 mon?s or ,lunations2 :i* fell #fa days %ort ( ! ,sol> ,ye>1 & s _! ye> became q vague & unfix$2 = :i* reason1 !y 7 =c$ to h a ,table publi%$ by ! ,high ,prie/1 to in=m !m :5 ! spr+ & o!r seasons began4 ,b ,julius ,cs>1 z already m5tion$1 #daa1 tak+ ?is tr\blesome affair into consid]ation1 re=m$ ! ,cal5d>1 by mak+ ! ye> to consi/ ( #cfe days #f h\rs4 ,sid5ote3 ,! orig9al ( ! ,gregorian1 or ,new ,/yle4 #dad4 ,! ye> ?us settl$1 is :at we /ill make use ( 9 ,brita93 b z x is some:at m ?an #aa m9utes long] ?an ! ,sol> ,tropical ,ye>1 ! times ( ! ,equ9oxes g backw>d1 & fall e>li] by "o day 9 ab\t #acj ye>s4 ,9 ! "t ( ! ,nic5e ,c\ncil 7,a4 ,d4 #cbe47 :i* 0 #adca ye>s ago1 ! v]nal ,equ9ox fell on ! #ba/ ( ,m>*3 &1 if we divide #adca by #acj1 x w quote #aa1 :i* is ! numb] ( days ! ,equ9ox has fall5 back s9ce ! ,c\ncil ( ,nice4 ,?is caus+ great di/urbances1 by unfix+ ! times ( ! celebration ( ,ea/]1 & consequ5tly ( all ! o!r moveable ,fea/s1 ,pope ,gregory ! #ac?1 9 ! ye> #aehb ord]$ t5 days to be at once /ruck out ( t ye>2 & ! next day aft] ! f\r? ( ,octob] 0 call$ ! fifte5?4 ,by ?is means ! v]nal ,equ9ox 0 re/or$ to ! #ba/ ( ,m>*2 & x 0 endeav\r$1 by ! omission ( ?ree int]cal>y days 9 #djj ye>s1 to make ! civil or political ye> keep pace ) ! ,sol> = "t to come4 ,?is new =m ( ! ye> is call$ ! ,gregorian ,acc\nt or ,new ,/yle2 :i* is receiv$ 9 all ,c\ntries :]e ! ,pope's ,au?ority is ackn[l$g$1 & ought to be 9 all places :]e tru? is reg>d$4 ,sid5ote3 ,mon?s4 #dae4 ,! pr9cipal division ( ! ye> is into ,mon?s1 :i* are ( two sorts1 namely ,a/ronomical & ,civil4 ,! ,a/ronomical mon? is ! "t 9 :i* ! ,moon runs ?r\gh ! ,zodiac1 & is ei!r ,p]iodical or ,synodical4 ,! ,p]iodical ,mon? is ! "t sp5t by ! ,moon 9 mak+ "o compleat ,revolution f any po9t ( ! ,zodiac to ! same aga92 :i* is #bg;d #g;h #dcm4 ,! ,synodical ,mon?1 call$ a ,lunation1 is ! "t conta9$ betwe5 ! ,moon's p>t+ ) ! ,sun at a ,conjunction1 & return+ to him aga92 :i* is 9 #bi;d #ab;h #ddm4 ,! ,civil ,mon?s are ^? :i* are fram$ = ! uses ( ,civil life2 & are diff]5t z to _! names1 numb] ( days1 & times ( beg9n+1 9 sev]al diff]5t ,c\ntries4 ,! fir/ mon? ( ! ,jewi% ,ye> fell accord+ to ! ,moon 9 our ,augu/ & ,septemb]1 ,old ,/yle2 ! second 9 ,septemb] & ,octob]1 & s on4 ,! fir/ mon? ( ! ,egyptian ,ye> began on ! #bi? ( our ,augu/4 ,! fir/ mon? ( ! ,arabic & ,turki% ,ye> began ! #af? ( ,july4 ,! fir/ mon? ( ! ,grecian ,ye> fell accord+ to ! ,moon 9 ,june & ,july1 ! second 9 ,july & ,augu/1 & s on1 z 9 ! foll[+ ,table4 ---------------------------------------- ------------------------- ,no ,! ,jewi% ye>4 ,days,no ,! ,egyptian ye>4 ,days ---------------------------------------- ------------------------- #a ,tisri ,aug4-,sept4 #cj #a ,?o? ,augu/ #bi #cj #b ,m>*esvan ,sept4-,oct4 #bi #b ,paophi ,septemb4 #bh #cj #c ,casleu ,oct4-,nov4 #cj #c ,a?ir ,octob] #bh #cj #d ,tebe? ,nov4-,dec4 #bi #d ,*ojac ,novemb4 #bg #cj #e ,%ebat ,dec4-,jan4 #cj #e ,tybi ,decemb4 #bg #cj #f ,ad> ,jan4-,feb4 #bi #f ,me*ir ,janu>y #bf #cj #g ,nisan or ,abib ,feb4-,m>4 #cj #g ,pham5o? ,febru>4 #be #cj #h ,ji> ,m>4-,apr4 #bi #h ,p>mu?i ,m>* #bg #cj #i ,sivan ,april-,may #cj #i ,pa*on ,april #bf #cj #aj ,tamuz ,may-,june #bi #aj ,payni ,may #bf #cj #aa ,ab ,june-,july #cj #aa ,epiphi ,june #be #cj #ab ,elul ,july-,aug4 #bi #ab ,mesori ,july #be #cj ---------------------------------------- ------------------------- ,days 9 ! ye> #ced ,epagom5 or days add$ #e ---------------------------------------- --------------------------- ,9 ! ,embolimic ye> aft] ,days 9 ! ye> #cfe ,ad> !y add$ a mon? call$ ,ve-,ad> ( #cj days4 ---------------------------------------- --------------------------- ---------------------------------------- --------------------------- ,no,! ,arabic & ,days,no,! anci5t ,grecian ye>4 ,days ,turki% ye>4 ---------------------------------------- --------------------------- #a ,muh>ram ,july #af #cj #a ,hecatombon ,june-,july #cj #b ,saph> ,augu/ #ae #bi #b ,metagitnion ,july-,aug4 #bi #c ,rabia ,i4 ,septemb4 #ac #cj #c ,bo$romion ,aug4-,sept4 #cj #d ,rabia ,,ii4 ,octob] #ac #bi #d ,pyanepsion ,sept4-,oct4 #bi #e ,jomada ,i4 ,novemb4 #aa #cj #e ,mmact]ion ,oct4-,nov4 #cj #f ,jomada ,,ii4 ,decemb4 #aa #bi #f ,posideon ,nov4-,dec4 #bi #g ,rajab ,janu>y #i #cj #g ,gamelion ,dec4-,jan4 #cj #h ,%asban ,febru>y #h #bi #h ,an!/]ion ,jan4-,feb4 #bi #i ,ramadan ,m>* #i #cj #i ,elapheloblion ,feb4-,m>4 #cj #aj ,%awal ,april #h #bi #aj ,muni*ion ,m>4-,apr4 #bi #aa ,dulhaadah ,may #g #cj #aa ,?>gelion ,april-,may #cj #ab ,dulheggia ,june #e #bi #ab ,s*irrophorion ,may-,june #bi ---------------------------------------- --------------------------- ,days 9 ! ye> #ced ,days 9 ! ye> #ced ---------------------------------------- ----------------------------- ,! ,arabians add #aa days at ! end ( e ye>1 :i* keep ! same mon?s to ! same seasons4 ---------------------------------------- --------------------------------- ,sid5ote3 ,weeks #daf4 ,a mon? is divid$ into f\r p>ts call$ ,weeks1 & a ,week into sev5 p>ts call$ ,days2 s t 9 a ,julian ,ye> !re are #ac su* ,mon?s1 or #eb ,weeks1 & "o ,day ov]4 ,! ,g5tiles gave ! names ( ! ,sun1 ,moon1 & ,planets to ! ,days ( ! ,week4 ,to ! fir/1 ! ,"n ( ! ,sun2 to ! second1 ( ! ,moon2 to ! ?ird1 ( ,m>s2 to ! f\r?1 ( ,m]cury2 to ! fif?1 ( ,jupit]2 & to ! six?1 ( ,saturn4 ,sid5ote3 ,days #dag4 ,a ,day is ei!r ,natural or ,artificial4 ,! ,natural ,day conta9s #bd h\rs2 ! ,artificial ! "t f ,sun-rise to ,sun-set4 ,! ,natural ,day is ei!r ,a/ronomical or ,civil4 ,! ,a/ronomical ,day beg9s at ,noon1 because ! increase & decrease ( ,days t]m9at$ by ! ,horizon are v unequal among !mselves2 :i* inequality is likewise augm5t$ by ! incon/ancy ( ! horizontal ,refractions #ahc3 & !re=e ! ,a/ronom] takes ! ,m]idian = ! limit ( diurnal ,revolutions2 reckon+ ,noon1 t is ! in/ant :5 ! ,sun's ,c5t] is on ! ,m]idian1 = ! beg9n+ ( ! ,day4 ,! ,briti%1 ,fr5*1 ,dut*1 ,g]mans1 ,spani>ds1 ,portuguese1 & ,egyptians1 beg9 ! ,civil ,day at mid-night3 ! anti5t ,greeks1 ,jews1 ,bohemians1 ,silesians1 ) ! mod]n ,italians1 & ,*9ese1 beg9 x at ,sun-sett+3 ,& ! anti5t ,babylonians1 ,p]sians1 ,syrians1 ) ! mod]n ,greeks1 at ,sun-ris+4 ,sid5ote3 ,h\rs #dah4 ,an ,h\r is a c]ta9 det]m9ate "p ( ! ,day1 & is ei!r equal or unequal4 ,an equal ,h\r is ! #bd? "p ( a mean natural ,day1 z %ewn by well regulat$ ,clocks & ,wat*es2 b ^? ,h\rs are n q equal z measur$ by ! returns ( ! ,sun to ! ,m]idian1 because ( ! obliquity ( ! ,ecliptic & ,sun's unequal motion 9 x #bbd-bde4 ,unequal ,h\rs are ^? by :i* ! ,artificial ,day is divid$ into twelve ,p>ts1 & ! ,night into z _m4 ,sid5ote3 ,m9utes1 ,seconds1 ,?irds1 & ,scruples4 #dai4 ,an ,h\r is divid$ into #fj equal p>ts call$ ,m9utes1 a m9ute into #fj equal p>ts call$ ,seconds1 & ^! aga9 into #fj equal p>ts call$ ,?irds4 ,! ,jews1 ,*aldeans1 & ,arabians1 divide ! ,h\r into #ajhj equal p>ts call$ ,scruples2 :i* numb] conta9s #ah times #fj1 s t "o m9ute conta9s #ah ,scruples4 ,sid5ote3 ,cycles1 ( ! ,sun1 ,moon1 & ,indiction4 #dbj4 ,a ,cycle is a p]petual r\nd1 or circulation ( ! same p>ts ( "t ( any sort4 ,! ,cycle ( ! ,sun is a revolution ( #bh ye>s1 9 :i* "t1 ! days ( ! mon?s return aga9 to ! same days ( ! week2 ! ,sun's ,place to ! same ,signs & ,degrees ( ! ,ecliptic on ! same mon?s & days1 s z n to diff] "o degree 9 #ajj ye>s2 & ! leap-ye>s beg9 ! same c\rse ov] aga9 ) respect to ! days ( ! week on :i* ! days ( ! mon?s fall4 ,! ,cycle ( ! ,moon1 commonly call$ ! ,gold5 ,numb]1 is a revolution ( #ai ye>s2 9 :i* "t1 ! ,conjunctions1 ,oppositions1 & o!r ,aspects ( ! ,moon are )9 an h\r & half ( be+ ! same z !y 7 on ! same days ( ! mon?s #ai ye>s be=e4 ,! ,indiction is a revolution ( #ae ye>s1 us$ only by ! ,romans = indicat+ ! times ( c]ta9 paym5ts made by ! subjects to ! republic3 ,x 0 e/abli%$ by ,con/ant9e1 ,a4,d4 #cab4 ,sid5ote3 ,to f9d ! ,ye>s ( ^! ,cycles4 #dba4 ,! ye> ( our ,,savi\r's ,bir?1 accord+ to ! vulg> ra1 0 ! #i? ye> ( ! ,sol> ,cycle2 ! fir/ ye> ( ! ,lun> ,cycle2 & ! #cab? ye> aft] 8 bir? 0 ! fir/ ye> ( ! ,roman ,indiction4 ,!re=e1 to f9d ! ye> ( ! ,sol> ,cycle1 add #i to any giv5 ye> ( ,,*ri/1 & divide ! sum by #bh1 ! ,quoti5t is ! numb] ( ,cycles elaps$ s9ce 8 bir?1 & ! rema9d] is ! ,cycle = ! giv5 ye>3 if no?+ rema9s1 ! ,cycle is #bh4 ,to f9d ! ,lun> ,cycle1 add #a to ! giv5 ye> ( ,,*ri/1 & divide ! sum by #ai2 ! ,quoti5t is ! numb] ( ,cycles elaps$ 9 ! int]val1 & ! rema9d] is ! ,cycle = ! giv5 ye>3 if no?+ rema9s1 ! ,cycle is #ai4 ,la/ly1 subtract #cab f ! giv5 ye> ( ,,*ri/1 & divide ! rema9d] by #ae2 & :at rema9s aft] ?is division is ! ,indiction = ! giv5 ye>3 if no?+ rema9s1 ! ,indiction is #ae4 ,sid5ote3 ,! defici5cy ( ! ,lun> ,cycle1 & consequ5ce !re(4 #dbb4 ,al?\gh ! above defici5cy 9 ! ,lun> ,cycle ( an h\r & half e #ai ye>s be b small1 yet 9 "t x becomes s s5sible z to make a :ole ,natural ,day 9 #caj ye>s4 ,s t1 al?\gh ?is ,cycle be ( use1 :5 rightly plac$ aga9/ ! days ( ! mon? 9 ! ,cal5d>1 z 9 our ,common ,pray] ,books1 = f9d+ ! days ( ! mean ,conjunctions or ,oppositions ( ! ,sun & ,moon1 & consequ5tly ! "t ( ,ea/]2 x w only s]ve = #caj ye>s ,old ,/yle4 ,= z ! ,new & ,full ,moons anticipate a day 9 t "t1 ! ,gold5 ,numb]s ought to be plac$ "o day e>li] 9 ! ,cal5d> = ! next #caj ye>s to come4 ,^! ,numb]s 7 rightly plac$ aga9/ ! days ( ,new ,moon 9 ! ,cal5d>1 by ! ,c\ncil ( ,nice1 ,a4 ,d4 #cbe2 b ! anticipation :i* has be5 neglect$ ev] s9ce1 is n[ gr[n almo/ into #e days3 & !re=e1 all ! ,gold5 ,numb]s ought n[ to be plac$ #e days high] 9 ! ,cal5d> = ! ,o4,s4 ?an !y 7 at ! "t ( ! said ,c\ncil2 or six days l[] = ! ,new ,/yle1 because at pres5t x diff]s #aa days f ! ,old4 ---------------------------------------- ------------ ,days,jan4,feb4,m>4,apr4,may ,jun4,jul4,aug4,sep4,oct4,nov4,dec4 ---------------------------------------- ------------ #a #i #i #ag #ag #f #aa #ai #b #ag #f #ad #ad #c #aa #ai #c #ag #f #ag #f #c #aa #ai #h #h #d #f #f #ad #ad #c #ai #h #af #e #ad #c #aa #aa #ai #h #af ---------------------------------------- ------------ #f #ad #c #ad #c #ai #af #e #e #g #c #c #aa #aa #ai #h #af #ac #h #aa #ai #h #h #af #e #e #ac #i #aa #ai #aa #ai #ac #b #aj #ai #h #h #af #af #e #ac #b #aj ---------------------------------------- ------------ #aa #ai #h #e #ac #b #b #aj #ab #h #af #h #af #af #e #aj #ah #ac #e #ac #ac #b #aj #ah #g #ad #af #e #af #e #b #aj #ah #ah #g #ae #e #e #ac #ac #b #g #ae ---------------------------------------- ------------ #af #ac #b #aj #aj #ah #g #ae #ag #ac #b #ac #b #ah #g #ae #d #d #ah #b #b #aj #aj #ah #ae #ab #ai #aj #ah #g #g #ae #d #d #ab #bj #aj #ah #aj #ah #ae #ab #a #a ---------------------------------------- ------------ #ba #ah #g #g #ae #d #ab #i #bb #ah #g #ae #d #d #ab #a #a #i #bc #g #ae #g #ae #ab #i #ag #ag #bd #ae #d #d #ab #a #i #f #be #ae #d #ab #a #i #ag #ag #f ---------------------------------------- ------------ #bf #d #d #ab #a #f #ad #bg #ab #a #a #i #i #ag #f #ad #bh #ab #a #ab #i #ag #f #ad #ad #c #c #bi #a #a #i #ag #c #aa #cj #ag #f #f #ad #c #aa ---------------------------------------- ------------ #ca #i #i #ad #c #aa #ai ---------------------------------------- ------------ ,sid5ote3 ,h[ to f9d ! day ( ! ,new ,moon by ! ,gold5 ,numb]4 #dbc4 ,9 ! annex$ ,table1 ! ,gold5 ,numb]s "u ! mon?s /& aga9/ ! days ( ,new ,moon 9 ! left h& column1 = ! ,new ,/yle2 adapt$ *iefly to ! second ye> aft] leap-ye> z be+ ! ne>e/ mean = all ! f\r2 & w s]ve till ! ye> #aijj4 ,!re=e1 to f9d ! day ( ,new ,moon 9 any mon? ( a giv5 ye> till t "t1 look = ! ,gold5 ,numb] ( t ye> "u ! desir$ mon?1 & aga9/ x1 y h ! day ( ,new ,moon 9 ! left h& column4 ,?us1 suppose x 7 requir$ to f9d ! day ( ,new ,moon 9 ,septemb] #ageg2 ! ,gold5 ,numb] = t ye> is #aj1 :i* ,i look = "u ,septemb] & "r aga9/ x 9 ! left h& column ,i f9d #ac1 :i* is ! day ( ,new ,moon 9 t mon?4 ,n4 ,b4 ,if all ! ,gold5 ,numb]s1 except #ag & #f1 7 set "o day l[] 9 ! ,table1 x w\ld s]ve f ! beg9n+ ( ! ye> #aijj till ! end ( ! ye> #baii4 ,! fir/ ,table aft] ?is *apt] %ews ! ,gold5 ,numb] = #djjj ye>s aft] ! bir? ( ,,*ri/1 by look+ = ! ev5 hundr$s ( any giv5 ye> at ! left h&1 & = ! re/ to make up t ye> at ! head ( ! ,table2 & :]e ! columns meet1 y h ! ,gold5 ,numb] 7:i* is ! same bo? 9 ,old & ,new ,/yle7 = ! giv5 ye>4 ,?us1 suppose ! ,gold5 ,numb] 0 want$ = ! ye> #ageg2 ,i look = #agjj at ! left h& ( ! ,table1 & = #eg at ! top ( x2 !n guid+ my eye d[nw>d f #eg to ov] aga9/ #agjj1 ,i f9d #aj1 :i* is ! ,gold5 ,numb] = t ye>4 ,sid5ote3 ,a p]petual ,table ( ! "t ( ,new ,moon to ! ne>e/ h\r1 = ! ,old ,/yle4 #dbd4 ,b because ! lun> ,cycle ( #ai ye>s sometimes includes five leap-ye>s1 & at o!r times only f\r1 ?is ,table w sometimes v>y a day f ! tru? 9 leap-ye>s aft] ,febru>y4 ,& x is impossible to h "o m correct1 unless we ext5d x to f\r times #ai or #gf ye>s2 9 :i* !re are #ai leap ye>s )\t a rema9d]4 ,b ev5 !n to h x ( p]petual use1 x mu/ be adapt$ to ! ,old ,/yle1 because 9 e c5turial ye> n divisible by #d1 ! regul> c\rse ( leap-ye>s is int]rupt$ 9 ! ,new2 z w be ! case 9 ! ye> #ahjj4 ,!re=e1 ^u ! regul> ,old ,/yle plan1 ,i h comput$ ! foll[+ ,table ( ! mean times ( all ! ,new ,moons to ! ne>e/ h\r = #gf ye>s2 beg9n+ ) ! ye> ( ,,*ri/ #agbd1 & end+ ) ! ye> #ahjj4 ,?is ,table may be made p]petual1 by d$uct+ #f h\rs f ! "t ( ,new ,moon 9 any giv5 ye> & mon? f #agbd to #ahjj1 9 ord] to h ! mean "t ( ,new ,moon 9 any ye> & mon? #gf ye>s aft]w>d2 or d$uct+ #ab h\rs = #aeb ye>s1 #ah h\rs = #bbh ye>s2 & #bd h\rs = #cjd ye>s1 because 9 t "t ! *anges ( ! ,moon anticipate almo/ a complete natural day4 ,& if ! l numb] ( h\rs be add$ = s _m ye>s pa/1 we %all h ! mean "t ( any ,new ,moon already elaps$4 ,suppose1 = example1 ! mean "t ( ,*ange 0 requir$ = ,janu>y #ahjb2 d$uct #gf ye>s & !re rema9s #agbf1 aga9/ :i* 9 ! foll[+ ,table "u ,janu>y ,i f9d ! "t ( ,new ,moon 0 on ! #ba/ day at #aa 9 ! ev5+3 f :i* take #f h\rs & !re rema9s ! #ba/ day at #e 9 ! ev5+ = ! mean "t ( ,*ange 9 ,janu>y #ahjb4 ,or1 if ! "t be requir$ = ,may1 ,a4 ,d4 #agja1 add #gf ye>s & x makes #aggg1 :i* ,i look = 9 ! ,table1 & aga9/ x "u ,may ,i f9d ! ,new ,moon 9 t ye> falls on ! #be? day at #i 9 ! ev5+2 to :i* add #f h\rs1 & x gives ! #bf? day at #c 9 ! ,morn+ = ! "t ( ,new ,moon 9 ,may1 ,a4 ,d4 #agja4 ,by ?is addition = "t pa/1 or subtraction = "t to come1 ! ,table w n v>y #bd h\rs f ! tru? 9 less ?an #adeib ye>s4 ,& if1 in/ead ( #f h\rs = e #gf ye>s1 we add or subtract only #e h\rs #eb m9utes1 x w n v>y a day 9 #aj millions ( ye>s4 ,al?\gh ?is ,table is calculat$ = #gf ye>s only1 & accord+ to ! ,old ,/yle1 yet by means ( two easy ,equations x may be made to answ] z exactly to ! ,new ,/yle1 = any "t to come4 ,?us1 because ! ye> #agbd 9 ?is ,table is ! fir/ ye> ( ! ,cycle = :i* x is made2 if f any ye> ( ,,*ri/ aft] #ahjj y subtract #agbc1 & divide ! ov]plus by #gf1 ! ,quoti5t w %ew h[ _m entire ,cycles ( #gf ye>s are elaps$ s9ce ! beg9n+ ( ! ,cycle "h provid$ =2 & ! rema9d] w %ew ! ye> ( ! curr5t ,cycle answ]+ to ! giv5 ye> ( ,,*ri/4 ,h5ce1 if ! rema9d] be #j1 y mu/ in/ead !re( put #gf1 & less5 ! ,quoti5t by unity4 ,!n1 look 9 ! left h& column ( ! ,table = ! numb] 9 y\r rema9d]1 & aga9/ x y w f9d ! times ( all ! mean ,new ,moons 9 t ye> ( ! pres5t ,cycle4 ,& :]eas 9 #gf ,julian ,ye>s ! ,moon anticipates #e h\rs #eb m9utes1 if !re=e ^! #e h\rs #eb m9utes be multipli$ by ! above f\nd ,quoti5t1 t is1 by ! numb] ( entire ,cycles pa/2 ! product subtract$ f ! times 9 ! ,table w leave ! correct$ times ( ! ,new ,moons to ! ,old ,/yle2 :i* may be r$uc$ to ! ,new ,/yle ?us3 ,divide ! numb] ( entire hundr$s 9 ! giv5 ye> ( ,,*ri/ by #d1 multiply ?is ,quoti5t by #c1 to ! product add ! rema9d]1 & f _! sum subtract #b3 ?is la/ rema9d] d5otes ! numb] ( days to be add$ to ! times above correct$1 9 ord] to r$uce !m to ! ,new ,/yle4 ,! reason ( ?is is1 t e #djj ye>s ( ! ,new ,/yle ga9s #c days ^u ! ,old ,/yle3 "o ( :i* x ga9s 9 ea* ( ! c5turial ye>s succe$+ t :i* is exactly divisible by #d )\t rema9d]2 b !n1 :5 y h f\nd ! days s ga9$1 #b mu/ be subtract$ f _! numb] on acc\nt ( ! rectifications made 9 ! ,cal5d> by ! ,c\ncil ( ,nice1 & s9ce by ,pope ,gregory4 ,x mu/ also be obs]v$1 t ! additional days f\nd z above direct$ d n take place 9 ! c5turial ,ye>s :i* are n multiples ( #d till ,febru>y #bi?1 ,o4 ,s4 = on t day beg9s ! diff]5ce betwe5 ! ,/yles2 till :i* day !re=e1 ^? t 7 add$ 9 ! prec$+ ye>s mu/ be us$4 ,! foll[+ ,example w make ?is accommodation pla94 ,requir$ ! mean "t ( ,new ,moon 9 ,june1 ,a4,d4 #aiji1 ,n4,s4 ,f #aiji take #agbc ,ye>s1 & !re rem4 #ahf ,:i* divid$ by #gf1 gives ! ,quoti5t #b & ! rema9d] #cd ,!n1 aga9/ #cd 9 ! ,table is ,june #e;d #h;h #jm ,aft]noon4 ,& #e;h #ebm multipli$ by #b make to be subtr4 #aa #dd ------------- ,rema9s ! mean "t accord+ to ! ,old ,/yle1 ,june #e;d #i;h #afm ,morn+4 ,entire hundr$ 9 #aiji are #ai1 :i* divid$ by #d1 quotes #d ,& leaves a rema9d] ( #c ,:i* ,quoti5t multipli$ by #c makes #ab1 & ! rema9d] add$ makes #ae ,f :i* subtract #b1 & !re rema9s #ac ,:i* numb] ( days add$ to ! above "t ,old ,/yle1 gives ,june #ah;d #i;h #afm ,morn4,n4,s4 ,s ! mean "t ( ,new ,moon 9 ,june #aiji ,new ,/yle is ! #ah? day at #af m9utes pa/ #i 9 ! ,morn+4 ,if #aa days be add$ to ! "t ( any ,new ,moon 9 ?is ,table1 x w give ! "t !re( accord+ to ! ,new ,/yle till ! ye> #ahjj4 ,& if #ad days #ah h\rs #bb m9utes be add$ to ! mean "t ( ,new ,moon 9 ei!r ,/yle1 x w give ! mean "t ( ! next ,full ,moon accord+ to t ,/yle4 ---------------------------------------- ---------------------------------------- ------------- ,a ,,table %ew+ ! times ( all ! mean ,*anges ( ! ,moon1 to ! ne>e/ ,h\r1 ?r\gh f\r ,lun> ,p]iods1 or #gf ye>s4 ,m signifies morn+1 ,a aft]noon4 ---------------------------------------- ---------------------------------------- ,yrs ,janu>y ,m>* ,may ,july ,sept4 ,novemb4 ( ,a4,d4 ,febru>y ,april ,june ,augu/ ,octob] ,decemb4 ! ---------------------------------------- ------------------------------------ ,cyc4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ---------------------------------------- ---------------------------------------- #a #agbdad #e;,a#ac #e,m#ac #f;,a#ab #g,m#aa #h;,a#aj #h,m #i #i;,a #h #aj,m #f #aj;,a #f #aa,m #d #ab;,a #d #a;,a #a #d,m #b #agbe #c #b,m #a #b;,a #c #c,m #a #d;,a #bi #f,m#bh #g;,a#bg #h,m#be #h;,a#be #i,m#bc #aj;,a#bc #aa,m #cj #e;,a #c #agbfba #aa;,a#bj #aa,m#ba #ab;,a#bj #a;,a#bj #a,m#ah #b;,a#ah #c,m#af #d;,a#ae #e,m#ad #e;,a#ac #f,m#ab #g;,a #b #d,m #d #agbgaa #h,m #i #i;,a#aa #i,m #i #aj;,a #i #aa,m #g #ab;,a #g #j;,a #f #a,m #d #a;,a #d #b,m #b #c;,a #ca #e;,a #e #agbhcj #f,m#bh #g;,a#bi #g,m#bg #h;,a#bg #h,m#be #i;,a#be #aj,m#bc #aa;,a#bb #aa,m#ba #ab;,a#bj #a;,a#bj #b,m #f #agbiah #b;,a#ag #c,m#ah #d;,a#ag #d,m#af #e;,a#ae #f,m#ad #g;,a#ab #g,m#aa #h;,a#aa #i,m #i #j;,a #i #aa,m #b #e,m #g #agcj #g #aa;,a #f #j;,a #h #a,m #f #a;,a #f #b,m #d #c;,a #d #c,m #b #d;,a #cj #g,m#bh #h;,a#bh #i,m #cj #f;,a #h #agcabf #i;,a#be #aj,m#bf #aj;,a#be #aa,m#bd #aa;,a#bc #j;,a#bc #a,m#ba #b;,a#bj #b,m#ai #c;,a#ah #d,m#ag #e;,a #i #agcbaf #e,m#ad #f;,a#ae #g,m#ac #h;,a#ac #h,m#aa #i;,a#aa #aj,m #i #aa;,a #h #aa,m #g #ab;,a #f #a;,a #f #b,m #a #f,m #aj #agcc #d #b;,a #c #c,m #d #d;,a #c #d,m #b #e;,a #cj #h,m#bh #h;,a#bg #i,m#bf #aj;,a#be #aa,m#bd #aa;,a #cj #g;,a #aa #agcdbc #j;,a#bb #a,m#bc #a;,a#bb #b,m#ba #b;,a#bj #c,m#ai #d;,a#ah #e,m#af #e;,a#af #f,m#ad #g;,a#ad #h,m #ab #agceab #i;,a#aa #i,m#ab #aj;,a#aa #aa,m#aj #aa;,a #i #j;,a #i #a,m #g #b;,a #f #b,m #e #c;,a #d #d,m #c #e;,a #b #e,m #a #g,m #ac #agcf ---- #bi #i,m#bh #i;,a#bg #aj,m#bf #aa;,a#be #j;,a#bc #ab;,a#bc #a;,a#bb #b,m#ba #c;,a #ca #f;,a #cj #h;,a #ad #agcgbj #c,m#ah #d;,a#bj #d,m#ah #e;,a#ah #e,m#af #f;,a#af #g,m#ad #h;,a#ac #h,m#ab #i;,a#aa #aj,m#aj #aa;,a #b #f,m #ae #agch #i #aa,m #g #ab;,a #i #a;,a #h #a,m #g #b;,a #f #c,m #e #d;,a #d #e,m #b #e;,a #cj #h,m#bi #h;,a #ca #g;,a #af #agcibh #i,m#bf #aj;,a#bh #aa,m#bf #ab;,a#bf #j;,a#be #a,m#bd #b;,a#bc #c,m#ba #c;,a#ba #d,m#ai #e;,a#ai #f,m #ag #agdjag #f;,a#af #g,m#af #h;,a#ae #i,m#ad #i;,a#ac #aj,m#ab #aa;,a#aa #j;,a#i #ab;,a #i #a;,a #h #b,m #g #c;,a #b #g,m #ah #agda #f #c,m #d #d;,a #f #d,m #d #e;,a #d #e,m #b #f;,a #cj #h,m#bh #i;,a#bh #aj,m#bf #aa;,a#bf #aa,m #ca #g;,a #ai #agdbbd #ab;,a#bc #a;,a#be #b,m#bc #c;,a#bc #c,m#ba #d;,a#ba #e,m#ai #f;,a#ah #f,m#ag #g;,a#af #h,m#ae #i;,a #bj #agdcad #i,m#ab #aj;,a#ad #aa,m#ab #ab;,a#ab #j;,a#aa #a,m#aj #b;,a #i #c,m #g #c;,a #g #d,m #e #e;,a #e #f,m #a #i,m #ba #agdd #c #f;,a #b #g,m #b #h;,a #cj #aj,m#bh #aa;,a#bh #j;,a#bf #ab;,a#be #a;,a#be #b,m#bc #c;,a#bc #c,m #cj #i;,a #bb #agdeba #d;,a#bj #e,m#ba #e;,a#bj #f,m#ai #f;,a#ah #g,m#ag #h;,a#af #h,m#ad #i;,a#ad #aj,m#ab #aa;,a#ab #j;,a #a #i;,a #bc #agdfaj #ab;,a#i #a;,a#aa #b,m #i #c;,a #i #c,m #g #d;,a #g #e,m #e #f;,a #d #f,m #c #g;,a #b #h,m #ca #aj,m #bd #agdgbi #aj;,a#bh #aa,m#bi #aa;,a#bh #j;,a#bg #ab;,a#bf #a;,a#bf #b,m#bd #c;,a#bc #c,m#bb #d;,a#ba #e,m#bj #f;,a #be #agdhai #f,m#ag #g;,a#ah #h,m#af #i;,a#af #i,m#ad #aj;,a#ad #aa,m#ab #ab;,a#aa #j;,a#aa #a,m #i #b;,a #i #c,m #b #i,m #bf #agdi #g #c;,a #f #d,m #g #e;,a #f #f,m #e #f;,a #d #g,m #c #h;,a #cj #aj,m#bi #aa;,a#bh #j;,a#bg #ab;,a #ca #i;,a #bg #agejbf #a;,a#be #b,m#bf #c;,a#be #d,m#bd #d;,a#bc #e,m#bb #f;,a#ba #g,m#ai #g;,a#ai #h,m#ag #i;,a#ag #aj,m #bh #ageaae #aj;,a#ad #aa,m#ae #aa;,a#ad #j;,a#ac #ab;,a#ab #a;,a#ab #b,m#aj #c;,a #i #c,m #h #d;,a #g #e,m #f #f;,a #b #i,m #bi #ageb #e #f,m #c #g;,a #d #h,m #b #i;,a #cj #aa,m#bi #ab;,a#bh #j;,a#bg #a,m#bf #b;,a#be #c,m#bd #c;,a #ca #aj;,a #cj #agecbc #d,m#ba #e;,a#bc #f,m#ba #g;,a#ba #g,m#ai #h;,a#ai #i,m#ag #aj;,a#af #aj,m#ae #aa;,a#ad #j;,a#ad #a,m #ca #agedab #a;,a#aa #b,m#ab #c;,a#aa #d,m#aj #d;,a #i #e,m #h #f;,a #g #g,m #e #g;,a #e #h,m #c #i;,a #c #aj,m #a #aj;,a #a #aa;,a #cb #agee ---- #bi #ab;,a#bi #a;,a#bh #b,m#bg #c;,a#be #c,m#bd #d;,a#bd #e,m#bb #f;,a#bb #f,m #ca #aa,m #ca #j;,a #cc #agefbj #g;,a#ai #h,m#ai #i;,a#ah #i,m#ag #aj;,a#af #aa,m#ae #ab;,a#ad #a;,a#ac #a,m#ab #b;,a#aa #c,m#aj #d;,a #a #ad;,a #cd #ageg #i #d,m #g #e;,a #i #f,m #g #g;,a #g #g,m #e #h;,a #e #i,m #c #aj;,a #b #aj,m #cj #a,m#bi #a;,a #ca #j;,a #ce #agehbh #b,m#bf #c;,a#bh #c,m#bf #d;,a#bf #d,m#bd #e;,a#bd #f,m#bb #g;,a#ba #g,m#bj #h;,a#ai #i,m#ah #aj;,a #cf #ageiag #aj,m#ae #aa;,a#ag #j;,a#af #a,m#ae #a;,a#ad #b,m#ac #c;,a#ab #b,m#aj #d;,a#aj #e,m #h #f;,a #h #g,m #a #ab;,a #cg #agfj #f #g;,a #e #h,m #e #i;,a #d #aj,m #c #aj;,a #b #aa,m #cj #a,m#bh #b;,a#bh #c,m#bf #d;,a#bf #d,m #ca #a;,a #ch #agfabd #e;,a#bc #f,m#bd #g;,a#bc #h,m#bb #i;,a#ba #aj,m#bj #aj;,a#ai #aa,m#ag #aa;,a#ag #j;,a#af #a,m#ae #b;,a #ci #agfbad #b,m#ab #c;,a#ad #c,m#ab #d;,a#ab #d,m#aj #e;,a#aj #f,m#h #g;,a #g #g,m #f #h;,a #e #i,m #d #aj;,a ---------------------------------------- ---------------------------------------- #a #a;,a #dj #agfc #c #aa,m #a #ab;,a #c #j;,a #b #a,m #bi #c;,a#bi #d,m#bg #d,m#bf #e,m#be #f;,a#bd #g,m#bc #g;,a #ca #b,m #da #agfdbb #h,m#bj #i;,a#ba #aj,m#ai #aa;,a#ai #aa,m#ag #ab;,a#ag #a;,a#af #b,m#ad #b;,a#ad #c,m#ab #d;,a#ab #e,m #a #a;,a #db #agfeaj #e;,a #i #f,m#aj #f;,a #i #g,m #h #g;,a #g #h,m #f #i;,a #e #aj,m #c #aj;,a #c #aa,m #a #ab;,a #ca #a,m #dc #agffbi #b;,a#bh #c,m#bi #d;,a#bh #e,m#bg #e;,a#bf #f,m#be #g;,a#bd #h,m#bb #h;,a#bb #i,m#bj #aj;,a#bj #aa,m #dd #agfgah #aa;,a#ag #j;,a#ai #a,m#ag #b;,a#ag #b,m#ae #c;,a#ae #d,m#ac #e;,a#ab #f,m#aa #f;,a#aj #g,m #i #h;,a #b #b,m #de #agfh #h #h,m #f #i;,a #g #aj,m #e #aa;,a #e #aa,m #c #ab;,a #c #a;,a #cj #c,m#bi #d;,a#bh #e,m#bg #e;,a #ca #b;,a #df #agfibf #f,m#bd #g;,a#bf #g,m#bd #h;,a#bd #h,m#bb #i;,a#bb #aj,m#bj #aa;,a#ai #aa,m#ah #ab;,a#ag #a;,a#ag #b,m #dg #aggjae #b;,a#ad #c,m#ae #d;,a#ad #e,m#ac #e;,a#ab #d,m#aa #g;,a#aj #h,m #h #h;,a #h #i,m #f #aj;,a #f #aa,m #a #d,m #dh #agga #d #aa,m #c #j;,a #e #a,m #c #b;,a #c #b,m #a #c;,a #bi #e,m#bg #f;,a#bg #g,m#be #h;,a#be #i,m #cj #e;,a #di #aggbbc #i;,a#bb #aj,m#bb #aj;,a#ba #aa,m#bj #aa;,a#ai #j;,a#ai #a,m#ag #b;,a#af #b,m#ae #c;,a#ad #d,m#ac #e;,a #ej #aggcab #e,m#aj #f;,a#ab #g,m#aj #h;,a#aj #h,m #h #i;,a #h #i,m #f #aj;,a #e #aa,m #d #ab;,a #c #a;,a #c #b,m #a #b;,a #a #d;,a #ea #aggd ---- #bi #e;,a#bi #f,m#bg #g;,a#bg #h,m#be #h;,a#bd #i,m#bc #aj;,a#bb #aa,m#ba #aa;,a #ca #c,m #ca #e,m #eb #aggebj #j;,a#ai #a,m#bj #b;,a#ai #c,m#ah #c;,a#ag #d,m#af #e;,a#ae #f,m#ac #f;,a#ac #g,m#aa #h;,a#aa #i,m #a #c;,a #ec #aggf #i #i;,a #h #aj,m #h #aj;,a #g #aa,m #f #ab;,a #e #j;,a #e #a,m #c #b;,a #b #b,m #bi #e;,a#bi #e,m #ca #d,m #ed #agggbg #f;,a#bf #g,m#bg #h;,a#bf #i,m#be #i;,a#bd #aj,m#bc #aa;,a#bb #j;,a#bj #ab;,a#bj #a;,a#ai #b,m#ah #c;,a #ee #agghag #c,m#ae #d;,a#ag #e,m#ae #f;,a#ae #f,m#ac #g;,a#ac #h,m#aa #i;,a#aj #i,m #i #aj;,a #h #aa,m #g #ab;,a #a #f,m #ef #aggi #f #j;,a #e #a,m #f #b;,a #e #c,m #d #c;,a #c #d,m #b #e;,a #bi #g,m#bh #h;,a#bg #i,m#bf #i;,a #cj #f;,a #eg #aghjbe #aj,m#bc #aa;,a#bd #aa,m#bb #ab;,a#bb #j;,a#ba #a,m#bj #b;,a#ai #c,m#ag #c;,a#ag #d,m#ae #e;,a#ae #f,m #eh #aghaac #f;,a#ab #g,m#ac #h;,a#ab #i,m#aa #i;,a#aj #aj,m #i #aa;,a #h #j;,a #f #ab;,a #f #a;,a #e #b,m #d #c;,a #a #f,m #ei #aghb #c #c,m #a #d;,a #c #e,m #a #f;,a #bi #h,m#bh #i;,a#bg #i,m#be #aj;,a#be #aa,m#bc #ab;,a#bc #j;,a #cj #g;,a #fj #aghcbb #a,m#bj #b;,a#bb #b,m#bj #c;,a#bj #c,m#ah #d;,a#ah #e,m#af #f;,a#ae #f,m#ad #g;,a#ac #h,m#ab #i;,a #a #f,m #fa #aghdaa #i,m #i #aj;,a#aj #aa,m #h #ab;,a #h #j;,a #g #a,m #f #b;,a #e #c,m #c #c;,a #c #d,m #a #e;,a #cj #f;,a #fb #aghebi #g,m#bg #h;,a#bi #i,m#bg #aj;,a#bg #aj,m#be #aa;,a#be #j;,a#bd #a,m#bb #a;,a#bb #b,m#bj #c;,a#bj #c,m #fc #aghfah #d;,a#ag #e,m#ah #e;,a#ag #f,m#af #f;,a#ae #g,m#ad #h;,a#ac #i,m#aa #i;,a#aa #aj,m #i #aa;,a #i #j;,a #a #f,m #fd #aghg #g #ab;,a #f #a;,a #h #b,m #f #c;,a #f #c,m #d #d;,a #d #e,m #b #f;,a #cj #h,m#bh #i;,a#bh #i,m #cj #g;,a #fe #aghhbf #aj;,a#be #aa,m#be #ab;,a#bd #a;,a#bd #a,m#bb #b;,a#bb #c,m#bj #d,m#ai #d,m#ah #e;,a#ag #f,m#af #g;,a #ff #aghiae #g,m#ac #h;,a#ae #i,m#ac #aj;,a#ac #aj,m#aa #aa;,a#aa #j;,a#aj #a,m #h #a;,a #h #b,m #f #c;,a #f #d,m #a #g,m #fg #agij #d #d;,a #c #e,m #d #e;,a #c #f,m #b #f;,a #cj #i,m#bh #i;,a#bg #aj,m#bf #aa;,a#be #j;,a#bd #ab;,a #cj #h;,a #fh #agiabc #a;,a#bb #b,m#bc #c;,a#bb #d,m#ba #d;,a#bj #e,m#ai #f;,a#ah #g,m#af #g;,a#af #h,m#ad #i;,a#ad #aj,m #fi #agibab #aj;,a#aa #aa,m#aa #ab;,a#aj #a;,a#aj #a,m #h #b;,a #h #c,m #f #d;,a #e #d;,a #d #e;,a #c #f,m #b #g;,a #a #g,m #a #i,m #gj #agic ---- #bi #aj,m#bh #aa;,a#bg #j;,a#bg #a,m#be #a;,a#bd #b,m#bc #c;,a#bb #d,m#ba #d;,a #cj #h;,a #cj #aj;,a #ga #agidbj #e,m#ah #f;,a#bj #f,m#ah #g;,a#ah #g,m#af #h;,a#af #i,m#ad #aj;,a#ac #aj,m#ab #aa;,a#aa #j;,a#aa #a,m #b #h,m #gb #agie #i #a;,a #h #b,m #i #c;,a #h #d,m #g #d;,a #f #e,m #e #f;,a #d #g,m #b #g;,a #cj #aj,m#bi #aj;,a #ca #i;,a #gc #agifbh #aa,m#bf #ab;,a#bg #j;,a#bf #a,m#be #a;,a#bd #b,m#bc #c;,a#bb #d,m#bj #d;,a#bj #e,m#ah #f;,a#ah #g,m #gd #agigaf #g;,a#ae #h,m#af #i;,a#ae #aj,m#ad #aj;,a#ac #aa,m#ab #ab;,a#aa #a;,a#aj #a,m #i #b;,a #h #c,m #g #d;,a #b #i,m #ge #agih #f #d,m #d #e;,a #f #f,m #d #g;,a #d #g,m #b #h;,a #cj #aj,m#bh #aa;,a#bh #j;,a#bg #a,m#bf #a;,a #ca #aj;,a #gf #agii #be #b,m#bc #c;,a#be #d,m#bc #e;,a#bc #e,m#ba #f;,a#ba #f,m#ai #h;,a#ah #h,m#ag #i;,a#af #aj,m#ae #aa;,a #a #ahjjad #aa;,a#ab #ab;,a#ac #j;,a#ab #a,m#aa #a;,a#aj #b,m #i #c;,a #h #d,m #f #d;,a #f #e,m #d #f;,a #d #g,m ---------------------------------------- ---------------------------------------- ,! ye> #ahjj beg9s a new ,cycle4 ,sid5ote3 ,ea/] ,cycle1 defici5t4 #dbe4 ,! ,cycle ( ,ea/]1 also call$ ! ,dionysian ,p]iod1 is a revolution ( #ecb ye>s1 f\nd by multiply+ ! ,sol> ,cycle #bh by ! ,lun> ,cycle #ai4 ,if ! ,new ,moons did n anticipate ^u ?is ,cycle1 ,ea/]-,day w\ld always be ! ,sunday next aft] ! fir/ ,full ,moon :i* succe$s ! #ba/ ( ,m>*4 ,b1 on acc\nt ( ! above anticipation #dbb1 to :i* no prop] reg>d 0 _h be=e ! late alt]ation ( ! ,/yle1 ! ,ecclesia/ic ,ea/] has sev]al times be5 a week diff]5t f ! true ,ea/] )9 ?is la/ ,c5tury3 :i* inconv5i5ce is n[ rem$i$ by mak+ ! ,table :i* us$ to f9d ,ea/] = ev]1 9 ! ,common ,pray] ,book1 ( no long] use ?an ! ,lun> diff]5ce f ! ,new ,/yle w admit (4 ,sid5ote3 ,numb] ( ,direction4 ,to f9d ! true ,ea/]4 #dbf4 ,! e>lie/ ,ea/] possible is ! #bb;d ( ,m>*1 ! late/ ! #be? ( ,april4 ,)9 ^! limits are #ce days1 & ! numb] belong+ to ea* ( !m is call$ ! ,numb] ( ,direction2 because !reby ! "t ( ,ea/] is f\nd = any giv5 ye>4 ,to f9d ! ,numb] ( ,direction1 accord+ to ! ,new ,/yle1 ent] ,table ,v foll[+ ?is ,*apt]1 ) ! compleat hundr$s ( any giv5 ye> at ! top1 & ! ye>s !re( 7if any7 bel[ an hundr$ at ! left h&2 & :]e ! columns meet is ! ,dom9ical ,lett] = ! giv5 ye>4 ,!n1 ent] ,table ,i1 ) ! compleat hundr$s ( ! same ye> at ! left h&1 & ! ye>s bel[ an hundr$ at ! top2 & :]e ! columns meet is ! ,gold5 ,numb] = ! same ye>4 ,la/ly1 ent] ,table ,,ii ) ! ,dom9ical ,lett] at ! left h& & ,gold5 ,numb] at ! top2 & :]e ! columns meet is ! ,numb] ( ,direction = t ye>2 :i* numb]1 add$ to ! #ba/ day ( ,m>* %ews on :at day ei!r ( ,m>* or ,april ,ea/] ,sunday falls 9 t ye>4 ,?us1 ! ,dom9ical ,lett] ,new ,/yle = ! ye> #ageg is ,b 7,table ,v7 & ! ,gold5 ,numb] is #aj1 7,table ,i7 by :i* 9 ,table ,,ii1 ! ,numb] ( ,direction is f\nd to be #bj2 :i*1 reckon$ f ! #ba/ ( ,m>*1 ends on ! #aj? ( ,april1 & t is ,ea/] ,sunday 9 ! ye> #ageg4 ,n4 ,b4 ,!re are always two ,dom9ical ,lett]s to ! leap-ye>1 ! fir/ ( :i* takes place to ! #bd? ( ,febru>y1 ! la/ = ! foll[+ "p ( ! ye>4 ,sid5ote3 ,dom9ical ,lett]4 #dbg4 ,! fir/ sev5 ,lett]s ( ! ,alphabet are commonly plac$ 9 ! annual ,almanacks to %ew on :at days ( ! week ! days ( ! mon?s fall ?r\gh\t ! ye>4 ,& because "o ( ^? sev5 ,lett]s mu/ necess>ily /& aga9/ ,sunday x is pr9t$ 9 a capital =m1 & call$ ! ,dom9ical ,lett]3 ! o!r six be+ ins]t$ 9 small *>act]s to d5ote ! o!r six days ( ! week4 ,n[1 s9ce a common ,julian ,ye> conta9s #cfe ,days1 if ?is numb] be divid$ by #g 7! numb] ( days 9 a week7 !re w rema9 "o day4 ,if !re _h be5 no rema9d]1 'tis pla9 ! ye> w\ld con/antly beg9 on ! same day ( ! week4 ,b s9ce "o rema9s1 'tis z pla9 t ! ye> mu/ beg9 & end on ! same day ( ! week2 & !re=e ! next ye> w beg9 on ! day foll[+4 ,h5ce1 :5 ,janu>y beg9s on ,sunday1 ,a is ! ,dom9ical or ,sunday ,lett] = t ye>3 !n1 because ! next ye> beg9s on ,monday1 ! ,sunday w fall on ! sev5? day1 to :i* is annex$ ! sev5? ,lett] ,g1 :i* !re=e w be ! ,dom9ical ,lett] = all t ye>3 & z ! ?ird ye> w beg9 on ,tuesday1 ! ,sunday w fall on ! six? day2 !re=e ,f w be ! ,sunday ,lett] = t ye>4 ,:5ce 'tis evid5t t ! ,sunday ,lett]s w g annually 9 a retrograde ord] ?us1 ,g1 ,f1 ,e1 ,d1 ,c1 ,b1 ,a4 ,& 9 ! c\rse ( sev5 ye>s1 if !y 7 all common ones1 ! same days ( ! week & ,dom9ical ,lett]s w\ld return to ! same days ( ! mon?s4 ,b because !re are #cff days 9 a leap-ye>1 if ?is numb] be divid$ by #g1 !re w rema9 two days ov] & above ! #eb weeks ( :i* ! ye> consi/s4 ,& !re=e1 if ! leap-ye> beg9s on ,sunday1 x w end on ,monday2 & ! next ye> w beg9 on ,tuesday1 ! fir/ ,sunday :]e( mu/ fall on ! six? ( ,janu>y1 to :i* is annex$ ! ,lett] ,f1 & n ,g z 9 common ye>s4 ,by ?is means1 ! leap-ye> return+ e f\r? ye>1 ! ord] ( ! ,dom9ical ,lett]s is int]rupt$2 & ! ,s]ies does n return to its fir/ /ate till aft] f\r times sev51 or #bh ye>s3 & !n ! same days ( ! mon? return 9 ord] to ! same days ( ! week4 ,sid5ote3 ,to f9d ! ,dom9ical ,lett]4 #dbh4 ,to f9d ! ,dom9ical ,lett] = any ye> ei!r be=e or aft] ! ,*ri/ian ra#hg3 ,9 ,table ,,iii or ,,iv = ,old ,/yle1 or ,v = ,new ,/yle1 look = ! hundr$s ( ye>s at ! head ( ! ,table1 & = ! ye>s bel[ an hundr$ 7to make up ! giv5 ye>7 at ! left h&3 & :]e ! columns meet y h ! ,dom9ical ,lett] = ! ye> desir$4 ,?us1 suppose ! ,dom9ical ,lett] be requir$ = ! ye> ( ,,*ri/ #ageh1 ,new ,/yle1 ,i look = #agjj at ! head ( ,table ,v1 & = #eh at ! left h& ( ! same ,table2 & 9 ! angle ( meet+1 ,i f9d ,a1 :i* is ! ,dom9ical ,lett] = t ye>4 ,if x 0 want$ = ! same ye> ,old ,/yle1 x w\ld be f\nd by ,table ,,iv to be ,d4 ,b to f9d ! ,dom9ical ,lett] = any giv5 ye> be=e ,,*ri/1 subtract "o f t ye> & !n proce$ 9 all respects z j n[ taught1 to f9d x by ,table ,,iii ,?us1 suppose ! ,dom9ical ,lett] be requir$ = ! #ehe? ye> be=e ! fir/ ye> ( ,,*ri/1 look = #ejj at ! head ( ,table ,,iii1 & = #hd at ! left h&2 9 ! meet+ ( ^! columns is ,,fe1 :i* 7 ! ,dom9ical ,lett]s = t ye>1 & %ews t x 0 a leap-ye>2 because1 leap-ye> has always two ,dom9ical ,lett]s4 ,sid5ote3 ,to f9d ! ,days ( ! ,mon?s4 #dbi4 ,to f9d ! day ( ! mon? answ]+ to any day ( ! week1 or ! day ( ! week answ]+ to any day ( ! mon?2 = any ye> pa/ or to come3 ,hav+ f\nd ! ,dom9ical ,lett] = ! giv5 ye>1 ent] ,table ,,vi1 ) ! ,dom9ical ,lett] at ! head2 & "u x1 all ! days 9 t column to ! "r h& are ,sundays1 9 ! divisions ( ! mon?s2 ! next column to ! "r are ,mondays2 ! next1 ,tuesdays2 & s on to ! la/ column "u ,g1 f :i* g back to ! column "u ,a1 & !nce proce$ t[>ds ! "r h& z be=e4 ,?us1 9 ! ye> #ageg1 ! ,dom9ical ,lett] ,new ,/yle is ,b1 9 ,table ,v1 !n 9 ,table ,,vi all ! days "u ,b are ,sundays 9 t ye>1 viz4 ! #b;d1 #i?1 #af?1 #bc;d1 & #cj? ( ,janu>y & ,octob]2 ! #f?1 #ac?1 #bj?1 & #bg? ( ,febru>y1 ,m>* & ,novemb]2 ! #c;d1 #aj?1 & #ag?1 ( ,april & ,july1 toge!r ) ! #ca/ ( ,july3 & s on to ! foot ( ! column4 ,!n1 ( c\rse1 all ! days "u ,c on ,mondays1 namely ! #c;d1 #aj?1 c4 ( ,janu>y & ,octob]2 & s ( all ! re/ 9 t column4 ,if ! day ( ! week answ]+ to any day ( ! mon? be requir$1 x is easily _h f ! same ,table by ! ,lett] t /&s at ! top ( ! column 9 :i* ! giv5 day ( ! mon? is f\nd4 ,?us1 ! ,lett] t /&s ov] ! #bh? ( ,may is ,a2 & 9 ! ye> #ehe be=e ,,*ri/ ! ,dom9ical ,lett] 0 f\nd to be ,,fe #dbh2 :i* be+ a leap-ye>1 & ,e tak+ place f ! #bd? ( ,febru>y to ! end ( t ye>1 %ews by ! ,table t ! #be? ( ,may 0 on a ,sunday2 & !re=e ! #bh? mu/ h be5 on a ,w$nesday3 = :5 ,e /&s = ,sunday1 ,f mu/ /& = ,monday1 ,g = ,tuesday1 ,a = ,w$nesday1 ,b = ,?ursday1 ,c = ,friday1 & ,d = ,saturday4 ,h5ce1 z x appe>s t ! fam\s ,eclipse ( ! ,sun =etold by ,,?ales1 by :i* a peace 0 br\ght ab\t betwe5 ! ,m$es & ,lydians1 happ5$ on ! #bh? ( ,may1 9 ! #ehe? ye> be=e ,,*ri/1 x c]ta9ly fell on a ,w$nesday4 ,sid5ote3 ,julian ,p]iod4 #dcj4 ,f ! multiplication ( ! ,sol> ,cycle ( #bh ye>s into ! ,lun> ,cycle ( #ai ye>s1 arises ! great ,julian ,p]iod consi/+ ( #gihj ye>s2 :i* _h its beg9n+ #gfd ye>s be=e ! suppos$ ye> ( ! creation 7:5 all ! ?ree ,cycles began toge!r7 & is n yet compleat$1 & !re=e x compreh5ds all o!r ,cycles1 ,p]iods & ras4 ,!re is b "o ye> 9 ! :ole ,p]iod :i* has ! same numb]s = ! ?ree ,cycles ( :i* x is made up3 & !re=e1 if hi/orians _h rem>k$ 9 _! writ+s ! ,cycles ( ea* ye>1 !re _h be5 no dispute ab\t ! "t ( any action record$ by !m4 ,sid5ote3 ,to f9d ! ye> ( ?is ,p]iod4 ,& ! ,cycles ( t ye>4 #dca4 ,! ,dionysian or vulg> ra ( ,*ri/'s bir? 0 ab\t ! end ( ! ye> ( ! ,julian ,p]iod #dgac2 & consequ5tly ! fir/ ye> ( 8 age1 accord+ to t acc\nt1 0 ! #dgad? ye> ( ! said ,p]iod4 ,!re=e1 if to ! curr5t ye> ( ,*ri/ we add #dgac1 ! ,sum w be ! ye> ( ! ,julian ,p]iod4 ,s ! ye> #ageg w be f\nd to be ! #fdgj? ye> ( t ,p]iod4 ,or1 to f9d ! ye> ( ! ,julian ,p]iod answ]+ to any giv5 ye> be=e ! fir/ ye> ( ,,*ri/1 subtract ! numb] ( t giv5 ye> f #dgad1 & ! rema9d] w be ! ye> ( ! ,julian ,p]iod4 ,?us1 ! ye> #ehe be=e ! fir/ ye> ( ,,*ri/ 7:i* 0 ! #ehd? be=e 8 bir?7 0 ! #dabi? ye> ( ! said ,p]iod4 ,la/ly1 to f9d ! ,cycles ( ! ,sun1 ,moon1 & ,indiction = any giv5 ye> ( ?is ,p]iod1 divide ! giv5 ye> by #bh1 #ai1 & #ae2 ! ?ree rema9d]s w be ! ,cycles s\ght1 & ! ,quoti5ts ! numb]s ( ,cycles run s9ce ! beg9n+ ( ! ,p]iod4 ,s 9 ! above #dgad? ye> ( ! ,julian ,p]iod ! ,cycle ( ! ,sun 0 #aj1 ! ,cycle ( ! ,moon #b1 & ! ,cycle ( ,indiction #d2 ! ,sol> ,cycle hav+ run ?r\gh #afh c\rses1 ! ,lun> #bdh1 & ! ,indiction #cad4 ,sid5ote3 ,! true ra ( ,,*ri/'s bir?4 #dcb4 ,! vulg> ra ( ,,*ri/'s bir? 0 nev] settl$ till ! ye> #ebg2 :5 ,dionysius ,exiguus1 a ,roman ,abbot1 fix$ x to ! end ( ! #dgac? ye> ( ! ,julian ,p]iod2 :i* 0 c]ta9ly f\r ye>s too late4 ,=1 our ,,savi\r 0 und\bt$ly born be=e ! ,dea? ( ,h]od ! ,great1 :o s\ght to kill him z soon z he he>d ( 8 bir?4 ,&1 accord+ to ! te/imony ( ,josephus 7,b4 xvii4 c4 #h47 !re 0 an eclipse ( ! ,moon 9 ! "t ( ,h]od's la/ illness3 :i* v eclipse our ,a/ronomical ,tables %ew to h be5 9 ! ye> ( ! ,julian ,p]iod #dgaj1 ,m>* #ac?1 #c h\rs #ba m9utes aft] mid-night1 at ,j]usalem4 ,n[1 z our ,,savi\r mu/ h be5 born "s mon?s be=e ,h]od's dea?1 s9ce 9 ! int]val he 0 c>ri$ into gypt2 ! late/ "t 9 :i* we c possibly fix ! true ra ( 8 bir? is ab\t ! end ( ! #dgji? ye> ( ! ,julian ,p]iod4 ,& ?is is f\r ye>s be=e ! vulg> ra !re(4 ,sid5ote3 ,! "t ( 8 crucifixion4 ,9 ! =m] edition ( ?is book1 ,i endeav\r$ to asc]ta9 ! "t ( ,,*ri/'s dea?2 by %ew+ 9 :at ye>1 ab\t ! reput$ "t ( ! ,passion1 !re 0 a ,passov] ,full ,moon on a ,friday3 on :i* day ( ! week1 & at ! "t ( ! ,passov]1 x is evid5t f ,m>k xv4 #db4 t our ,,savi\r 0 crucifi$4 ,& 9 comput+ ! times ( all ! ,passov] ,full ,moons f ! #bj? to ! #dj? ye> ( ,,*ri/1 aft] ! ,jewi% mann]1 :i* 0 to add #ad days to ! "t :5 ! ,new ,moon next be=e ! ,passov] 0 fir/ visible at ,j]usalem1 9 ord] to h _! day ( ! ,passov] ,full ,moon1 ,i f\nd t ! only ,passov] ,full ,moon :i* fell on a ,friday1 9 all t "t1 0 9 ! ye> ( ! ,julian ,p]iod #dgdf1 on ! ?ird day ( ,april3 :i* ye> 0 ! #cc;d ye> ( ,,*ri/'s age1 reckon+ f ! vulg> ra ( 8 bir?1 b ! #cg? c\nt+ f ! true ra !re(3 & 0 also ! la/ ye> ( ! #djb;d ,olympiad#hh1 9 :i* v ye> ,phlegon an ,hea!n writ] tells u1 !re 0 ! mo/ extraord9>y ,eclipse ( ! ,sun t ev] 0 kn[n1 & t x 0 night at ! six? h\r ( ! day4 ,:i* agrees exactly ) ! "t t ! d>kness at ! crucifixion began1 accord+ to ! ?ree ,evangeli/s :o m5tion x#hi3 & !re=e mu/ h be5 ! v same d>kness1 b mi/ak5 by ,phlegon = a natural ,eclipse ( ! ,sun2 :i* 0 impossible on two acc\nts1 #a4 because x 0 at ! "t ( ,full ,moon2 & #b4 because :oev] takes ! pa9s to calculate1 w f9d t !re c\ld be no regul> & total ,eclipse ( ! ,sun t ye> 9 any "p ( ,judea1 nor any :]e betwe5 ,j]usalem & ,egypt3 s t ?is d>kness mu/ h be5 q out ( ! common c\rse ( nature4 ,f ! co-incid5ce ( ^! *>act]s1 ,i made no d\bt ( hav+ asc]ta9$ ! true ye> & day ( our ,,savi\r's dea?4 ,b hav+ v lately read :at "s em95t au?ors h wrote on ! same subject1 ( :i* ,i 0 really ignorant be=e2 & he>d ! op9ions ( o!r c&id & +5i\s enquir]s aft] tru? 7:i* e hone/ man w foll[ :]ev] x leads him7 & :o ?9k !y h /rong reasons = believ+ t ! "t ( ,,*ri/'s dea? 0 n 9 ! ye> ( ! ,julian ,p]iod #dgdf1 b 9 ! ye> #dgdc2 ,i f9d difficulties on bo? sides1 n easily got ov]3 & %all !re=e /ate ! case bo? ways z fairly z ,i c2 leav+ ! read] to take :i* side ( ! ,"q he pleases4 ,bo? ,dr4 ,prideaux & ,sir ,isaac ,newton are ( op9ion t ,daniel's sev5ty weeks1 consi/+ ( #dij ye>s 7,dan4 *ap4 ix4 v4 #bc-bf7 began ) ! "t :5 ,ezra receiv$ 8 commission f ,artax]xes to g to ,j]usalem1 :i* 0 9 ! sev5? ye> ( t ,k+'s reign 7,ezra *4 vii4 v4 #aa-bf7 & end$ ) ! dea? ( ,,*ri/4 ,=1 by jo9+ ! accompli%m5t ( t prophecy ) ! expiation ( ,s91 ^? weeks _c well be suppos$ to end at any o!r "t4 ,& bo? ^! au?ors agree t ?is 0 ,artax]xes ,longimanus1 n ,artax]xes ,mnemon4 ,! ,doctor ?9ks t ! la/ ( ^? annual weeks 0 equally divid$ betwe5 ,john's m9i/ry & ,,*ri/'s4 ,&1 z to ! half week1 m5tion$ by ,daniel *ap4 ix4 v4 #bg4 ,sir ,isaac ?9ks x made no "p ( ! above sev5ty2 b only meant ! ?ree ye>s & an half 9 :i* ! ,romans made w> ^u ! ,jews f spr+ 9 ,a4,d4 #fg to autumn 9 ,a4,d4 #gj1 :5 a f9al ,p]iod 0 put to _! sacrifices & oblations by de/roy+ _! city & sanctu>y1 on :i* !y 7 utt]ly disp]s$4 ,n[1 bo? by ! und\bt$ ,canon ( ,ptolemy1 & ! fam\s ra ( ,nabonass>1 :i* is s well v]ifi$ by ,eclipses t x _c deceive u1 ! beg9n+ ( ^! sev5ty weeks1 or ! sev5? ye> ( ! reign ( ,artax]xes ,longimanus1 is p9n$ d[n to ! ye> ( ! ,julian ,p]iod #dbef3 f :i* c\nt #dij ye>s to ! dea? ( ,,*ri/1 & ! same w fall 9 ! above ye> ( ! ,julian ,p]iod #dgdf3 :i* w\ld seem to asc]ta9 ! true ye> beyond dispute4 ,b z ,josephus's ,eclipse ( ! ,moon 9 a great measure fixes our ,,savi\r's bir? to ! end ( ! #dgac? ye> ( ! ,julian ,p]iod1 & a ,friday ,passov] ,full ,moon fixes ! "t ( 8 dea? to ! ?ird ( ,april 9 ! #dgdf? ye> ( t ,p]iod1 ! same z above by ,daniel's weeks1 ?is supposes our ,,savi\r to h be5 crucifi$ 9 ! #cg? ye> ( 8 age4 ,& z ,/4 ,luke *ap4 iii4 v]4 #bc4 fixes ! "t ( ,,*ri/'s baptism to ! beg9n+ ( 8 #cj? ye>1 x w\ld h5ce seem t 8 publick m9i/ry1 to :i* 8 baptism 0 ! initiation1 la/$ sev5 ye>s4 ,b1 z x w\ld be v difficult to f9d acc\nt 9 all ! ,evangeli/s ( m ?an f\r ,passov]s :i* he kept at ,j]usalem dur+ ! "t ( 8 m9i/ry1 o!rs ?9k t he suff]$ 9 ! vulg> #cj? ye> ( 8 age1 :i* 0 really ! #cc;d2 namely 9 ! ye> ( ! ,julian ,p]iod #dgdc4 ,& ?is op9ion is f>!r /r5g!n$ by consid]+ t our ,,savi\r eat 8 la/ ,pas*al ,supp] on a ,?ursday ev5+1 ! day imm$iately be=e 8 crucifixion3 & t z he subject$ himself to ! law1 he w\ld n break ! law by keep+ ! ,passov] on ! day be=e ! law prescrib$2 nei!r w\ld ! ,prie/s h suff]$ ! ,lamb to be kill$ = him be=e ! f\rte5? day ( ,nisan :5 x 0 kill$ = all ! p1 ,exod4 xii4 v]4 #f4 ,& h5ce !y inf] t he kept ?is ,passov] at ! same "t ) ! re/ ( ! ,jews1 9 ! vulg> #cj? ye> ( 8 age3 at :i* "t x is evid5t by calculation t !re 0 a ,passov] ,full ,moon on ,?ursday ,april ! #f?4 ,b ?is is press$ ) two difficulties4 #a4 ,x drops ! la/ half ( ,daniel's sev5tie? week1 z ( no mom5t 9 ! prophecy2 & #b4 x sets aside ! te/imony ( ,phlegon1 z if he _h mi/ak5 almo/ a :ole ,olympiad4 ,o!rs aga9 endeav\r to reconcile ! :ole diff]5ce1 by suppos+1 t z ,,*ri/ express$ himself only 9 r\nd numb]s conc]n+ ! "t he 0 to lie 9 ! grave1 ,matt4 xii4 #dj4 s might ,/4 ,luke possibly h done ) reg>d to ! ye> ( 8 baptism3 :i* w\ld really seem to be ! case :5 we consid]1 t ! ,jews told our ,,savi\r1 sometime be=e 8 dea?1 ,?\ art n yet fifty ye>s old1 ,john vii4 #eg4 :i* inde$ 0 m likely to be said to a p]son ne> =ty ?an to "o b j turn$ ( ?irty4 ,& z to 8 eat+ ! above ,passov] on ,?ursday1 :i* mu/ h be5 on ! ,jewi% ,full ,moon day1 !y ?9k x may be easily accommodat$ to ! #cg? ye> ( 8 age2 s9ce1 z ! ,jews always began _! day 9 ! ev5+1 _! ,friday ( c\rse began on ! ev5+ ( our ,?ursday4 ,& x is evid5t1 z above-m5tion$1 t ! only ,jewi% ,friday ,full ,moon1 at ! "t ( _! ,passov]1 0 9 ! vulg> #cc;d1 b ! real #cg? ye> ( ,,*ri/'s age2 :i* 0 ! #dgdf? ye> ( ! ,julian ,p]iod1 & ! la/ ye> ( ! #bjb;d ,olympiad4 ,sid5ote3 ras or ,epo*as4 #dcc4 ,z !re are c]ta9 fix$ po9ts 9 ! ,heav5s f :i* ,a/ronom]s beg9 _! computations1 s !re are c]ta9 po9ts ( "t f :i* hi/orians beg9 to reckon2 & ^! po9ts or roots ( "t are call$ ras or ,epo*as4 ,! mo/ rem>kable ras are ^? ( ! ,creation1 ! ,greek ,olympiads1 ! build+ ( ,rome1 ! ra ( ,nabonass>1 ! dea? ( ,alex&]1 ! bir? ( ,,*ri/1 ! ,arabian ,hegira1 & ! ,p]sian ,jesdegird3 ,all :i*1 toge!r ) sev]al o!rs ( less note1 h _! beg9n+s 9 ! foll[+ ,table fix$ to ! ye>s ( ! ,julian ,p]iod1 to ! age ( ! _w at ^? times1 & to ! ye>s be=e & aft] ! bir? ( ,,*ri/4 ,julian ,p]iod4 ,y4 ( ! ,_w4 ,be=e ,*ri/4 #a4 ,! creation ( ! _w1 accord+ to ,/rau*ius #gfd #a #cidi #b4 ,! ,deluge1 or ,noah's ,flood #bdbj #afef #bbic #c4 ,! ,assyrian ,mon>*y by ,nimrod #becg #aggc #bagf #d4 ,! ,bir? ( ,abraham #bgab #aidh #bjja #e4 ,! beg9n+ ( ! ,k+dom ( ! ,argives #bhef #bjib #aheg #f4 ,! beg94 ( ! ,k+dom ( ,a!ns by ,cecrops #caeg #bcic #aeef #g4 ,! dep>ture ( ! ,israelites f ,egypt #cbaf #bdeb #adig #h4 ,_! entrance into ,canaan1 or ! ,jubilee #cbef #bdib #adeg #i4 ,! de/ruction ( ,troy #cebi #bhfe #aahd #aj4 ,! beg9n+ ( ,k+ ,david's reign #cfec #bhhi #ajfj #aa4 ,! f\ndation ( ,solomon's ,temple #cfif #bicb #ajag #ab4 ,! ,argonautic exp$ition #cggf #cjab #icg #ac4 ,arbaces1 ! fir/ ,k+ ( ! ,m$es #chch #cjgd #age #ad4 ,m&aucus ! second #chfe #caja #hdh #ae4 ,sos>mus ! ?ird #ciae #caea #gih #af4 ,artica ! f\r? #cide #caha #gfh #ag4 ,c>dica ! fif? #ciif #cbcb #gah #ah4 ,phraortes ! six? #djeg #cbic #fef #ai4 ,cyax>es ! sev5? #djhj #ccaf #fcc #bj4 ,! beg9n+ ( ! ,olympiads #cich #cagd #gge #ba4 ,! ,catonian ,epo*a ( ! build+ ( ,rome #cifa #caig #geb #bb4 ,! ra ( ,nabonass> #cifg #cbjb #gdf #bc4 ,! de/ruction ( ,sam>ia #ciij #cbbf #gbc #bd4 ,! ,babyloni% captivity #dacc #ccdi #fjj #be4 ,! de/ruction ( ,solomon's ,temple #dabd #ccfj #ehi #bf4 ,! ,p]sian mon>*y f\nd$ by ,cyrus #daed #ccij #eei #bg4 ,! battle ( ,m>a?on #dbbd #cdfj #dhi #bh4 ,! beg94 ( ! reign ( ,art4 ,longimanus #dbdi #cdhe #dfd #bi4 ,! beg9n+ ( ,daniel's #gj weeks #dbef #cdib #deg #cj4 ,! beg9n+ ( ! ,peloponnesian w> #dbhb #ceah #dca #ca4 ,! dea? ( ,alex&] #dcij #cfbf #cbc #cb4 ,! re/oration ( ! ,jews #dedh #cghd #abi #cc4 ,! corr4 ( ! ,cal5d> by ,julius ,cs> #dffi #cije #dd #cd4 ,! beg9n+ ( ! reign ( ,h]od #dfgc #ciji #dj #ce4 ,! ,spani% ra #dfge #ciaa #ch #cf4 ,! battle at ,actium #dfhc #ciai #cj #cg4 ,! tak+ ( ,alex&ria #dfhc #ciai #cj #ch4 ,! ,epo* ( ! title ( ,augu/us #dfhf #cibb #bg #ci4 ,! true ra ( ,,*ri/'s bir? #dgji #cide #d #dj4 ,! dea? ( ,h]od #dgaj #cidf #c #da4 ,! ,diony4 or vulg4 ra ( ! bir? ( ,,*ri/ #dgac #cidi ,,ad#j #db4 ,! true ye> ( ,,*ri/'s dea? #dgdf #cihb #cc #dc4 ,! de/ruction ( ,j]usalem #dghc #djai #gj #dd4 ,! ,dioclesian p]secution #ejae #dbea #cjb #de4 ,! ,epo* ( ,con/ant9e ! ,great #ejai #dbee #cjf #df4 ,! ,c\ncil ( ,nice #ejch #dbgd #cbe #dg4 ,! ,epo*a ( ! ,hegira #ecce #dega #fbb #dh4 ,! ,epo* ( ,yesdej]d #ecdd #dehj #fca #di4 ,! ,jellalan ,epo*a #egia #ejbg #ajgh #ej4 ,! ,epo*a ( ! re=mation #fbcj #edff #aeag ---------------------------------------- -------------------------------- ,,tab4 ,i4 ,%ew+ ! ,gold5 ,numb] 7:i* is ! same bo? 9 ! ,old & ,new ,/yle7 f ! ,*ri/ian ra to ,a4,d4 #djjj4 ---------------------------------------- -------------------------------- ,ye>s less ?an an ,hundr$4 ---------------------------------------- -------------- #j #a #b #cd #ef #g #h #iajaaabacadaeafagah #aibjbabbbcbdbebfbgbhbicjcacbcccdcecfcg ,hundr$s ( #chcidjdadbdcdddedfdgdhdiejeaebecedeeef ,ye>s4 #egeheifjfafbfcfdfefffgfhfigjgagbgcgdge #gfggghgihjhahbhchdhehfhghhhiijiaibicid #ieifigihii -------------- #jaijjchjj #a #b #c #d #e #f #g #h #iajaaabacadaeafagahai #ajjbjjjcijj #f #g #h #iajaaabacadaeafagahai #a #b #c #d #e #bjjbajjdjjjaaabacadaeafagahai #a #b #c #d #e #f #g #h #iaj #cjjbbjj c4#afagahai #a #b #c #d #e #f #g #h #iajaaabacadae #djjbcjj -- #b #c #d #e #f #g #h #iajaaabacadaeafagahai #a ---------------------------------------- ---------- #ejjbdjj -- #g #h #iajaaabacadaeafagahai #a #b #c #d #e #f #fjjbejj -- #abacadaeafagahai #a #b #c #d #e #f #g #h #iajaa #gjjbfjj -- #agahai #a #b #c #d #e #f #g #h #iajaaabacadaeaf #hjjbgjj -- #c #d #e #f #g #h #iajaaabacadaeafagahai #a #b #ijjbhjj -- #h #iajaaabacadaeafagahai #a #b #c #d #e #f #g ---------------------------------------- ---------- #ajjjbijj -- #acadaeafagahai #a #b #c #d #e #f #g #h #iajaaab #aajjcjjj -- #ahai #a #b #c #d #e #f #g #h #iajaaabacadaeafag #abjjcajj -- #d #e #f #g #h #iajaaabacadaeafagahai #a #b #c #acjjcbjj -- #iajaaabacadaeafagahai #a #b #c #d #e #f #g #h #adjjccjj -- #adaeafagahai #a #b #c #d #e #f #g #h #iajaaabac ---------------------------------------- ---------- #aejjcdjj -- #ai #a #b #c #d #e #f #g #h #iajaaabacadaeafagah #afjjcejj -- #e #f #g #h #iajaaabacadaeafagahai #a #b #c #d #agjjcfjj -- #ajaaabacadaeafagahai #a #b #c #d #e #f #g #h #i #ahjjcgjj -- #aeafagahai #a #b #c #d #e #f #g #h #iajaaabacad ---------------------------------------- ---------- ---------------------------------------- ---------------------- ,,tab4 ,,ii4 ,%ew+ ! ,numb] ( ,direction1 = f9d+ ,ea/] ,sunday by ! ,gold5 ,numb] & ,dom9ical ,lett]4 ---------------------------------------- --- ,g4 ,n4 #a #b #c #d #e #f #g #h #iajaaabacadaeafagahai ---------------------------------------- --- ,a #bfai #ebfabccaiabbfai #ebfab #ebfabccaiab ,b #bgac #fbgaccdbjacbgbj #fbgac #fbjaccdbj #f ,c #bhad #gbaadceba #gbhba #gbhad #gbaadbhba #g ,d #biae #hbbaebibb #hbiae #hbiae #abbaebibb #h ,e #cjaf #bbcafcjbc #icjaf #ibcaf #bbc #icjbc #i ,f #bdag #cbdajcabdajcaagajbdag #cbdajcaagaj ,g #beah #dbeaacbahaacbah #dbeah #dbeaacbahaa ---------------------------------------- --- ,?is ,table is adapt$ to ! ,new ,/yle4 ---------------------------------------- ---------------------- ,,tab4 ,,iii4 ,%ew+ ! ,dom9ical ,lett]s1 ,old ,/yle1 = #dbjj ,ye>s be=e ! ,*ri/ian ra4 ---------------------------------------- --------------------------- ,be=e ,*ri/ ,hundr$s ( ,ye>s4 ---------------------------------------- --------------------- #j #ajj #bjj #cjj #djj #ejj #fjj #gjj #hjj #ijj #ajjj #aajj #abjj #acjj ,ye>s less #adjj #aejj #afjj #agjj #ahjj #aijj #bjjj ?an an #bajj #bbjj #bcjj #bdjj #bejj #bfjj #bgjj ,hundr$4 #bhjj #bijj #cjjj #cajj #cbjj #ccjj #cdjj #cejj #cfjj #cgjj #chjj #cijj #djjj #dajj ---------------------------------------- ------------------ #j #bh #ef #hd ,d ,c ,c ,b ,b ,a ,a ,g ,g ,f ,f ,e ,e ,d ---------------------------------------- ------------------ #a #bi #eg #he ,e ,d ,c ,b ,a ,g ,f #b #cj #eh #hf ,f ,e ,d ,c ,b ,a ,g #c #ca #ei #hg ,g ,f ,e ,d ,c ,b ,a #d #cb #fj #hh ,b ,a ,a ,g ,g ,f ,f ,e ,e ,d ,d ,c ,c ,b ---------------------------------------- ------------------ #e #cc #fa #hi ,c ,b ,a ,g ,f ,e ,d #f #cd #fb #ij ,d ,c ,b ,a ,g ,f ,e #g #ce #fc #ia ,e ,d ,c ,b ,a ,g ,f #h #cf #fd #ib ,g ,f ,f ,e ,e ,d ,d ,c ,c ,b ,b ,a ,a ,g ---------------------------------------- ------------------ #i #cg #fe #ic ,a ,g ,f ,e ,d ,c ,b #aj #ch #ff #id ,b ,a ,g ,f ,e ,d ,c #aa #ci #fg #ie ,c ,b ,a ,g ,f ,e ,d #ab #dj #fh #if ,e ,d ,d ,c ,c ,b ,b ,a ,a ,g ,g ,f ,f ,e ---------------------------------------- ------------------ #ac #da #fi #ig ,f ,e ,d ,c ,b ,a ,g #ad #db #gj #ih ,g ,f ,e ,d ,c ,b ,a #ae #dc #ga #ii ,a ,g ,f ,e ,d ,c ,b #af #dd #gb ,c ,b ,b ,a ,a ,g ,g ,f ,f ,e ,e ,d ,d ,c ---------------------------------------- ------------------ #ag #de #gc ,d ,c ,b ,a ,g ,f ,e #ah #df #gd ,e ,d ,c ,b ,a ,g ,f #ai #dg #ge ,f ,e ,d ,c ,b ,a ,g #bj #dh #gf ,a ,g ,g ,f ,f ,e ,e ,d ,d ,c ,c ,b ,b ,a ---------------------------------------- ------------------ #ba #di #gg ,b ,a ,g ,f ,e ,d ,c #bb #ej #gh ,c ,b ,a ,g ,f ,e ,d #bc #ea #gi ,d ,c ,b ,a ,g ,f ,e #bd #eb #hj ,f ,e ,e ,d ,d ,c ,c ,b ,b ,a ,a ,g ,g ,f ---------------------------------------- ------------------ #be #ec #ha ,g ,f ,e ,d ,c ,b ,a #bf #ed #hb ,a ,g ,f ,e ,d ,c ,b #bg #ee #hc ,b ,a ,g ,f ,e ,d ,c ---------------------------------------- ------------------ ,,tab4 ,,iv4 ,%ew+ ! ,dom9ical ,lett]s1 ,old ,/yle1 = #dbjj ,ye>s aft] ! ,*ri/ian ra4 ---------------------------------------- --------------------------- ,aft] ,*ri/ ,hundr$s ( ,ye>s4 ---------------------------------------- --------------------- #j #ajj #bjj #cjj #djj #ejj #fjj #gjj #hjj #ijj #ajjj #aajj #abjj #acjj ,ye>s less #adjj #aejj #afjj #agjj #ahjj #aijj #bjjj ?an an #bajj #bbjj #bcjj #bdjj #bejj #bfjj #bgjj ,hundr$4 #bhjj #bijj #cjjj #cajj #cbjj #ccjj #cdjj #cejj #cfjj #cgjj #chjj #cijj #djjj #dajj ---------------------------------------- ------------------ #j #bh #ef #hd ,d ,c ,e ,d ,f ,e ,g ,f ,a ,g ,b ,a ,c ,b ---------------------------------------- ------------------ #a #bi #eg #he ,b ,c ,d ,e ,f ,g ,a #b #cj #eh #hf ,a ,b ,c ,d ,e ,f ,g #c #ca #ei #hg ,g ,a ,b ,c ,d ,e ,f #d #cb #fj #hh ,f ,e ,g ,f ,a ,g ,b ,a ,c ,b ,d ,c ,e ,d ---------------------------------------- ------------------ #e #cc #fa #hi ,d ,e ,f ,g ,a ,b ,c #f #cd #fb #ij ,c ,d ,e ,f ,g ,a ,b #g #ce #fc #ia ,b ,c ,d ,e ,f ,g ,a #h #cf #fd #ib ,a ,g ,b ,a ,c ,b ,d ,c ,e ,d ,f ,e ,g ,f ---------------------------------------- ------------------ #i #cg #fe #ic ,f ,g ,a ,b ,c ,d ,e #aj #ch #ff #id ,e ,f ,g ,a ,b ,c ,d #aa #ci #fg #ie ,d ,e ,f ,g ,a ,b ,c #ab #dj #fh #if ,c ,b ,d ,c ,e ,d ,f ,e ,g ,f ,a ,g ,b ,a ---------------------------------------- ------------------ #ac #da #fi #ig ,a ,b ,c ,d ,e ,f ,g #ad #db #gj #ih ,g ,a ,b ,c ,d ,e ,f #ae #dc #ga #ii ,f ,g ,a ,b ,c ,d ,e #af #dd #gb ,e ,d ,f ,e ,g ,f ,a ,g ,b ,a ,c ,b ,d ,c ---------------------------------------- ------------------ #ag #de #gc ,c ,d ,e ,f ,g ,a ,b #ah #df #gd ,b ,c ,d ,e ,f ,g ,a #ai #dg #ge ,a ,b ,c ,d ,e ,f ,g #bj #dh #gf ,g ,f ,a ,g ,b ,a ,c ,b ,d ,c ,e ,d ,f ,e ---------------------------------------- ------------------ #ba #di #gg ,e ,f ,g ,a ,b ,c ,d #bb #ej #gh ,d ,e ,f ,g ,a ,b ,c #bc #ea #gi ,c ,d ,e ,f ,g ,a ,b #bd #eb #hj ,b ,a ,c ,b ,d ,c ,e ,d ,f ,e ,g ,f ,a ,g ---------------------------------------- ------------------ #be #ec #ha ,g ,a ,b ,c ,d ,e ,f #bf #ed #hb ,f ,g ,a ,b ,c ,d ,e #bg #ee #hc ,e ,f ,g ,a ,b ,c ,d ---------------------------------------- ------------------ ,,tab4 ,v4 ,! ,dom9ical ,lett]1 ,new ,/yle1 = #djjj ,ye>s aft] ! ,*ri/ian ra4 ---------------------------------------- ------ ,aft] ,*ri/4 ,hundr$s ( ,ye>s4 ---------------------------------------- --- #ajj #bjj #cjj #djj #ejj #fjj #gjj #hjj #ijj #ajjj #aajj #abjj #acjj #adjj #aejj #afjj #agjj #ahjj #aijj #bjjj ,ye>s less ?an #bajj #bbjj #bcjj #bdjj an ,hundr$4 #bejj #bfjj #bgjj #bhjj #bijj #cjjj #cajj #cbjj #ccjj #cdjj #cejj #cfjj #cgjj #chjj #cijj #djjj ------------------------ ,c ,e ,g ,b ,a ---------------------------------------- #a #bi #eg #he ,b ,d ,f ,g #b #cj #eh #hf ,a ,c ,e ,f #c #ca #ei #hg ,g ,b ,d ,e #d #cb #fj #hh ,f ,e ,a ,g ,c ,b ,d ,c ---------------------------------------- #e #cc #fa #hi ,d ,f ,a ,b #f #cd #fb #ij ,c ,e ,g ,a #g #ce #fc #ia ,b ,d ,f ,g #h #cf #fd #ib ,a ,g ,c ,b ,c ,d ,f ,e ---------------------------------------- #i #cg #fe #ic ,f ,a ,c ,d #aj #ch #ff #id ,e ,g ,b ,c #aa #ci #fg #ie ,d ,f ,a ,b #ab #dj #fh #if ,c ,b ,e ,d ,g ,f ,a ,g ---------------------------------------- #ac #da #fi #ig ,a ,c ,e ,f #ad #db #gj #ih ,g ,b ,d ,e #ae #dc #ga #ii ,f ,a ,c ,d #af #dd #gb ,e ,d ,g ,f ,b ,a ,c ,b ---------------------------------------- #ag #de #gc ,c ,e ,g ,a #ah #df #gd ,b ,d ,f ,g #ai #dg #ge ,a ,c ,e ,f #bj #dh #gf ,g ,f ,b ,a ,d ,c ,e ,d ---------------------------------------- #ba #di #gg ,e ,g ,b ,c #bb #ej #gh ,d ,f ,a ,b #bc #ea #gi ,c ,e ,g ,a #bd #eb #hj ,b ,a ,d ,c ,f ,e ,g ,f ---------------------------------------- #be #ec #ha ,g ,b ,d ,e #bf #ed #hb ,f ,a ,c ,d #bg #ee #hc ,e ,g ,b ,c #bh #ef #hd ,d ,c ,f ,e ,a ,g ,b ,a ---------------------------------------- ,,tab4 ,,vi4 ,%ew+ ! ,days ( ! ,mon?s = bo? ,/yles by ! ,dom9ical ,lett]s4 ---------------------------------------- - ,week ,day4 ,a ,b ,c ,d ,e ,f ,g ---------------------------------------- - #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad ,janu>y #ca #ae #af #ag #ah #ai #bj #ba ,octob] #ca #bb #bc #bd #be #bf #bg #bh #bi #cj #ca ---------------- ------------------------- #a #b #c #d #e #f #g #h #i #aj #aa ,feb4 #bh-bi #ab #ac #ad #ae #af #ag #ah ,m>* #ca #ai #bj #ba #bb #bc #bd #be ,nov4 #cj #bf #bg #bh #bi #cj #ca ---- ------------------------------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae ,april #cj #af #ag #ah #ai #bj #ba #bb ,july #ca #bc #bd #be #bf #bg #bh #bi #cj #ca -------------------- --------------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai ,augu/ #ca #bj #ba #bb #bc #bd #be #bf #bg #bh #bi #cj #ca -------- --------------------------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af ,septemb4 #cj #ag #ah #ai #bj #ba #bb #bc ,decemb4 #ca #bd #be #bf #bg #bh #bi #cj #ca ------------------------ ----------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj ,may #ca #ba #bb #bc #bd #be #bf #bg #bh #bi #cj #ca ------------ ----------------------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag ,june #cj #ah #ai #bj #ba #bb #bc #bd #be #bf #bg #bh #bi #cj ---------------------------------------- - ,,*ap4 ,,xxii4 ,a ,description ( ! ,a/ronomical ,ma*9]y s]v+ to expla9 & illu/rate ! =ego+ "p ( ?is ,treatise4 ,sid5ote3 ,front+ ! ,title ,page4 ,! ,,orr]y4 #dcd4 ,! ,,orr]y4 ,?is ,ma*9e %ews ! ,motions ( ! ,sun1 ,m]cury1 ,v5us1 ,e>?1 & ,moon2 & occasionally1 ! sup]ior ,planets1 ,m>s1 ,jupit]1 & ,saturn may be put on2 ,jupit]'s f\r ,satellites are mov$ r\nd him 9 _! prop] times by a small ,w9*2 & ,saturn has 8 five ,satellites1 & 8 ,r+ :i* keeps its p>allelism r\nd ! ,sun2 & by a ,lamp put 9 ! ,sun's place1 ! ,r+ %ews all ! ,phases describ$ 9 ! #bjd? ,article4 ,sid5ote3 ,! ,sun4 ,! ,ecliptic4 ,9 ! ,c5t]1 ,no #a4 repres5ts ! ,,sun1 support$ by x's ,axis incl9+ almo/ #h ,degrees f ! ,axis ( ! ,ecliptic2 & turn+ r\nd 9 #be-a_/d days on its ,axis1 ( :i* ! ,nor? ,pole incl9es t[>d ! #h? ,degree ( ,pisces 9 ! great ,ecliptic 7,no4 #aa47 :]eon ! ,mon?s & ,days are engrav5 ov] ! ,signs & ,degrees 9 :i* ! ,sun appe>s1 z se5 f ! ,e>?1 on ! diff]5t days ( ! ye>4 ,sid5ote3 ,m]cury4 ,! ne>e/ ,planet 7,no4 #b7 to ! ,sun is ,m]cury1 :i* goes r\nd him 9 #hg days #bc h\rs1 or #hg-bc_/bd diurnal rotations ( ! ,e>?2 b has no ,motion r\nd its ,axis 9 ! ,ma*9e1 because ! "t ( its diurnal ,motion 9 ! ,heav5s is n kn[n to u4 ,sid5ote3 ,v5us4 ,! next ,planet 9 ord] is ,v5us 7,no4 #c7 :i* p]=ms h] annual ,c\rse 9 #bbd days #ag h\rs2 & turns r\nd h] ,axis 9 #bd days #h h\rs1 or 9 #bd-a_/c diurnal rotations ( ! ,e>?4 ,h] ,axis incl9es #ge ,degrees f ! ,axis ( ! ,ecliptic1 & h] ,nor? ,pole incl9es t[>ds ! #bj? ,degree ( ,aqu>ius1 accord+ to ! obs]vations ( ,bian*9i4 ,%e %ews all ! ,ph5om5a describ$ f ! #cj? to ! #dd? ,article 9 ,*ap4 ,i4 ,sid5ote3 ,! ,e>?4 ,next )\t ! ,orbit ( ,v5us is ! ,e>? 7,no4 #d7 :i* turns r\nd its ,axis1 to any fix$ po9t at a great di/ance1 9 #bc h\rs #ef m9utes #d seconds ( mean sol> "t 7#bba seq47 b f ! ,sun to ! ,sun aga9 9 #bd h\rs ( ! same "t4 ,no4 #f is a sid]eal ,dial-,plate "u ! ,e>?2 & ,no4 #g a sol> ,dial-,plate on ! cov] ( ! ,ma*9e4 ,! ,index ( ! =m] %ews sid]eal1 & ( ! latt]1 sol> "t2 & h5ce1 ! =m] ,index ga9s "o entire revolution on ! latt] e ye>1 z #cfe sol> or natural days conta9 #cff sid]eal days1 or app>5t revolutions ( ! ,/>s4 ,9 ! "t t ! ,e>? makes #cfe-a_/d diurnal rotations on its ,axis1 x goes once r\nd ! ,sun 9 ! ,plane ( ! ,ecliptic2 & always keeps opposite to a mov+ ,index 7,no4 #aj7 :i* %ews ! ,sun's daily *ange ( place1 & also ! days ( ! mon?s4 ,! ,e>? is half cov]$ ) a black cap = divid+ ! app>5tly enlight5$ half next ! ,sun1 f ! o!r half1 :i* :5 turn$ away f him is 9 ! d>k4 ,! edge ( ! cap repres5ts ! ,circle b\nd+ ,light & ,d>kness1 & %ews at :at "t ! ,sun rises & sets to all places ?r\gh\t ! ye>4 ,! ,e>?'s ,axis incl9es #bc-a_/b ,degrees f ! ,axis ( ! ,ecliptic1 ! ,nor? ,pole incl9es t[>d ! beg9n+ ( ,canc]2 & keeps its p>allelism ?r\gh\t its annual ,c\rse #dh1 #bjb2 s t 9 ,summ] ! nor!rn p>ts ( ! ,e>? incl9e t[>ds ! ,sun1 & 9 ! ,w9t] f him3 by :i* means1 ! diff]5t l5g?s ( days & nights1 & ! cause ( ! v>i\s seasons1 are demon/rat$ to sight4 ,!re is a broad ,horizon1 to ! upp] side ( :i* is fix$ a ,m]idian ,semi-circle 9 ! ,nor? & ,s\? ,po9ts1 graduat$ on bo? sides f ! ,horizon to #ij 9 ! ,z5i?1 or v]tical ,po9t4 ,! edge ( ! ,horizon is graduat$ f ! ,ea/ & ,we/ to ! ,s\? & ,nor? ,po9ts1 & )9 ^! ,divisions are ! ,po9ts ( ! ,compass4 ,on ! l[] side ( ?is ?9 ,horizon ,plate /& out f\r small ,wires1 to :i* is fix$ a ,twilight ,circle #ah ,degrees f ! graduat$ side ( ! ,horizon all r\nd4 ,?is ,horizon may be put ^u ! ,e>? 7:5 ! cap is tak5 away7 & rectifi$ to ! ,latitude ( any place3 & !n1 by a small ,wire call$ ! ,sol> ,ray1 :i* may be put on s z to proce$ directly f ! ,sun's ,c5t] t[>ds ! ,e>?'s1 b to come no f>!r ?an almo/ to t\* ! ,horizon1 ! beg9n+ ( ,twilight1 "t ( ,sun-ris+1 ) 8 ,amplitude1 ,m]idian ,altitude1 "t ( ,sett+1 ,amplitude1 & end ( ,twilight1 are %ewn = e day ( ! ye>1 at t place to :i* ! ,horizon is rectifi$4 ,sid5ote3 ,! ,moon4 ,! ,moon 7,no4 #e7 goes r\nd ! ,e>?1 f betwe5 x & any fix$ po9t at a great di/ance1 9 #bg days #g h\rs #dc m9utes1 or ?r\gh all ! ,signs & ,degrees ( h] ,orbit2 :i* is call$ h] ,p]iodical ,revolution2 b %e goes r\nd f ! ,sun to ! ,sun aga91 or f ,*ange to ,*ange1 9 #bi days #ab h\rs #de m9utes1 :i* is h] ,synodical ,revolution2 & 9 t "t %e exhibits all ! ,phases already describ$ #bee4 ,:5 ! above-m5tion$ ,horizon is rectifi$ to ! ,latitude ( any giv5 place1 ! times ( ! ,moon's ris+ & sett+1 toge!r ) h] ,amplitude1 are %ewn to t place z well z ! ,sun's2 & all ! v>i\s ,ph5om5a ( ! ,h>ve/ ,moon #bgc seq4 made obvi\s to sight4 ,sid5ote3 ,! ,nodes4 ,! ,moon's ,orbit 7,no4 #i47 is incl9$ to ! ,ecliptic1 7,no4 #aa47 "o half be+ above1 & ! o!r bel[ x4 ,! ,nodes1 or ,po9ts at #j & #j lie 9 ! ,plane ( ! ,ecliptic1 z describ$ #cag1 #cah1 & %ift backw>d ?r\gh all x's ,signs & ,degrees 9 #ah-b_/c ye>s4 ,! ,degrees ( ! ,moon's ,latitude1 to ! highe/ at ,,nl 7,nor? ,latitude7 & l[e/ at ,,sl 7,s\? ,latitude7 are engrav5 bo? ways f h] ,nodes at #j & #j2 &1 z ! ,moon rises & falls 9 h] ,orbit accord+ to its incl9ation1 h] ,latitude & ,di/ance f h] ,nodes are %ewn = e day2 hav+ fir/ rectifi$ h] ,orbit s z to set ! ,nodes to _! prop] places 9 ! ,ecliptic3 & !n1 z !y come ab\t at diff]5t1 & almo/ opposite times ( ! ye> #cai1 & !n po9t t[>ds ! ,sun1 all ! ,eclipses may be %ewn = hundr$s ( ye>s 7)\t any new rectification7 by turn+ ! ,ma*9]y backw>d = "t pa/1 or =w>d = "t to come4 ,at #ag ,degrees di/ance f ea* ,node1 on bo? ,sides1 is engrav$ a small ,sun2 & at #ab ,degrees di/ance1 a small ,moon2 :i* %ew ! limits ( sol> & lun> ,eclipses #cag3 & :51 at any *ange1 ! ,moon falls betwe5 ei!r ( ^! ,suns & ! ,node1 ! ,sun w be eclips$ on ! day po9t$ to by ! annual ,index 7,no4 #aj17 & z ! ,moon has !n ,nor? or ,s\? ,latitude1 "o may easily judge :e!r t ,eclipse w be visible 9 ! ,nor!rn or ,s\!rn ,hemisph]e2 especially z ! ,e>?'s ,axis incl9es t[>ds ! ,sun or f him at t "t4 ,& :51 at any ,full1 ! ,moon falls betwe5 ei!r ( ! little ,moon's & ,node1 %e w be eclips$1 & ! annual ,index %ews ! day ( t ,eclipse4 ,!re is a ,circle ( #bi-a_/b equal p>ts 7,no4 #h47 on ! cov] ( ! ,ma*9e1 on :i* an ,index %ews ! days ( ! ,moon's age4 ,sid5ote3 ,,plate ,,ix4 ,fig4 ,x4 ,!re are two ,semi-circles fix$ to an elliptical ,r+1 :i* be+ put l a cap ^u ! ,e>?1 & ! =k$ "p ,f ^u ! ,moon1 %ews ! ,tides z ! ,e>? turns r\nd )9 !m1 & !y are l$ r\nd x by ! ,moon4 ,:5 ! diff]5t ,places come to ! ,semi-circle ,aa,eb,b1 !y h ,tides ( ,flood2 & :5 !y come to ! ,semicircle ,,c$ !y h ,tides ( ,ebb #cjd1 #cje2 ! ,index on ! h\r ,circle 7,no4 #g47 %ew+ ! times ( ^! ,ph5om5a4 ,!re is a jo9t$ ,wire1 ( :i* "o end be+ put into a hole 9 ! upright /em t holds ! ,e>?'s cap1 & ! ,wire laid into a small =k$ piece :i* may be occasionally put ^u ,v5us or ,m]cury1 %ews ! direct & retrograde ,motions ( ^! two ,planets1 ) _! /ation>y ,times & ,places z se5 f ! ,e>?4 ,! :ole ,ma*9]y is turn$ by a w9* or h&le 7,no4 #ab17 & is s easily mov$ t a clock might turn x )\t any dang] ( /opp+4 ,to give a ,plate ( ! :eel-"w ( ?is ,ma*9e1 w\ld answ] no purpose1 because _m ( ! :eels lie s beh9d o!rs z to hide !m f sight 9 any view :atsoev]4 ,sid5ote3 ,ano!r ,,orr]y4 ,,plate ,,vi4 ,fig4 ,i4 #dce4 ,ano!r ,,orr]y4 ,9 ?is ,ma*9e1 :i* is ! simple/ ,i ev] saw1 = %ew+ ! diurnal & annual motions ( ! ,e>?1 toge!r ) ! motion ( ! ,moon & h] ,nodes2 ,a & ,b are two oblong squ>e ,plates held toge!r by f\r upright pill>s2 ( :i* ?ree appe> at f1 g1 & g#b4 ,"u ! ,plate ,a is an endless screw on ! ,axis ( ! h&le b1 :i* works 9 a :eel fix$ on ! same ,axis ) ! d\ble groov$ :eel ,e2 & on ! top ( ?is ,axis is fix$ ! too!d :eel i1 :i* turns ! p9ion k1 on ! top ( ^: ,axis is ! p9ion k#b :i* turns ano!r p9ion b#b1 & t o!r turns a ?ird1 on ! ,axis a#b ( :i* is ! ,e>? ,u turn+ r\nd2 ?is la/ ,axis incl9+ #bc-a_/b ,degrees4 ,! support] ,x#b1 9 :i* ! ,axis ( ! ,e>? turns1 is fix$ to ! moveable ,plate ,c4 ,9 ! fix$ ,plate ,b1 beyond ,h1 is fix$ ! /rong wire d1 on :i* hangs ! ,sun ,t s z x may turn r\nd ! wire4 ,to ?is ,sun is fix$ ! wire or sol> ray ,z1 :i* 7z ! ,e>? ,u turns r\nd its ,axis7 po9ts to all ! places t ! ,sun passes v]tically ov]1 e day ( ! ye>4 ,! ,e>? is half cov]$ ) a black cap a1 z 9 ! =m] ,orr]y1 = divid+ ! day f ! night2 &1 z ! diff]5t places come out f bel[ ! edge ( ! cap1 or g 9 bel[ x1 !y %ew ! times ( ,sun-ris+ & sett+ e day ( ! ye>4 ,?is cap is fix$ on ! wire b1 :i* has a =k$ piece ,c turn+ r\nd ! wire d3 &1 z ! ,e>? goes r\nd ! ,sun1 x c>ries ! ,cap1 ,wire1 & sol> ,ray r\nd him2 s t ! sol> ,ray con/antly po9ts t[>ds ! ,e>?'s ,c5t]4 ,on ! ,axis ( ! p9ion k is ! p9ion m1 :i* turns a :eel on ! cock or support] n1 & on ! ,axis ( ?is :eel ne>e/ n is a p9ion 7hid f view7 "u ! ,plate ,c1 :i* p9ion turns a :eel t c>ries ! ,moon ,v r\nd ! ,e>? ,u2 ! ,moon's ,axis ris+ & fall+ 9 ! socket ,w1 :i* is fix$ to ! triangul> piece above ,z2 & ?is piece is fix$ to ! top ( ! ,axis ( ! la/ m5tion$ :eel4 ,! socket ,w is slit on ! out]mo/ side2 & 9 ?is slit ! two p9s ne> ,y1 fix$ 9 ! ,moon's ,axis1 move up & d[n2 "o ( !m be+ above ! incl9$ ,plane ,,yx1 & ! o!r bel[ x4 ,by ?is me*anism1 ! ,moon ,v moves r\nd ! ,e>? ,t 9 ! incl9$ ,orbit q1 p>allel to ! ,plane ( ! ,r+ ,,yx2 ( :i* ! ,desc5d+ ,node is at ,x1 & ! ,asc5d+ ,node opposite to x1 b hid by ! support] ,x#b4 ,! small :eel ,e turns ! l>ge :eels ,d & ,f1 ( equal diamet]s1 by cat-gut /r+s cross+ betwe5 !m3 & ! ,axis ( ^! two :eels are crank$ at ,g & ,h1 above ! ,plate ,b4 ,! upright /ems ( ^! cranks go+ ?r\gh ! ,plate ,c1 c>ry x ov] & ov] ! fix$ ,plate ,b1 ) a motion :i* c>ries ! ,e>? ,u r\nd ! ,sun ,t1 keep+ ! ,e>?'s ,axis always p>allel to itself2 or /ill incl9+ t[>ds ! left-h& ( ! ,plate2 & %ew+ ! vicissitudes ( seasons1 z describ$ 9 ! t5? *apt]4 ,z ! ,e>? goes r\nd ! ,sun ! p9ion k goes r\nd ! :eel i1 = ! ,axis ( k nev] t\*es ! fix$ ,plate ,b2 b turns on a wire fix$ into ! ,plate ,c4 ,on ! top ( ! crank ,g is an ,index ,l1 :i* goes r\nd ! ,circle m#b 9 ! "t t ! ,e>? goes r\nd ! ,sun2 & po9ts to ! days ( ! mon?s2 :i*1 toge!r ) ! names ( ! seasons1 are m>k$ 9 ?is ,circle4 ,?is ,index has a small groov$ :eel ,l fix$ ^u x1 r\nd :i*1 & ! ,plate ,z1 goes a cat-gut /r+ cross+ betwe5 !m2 & by ?is means ! ,moon's incl9$ ,plane ,,yx ) its ,nodes is turn$ backw>d1 = %ew+ ! times & returns ( ,eclipses #cai1 #cbj4 ,! foll[+ p>ts ( ?is ma*9e mu/ be consid]$ z di/9ct f ^? already describ$4 ,t[>ds ! "r h&1 let ,s be ! ,e>? hung on ! wire e1 :i* is fix$ into ! ,plate ,b2 & let ,o be ! ,moon fix$ on ! ,axis ,m1 & turn+ r\nd )9 ! cap ,p1 9 :i*1 & 9 ! ,plate ,c ! crook$ wire ,q is fix$4 ,on ! ,axis ,m is also fix$ ! ,index ,k1 :i* goes r\nd a ,circle h#b1 divid$ into #bi-a_/b equal p>ts1 :i* are ! days ( ! ,moon's age3 b to avoid confusion 9 ! s*eme1 x is only m>k$ ) ! num]al figures #a #b #c #d1 = ! ,qu>t]s4 ,z ! crank ,h c>ries ?is ,moon r\nd ! ,e>? ,s 9 ! ,orbit t1 %e %ews all h] ,phases by means ( ! cap ,p = ! diff]5t days ( h] age1 :i* are %ewn by ! ,index ,k2 ?is ,index1 turn+ j z ! ,moon ,o does1 demon/rates h] turn+ r\nd h] ,axis z %e /ill keeps ! same side t[>ds ! ,e>? ,s #bfb4 ,sid5ote3 ,,pl4 ,,viii4 ,at ! o!r end ( ! ,plate ,c1 a ,moon ,n goes r\nd an ,e>? ,r 9 ! ,orbit p2 b ?is ,moon's ,axis is /uck fa/ into ! ,plate ,c at ,s#b2 s t nei!r ,moon nor ,axis c turn r\nd2 & z ?is ,moon goes r\nd h] ,e>? %e %ews h]self all r\nd to x2 :i* proves1 t if ! ,moon 0 se5 all r\nd f ! ,e>? 9 a ,lunation1 %e c\ld n turn r\nd h] ,axis4 ,n4 ,b4 ,if !re 7 only ! two :eels ,d & ,f1 ) a cat-gut /r+ ov] !m1 b n cross+ betwe5 !m1 ! ,axis ( ! ,e>? ,u w\ld keep its p>allelism r\nd ! ,sun ,t1 & %ew all ! seasons2 z ,i sometimes make ^! ,ma*9es3 & ! ,moon ,o w\ld g r\nd ! ,e>? ,s1 %ew+ h] ,phases z above2 z likewise w\ld ! ,moon ,n r\nd ! ,e>? ,r2 b !n1 nei!r c\ld ! diurnal motion ( ! ,e>? ,u on its ,axis be %ewn1 nor ! motion ( ! ,moon ,v r\nd t ,e>?4 ,sid5ote3 ,! ,,calculator4 #dcf4 ,9 ! ye> #agdf ,i contriv$ a v simple ,ma*9e1 & describ$ x's p]=mance 9 a small treatise ^u ! ,ph5om5a ( ! ,h>ve/ ,moon1 publi%$ 9 ! ye> #agdg4 ,i improv$ x soon aft]1 by add+ ano!r :eel1 & call$ x ! ,calculator4 ,x may be easily made by any ,g5tleman :o has a me*anical ,g5ius4 ,sid5ote3 ,fig4 ,i4 ,! great flat ,r+ support$ by twelve pill>s1 & on :i* ! twelve ,signs ) _! respective ,degrees are laid d[n1 is ! ,ecliptic2 ne>ly 9 ! c5t] ( x is ! ,sun ,s support$ by ! /rong crook$ ,wire ,i2 & f ! ,sun proce$s a ,wire ,w1 call$ ! ,sol> ,ray1 po9t+ t[>ds ! c5t] ( ! ,e>? ,e1 :i* is furni%$ ) a moveable ,horizon ,h1 toge!r ) a braz5 ,m]idian1 & ,quadrant ( ,altitude4 ,r is a small ,ecliptic1 ^: ,plane co-incides ) t ( ! great "o1 & has ! l ,signs & ,degrees m>k$ ^u x2 & is support$ by two ,wires ,d & ,d1 :i* ent] into ! ,plate ,,pp1 b may be tak5 (f at pleasure4 ,z ! ,e>? goes r\nd ! ,sun1 ! ,signs ( ?is small ,circle keep p>allel to !mselves1 & to ^? ( ! great ,ecliptic4 ,:5 x is tak5 (f1 & ! sol> ,ray ,w drawn f>!r out1 s z almo/ to t\* ! ,horizon ,h1 or ! ,quadrant ( ,altitude1 ! ,horizon be+ rectifi$ to any giv5 ,latitude1 & ! ,e>? turn$ r\nd its ,axis by h&1 ! po9t ( ! ,wire ,w %ews ! ,sun's ,decl9ation 9 pass+ ov] ! graduat$ brass ,m]idian1 & 8 height at any giv5 "t ^u ! ,quadrant ( ,altitude1 toge!r ) 8 ,azimu?1 or po9t ( ,be>+ ^u ! ,horizon at t "t2 & likewise 8 ,amplitude1 & "t ( ,ris+ & ,sett+ by ! h\r ,index1 = any day ( ! ye> t ! annual ,index ,u po9ts to 9 ! ,circle ( ,mon?s bel[ ! ,sun4 ,m is a sol> ,index or ,po9t] support$ by ! ,wire ,l :i* is fix$ into ! knob ,k3 ! use ( ?is ,index is to %ew ! ,sun's place 9 ! ,ecliptic e day 9 ! ye>2 = x goes ov] ! ,signs & ,degrees z ! ,index ,u goes ov] ! mon?s & days2 or r z !y pass "u ! ,index ,u1 9 mov+ ! cov] plate ) ! ,e>? & its ,furniture r\nd ! ,sun2 = ! ,index ,u is fix$ tight on ! immoveable ,axis 9 ! ,c5t] ( ! ,ma*9e4 ,k is a knob or h&le = mov+ ! ,e>? r\nd ! ,sun1 & ! ,moon r\nd ! ,e>?4 ,z ! ,e>? is c>ri$ r\nd ! ,sun1 its ,axis con/antly keeps ! same oblique direction1 or p>allel to itself #dh1 #bjb1 %ew+ !reby ! diff]5t l5g?s ( days & nights at diff]5t times ( ! ye>1 ) all ! v>i\s seasons4 ,&1 9 "o annual revolution ( ! ,e>?1 ! ,moon ,m goes #ab-a_/c times r\nd x f ,*ange to ,*ange1 hav+ an occasional provision = %ew+ h] diff]5t ,phases4 ,! l[] end ( ! ,moon's ,axis be>s by a small friction :eel ^u ! incl9$ ,plane ,t1 :i* causes ! ,moon to rise above & s9k bel[ ! ,ecliptic ,r 9 e ,lunation2 cross+ x 9 h] ,nodes1 :i* %ift backw>d ?r\gh all ! ,signs & ,degrees ( ! said ,ecliptic1 by ! retrograde ,motion ( ! incl9$ ,plane ,t1 9 #ah ye>s & #bbe days4 ,on ?is ,plane ! ,degrees & ,p>ts ( ! ,moon's ,nor? & ,s\? ,latitude are laid d[n f bo? ! ,nodes1 "o ( :i*1 viz4 ! ,desc5d+ ,node appe>s at #j1 by ,,dn above ,b2 ! o!r ,node be+ hid f ,sight on ?is ,plane by ! plate ,,pp2 & f bo? ,nodes1 at prop] di/ances1 z 9 ! o!r ,orr]y1 ! limits ( ,eclipses are m>k$1 & all ! sol> & lun> ,eclipses are %ewn 9 ! same mann]1 = any giv5 ye>1 )9 ! limits ( #fjjj1 ei!r be=e or aft] ! ,*ri/ian ra4 ,on ! plate t cov]s ! :eel-"w1 "u ! ,sun ,s1 & r\nd ! knob ,k are ,a/ronomical ,tables1 by :i* ! ,ma*9e may be rectifi$ to ! beg9n+ ( any giv5 ye> )9 ^! limits1 9 ?ree or f\r m9utes ( "t2 & :5 once set "r1 may be turn$ backw>d = #cjj ye>s pa/1 or =w>d = z _m to come1 )\t requir+ any new rectification4 ,!re is a me?od = its add+ up ! #bi? ( ,febru>y e f\r? ye>1 & all[+ only #bh days to t mon? = e o!r ?ree3 b all ?is be+ p]=m$ by a p>ticul> mann] ( cutt+ ! tee? ( ! :eels1 & divid+ ! mon? circle1 too long & intricate to be describ$ "h1 ,i %all only %ew h[ ^! motions may be p]=m$ ne> en\gh = common use1 by :eels ) grooves & cat-gut /r+s r\nd !m1 only "h ,i mu/ put ! ,op]ator 9 m9d t ! grooves are to be made %>p 7n r\nd7 bottom$ to keep ! /r+s f slipp+4 ,! ,moon's ,axis moves up & d[n 9 ! socket ,n fix$ into ! b> ,o 7:i* c>ries h] r\nd ! ,e>?7 z %e rises above or s9ks bel[ ! ,ecliptic2 & imm$iately bel[ ! incl9$ ,plane ,t is a flat circul> plate 7betwe5 ,y & ,t7 on :i* ! diff]5t ,exc5tricities ( ! ,moon's ,orbit are laid d[n2 & likewise h] mean ,anomaly & elliptic ,equation by :i* h] true ,place may be v ne>ly f\nd at any "t4 ,bel[ ?is ,apogee-plate1 :i* %ews ! ,anomaly1 c4 is a ,circle ,y divid$ into #bi-a_/b equal p>ts :i* are ! days ( ! ,moon's age3 & ! =k$ end ,a ( ! ,index ,,ab 7,fig ,,ii7 may be put into ! ,apogee-"p ( ?is plate2 !re be+ j su* ano!r ,index to put into ! incl9$ ,plane ,t at ! ,asc5d+ ,node2 & !n ! curv$ po9ts ,b ( ^! ,indexes %ew ! direct motion ( ! ,apogee1 & retrograde motion ( ! ,nodes ?r\gh ! ,ecliptic ,r1 ) _! ,places 9 x at any giv5 "t4 ,z ! ,moon ,m goes r\nd ! ,e>? ,e1 %e %ews h] ,place e day 9 ! ,ecliptic ,r1 & ! l[] end ( h] ,axis %ews h] ,latitude & di/ance f h] ,node on ! incl9$ ,plane ,t1 also h] di/ance f h] ,apogee & ,p]igee1 toge!r ) h] mean ,anomaly1 ! !n ,exc5tricity ( h] ,orbit1 & h] elliptic ,equation1 all on ! ,apogee ,plate1 & ! day ( h] age 9 ! ,circle ,y ( #bi-a_/b equal p>ts2 = e day ( ! ye> po9t$ out by ! annual ,index ,u 9 ! ,circle ( mon?s4 ,hav+ rectifi$ ! ,ma*9e by ! ,tables = ! beg9n+ ( any ye>1 move ! ,e>? & ,moon =w>d by ! knob ,k1 until ! annual ,index comes to any giv5 day ( ! mon?2 !n /op1 & n only all ! above ,ph5om5a may be %ewn = t day1 b also1 by turn+ ! ,e>? r\nd its ,axis1 ! ,decl9ation1 ,azimu?1 ,amplitude1 ,altitude ( ! ,moon at any h\r1 & ! times ( h] ,ris+ & ,sett+1 are %ewn by ! ,horizon1 ,quadrant ( ,altitude1 & h\r ,index4 ,& 9 mov+ ! ,e>? r\nd ! ,sun1 ! days ( all ! ,new & ,full ,moons & ,eclipses 9 any giv5 ye> are %ewn4 ,! ,ph5om5a ( ! ,h>ve/ ,moon1 & ^? ( ! ,tides1 by su* a cap z t 9 ,plate #i ,fig4 #aj4 put ^u ! ,e>? & ,moon1 toge!r ) ! solution ( _m problems n "h relat$1 are made conspicu\s4 ,sid5ote3 ,,pl4 ,,viii4 ,! easie/1 ?\gh n ! be/ way1 t ,i c in/ruct any me*anical p]son to make ! :eel-"w ( su* a ma*9e1 is z foll[s2 :i* is ! way t ,i made x1 be=e ,i ?\ght ( numb]s exact en\gh to make x wor? ! tr\ble ( cutt+ tee? 9 ! :eels4 ,sid5ote3 ,fig4 ,,iii4 ,fig4 #c;d ( ,plate #h is a section ( ?is ,ma*9e2 9 :i* ,,abcd is a frame ( wood held toge!r by f\r pill>s at ! corn]s1 :]e( two appe> at ,,ac & ,,bd4 ,9 ! l[] ,plate ,,cd ( ?is ,frame are ?ree small friction-:eels1 at equal di/ances f ea* o!r2 two ( !m appe>+ at e & e4 ,z ! frame is mov$ r\nd1 ^! :eels run ^u ! fix$ bottom ,plate ,,ee :i* supports ! :ole "w4 ,9 ! ,c5t] ( ?is la/ m5tion$ ,plate is fix$ ! upright ,axis f ,,ffg1 & on ! same ,axis is fix$ ! :eel ,,hhh 9 :i* are f\r grooves ,i1 ,x1 k1 ,l ( diff]5t ,diamet]s4 ,9 ^! grooves are cat-gut /r+s go+ also r\nd ! sep>ate :eels ,m1 ,n1 ,o & ,p4 ,! :eel ,m is fix$ on a solid ,sp9dle or ,axis1 ! l[] pivot ( :i* turns at ,r 9 ! "u ,plate ( ! moveable frame ,,abcd2 & on ! upp] end ( ?is ,axis is fix$ ! ,plate o o 7:i* is ,,pp1 "u ! ,e>?1 9 ,fig4 ,i47 & to ?is ,plate is fix$1 at an ,angle ( #bc-a_/b ,degrees incl9ation1 ! ,dial-plate bel[ ! ,e>? ,t2 on ! ,axis ( :i*1 ! ,index q is turn$ r\nd by ! ,e>?4 ,?is ,axis1 toge!r ) ! ,:eel ,m1 & ,plate o o1 keep _! p>allelism 9 go+ r\nd ! ,sun ,s4 ,on ! ,axis ( ! :eel ,m is a moveable socket on :i* ! small :eel ,n is fix$1 & on ! upp] end ( ?is socket is put on tight 7b s z x may be occasionally turn$ by h&7 ! b> ,,zz 7viz4 ! b> ,o 9 ,fig4 ,i47 :i* c>ries ! ,moon m r\nd ! ,e>? ,t1 by ! ,socket n1 fix$ into ! b>4 ,z ! ,moon goes r\nd ! ,e>? h] ,axis rises & falls 9 ! ,socket n2 because1 on ! l[] end ( h] ,axis1 :i* is turn$ inw>d1 !re is a small friction ,:eel s runn+ on ! incl9$ ,plane ,x 7:i* is ,t 9 ,fig4 ,i47 & s causes ! ,moon alt]nately to rise above & s9k bel[ ! little ,ecliptic ,,vv 7,r 9 ,fig4 ,i47 9 e ,lunation4 ,on ! ,socket or holl[ ,axis ( ! ,:eel ,n1 !re is ano!r ,socket on :i* ! ,:eel ,o is fix$2 & ! ,moon's incl9$ ,plane ,x is put tightly on ! upp] end ( ?is ,socket1 n on a squ>e1 b on a r\nd1 t x may be occasionally set by h& )\t wr5*+ ! ,:eel or ,axle4 ,la/ly1 on ! holl[ ,axis ( ! ,:eel ,o is ano!r ,socket on :i* is fix$ ! ,:eel ,p1 & on ! upp] end ( ?is ,socket is put on tightly ! ,apogee-plate ,y1 7t imm$iately bel[ ,t 9 ,fig4 ,i47 all ^! ,axles turn 9 ! upp] ,plate ( ! moveable frame at ,q :i* ,plate is cov]$ ) ! ?9 ,plate cc 7screw$ to x7 :]eon are ! =e-m5tion$ ,tables & mon? ,circle 9 ,fig4 ,i4 ,! middle "p ( ! ?ick fix$ ,:eel ,,hhh is mu* broad] ?an ! re/ ( x1 & comes out betwe5 ! ,:eels ,m & ,o almo/ to ! ,:eel ,n4 ,to adju/ ! diamet]s ( ! grooves ( ?is fix$ :eel to ! grooves ( ! sep>ate ,:eels ,m1 ,n1 ,o & ,p1 s z !y may p]=m _! motions 9 ! prop] times1 ! foll[+ me?od mu/ be obs]v$4 ,! ,groove ( ! ,:eel ,m1 :i* keeps ! p>allelism ( ! ,e>?'s ,axis1 mu/ be precisely ( ! same ,diamet] z ! l[] ,groove ,i ( ! fix$ ,:eel ,,hhh2 b1 :5 ?is ,groove is s well adju/$ z to %ew1 t 9 ev] s _m annual revolutions ( ! ,e>?1 its ,axis keeps its p>allelism1 z may be obs]v$ by ! sol> ,ray ,w 7,fig4 ,i47 always com+ precisely to ! same ,degree ( ! small ,ecliptic ,r at ! end ( e annual revolution1 :5 ! ,index ,m po9ts to ! l ,degree 9 ! great ,ecliptic2 !n1 ) ! edge ( a ?9 ,file give ! ,groove ( ! ,:eel ,m a small rub all r\nd2 & by t means1 less5+ ! ,diamet] ( ! ,groove1 p]haps ab\t ! #bj? "p ( a hair's bread?1 x w cause ! ,e>? to %ew ! precession ( ! ,equ9oxes2 :i*1 9 _m annual revolutions w beg9 to be s5sible z ! ,e>?'s ,axis sl[ly deviates f its p>allelism #bdf1 t[>ds ! antec$5t ,signs ( ! ,ecliptic4 ,! ,diamet] ( ! ,groove ( ! ,:eel ,n1 :i* c>ries ! ,moon r\nd ! ,e>?1 mu/ be to ! ,diamet] ( ! ,groove ,x z a ,lunation is to a ye>2 t is1 z #bi-a_/b to #cfe-a_/d4 ,! ,diamet] ( ! ,groove ( ! ,:eel ,o1 :i* turns ! incl9$ ,plane ,x ) ! ,moon's ,nodes backw>d1 mu/ be to ! ,diamet] ( ! ,groove k z #bj to #ah-bbe_/cfe4 ,&1 ,la/ly1 ! ,diamet] ( ! ,groove ( ! ,:eel ,p1 :i* c>ries ! ,moon's ,apogee =w>d1 mu/ be to ! ,diamet] ( ! ,groove ,l z #gj to #fb4 ,sid5ote3 ,,plate ,,iv4 ,b1 aft] all ?is nice adju/m5t ( ! ,grooves to ! proportional times ( _! respective ,:eels turn+ r\nd1 & :i* seems to promise v well 9 ,!ory1 !re w /ill be f\nd a necessity ( a f>!r adju/m5t by h&2 because prop] all[ance mu/ be made = ! ,diamet]s ( ! cat-gut /r+s3 & ! ,grooves mu/ be s adju/$ by h&1 z1 t 9 ! "t ! ,e>? is mov$ once r\nd ! ,sun1 ! ,moon mu/ p]=m #ab synodical revolutions r\nd ! ,e>?1 & be almo/ #aa days old 9 h] #ac? revolution4 ,! incl9$ ,plane ) its ,nodes mu/ g once r\nd backw>d ?r\gh all ! ,signs & ,degrees ( ! small ,ecliptic 9 #ah annual revolutions ( ! ,e>? & #bbe days ov]4 ,& ! ,apogee-plate mu/ g once r\nd =w>d1 s z its ,index may g ov] all ! ,signs & ,degrees ( ! small ,ecliptic 9 eight ye>s 7or s _m annual revolutions ( ! ,e>?7 & #cab days ov]4 ,n4 ,b4 ,! /r+ :i* goes r\nd ! ,grooves ,x & ,n = ! ,moon's ,motion mu/ cross betwe5 ^! ,:eels2 b all ! re/ ( ! /r+s g 9 _! respective ,grooves ,,im1 k,o1 & ,,lp )\t cross+4 ,sid5ote3 ,! ,,comet>ium4 #dcg4 ,! ,,comet>ium4 ,?is curi\s ,ma*9e %ews ! ,motion ( a ,comet or exc5tric ,body mov+ r\nd ! ,sun1 describ+ equal ,areas 9 equal times #aeb1 & may be s contriv$ z to %ew su* a ,motion = any ,degree ( ,exc5tricity4 ,x 0 inv5t$ by ! late ,dr4 ,desaguli]s4 ,sid5ote3 ,fig4 ,,iv4 ,! d>k elliptical ,groove r\nd ! lett]s abcdefghiklm is ! ,orbit ( ! ,comet ,y3 ?is ,comet is c>ri$ r\nd 9 ! ,groove accord+ to ! ord] ( lett]s1 by ! ,wire ,w1 fix$ 9 ! ,sun ,s1 & slides on ! ,wire z x approa*es ne>] to or rec$es f>!r f ! ,sun1 be+ ne>e/ ( all 9 ! ,p]ihelion a1 & f>!/ 9 ! ,aphelion g4 ,! ,areas a,sb1 b,sc1 c,sd c4 or cont5ts ( ^! sev]al ,triangles are all equal2 & 9 e turn ( ! ,w9* ,n ! ,comet ,y is c>ri$ ov] "o ( ^! ,areas2 consequ5tly 9 z mu* "t z x moves1 f f to g1 or f g to h1 x moves f m to a1 or f a to b2 & s ( ! re/1 be+ quicke/ ( all at a1 & sl[e/ at g4 ,?us1 ! ,comet's velocity 9 its ,orbit cont9ually decreases f ! ,p]ihelion a to ! ,aphelion g2 & increases 9 ! same proportion f g to a4 ,sid5ote3 ,,plate ,,iv4 ,! elliptic ,orbit is divid$ into #ab equal ,p>ts or ,signs ) _! respective ,degrees1 & s is ! ,circle n o p q r s t n :i* repres5ts a great ,circle 9 ! ,heav5s1 & to :i* all ! fix$ ,/>s 9 ! ,comet's way are ref]r$4 ,:il/ ! ,comet moves f f to g 9 its ,orbit x appe>s to move only ab\t #e ,degrees 9 ?is ,circle1 z is %ewn by ! small knob on ! end ( ! ,wire ,w2 b 9 z %ort "t z ! ,comet moves f m to a1 or f a to b1 & x appe>s to describe ! l>ge space tn or no 9 ! ,heav5s1 ei!r ( :i* spaces conta9s #abj ,degrees or f\r ,signs4 ,7 ! ,exc5tricity ( its ,orbit great]1 ! great] /ill w\ld be ! diff]5ce ( its ,motion1 & vice v]s4 ,,abcdefghiklma is a circul> ,orbit = %ew+ ! equable ,motion ( a ,body r\nd ! ,sun ,s1 describ+ equal ,areas ,,asb1 ,,bsc1 c4 9 equal times ) ^? ( ! ,body ,y 9 its elliptical ,orbit above m5tion$2 b ) ?is diff]5ce1 t ! circul> ,motion describes ! equal ,arcs ,,ab1 ,,bc1 c4 9 ! same equal times t ! elliptical ,motion describes ! unequal ,arcs ab1 bc1 c4 ,n[1 suppose ! two ,bodies ,y & ,i to />t f ! ,po9ts a & ,a at ! same mom5t ( "t1 & ea* hav+ gone r\nd its respective ,orbit1 to arrive at ^! ,po9ts aga9 at ! same in/ant1 ! ,body ,y w be =w>d] 9 its ,orbit ?an ! ,body ,i all ! way f a to g1 & f ,a to ,g2 b ,i w be =w>d] ?an ,y ?r\gh all ! o!r half ( ! ,orbit2 & ! diff]5ce is equal to ! ,equation ( ! ,body ,y 9 its ,orbit4 ,at ! ,po9ts a1 ,a1 & g1 ,g1 t is1 9 ! ,p]ihelion & ,aphelion1 !y w be equal2 & !n ! ,equation vani%es4 ,?is %ews :y ! ,equation ( a ,body mov+ 9 an elliptic ,orbit1 is add$ to ! mean or suppos$ circul> ,motion f ! ,p]ihelion to ! ,aphelion1 & subtract$ f ! ,aphelion to ! ,p]ihelion1 9 ,bodies mov+ r\nd ! ,sun1 or f ! ,p]igee to ! ,apogee1 & f ! ,apogee to ! ,p]igee 9 ! ,moon's ,motion r\nd ! ,e>?1 accord+ to ! ,precepts 9 ! #cee? ,article2 only we are to consid]1 t :5 ,motion is turn$ into ,"t1 x rev]ses ! titles 9 ! ,table ( ,! ,moon's elliptic ,equation4 ,sid5ote3 ,fig4 ,v4 ,?is curi\s ,motion is p]=m$ 9 ! foll[+ mann]4 ,,abc is a wood5 b> 79 ! box conta9+ ! :eel-"w7 above :i* are ! :eels ,d & ,e2 & bel[ x ! elliptic ,plates ,,ff & ,,gg2 ea* ,plate be+ fix$ on an ,axis 9 "o ( its ,focuses1 at ,e & ,k2 & ! ,:eel ,e is fix$ on ! same ,axis ) ! ,plate ,,ff4 ,^! ,plates h ,grooves r\nd _! edges precisely ( equal ,diamet]s to "o ano!r1 & 9 ^! ,grooves is ! cat-gut /r+ gg1 gg cross+ betwe5 ! ,plates at h4 ,on ,h1 ! ,axis ( ! h&le or w9* ,n 9 ,fig4 #d?1 is an endless screw 9 ,fig4 #e1 work+ 9 ! ,:eels ,d & ,e1 ^: numb]s ( tee? be+ equal1 & %\ld be equal to ! numb] ( l9es a,s1 b,s1 c,s1 c4 9 ,fig4 #d1 !y turn r\nd _! ,axes 9 equal times to "o ano!r1 & to ! ,motion ( ! elliptic ,plates4 ,=1 ! ,:eels ,d & ,e hav+ equal numb]s ( tee?1 ! ,plate ,,ff be+ fix$ on ! same ,axis ) ! ,:eel ,e1 & ! ,plate ,,ff turn+ ! equally big ,plate ,,gg by a cat-gut /r+ r\nd !m bo?1 !y mu/ all g r\nd _! ,axes 9 z _m turns ( ! h&le ,n z ei!r ( ! ,:eels has tee?4 ',tis easy to see1 t ! end h ( ! elliptical ,plate ,,ff be+ f>!r f its ,axis ,e ?an ! opposite end i is1 mu/ describe a ,circle s mu* ! l>g] 9 proportion2 & !re=e move ?r\gh s mu* m space 9 ! same "t2 & = t reason ! end h moves s mu* fa/] ?an ! end i1 al?\gh x goes no soon] r\nd ! ,c5t] ,e4 ,b !n1 ! quick-mov+ end h ( ! ,plate ,,ff leads ab\t ! %ort end h,k ( ! ,plate ,,gg ) ! same velocity2 & ! sl[ mov+ end i ( ! ,plate ,,ff com+ half r\nd z to ,b1 mu/ !n lead ! long end k ( ! ,plate ,,gg z sl[ly ab\t3 ,s t ! elliptical ,plate ,,ff & x's ,axis ,e move uni=mly & equally quick 9 e "p ( its revolution2 b ! elliptical ,plate ,,gg1 toge!r ) its ,axis ,k mu/ move v unequally 9 diff]5t p>ts ( its revolution2 ! diff]5ce be+ always inv]sely z ! di/ance ( any po9t ( ! ,circumf]5ce ( ,,gg f its ,axis at ,k3 or 9 o!r words1 to in/ance 9 two po9ts1 if ! di/ance ,kk be f\r1 five1 or six times z great z ! di/ance ,kh1 ! ,po9t h w move 9 t position f\r1 five1 or six times z fa/ z ! ,po9t k does1 :5 ! ,plate ,,gg has gone half r\nd3 & s on = any o!r ,exc5tricity or diff]5ce ( ! ,di/ances ,kk & ,kh4 ,! too? i on ! ,plate ,,ff falls 9 betwe5 ! two tee? at k on ! ,plate ,,gg1 by :i* means ! revolution ( ! latt] is s adju/$ to t ( ! =m]1 t !y c nev] v>y f "o ano!r4 ,on ! top ( ! ,axis ( ! equally mov+ ,:eel ,d1 9 ,fig4 #e?1 is ! ,sun ,s 9 ,fig4 #d?2 :i* ,sun1 by ! ,wire ,z fix$ to x1 c>ries ! ,ball ,i r\nd ! ,circle ,,abcd1 c4 ) an equable ,motion accord+ to ! ord] ( ! lett]s3 & on ! top ( ! ,axis ,k ( ! unequally mov+ ,ellipsis ,,gg1 9 ,fig4 #e?1 is ! ,sun ,s 9 ,fig4 #d?1 c>ry+ ! ,ball ,y unequably r\nd 9 ! elliptical ,groove a b c d1 c4 ,n4,b4 ,?is elliptical ,groove mu/ be precisely equal & simil> to ! v]ge ( ! ,plate ,,gg1 :i* is also equal to t ( ,,ff4 ,9 ?is mann]1 ,ma*9es may be made to %ew ! true ,motion ( ! ,moon ab\t ! ,e>?1 or ( any ,planet ab\t ! ,sun2 by mak+ ! elliptical ,plates ( ! same ,exc5tricities1 9 proportion to ! ,radius1 z ! ,orbits ( ! ,planets are ^: ,motions !y repres5t3 & s1 _! diff]5t ,equations 9 diff]5t p>ts ( _! ,orbits may be made pla9 to sight2 & cle>] ,ideas ( ^! ,motions & ,equations acquir$ 9 half an h\r1 ?an c\ld be ga9$ f read+ half a day ab\t su* ,motions & ,equations4 ,sid5ote3 ,! improv$ ,,cele/ial ,,globe4 ,,plate ,,iii4 ,fig4 ,,iii4 #dch4 ,! ,improv$ ,cele/ial ,globe4 ,on ! ,nor? ,pole ( ! ,axis1 above ! ,h\r ,circle1 is fix$ an ,ar* ,,mkh ( #bc-a_/b ,degrees2 & at ! end ,h is fix$ an upright p9 ,,hg1 :i* /&s directly ov] ! ,nor? ,pole ( ! ,ecliptic1 & p]p5dicul> to t "p ( ! surface ( ! ,globe4 ,on ?is p9 are two moveable ,collets at ,d & ,h1 to :i* are fix$ ! quadrantal ,wires ,n & ,o1 hav+ two little ,balls on _! ends = ! ,sun & ,moon1 z 9 ! ,figure4 ,! ,collet ,d is fix$ to ! circul> ,plate ,f :]eon ! #bi-a_/b days ( ! ,moon's age are engrav51 beg9n+ j "u ! ,sun's ,wire ,n2 & z ?is ,wire is mov$ r\nd ! ,globe1 ! ,plate ,f turns r\nd ) x4 ,^! ,wires are easily turn$ if ! ,screw ,g be slack5$2 & :5 !y are set to _! prop] places1 ! ,screw s]ves to fix !m !re s1 z 9 turn+ ! ,ball ( ! ,globe1 ! ,wires ) ! ,sun & ,moon g r\nd ) x2 & ^! two little ,balls rise & set at ! same times1 & on ! same po9ts ( ! ,horizon1 = ! day to :i* !y are rectifi$1 z ! ,sun & ,moon d 9 ! ,heav5s4 ,because ! ,moon keeps n h] c\rse 9 ! ,ecliptic 7z ! ,sun appe>s to d7 b has a ,decl9ation ( #e-a_/c ,degrees on ea* side f x 9 e ,lunation #cag1 h] ,ball may be screw$ z _m ,degrees to ei!r side ( ! ,ecliptic z h] ,latitude or ,decl9ation f ! ,ecliptic am\nts to at any giv5 "t2 & = ?is purpose ,s is a small piece ( pa/ebo>d1 ( :i* ! curv$ edge ,s is to be set ^u ! ,globe at "r ,angles to ! ,ecliptic1 & ! d>k l9e ov] ,s to /& upright ^u x4 ,f ?is l9e1 on ! convex edge1 are drawn ! #e-a_/c ,degrees ( ! ,moon's ,latitude on bo? sides ( ! ,ecliptic2 & :5 ?is piece is set upright on ! ,globe1 x's graduat$ edge rea*es to ! ,moon on ! ,wire ,o1 by :i* means %e is easily adju/$ to h] ,latitude f\nd by an ,ephem]is4 ,! ,horizon is support$ by two semicircul> ,ar*es1 because ,pill>s w\ld /op ! progress ( ! ,balls :5 !y g bel[ ! ,horizon 9 an oblique sph]e4 ,sid5ote3 ,to rectify x4 ,to rectify ! ,globe4 ,elevate ! ,pole to ! ,latitude ( ! ,place2 !n br+ ! ,sun's place 9 ! ,ecliptic = ! giv5 day to ! bras5 ,m]idian1 & set ! ,h\r ,index to ,,xii at noon1 t is1 to ! upp] ,,xii on ! ,h\r ,circle2 keep+ ! ,globe 9 t situation1 slack5 ! ,screw ,g1 & set ! ,sun directly ov] 8 place on ! ,m]idian2 :i* done1 set ! ,moon's ,wire "u ! numb] t expresses h] age = t day on ! ,plate ,f1 & %e w !n /& ov] h] place 9 ! ,ecliptic1 & %ew :at ,con/ellation %e is 94 ,la/ly1 fa/5 ! ,screw ,g1 & lay+ ! curv$ edge ( ! pa/ebo>d ,s ov] ! ,ecliptic bel[ ! ,moon1 adju/ ! ,moon to h] ,latitude ov] ! graduat$ edge ( ! pa/ebo>d2 & ! ,globe w be rectifi$4 ,sid5ote3 ,x's use4 ,hav+ ?us rectifi$ ! ,globe1 turn x r\nd1 & obs]ve on :at po9ts ( ! ,horizon ! ,sun & ,moon ,balls rise & set1 = ^! agree ) ! po9ts ( ! ,compass on :i* ! ,sun & ,moon rise & set 9 ! ,heav5s on ! giv5 day2 & ! ,h\r ,index %ews ! times ( _! ris+ & sett+2 & likewise ! "t ( ! ,moon's pass+ ov] ! ,m]idian4 ,?is simple ,app>atus %ews all ! v>ieties t c happ5 9 ! ris+ & sett+ ( ! ,sun & ,moon2 & makes ! =em5tion$ ,ph5om5a ( ! ,h>ve/ ,moon 7,*ap4 xvi47 pla9 to ! ,eye4 ,x is also v useful 9 read+ ,lectures on ! ,globes1 because a l>ge company c see ?is ,sun & ,moon go+ r\nd1 ris+ above & sett+ bel[ ! ,horizon at diff]5t times1 accord+ to ! seasons ( ! ye>2 & mak+ _! appulses to diff]5t fix$ ,/>s4 ,b1 9 ! usual way1 :]e !re is only ! places ( ! ,sun & ,moon 9 ! ,ecliptic to keep ! ,eye ^u1 !y are easily lo/ sight (1 unless cov]$ ) ,pat*es4 ,sid5ote3 ,! ,,planet>y ,,globe4 ,,pl4 ,,viii4 ,fig4 ,,iv4 #dci4 ,! ,planet>y ,globe4 ,9 ?is ,ma*9e1 ,t is a t]re/rial ,globe fix$ on its ,axis /&+ upright on ! ,p$e/al ,,cde1 on :i* is an ,h\r ,circle1 hav+ its ,index fix$ on ! ,axis1 :i* turns some:at tightly 9 ! ,p$e/al1 s t ! ,globe may n be liable to %ake2 to prev5t :i*1 ! ,p$e/al is ab\t two ,in*es ?ick1 & ! ,axis goes q ?r\gh x1 be>+ on a %\ld]4 ,! ,globe is hung 9 a graduat$ bras5 ,m]idian1 mu* 9 ! usual way2 & ! ?9 ,plate ,n1 ,,ne1 ,e1 is a moveable ,horizon1 graduat$ r\nd ! out] edge1 = %ew+ ! ,be>+s & ,amplitudes ( ! ,sun1 ,moon1 & ,planets4 ,! bras5 ,m]idian is groov$ r\nd ! out] edge2 & 9 ?is ,groove is a sl5d] ,semi-circle ( brass1 ! ends ( :i* are fix$ to ! ,horizon 9 its ,nor? & ,s\? ,po9ts3 ?is ,semi-circle slides 9 ! ,groove z ! ,horizon is mov$ 9 rectify+ x = diff]5t ,latitudes4 ,to ! middle ( ! ,semi-circle is fix$ a ,p9 :i* always keeps 9 ! ,z5i? ( ! ,horizon1 & on ?is ,p9 ! ,quadrant ( ,altitude q turns2 ! l[] end ( :i*1 9 all ,positions1 t\*es ! ,horizon z x is mov$ r\nd ! same4 ,?is ,quadrant is divid$ into #ij ,degrees f ! ,horizon to ! z5i?al ,p9 on :i* x is turn$1 at #ij4 ,! great flat ,circle or ,plate ,,ab is ! ,ecliptic1 on ! out] edge ( :i*1 ! ,signs & ,degrees are laid d[n2 & e fif? ,degree is drawn ?r\gh ! re/ ( ! surface ( ?is ,plate t[>ds its ,c5t]4 ,on ?is ,plate are sev5 ,grooves1 to :i* sev5 little ,balls are adju/$ by slid+ ,wires1 s t !y are easily mov$ 9 ! ,grooves1 )\t dang] ( />t+ out ( !m4 ,! ,ball next ! t]re/rial ,globe is ! ,moon1 ! next )\t x is ,m]cury1 ! next ,v5us1 ! next ! ,sun1 !n ,m>s1 !n ,jupit]1 & la/ly ,saturn2 & 9 ord] to "k !m1 !y are sep>ately /ampt ) ! foll[+ ,*>act]s2 1 1 1 1 1 1 4 ,?is ,plate or ,ecliptic is support$ by f\r /rong ,wires1 hav+ _! l[] ends fix$ into ! ,p$e/al1 at ,c1 ,d1 & ,e1 ! f\r? be+ hid by ! ,globe4 ,! ,ecliptic is incl9$ #bc-a_/b ,degrees to ! ,p$e/al1 & is !re=e prop]ly incl9$ to ! ,axis ( ! ,globe :i* /&s upright on ! ,p$e/al4 ,sid5ote3 ,to rectify x4 ,to rectify ?is ,ma*9e4 ,set all ! planet>y ,balls to _! geoc5tric places 9 ! ,ecliptic = any giv5 "t by an ,ephem]is3 !n1 set ! ,nor? ,po9t ( ! ,horizon to ! ,latitude ( y\r place on ! bras5 ,m]idian1 & ! ,quadrant ( ,altitude to ! ,s\? ,po9t ( ! ,horizon2 :i* done1 turn ! ,globe ) its ,furniture till ! ,quadrant ( ,altitude comes "r aga9/ ! ,sun1 viz4 to 8 place 9 ! ,ecliptic2 & keep+ x !re1 set ! ,h\r ,index to ! ,,xii next ! lett] ,c2 & ! ,ma*9e w be rectifi$1 n only = ! foll[+ ,problems1 b = sev]al o!rs1 :i* ! ,arti/ may easily f9d out4 ,,problem ,i4 ,to f9d ! ,amplitudes1 ,m]idian ,altitudes1 & times ( ,ris+1 ,culm9at+1 & ,sett+1 ( ! ,sun1 ,moon1 & ,planets4 ,sid5ote3 ,x's use4 ,turn ! ,globe r\nd ea/w>d1 or accord+ to ! ord] ( ,signs2 & z ! ea/]n edge ( ! ,horizon comes "r aga9/ ! ,sun1 ,moon1 or any ,planet1 ! ,h\r ,index w %ew ! "t ( x's ris+2 & ! inn] edge ( ! ,ecliptic w cut x's ris+ ,amplitude 9 ! ,horizon4 ,turn on1 & z ! ,quadrant ( ,altitude comes "r aga9/ ! ,sun1 ,moon1 or ,planets1 ! ,ecliptic cuts _! m]idian ,altitudes 9 ! ,quadrant1 & ! ,h\r ,index %ews ! times ( _! com+ to ! ,m]idian4 ,cont9ue turn+1 & z ! we/]n edge ( ! ,horizon comes "r aga9/ ! ,sun1 ,moon1 or ,planets1 _! sett+ ,amplitudes are cut 9 ! ,horizon by ! ,ecliptic2 & ! times ( _! sett+ are %ewn by ! ,index on ! ,h\r ,circle4 ,,problem ,,ii4 ,to f9d ! ,altitude & ,azimu? ( ! ,sun1 ,moon1 & ,planets1 at any "t ( _! be+ above ! ,horizon4 ,turn ! ,globe till ! ,index comes to ! giv5 "t 9 ! ,h\r ,circle2 !n keep ! ,globe /eady1 & mov+ ! ,quadrant ( ,altitude to ea* ,planet respectively1 ! edge ( ! ,ecliptic w cut ! ,planet's mean ,altitude on ! ,quadrant1 & ! ,quadrant w cut ! ,planet's ,azimu?1 or ,po9t ( ,be>+ on ! ,horizon4 ,,problem ,,iii4 ,! ,sun's ,altitude be+ giv5 at any "t ei!r be=e or aft] ,noon1 to f9d ! ,h\r ( ! ,day1 & ! ,v>iation ( ! ,compass1 9 any kn[n ,latitude4 ,) "o h& hold ! edge ( ! ,quadrant "r aga9/ ! ,sun2 &1 ) ! o!r h&1 turn ! ,globe we/w>d1 if x be 9 ! =5oon1 or ea/w>d if x be 9 ! aft]noon1 until ! ,sun's place at ! inn] edge ( ! ,ecliptic cuts ! ,quadrant 9 ! ,sun's obs]v$ ,altitude2 & !n ! ,h\r ,index w po9t out ! "t ( ! day1 & ! ,quadrant w cut ! true ,azimu?1 or ,be>+ ( ! ,sun = t "t3 ! diff]5ce betwe5 :i*1 & ! ,be>+ %ewn by ! ,azimu? ,compass1 %ews ! v>iation ( ! ,compass 9 t place ( ! ,e>?4 ,sid5ote3 ,! ,,trajectorium ,,lun>e4 ,,pl4 ,,vii4 ,fig4 ,v4 #ddj4 ,! ,trajectorium ,lun>e4 ,?is ,ma*9e is = del9eat+ ! pa?s ( ! ,e>? & ,moon1 %ew+ :at sort ( ,curves !y make 9 ! e!rial regions2 & 0 j m5tion$ 9 ! #bff? ,article4 ,s is ! ,sun1 & ,e ! ,e>?1 ^: ,c5t]s are #ha ,in*es di/ant f ea* o!r2 e ,in* answ]+ to a ,million ( ,miles #dg4 ,m is ! ,moon1 ^: ,c5t] is #bd_/ajj p>ts ( an ,in* f ! ,e>?'s 9 ?is ,ma*9e1 ?is be+ 9 j proportion to ! ,moon's di/ance f ! ,e>? #eb4 ,,aa is a ,b> ( ,wood1 to be mov$ by h& r\nd ! ,axis g :i* is fix$ 9 ! ,:eel ,y4 ,! ,circumf]5ce ( ?is ,:eel is to ! ,circumf]5ce ( ! small ,:eel ,l 7bel[ ! o!r end ( ! ,b>7 z #cfe-a_/d days is to #bi-a_/b2 or z a ,ye> is to a ,lunation4 ,! ,:eels are groov$ r\nd _! edges1 & 9 ! ,grooves is ! cat-gut /r+ ,,gg cross+ betwe5 ! ,:eels at ,x4 ,on ! ,axis ( ! ,:eel ,l is ! ,index ,f1 9 :i* is fix$ ! ,moon's ,axis ,m = c>ry+ h] r\nd ! ,e>? ,e 7fix$ on ! ,axis ( ! ,:eel ,l7 9 ! "t t ! ,index goes r\nd a ,circle ( #bi-a_/b equal p>ts1 :i* are ! days ( ! ,moon's age4 ,! ,:eel ,y has ! ,mon?s & ,days ( ! ye> all r\nd x's ,limb2 & 9 ! ,b> ,,aa is fix$ ! ,index ,i1 :i* po9ts out ! ,days ( ! ,mon?s answ]+ to ! ,days ( ! ,moon's age1 %ewn by ! ,index ,f1 9 ! ,circle ( #bi-a_/b equal p>ts at ! o!r end ( ! ,b>4 ,on ! ,axis ( ! ,:eel ,l is put ! piece ,d1 bel[ ! ,cock ,c1 9 :i* ?is ,axis turns r\nd2 & 9 ,d are put ! ,p5cils e & m1 directly "u ! ,e>? ,e & ,moon ,m2 s t m is c>ri$ r\nd e z ,m is r\nd ,e4 ,sid5ote3 ,x's use4 ,lay ! ,ma*9e on an ev5 ,floor1 press+ g5tly on ! ,:eel ,y to cause its spik$ ,feet 7( :i* two appe> at ,p & ,p1 ! ?ird be+ suppos$ to be hid f sight by ! ,:eel7 ent] a little into ! ,floor to secure ! ,:eel f turn+4 ,!n lay a pap] ab\t f\r foot long "u ! ,p5cils e & m1 cross-wise to ! ,b>3 :i* done1 move ! ,b> sl[ly r\nd ! ,axis g ( ! ,:eel ,y2 &1 z ! ,e>? ,e goes r\nd ! ,sun ,s1 ! ,moon ,m w g r\nd ! ,e>? ) a duly proportion$ velocity2 & ! friction ,:eel ,w runn+ on ! ,floor1 w keep ! ,b> f be>+ too heavily on ! ,p5cils e & m1 :i* w del9eate ! pa?s ( ! ,e>? & ,moon1 z 9 ,fig4 #b;d1 already describ$ at l>ge1 #bff1 #bfg4 ,z ! ,index ,i po9ts out ! ,days ( ! ,mon?s1 ! ,index ,f %ews ! ,moon's age on ^! ,days1 9 ! ,circle ( #bi-a_/b equal p>ts4 ,& z ?is la/ ,index po9ts to ! diff]5t ,days 9 x's ,circle1 ! l num]al ,figures may be set to ^? p>ts ( ! ,curves ( ! ,e>?'s ,pa? & ,moon's1 :]e ! ,p5cils e & m are at ^? times respectively1 to %ew ! places ( ! ,e>? & ,moon4 ,if ! ,p5cil e be pu%$ a v little (f1 z if f ! ,p5cil m1 to ab\t #a_/dj "p ( _! di/ance1 & ! ,p5cil m pu%$ z mu* t[>ds e1 to br+ !m to ! same di/ances aga91 ?\gh n to ! same po9ts ( space2 !n z m goes r\nd e1 e w g z x 7 r\nd ! ,c5t] ( ,gravity betwe5 ! ,e>? e & ,moon m #bih3 b ?is ,motion w n s5sibly alt] ! ,figure ( ! ,e>?'s ,pa? or ! ,moon's4 ,if a ,p9 z p be put ?r\gh ! ,p5cil m1 ) its head t[>ds t ( ! ,p9 q 9 ! ,p5cil e1 its head w always keep !reto z m goes r\nd e1 or z ! same side ( ! ,moon is /ill obv]t$ to ! ,e>?4 ,b ! ,p9 p1 :i* may be consid]$ z an equatoreal ,diamet] ( ! ,moon1 w turn q r\nd ! ,po9t m1 mak+ all possible ,angles ) ! ,l9e ( its progress or l9e ( ! ,moon's ,pa?4 ,?is is an ocul> pro( ( ! ,moon's turn+ r\nd h] ,axis4 ,sid5ote3 ,! ,,tide ,,dial4 ,,plate ,,ix4 ,fig4 ,,vii4 ,x's use4 #dda4 ,! ,,tide-,,dial4 ,! outside p>ts ( ?is ,ma*9e consi/ (1 #a4 ,an eight-sid$ ,box1 on ! top ( :i* at ! corn] is %ewn ! ,phases ( ! ,moon at ! ,octants1 ,qu>t]s1 & ,full4 ,)9 ^! is a ,circle ( #bi-a_/b equal p>ts1 :i* are ! days ( ! ,moon's age acc\nt$ f ! ,sun at ,new ,moon r\nd to ! same aga94 ,)9 ?is ,circle is "o ( #bd h\rs divid$ into _! respective ,halves & ,qu>t]s4 #b4 ,a mov+ elliptical ,plate pa9t$ blue to repres5t ! ris+ ( ! ,tides "u & opposite to ! ,moon2 & has ! words1 ,high ,wat]1 ,tide fall+1 ,l[ ,wat]1 ,tide ris+1 m>k$ ^u x4 ,to "o end ( ?is ,plate is fix$ ! ,moon ,m by ! ,wire ,w1 & goes along ) x4 #c4 ,above ?is elliptical ,plate is a r\nd "o1 ) ! ,po9ts ( ! ,compass ^u x1 & also ! names ( above #bjj places 9 ! l>ge ,ma*9e 7b only #cb 9 ! ,figure to avoid confusion7 set ov] ^? ,po9ts on :i* ! ,moon be>s :5 %e raises ! ,tides to ! greate/ heights at ^! ,places twice 9 e lun> day3 & to ! ,nor? & ,s\? ,po9ts ( ?is ,plate are fix$ two ,indexes ,i & ,k1 :i* %ew ! times ( ,high ,wat] 9 ! ,h\r ,circle at all ^! places4 #d4 ,bel[ ! elliptical ,plate are f\r small ,plates1 two ( :i* project out f bel[ its ends at ,new & ,full ,moon2 & s1 by l5g!n+ ! ,ellipse %ew ! ,spr+ ,tides1 :i* are !n rais$ to ! greate/ heights by ! unit$ attractions ( ! ,sun & ,moon #cjb4 ,! o!r two ( ^! small ,plates appe> at l[ wat] :5 ! ,moon is 9 h] ,quadratures1 or at ! sides ( ! elliptic ,plate1 to %ew ! ,nepe ,tides2 ! ,sun & ,moon !n act+ cross-wise to ea* o!r4 ,:5 any two ( ^! small ,plates appe>1 ! o!r two are hid2 & :5 ! ,moon is 9 h] ,octants !y all disappe>1 !re be+ nei!r ,spr+ nor ,nepe ,tides at ^? times4 ,)9 ! ,box are a few ,:eels = p]=m+ ^! ,motions by ! ,h&le or ,w9* ,h4 ,illu/ration3 ,plate ,,xiii4 ,j4 ,f]guson inv4 et del4 ,j4 ,mynde ,sculp4 ,turn ! ,h&le until ! ,moon ,m comes to any giv5 day ( h] age 9 ! ,circle ( #bi-a_/b equal p>ts1 & ! ,moon's ,wire ,w w cut ! "t ( h] com+ to ! ,m]idian on t day1 9 ! ,h\r ,circle2 ! ,,xii "u ! ,sun be+ ,mid-day1 & ! opposite ,,xii ,mid-night3 !n look+ = ! "n ( any giv5 place on ! r\nd ,plate 7:i* makes #bi-a_/b rotations :il/ ! ,moon ,m makes only "o revolution f ! ,sun to ! ,sun aga97 turn ! ,h&le till t place comes to ! ^w ,high ,wat] "u ! ,moon1 & ! ,index :i* falls among ! ,aft]noon ,h\rs w %ew ! "t ( high wat] at t place 9 ! ,aft]noon ( ! giv5 day3 !n turn ! ,plate half r\nd1 till ! same place comes to ! opposite ,high ,wat] ,m>k1 & ! ,index w %ew ! "t ( ,high ,wat] 9 ! ,=5oon at t place4 ,& ?us1 z all ! diff]5t places come successively "u & opposite to ! ,moon1 ! ,indexes %ew ! times ( ,high ,wat] at !m 9 bo? p>ts ( ! day3 & :5 ! same places come to ! ,l[ ,wat] ,m>ks ! ,indexes %ew ! times ( ,l[ ,wat]4 ,= ab\t two days be=e & aft] ! times ( ,new & ,full ,moon1 ! two small ,plates come out a little way f bel[ ! ,high ,wat] ,m>ks on ! elliptical ,plate1 to %ew t ! ,tides rise /ill high] ab\t ^! times3 & ab\t ! ,qu>t]s1 ! o!r two ,plates come out a little f "u ! ,l[ ,wat] ,m>ks t[>ds ! ,sun & on ! opposite side1 %ew+ t ! ,tides ( ,flood rise n !n s high1 nor d ! ,tides ( ,ebb fall s l[1 z at o!r times4 ,by pull+ ! ,h&le a little way outw>d1 x is dis5gag$ f ! ,:eel-"w1 & !n ! upp] ,plate may be turn$ r\nd quickly by h& s1 z ! ,moon may be br\ght to any giv5 day ( h] age 9 ab\t a qu>t] ( a m9ute4 ,sid5ote3 ,! inside "w describ$4 ,fig4 ,,viii4 ,on ,,ab1 ! ,axis ( ! ,h&le ,h1 is an endless ,screw ,c :i* turns ! ,:eel ,,f$ ( #bd tee? r\nd 9 #bd revolutions ( ! ,h&le3 ?is ,:eel turns ano!r ,,ong ( #dh tee?1 & on its ,axis is ! ,p9ion ,,pq ( f\r leaves :i* turns ! ,:eel ,,lki ( #ei tee? r\nd 9 #bi-a_/b turn+s or rotations ( ! ,:eel ,,f$1 or 9 #gjh revolutions ( ! ,h&le1 :i* is ! numb] ( ,h\rs 9 a synodical revolution ( ! ,moon4 ,! r\nd ,plate ) ! names ( ,places ^u x is fix$ on ! ,axis ( ! ,:eel ,,f$2 & ! ,elliptical or ,tide-,plate ) ! ,moon fix$ to x is ^u ! ,axis ( ! ,:eel ,,lki2 consequ5tly1 ! =m] makes #bi-a_/b revolutions 9 ! "t t ! latt] makes "o4 ,! :ole ,:eel ,,f$ ) ! endless ,screw ,c1 & dott$ "p ( ! ,axis ( ! ,h&le ,,ab1 toge!r ) ! dott$ "p ( ! ,:eel ,,ong1 lie hid bel[ ! l>ge ,:eel ,,lki4 ,fig4 #i? repres5ts ! "u side ( ! ,elliptical or ,tide-,plate abcd1 ) ! f\r small ,plates ,,abcd1 ,,efgh1 ,,iklm1 ,,nopq ^u x3 ea* ( :i* has two slits z ,,tt1 ,,ss1 ,,rr1 ,,uu slid+ on two ,p9s z nn1 fix$ 9 ! elliptical ,plate4 ,9 ! f\r small ,plates are fix$ f\r ,p9s at ,w1 ,x1 ,y1 & ,z2 all ( :i* "w 9 an elliptic ,groove oooo on ! cov] ( ! ,box bel[ ! elliptical ,plate2 ! longe/ ,axis ( ?is ,groove be+ 9 a "r l9e ) ! ,sun & ,full ,moon4 ,consequ5tly1 :5 ! ,moon is 9 ,conjunction or ,opposition1 ! ,p9s ,w & ,x ?ru/ out ! ,plates ,,abcd & ,,iklm a little beyond ! ends ( ! elliptic ,plate at d & b1 to f & e2 :il/ ! ,p9s ,y & ,z draw 9 ! ,plates ,,efgh & ,,nopq q "u ! elliptic ,plate to g & h4 ,b1 :5 ! ,moon comes to h] fir/ or ?ird ,qu>t]1 ! elliptic ,plate lies across ! fix$ elliptic ,groove 9 :i* ! ,p9s "w2 & !re=e ! end ,plates ,,abcd & ,,iklm are drawn 9 bel[ ! great ,plate1 & ! o!r two ,plates ,,efgh & ,,nopq are ?ru/ out beyond x to a & c4 ,:5 ! ,moon is 9 h] ,octants ! ,p9s ,v1 ,x1 ,y1 ,z are 9 ! p>ts o1 o1 o1 o ( ! elliptic ,groove1 :i* p>ts are at a mean betwe5 ! greate/ & lea/ di/ances f ! ,c5t] q1 & !n all ! f\r small ,plates disappe> bel[ ! great "o4 ,sid5ote3 ,! ,,eclips>eon4 ,pl4 ,,xiii4 #ddb4 ,! ,,eclips>eon4 ,?is ,piece ( ,me*anism exhibits ! ,"t1 ,quantity1 ,duration1 & ,progress ( sol> ,eclipses1 at all ,p>ts ( ! ,e>?4 ,! pr9cipal p>ts ( ?is ,ma*9e are1 #a4 ,a t]re/rial ,globe ,a turn$ r\nd its ,axis ,b by ! ,h&le or ,w9* ,m2 ! ,axis ,b incl9es #bc-a_/b ,degrees1 & has an ,index :i* goes r\nd ! ,h\r ,circle ,d 9 ea* rotation ( ! ,globe4 #b4 ,a circul> ,plate ,e on ! ,limb ( :i* ! ,mon?s & ,days ( ! ye> are ins]t$4 ,?is ,plate supports ! ,globe1 & gives its ,axis ! same position to ! ,sun1 or to a c&le prop]ly plac$1 t ! ,e>?'s ,axis has to ! ,sun ^u any day ( ! ye> #cch1 by turn+ ! ,plate till ! giv5 ,day ( ! ,mon? comes to ! fix$ ,po9t] or annual ,index ,g4 #c4 ,a crook$ ,wire ,f :i* po9ts t[>ds ! middle ( ! ,e>?'s enlight5$ ,disc at all times1 & %ews to :at place ( ! ,e>? ! ,sun is v]tical at any giv5 "t4 #d4 ,a ,p5umbra1 or ?9 circul> ,plate ( brass ,i divid$ into #ab ,digits by #ab conc5tric ,circles1 :i* repres5t a ,section ( ! ,moon's ,p5umbra1 & is proportion$ to ! size ( ! ,globe2 s t ! %ad[ ( ?is ,plate1 =m$ by ! ,sun1 or a c&le plac$ at a conv5i5t di/ance1 ) x's ,rays transmitt$ ?r\gh a convex ,l5s to make !m fall p>allel on ! ,globe1 cov]s exactly all ^? places ^u x t ! ,moon's ,%ad[ & ,p5umbra d on ! ,e>?3 s t ! ,ph5om5a ( any sol> ,eclipse may be %ewn by ?is ,ma*9e ) c&le-light1 almo/ z well z by ! light ( ! ,sun4 #e4 ,an upright frame ,,hhhh1 on ! sides ( :i* are ,scales ( ! ,moon's ,latitude or ,decl9ation f ! ,ecliptic4 ,to ^! ,scales are fitt$ two ,slid]s ,k & ,k1 ) ,indexes = adju/+ ! ,p5umbra's ,c5t] to ! ,moon's ,latitude1 z x is ,nor? or ,s\? ,asc5d+ or ,desc5d+4 #f4 ,a sol> ,horizon ,c1 divid+ ! enlight5$ ,hemisph]e ( ! ,globe f t :i* is 9 ! d>k at any giv5 "t1 & %ew+ at :at places ! g5]al ,eclipse beg9s & ends ) ! ris+ or sett+ ,sun4 #g4 ,a ,h&le ,m1 :i* turns ! ,globe r\nd x's ,axis by :eel-"w1 & at ! same "t moves ! ,p5umbra across ! frame by ?reads ov] ! ,pullies ,l1 ,l1 ,l1 ) ! velocity duly proportion$ to t ( ! ,moon's %ad[ ov] ! ,e>?1 z ! ,e>? turns on its ,axis4 ,& z ! ,moon's ,motion is quick] or sl[]1 accord+ to h] diff]5t di/ances f ! ,e>?1 ! p5umbral ,motion is easily regulat$ 9 ! ,ma*9e by *ang+ "o ( ! ,pullies4 ,sid5ote3 ,to rectify x4 ,to rectify ! ,ma*9e = use4 ,! true "t ( ,new ,moon & h] ,latitude be+ kn[n by ! =ego+ ,precepts #cee1 #cfc1 if h] ,latitude exce$s ! numb] ( m9utes or divisions on ! ,scales 7:i* are on ! side ( ! frame hid f view 9 ! ,figure ( ! ,ma*9e7 !re c be no ,eclipse ( ! ,sun at t ,conjunction2 b if x does n1 ! ,sun w be eclips$ to "s places ( ! ,e>?2 &1 to %ew ! times & v>i\s appe>ances ( ! ,eclipse at ^? places1 proce$ 9 ord] z foll[s4 ,to rectify ! ,ma*9e = p]=m+ by ! ,light ( ! ,sun4 #a4 ,move ! ,slid]s ,,kk till _! ,indexes po9t to ! ,moon's ,latitude on ! ,scales1 z x is ,nor? & ,s\? ,asc5d+ or ,desc5d+1 at t "t4 #b4 ,turn ! ,mon? ,plate ,e till ! day ( ! giv5 ,new ,moon comes to ! annual ,index ,g4 #c4 ,unscrew ! ,coll> ,n a little on ! ,axis ( ! ,h&le1 to loos5 ! contigu\s ,socket on :i* ! ?reads t move ! ,p5umbra are w\nd2 & set ! ,p5umbra by ,h& till its ,c5t] comes to ! p]p5dicul> ?read 9 ! middle ( ! frame2 :i* ?read repres5ts ! ,axis ( ! ,ecliptic #cga4 #d4 ,turn ! ,h&le till ! ,m]idian ( ,london on ! ,globe comes j "u ! po9t ( ! crook$ ,wire ,f2 !n /op1 & turn ! ,h\r ,circle ,d by ,h& till ,,xii at ,noon comes to its ,index4 #e4 ,turn ! ,h&le till ! ,h\r ,index po9ts to ! "t ( ,new ,moon 9 ! ,circle ,d2 & hold+ x !re1 screw fa/ ! ,coll> ,n4 ,la/ly1 elevate ! ,ma*9e till ! ,sun %9es ?r\gh ! ,sight-,holes 9 ! small upright ,plates ,o1 ,o1 on ! ,p$e/al2 & ! :ole ,ma*9e w be rectifi$4 ,to rectify ! ,ma*9e = %ew+ ! ,c&le-,light1 proce$ 9 e respect z above1 except 9 t "p ( ! la/ p>agraph :]e ! ,sun is m5tion$2 in/ead ( :i* place a ,c&le be=e ! ,ma*9e1 ab\t f\r y>ds f x1 s z ! %ad[ ( ,int]section ( ! cross ?reads 9 ! middle ( ! frame may fall precisely on t "p ( ! ,globe to :i* ! crook$ ,wire ,f po9ts3 !n1 ) a pair ( ,compasses take ! di/ance betwe5 ! ,p5umbra's ,c5t] & ,int]section ( ! ?reads2 & equal to t di/ance set ! ,c&le high] or l[] z ! ,p5umbra's ,c5t] is above or bel[ ! said ,int]section4 ,la/ly1 place a l>ge convex ,l5s betwe5 ! ,ma*9e & ,c&le1 s z ! ,c&le may be 9 ! ,focus ( ! ,l5s1 & !n ! ,rays w fall p>allel1 & ca/ a /rong light on ! ,globe4 ,sid5ote3 ,x's use4 ,^! ?+s done1 :i* may be soon] ?an express$1 turn ! ,h&le backw>d until ! ,p5umbra almo/ t\*es ! side ,,hf ( ! frame2 !n turn+ x gradually =w>d1 obs]ve ! foll[+ ,ph5om5a4 #a4 ,:]e ! ea/]n edge ( ! ,%ad[ ( ! p5umbral ,plate ,i fir/ t\*es ! ,globe at ! sol> ,horizon1 ^? :o inhabit ! correspond+ "p ( ! ,e>? see ! ,eclipse beg9 on ! upp]mo/ edge ( ! ,sun1 j at ! "t ( its ris+4 #b4 ,9 t place :]e ! ,p5umbra's ,c5t] fir/ t\*es ! ,globe1 ! inhabitants h ! ,sun ris+ ^u !m c5trally eclips$4 #c4 ,:5 ! :ole ,p5umbra j falls ^u ! ,globe1 its we/]n edge1 at ! sol> ,horizon1 t\*es & leaves ! place :]e ! ,eclipse ends at ,sun-rise on 8 l[]mo/ edge4 ,cont9ue turn+1 &1 #d4 ! cross l9es 9 ! ,c5t] ( ! ,p5umbra w g ov] all ^? places on ! ,globe :]e ! ,sun is c5trally eclips$4 #e4 ,:5 ! ea/]n edge ( ! ,%ad[ t\*es any place ( ! ,globe1 ! ,eclipse beg9s !re3 :5 ! v]tical l9e 9 ! ,p5umbra comes to any place1 !n is ! greate/ obscuration at t place2 & :5 ! we/]n edge ( ! ,p5umbra leaves ! place1 ! ,eclipse ends !re2 ! times ( all :i* are %ewn on ! ,h\r ,circle3 & f ! beg9n+ to ! end1 ! ,%ad[s ( ! conc5tric p5umbral ,circles %ew ! numb] ( ,digits eclips$ at all ! int]m$iate times4 #f4 ,:5 ! ea/]n edge ( ! ,p5umbra leaves ! ,globe at ! sol> ,horizon ,c1 ! inhabitants see ! ,sun beg9n+ to be eclips$ on 8 l[]mo/ edge at its sett+4 #g4 ,:]e ! ,p5umbra's ,c5t] leaves ! ,globe1 ! inhabitants see ! ,sun set c5trally eclips$4 ,& la/ly1 :]e ! ,p5umbra is :olly dep>t+ f ! ,globe1 ! inhabitants see ! ,eclipse end+ on ! upp]mo/ "p ( ! ,sun's edge1 at ! "t ( its disappe>+ 9 ! ,horizon #cdc4 ,n4,b4 ,if any giv5 day ( ! ye> on ! ,plate ,e be set to ! annual ,index ,g1 & ! ,h&le turn$ till ! ,m]idian ( any place comes "u ! po9t ( ! crook$ ,wire1 & !n ! ,h\r ,circle ,d set by ! h& till ,,xii comes to its ,index2 9 turn+ ! ,globe r\nd by ! ,h&le1 :5 ! said place t\*es ! ea/]n edge ( ! ,hoop or sol> ,horizon ,c1 ! ,index %ews ! "t ( ,sun-sett+ at t place2 & :5 ! place is j com+ out f bel[ ! o!r edge ( ! ,hoop ,c1 ! ,index %ews ! "t t ! ev5+ ,twilight ends to x4 ,:5 ! place has gone ?r\gh ! d>k "p ,a1 & comes ab\t s to t\* "u ! back ( ! ,hoop ,c on ! o!r side1 ! ,index %ews ! "t t ! ,morn+ ,twilight beg9s2 & :5 ! same place is j com+ out f bel[ ! edge ( ! ,hoop next ! frame1 ! ,index po9ts out ! "t ( ,sun-ris+4 ,& ?us1 ! times ( ,sun-ris+ & sett+ are %ewn at all places 9 "o rotation ( ! ,globe1 = any giv5 day ( ! ye>3 & ! po9t ( ! crook$ ,wire ,f %ews all ! places t ! ,sun passes v]tically ov] on t day4 ,,f9is4 ,,index4 ,! num]al ,figures ref] to ! ,articles1 & ! small n to ! ,notes on ! ,articles4 ,a4 ,accel]ation ( ! ,/>s1 #bba4 ,angle1 :at1 #ahe4 ,annual ,p>allax ( ! ,/>s1 #aif4 ,anomaly1 :at1 #bci4 ,anti5ts1 _! sup]/iti\s notions ( ,eclipses1 #cbi4 ,_! me?od ( divid+ ! ,zodiac1 #cih4 ,antipodes1 :at1 #abb4 ,apsides1 l9e (1 #bch4 ,,ar*im$es1 8 ideal ,problem = mov+ ! ,e>?1 #aei4 ,areas describ$ by ! ,planets1 equal 9 times1 #aec4 ,a/ronomy1 ! great advantages aris+ f x bo? 9 our religi\s & civil conc]ns1 #a ,discov]s ! laws by :i* ! ,planets move1 & are reta9$ 9 _! ,orbits1 #b ,atmosph]e1 ! high] ! ?9n]1 #agd4 ,x's prodigi\s expansion1 ib4 ,x's :ole weight on ! ,e>?1 #age4 ,g5]ally ?\ght to be heavie/ :5 x is lighte/1 #agf4 ,)\t x ! ,heav5s w\ld appe> d>k 9 ! day-"t1 #agg4 ,is ! cause ( twilight1 ib4 ,x's height1 ib4 ,refracts ! ,sun's rays1 #agh4 ,cause? ! ,sun & ,moon to appe> above ! ,horizon :5 !y are really bel[ x1 ib4 ,foggy1 deceives u 9 ! bulk & di/ance ( objects1 #ahe4 ,attraction1 #aja-aje4 ,decreases z ! squ>e ( ! di/ance increases1 #ajf4 ,great] 9 ! l>g] ?an 9 ! small] ,planets1 #aeh4 ,great] 9 ! ,sun ?an 9 all ! ,planets if put toge!r1 ib4 ,axes ( ! ,planets1 :at1 #ai4 ,_! diff]5t positions ) respect to "o ano!r1 #abj4 ,axis ( ! ,e>?1 x's p>allelism1 #cjb4 ,x's position v>iable z se5 f ! ,sun or ,moon1 #cch4 ! ,ph5om5a !nce aris+1 #cdj4 ,b4 ,bodies1 on ! ,e>?1 lose ( _! weight ! ne>] !y are to ! ,equator1 #aag4 ,h[ !y might lose all _! weight1 #aah1 ,h[ !y become visible1 #afg4 ,c4 ,calculator1 7an ,in/rum5t7 describ$1 #dcf4 ,cal5d>1 h[ to inscribe ! ,gold5 ,numb]s rightly 9 x = %ew+ ! days ( ,new ,moons1 #dbc4 ,cannon-,ball1 x's swiftness1 #hi4 ,9 :at times x w\ld fly f ! ,sun to ! diff]5t ,planets & fix$ ,/>s1 ib4 ,,cass9i1 8 acc\nt ( a d\ble ,/> eclips$ by ! ,moon1 #eh4 ,8 ,diagrams ( ! ,pa?s ( ! ,planets1 #ach4 ,catalogue ( ! ,eclipses1 #cbg4 ,( ! ,con/ellations & ,/>s1 #cfg4 ,( rem>kable ras & ev5ts1 #dcc4 ,cele/ial ,globe improv$1 #dch4 ,c5tripetal & c5trifugal =ces1 h[ !y alt]nately ov]come ea* o!r 9 ! motions ( ! ,planets1 #aeb-aed4 ,*anges 9 ! ,heav5s1 #djc4 ,*ords1 l9e (1 h[ to make1 #cfi4 ,circles1 ( p]petual ,app>ition & ,occultation1 #abh4 ,( ! ,sph]e1 #aih4 ,conta9 #cfj ,degrees :e!r !y be great or small1 #bjg4 ,civil ,ye>1 :at1 #daa4 ,,columbus 7,,*ri/oph]7 8 /ory conc]n+ an ,eclipse1 #ccj4 ,clocks & ,wat*es1 an easy me?od ( kn[+ :e!r !y g true or false1 #bbc4 ,:y !y seldom agree ) ! ,sun if !y g true1 #bbh-bde4 ,h[ to regulate !m by ,equation ,tables & a ,m]idian l9e1 #bbe1 #bbf4 ,cl\dy ,/>s1 #djb4 ,comet>ium 7an ,in/rum5t7 describ$1 #dcg4 ,con/ellations1 anti5t1 _! numb]1 #cif4 ,! numb] ( ,/>s 9 ea*1 accord+ to diff]5t ,a/ronom]s1 #cii4 ,cycle1 ,sol>1 ,lun>1 & ,romi%1 #dbj4 ,( ,ea/]1 #dbe4 ,d4 ,d>kness at our ,,savi\r's crucifixion sup]natural1 #ceb1 #dcb4 ,day1 natural & artificial1 :at1 #dag4 ,& ,night1 always equally long at ! ,equator1 #abf4 ,natural1 n compleat$ 9 an absolute turn ( ! ,e>? on x's ,axis1 #bbb4 ,degree1 :at1 #bjg4 ,digit1 :at1 #cba1 n4 ,direction1 7,numb] (7 #dbf4 ,di/ances ( ! ,planets f ! ,sun1 an idea !re(1 #hi4 ,a ,table !re(1 #ih4 ,h[ f\nd1 #aij4 ,diurnal & annual ,motions ( ! ,e>? illu/rat$1 #bjj1 #bjb4 ,dom9ical ,lett]1 #dbg4 ,d\ble projectile =ce1 a balance to a ,quadruple ,p[] ( ,gravity1 #aec4 ,/> cov]$ by ! ,moon1 #eh4 ,e4 ,e>?1 x's bulk b a po9t z se5 f ! ,sun1 #c ,x's ,diamet]1 annual ,p]iod1 & ,di/ance f ! ,sun1 #dg4 ,turns r\nd x's ,axis1 ib4 ,velocity ( x's equatoreal ,p>ts1 ib4 ,velocity 9 x's annual ,orbit1 ib4 ,incl9ation ( x's ,axis1 #dh4 ,pro( ( x's be+ globul>1 or ne>ly s1 #di1 #cad4 ,measurem5t ( x's surface1 #ej1 #ea4 ,diff]5ce betwe5 x's ,equatoreal & ,pol> ,diamet]s1 #gf4 ,x's motion r\nd ! ,sun demon/rat$ by gravity1 #ajh1 #aaa4 by ,dr4 ,,bradley's obs]vations1 #aac4 by ! ,eclipses ( ,jupit]'s ,satellites1 #bai4 ,x's diurnal motion highly probable f ! absurdity t mu/ foll[ ^u suppos+ x n to move1 #aaa4 #abj4 & demon/rable f x's figure1 #aaf4 ?is motion _c be felt1 #aai4 ,objections aga9/ x's motion answ]$1 #aab1 #aba4 ,x has no su* ?+ z an upp] or "u side1 #abb4 9 :at case x might1 #abc4 ,! swiftness ( x's motion 9 x's ,orbit comp>$ ) ! velocity ( light1 #aig4 ,x's diurnal & annual motions illu/rat$ by an easy exp]im5t1 #bjj4 ,prov$ to be less ?an ! ,sun & bigg] ?an ! ,moon1 #cae4 ,ea/] ,cycle1 #dbe4 ,eclips>eon 7an ,in/rum5t7 describ$1 #ddb4 ,eclipses1 ( ,jupit]'s ,satellites1 h[ ! ,longitude is f\nd by !m1 #bjg-bah4 !y demon/rate ! velocity ( light1 #baf4 ,( ! ,sun & ,moon1 #cab-cbg4 ,:y !y happ5 n 9 e mon?1 #caf4 ,:5 !y mu/ be1 #cag4 ,_! limits1 ib4 ,_! ,p]iod1 #cbj1 #cbf4 ,a diss]tation on _! progress1 #cba-cbd4 ,a l>ge catalogue ( !m1 #cbg4 ,hi/orical ones1 #cbh4 ,m ( ! ,sun ?an ( ! ,moon1 & :y1 #cca4 ,! prop] ,elem5ts = _! calculation & projection1 #cec-cij4 ,ecliptic1 x's ,signs1 _! names & *>act]s1 #ia4 ,makes diff]5t ,angles ) ! ,horizon e h\r & m9ute1 #bge4 h[ ^! ,angles may be e/imat$ by ! position ( ! ,moon's horns1 #bfj4 ,x's obliquity to ! ,equator less n[ ?an x 0 =m]ly1 #dje4 ,h[ x's ,signs are numb]$1 #ced4 ,elongations1 ( ! ,planets1 z se5 by an obs]v] at re/ on ! outside ( all _! ,orbits1 #acc4 ,( ,m]cury & ,v5us z se5 f ! ,e>?1 illu/rat$1 #adb4 x's quantity1 #adc4 ,( ,m]cury1 ,v5us1 ! ,e>?1 ,m>s1 & ,jupit]2 x's quantity z se5 f ,saturn1 #adg4 ,epo*as or ras1 #dcc4 ,equation ( "t1 #bbd-bde4 ,( ! ,moon's ,place1 #cee4 ,( ! ,sun's ,place1 ib4 ,( ! ,nodes1 #cfc4 ,equator1 day & night always equal !re1 #abf4 ,makes always ! same ,angle ) ! ,horizon ( ! same place2 ! ,ecliptic n1 #bgd1 #bge4 ,equ9octial ,po9ts 9 ! ,heav5s1 _! precession1 #bdf1 a v diff]5t ?+ f ! recession or anticipation ( ! ,equ9oxes on ,e>?1 ! "o no ways occasion$ by ! o!r1 #bdi4 ,exc5tricities ( ! ,planets ,orbits1 #aee4 ,f4 ,fallacies 9 judg+ ( ! bulk ( objects by _! app>5t di/ance1 #ahe2 appli$ to ! solution ( ! horizontal ,moon1 #ahg4 ,fir/ ,m]idian1 :at1 #bjg4 ,fix$ ,/>s1 :y !y appe> ( less magnitude :5 view$ ?r\gh a telescope ?an by ! b>e eye1 #cia4 ,_! numb]1 #cib4 ,_! division into diff]5t ,classes & ,con/ellations1 #cie-cii4 ,g4 ,g5]al ,ph5om5a ( a sup]ior ,planet z se5 f an inf]ior1 #adi4 ,gravity1 demon/rable1 #aja-ajd4 ,keeps all bodies on ! ,e>? to x's surface1 or br+s !m back :5 ?r[n upw>d2 & con/itutes _! weight1 #aja1 #abb4 ,reta9s all ! ,planets 9 _! ,orbits1 #ajc4 ,decreases z ! squ>e ( ! di/ance increases1 #ajf4 ,proves ! ,e>?'s annual motion1 #ajh4 ,demon/rat$ to be great] 9 ! l>g] ,planets ?an 9 ! small]2 & /rong] 9 ! ,sun ?an 9 all ! ,planets toge!r1 #aeh4 ,h>d to und]/& :at x is1 #afj4 ,acts e mom5t1 #afb4 ,globe1 improv$ cele/ial1 #dch4 ,great ,ye>1 #bea4 ,h4 ,h>mony ( ! cele/ial motions1 #aaa4 ,h>ve/-,moon1 #bgc-bic4 ,none at ! ,equator1 #bgc4 ,rem>kable at ! ,pol> ,circles1 #bhe4 ,9 :at ye>s mo/ & lea/ advantage\s1 #bib4 ,heat1 decreases z ! squ>e ( ! di/ance f ! ,sun increases1 #afi4 ,:y n greate/ :5 ! ,e>? is ne>e/ ! ,sun1 #bje4 ,:y great] ab\t ?ree o',clock 9 ! aft]noon ?an :5 ! ,sun is on ! ,m]idian1 #cjj4 ,heav5s1 seem to turn r\nd ) diff]5t velocities z se5 f ! diff]5t ,planets2 & on diff]5t ,axes z se5 f mo/ ( !m1 #abj4 ,only "o ,hemisph]e ( !m se5 at once f any "o ,planet's surface1 #abe4 ,! ,sun's ,c5t] ! only po9t f :i* _! true ,motions c\ld be se51 #ace4 ,*anges 9 !m1 #djc4 ,horizon1 :at1 #abe1 n4 ,horizontal-,moon expla9$1 #ahg4 ,horizontal ,p>allax1 ( ! ,moon1 #aij2 ( ! ,sun1 #aia2 be/ obs]v$ at ! ,equator1 #aic4 ,h\r-,circles1 :at1 #bjh4 ,h\r ( "t equal to #ae degrees ( motion1 ib4 ,h[ divid$ by ! ,jews1 ,*aldeans1 & ,arabians1 #dai4 ,,huyg5ius1 8 ?\ghts conc]n+ ! di/ance ( "s ,/>s1 #e ,i4 ,j4 ,incl9ation ( ,v5us's ,axis1 #bi4 ,( ! ,e>?'s1 #dh4 ,( ! ,axis or ,orbit ( a ,planet only relative1 #bja4 ,inhabitants ( ! ,e>? 7or any o!r ,planet7 /& on opposite sides ) _! feet t[>d "o ano!r1 yet ea* ?9ks himself on ! upp] side1 #abb4 ,julian ,p]iod1 #dcj4 ,jupit]1 x's di/ance1 diamet]1 diurnal & annual revolutions1 #fg-fi4 ,! ,ph5om5a ( x's ,belts1 #gj4 ,has no diff]5ce ( seasons1 #ga4 ,has f\r ,moons1 #gb1 _! gr& ,p]iod1 #gc1 ! ,angles :i* _! ,orbits subt5d z se5 f ! ,e>?1 #gd1 mo/ ( !m are eclips$ 9 e revolution1 #ge4 ,! great diff]5ce betwe5 x's equatoreal & pol> ,diamet]s1 #gf4 ,! incl9ation ( x's ,orbit1 & place ( x's ,asc5d+ ,node1 #gg4 ,! ,sun's light #cjjj times z /rong on x z ,full ,moon-light is on ! ,e>?1 #he4 ,is probably inhabit$1 #hf4 ,! amaz+ /r5g? requir$ to put x 9 motion1 #aeh4 ,! figures ( ! ,pa?s describ$ by x's ,satellites1 #bfi4 ,l4 ,light1 ! inconceivable smallness ( x's p>ticles1 #afe1 & ! dreadful mis*ief !y w\ld d if !y 7 l>g]1 #aff4 ,x's surpris+ velocity1 #aff1 comp>$ ) ! swiftness ( ! ,e>?'s annual motion1 #aig4 ,decreases z ! squ>e ( ! di/ance f ! lum9\s body increases1 #afi4 ,is refract$ 9 pass+ ?r\gh diff]5t ,m$iums1 #aga-agc4 ,af=ds a pro( ( ! ,e>?'s annual motion1 #aig1 #bai4 ,9 :at "t x comes f ! ,sun to ! ,e>?1 #baf1 ?is expla9$ by a figure1 #bag4 ,limits ( ,eclipses1 #cag4 ,l9e1 ( ! ,nodes1 :at1 #cag2 has a retrograde motion1 #cai4 ,( ,s9es & ,*ords1 h[ to make1 #cfi4 ,,long 7,rev4 ,dr47 8 me?od ( comp>+ ! quantity ( ! surface ( dry l& ) t ( ! ,sea1 #ea4 ,8 glass sph]e1 #abf4 ,longitude1 h[ f\nd1 #bjg-bac4 ,lucid ,spots 9 ! ,heav5s1 #dja4 ,lun> ,cycle defici5t1 #dbb4 ,m4 ,magellanic ,cl\ds1 #djb4 ,man1 ( a middle size1 h[ mu* press$ by ! weight ( ! ,atmosph]e1 #age2 :y ?is pressure is n felt1 ib4 ,m>s1 x's ,diamet]1 ,p]iod1 ,di/ance1 & o!r ,ph5om5a1 #fd-fg4 ,matt]1 x's prop]ties1 #ii4 ,mean ,anomaly1 :at1 #bci4 ,m]cury1 x's ,diamet]1 ,p]iod1 ,di/ance1 c4 #bb4 ,appe>s 9 all ! %apes ( ! ,moon1 #bc4 ,:5 x w be se5 on ! ,sun1 #bd4 ,! incl9ation ( x's ,orbit & ,place ( x's ,asc5d+ ,node1 ib4 ,x's ,pa? del9eat$1 #ach4 ,exp]im5t to %ew x's ,phases & app>5t ,motion1 #adb4 ,m]cury 7,quicksilv]7 9 ! ,b>omet]1 :y n affect$ by ! ,moon's rais+ ,tides 9 ! ,air1 #caa4 ,m]idian1 fir/1 #bjg4 ,l9e1 h[ to draw "o1 #bbf4 ,milky ,way1 :at1 #djj4 ,mon?s1 ,jewi%1 ,arabian1 ,egyptian1 & ,grecian1 #dae4 ,moon1 h] ,diamet] & ,p]iod1 #eb4 ,h] phases1 #ec1 #bee4 ,%9es n by h] own light1 #ed4 ,has no diff]5ce ( seasons1 #ee4 ,! ,e>? is a ,moon to h]1 #ef4 ,has no ,atmosph]e ( any visible ,d5sity1 #eh2 nor ,seas1 #ei4 ,h[ h] inhabitants may be suppos$ to measure _! ye>1 #fb4 ,h] light comp>$ ) day-light1 #he4 ,! exc5tricity ( h] ,orbit1 #ih4 ,is ne>] ! ,e>? n[ ?an %e 0 =m]ly1 #afc4 ,appe>s bigg] 9 ! ,horizon ?an at any consid]able height above x1 & :y1 #ahg2 yet is se5 mu* "u ! same ,angle 9 bo? cases1 #ahh4 ,h] surface m\nta9\s1 #beb3 if smoo? %e c\ld give u no light1 ib4 ,:y no hills appe> r\nd h] edge1 #bec4 ,has no ,twilight1 #bed4 ,appe>s n always q r\nd :5 full1 #bef4 ,h] phases agreeably repres5t$ by a globul> ,/one view$ 9 ,sun-%9e :5 %e is above ! ,horizon1 & ! obs]v] plac$ z if he saw h] on ! top ( ! ,/one1 #beh4 ,turns r\nd h] ,axis1 #bfb4 ,! l5g? ( h] ,sol> & ,sid]eal ,day1 ib4 ,h] p]iodical & synodical revolution repres5t$ by ! motions ( ! h\r & m9ute h&s ( a ,wat*1 #bfd4 ,h] ,pa? del9eat$1 & %ewn to be always concave to ! ,sun1 #bfe-bfh4 ,h] motion alt]nately ret>d$ & accel]at$1 #bfg4 ,h] gravity t[>d ! ,sun great] ?an t[>d ! ,e>? at h] ,conjunction1 & :y %e does n !n ab&on ! ,e>? on t acc\nt1 #bfh4 ,rises ne>] ! "t ( ,sun-set :5 ab\t ! full 9 h>ve/ = a :ole week ?an :5 %e is ab\t ! full at any o!r "t ( ! ye>1 & :y1 #bgc-bhd3 ?is ris+ goes ?r\gh a c\rse ( increas+ & decreas+ b5efit to ! f>m]s e #ai ye>s1 #bib4 ,cont9ues above ! ,horizon ( ! ,poles = f\rte5 ( our natural ,days toge!r1 #bic4 ,prov$ to be globul>1 #cad4 & to be less ?an ! ,e>?1 #cae4 ,h] ,nodes1 #cag4 asc5d+ & desc5d+1 #cah4 _! retrograde motion1 #cai4 ,h] accel]ation prov$ f anti5t ,eclipses1 #cbb1 n4 ,h] ,apogee & ,p]igee1 #ccf4 ,n invisible :5 %e is totally eclips$1 & :y1 #cdf4 ,h[ to calculate h] ,conjunctions1 ,oppositions1 & ,eclipses1 #cee-cij4 ,h[ to f9d h] age 9 any ,lunation by ! ,gold5 ,numb]1 #dbc4 ,morn+ & ,ev5+ ,/>1 :at1 #ade4 ,motion1 naturally rectil9eal1 #ajj4 ,app>5t1 ( ! ,planets z se5 by a spectator at re/ on ! outside ( all _! ,orbits1 #acc2 & ( ! ,heav5s z se5 f any ,planet1 #aed4 ,n4 ,natural ,day1 n compleat$ 9 ! "t t ! ,e>? turns r\nd x's ,axis1 #bbb4 ,new & ,full ,moon1 to calculate ! times ( #cee4 ,new ,/>s1 #djc1 _c be ,comets1 #djd4 ,new ,/yle1 x's orig9al1 #dad4 ,,nicias's ,eclipse1 #cbh4 ,nodes1 ( ! ,planet's ,orbits1 _! places 9 ! ,ecliptic1 #bj4 ,( ! ,moon's ,orbit1 #cag4 _! retrograde motion1 #cai4 ,nonagesimal ,degree1 :at1 #bei4 ,numb] ( ,direction1 #dbf4 ,o4 ,objects1 we (t5 mi/ake _! bulk by mi/ak+ _! di/ance1 #ahe4 ,appe> bigg] :5 se5 ?r\gh a fog ?an ?r\gh cle> ,air1 & :y1 ib4 ?is appli$ to ! solution ( ! ,horizontal ,moon1 #ahg4 ,oblique ,sph]e1 :at1 #aca4 ,olympiads1 :at1 #cbc4 n4 ,orbits ( ! ,planets n solid1 #ba4 ,orr]y describ$1 #dcd1 #dce1 #dcf4 ,p4 ,p>allax1 ,horizontal1 :at1 #aij4 ,p>allel ,sph]e1 :at1 #aca4 ,pa? ( ! ,moon1 #bfe1 #bff1 #bfg4 ,( ,jupit]'s ,moons1 #bfi4 ,p5dulums1 _! vibrat+ sl[] at ! ,equator ?an ne> ! ,poles proves t ! ,e>? turns on x's ,axis1 #aag4 ,p5umbra1 :at1 #ccf4 ,x's velocity on ! ,e>? 9 ,sol> ,eclipses1 #ccg4 ,p]iod ( ,eclipses1 #cbj1 #cbf4 ,phases ( ! ,moon1 #beb-bfh4 ,planets1 mu* ( ! same nature ) ! ,e>?1 #aa4 ,"s h ,moons belong+ to !m1 #ab4 ,move all ! same way z se5 f ! ,sun1 b n z se5 f "o ano!r1 #ah4 ,_! ,moons d5ote !m to be inhabit$1 #hf4 ,! proportional bread? ( ! ,sun's ,disc z se5 f ea* ( !m1 #hg4 ,_! proportional bulks z se5 f ! ,sun1 #hh4 ,an idea ( _! di/ances f ! ,sun1 #hi4 ,appe> bigg] & less by turns1 & :y1 #ij4 ,are kept 9 _! ,orbits by ! p[] ( gravity1 #aja1 #aej-aeh4 ,_! motions v irregul> z se5 f ! ,e>?1 #acg4 ,! app>5t motions ( ,m]cury & ,v5us del9eat$ by ,p5cils 9 an ,orr]y1 #ach4 ,elongations ( all ! re/ z se5 f ,saturn1 #adg4 ,describe equal areas 9 equal times1 #aec4 ,! exc5tricities ( _! ,orbits1 #aee4 ,9 :at times !y w\ld fall to ! ,sun by ! p[] ( gravity1 #aeg4 ,di/urb "o ano!r's motions1 ! consequ5ce !re(1 #afc4 ,appe> dimm] :5 se5 ?r\gh telescopes ?an by ! b>e eye1 ! reason ( ?is1 #agj4 ,planet>y ,globe describ$1 #dci4 ,pol> ,circles1 #aih4 ,poles1 ( ! ,planets1 :at1 #ai4 ,( ! _w1 :at1 #abb4 ,cele/ial1 seem to keep on ! same po9ts ( ! ,heav5s all ! ye>1 & :y1 #aif4 ,projectile ,=ce1 #aej2 if d\bl$ w\ld require a quadruple p[] ( gravity to reta9 ! ,planets 9 _! ,orbits1 #aec4 ,is evid5tly an impulse f ! h& ( ! ,,almighty1 #afa4 ,precession ( ! ,equ9oxes1 #bdf-bea4 ,ptolemean ,sy/em absurd1 #if1 #adj4 ,r4 ,rays ( ,light1 if n di/urb$1 move 9 /raight l9es1 & h9d] n "o ano!r's motions1 #afh4 ,are refract$ 9 pass+ ?r\gh diff]5t m$iums1 #aga4 ,reflection ( ! ,atmosph]e causes ! ,twilight1 #agg4 ,refraction ( ! ,atmosph]e b5ds ! rays ( light f /raight l9es1 & keeps ! ,sun & ,moon long] 9 sight ?an !y w\ld o!rwise be1 #agh4 ,a surpris+ in/ance ( ?is1 #ahc4 ,mu/ be all[$ = 9 tak+ ! ,altitudes ( ! cele/ial bodies1 ib4 ,"r ,sph]e1 #aca4 ,s4 ,satellites2 ! times ( _! revolutions r\nd _! prim>y ,planets1 #eb1 #gc1 #hj4 ,_! ,orbits comp>$ ) ea* o!r1 ) ! ,orbits ( ! prim>y ,planets1 & ) ! ,sun's circumf]5ce1 #bga4 ,:at sort ( ,curves !y describe1 #bgb4 ,saturn1 ) 8 ,r+ & ,moon's1 _! ,ph5om5a1 #gh1 #gi1 #hb4 ,! ,sun's light #ajjj times z /rong to him z ! light ( ! ,full ,moon is to u1 #he4 ,! ,ph5om5a ( 8 ,r+ f>!r expla9$1 #bjd4 ,our bless$ ,,savi\r1 ! d>kness at 8 crucifixion sup]natural1 #ceb4 ,! prophetic ye> ( 8 crucifixion f\nd to agree ) an a/ronomical calculation1 #dcb4 ,seasons1 diff]5t1 illu/rat$ by an easy exp]im5t1 #bjj2 by a figure1 #bjb4 ,%ad[1 :at1 #cab4 ,sid]eal ,"t1 :at1 #bba2 ! numb] ( ,sid]eal ,days 9 a ye> exce$s ! numb] ( ,sol> ,days by "o1 & :y1 #bbb4 ,an easy me?od = regulat+ ,clocks & ,wat*es by x1 #bbc4 ,signs ( ! ,zodiac1 _! names & *>act]s1 #ia1 #cfe4 ,h[ !y are numb]$ by ,a/ronom]s1 #ced4 ,s9es1 l9e (1 h[ to make1 #cfi4 ,,smi?1 7,rev4 ,dr47 8 companion betwe5 ,moon-light & ,day-light1 #he4 ,8 demon/ration t light decreases z ! squ>e ( ! di/ance f ! lum9\s body increases1 #afi4 7,mr4 ,,george7 8 ,diss]tation on ! ,progress ( a ,sol> ,eclipse1 #cba-cbd4 ,sol> ,a/ronom]1 ! judgm5t he might be suppos$ to make conc]n+ ! ,planets & ,/>s1 #ace1 #acf4 ,sph]e1 p>allel1 oblique1 & "r1 #aca4 ,x's ,circles1 #aih4 ,spr+ & ,neap ,tides1 #cjb4 ,/>s1 _! va/ di/ance f ! ,e>?1 #c1 #aif4 ,probably n all at ! same di/ance1 #d ,%9e by _! own light1 & are !re=e ,suns #g1 probably to o!r worlds1 #h ,a demon/ration t !y d n move r\nd ! ,e>?1 #aaa4 ,h an app>5t sl[ motion r\nd ! ,poles ( ! ,ecliptic1 & :y1 #bea4 ,a catalogue ( !m1 #cii4 ,cl\dy1 #djb4 ,new1 #djc4 ,"s ( !m *ange _! places1 #djd4 ,/>ry ,heav5s h ! same appe>ance f any "p ( ! ,sol> ,sy/em1 #acb4 ,,sun appe>s bigg] ?an ! ,/>s1 & :y1 #d ,turns r\nd 8 ,axis1 #ah4 ,8 proportional bread? z se5 f ! diff]5t ,planets1 #hg4 ,describes unequal arcs above & bel[ ! ,horizon at diff]5t times1 & :y1 #acj4 ,8 ,c5t] ! only place f :i* ! true motions ( ! ,planets c\ld be se51 #ace4 ,is = half a ye> toge!r visible at ea* ,pole 9 x's turn1 & z long 9 visible1 #bjj1 #bid4 ,is ne>] ! ,e>? 9 ,w9t] ?an 9 ,summ]1 #bje4 ,:y 8 motion agrees s seldom ) ! motion ( a well regulat$ ,clock1 #bbd-bde4 ,w\ld m ?an fill ! ,moon's ,orbit1 #bga4 ,prov$ to be mu* bigg] ?an ! ,e>?1 & ! ,e>? to be bigg] ?an ! ,moon1 #cae4 ,to calculate 8 true place1 #cfj4 ,sy/ems1 ! ,sol>1 #ag-ie2 ! ,ptolemean1 #if2 ! ,ty*onic1 #ig4 ,t4 ,table1 ( ! ,p]iods1 ,revolutions1 ,magnitudes1 ,di/ances1 c4 ( ! ,planets1 fac+ #ii4 ,( ! ,air's r>ity1 compression1 & expansion at diff]5t heights1 #agd4 ,( refractions1 #ahb4 ,= conv]t+ "t into motion1 & ! rev]se1 #bbj4 ,= %ew+ h[ mu* ( ! cele/ial ,equator passes ov] ! ,m]idian 9 any "p ( a mean ,sol> ,day2 & h[ mu* ! ,/>s accel]ate ^u ! mean ,sol> "t = a mon?1 #bba4 ,( ! fir/ "p ( ! ,equation ( "t1 #bbi2 ( ! second "p1 #bda4 ,( ! precession ( ! ,equ9ox1 #bdg4 ,( ! l5g? ( ,sid]eal1 ,julian1 & ,tropical ,ye>s1 #bea4 ,( ! ,sun's place & ,anomaly1 foll[+ #bea4 ,( ! ,equation ( natural ,days1 foll[+ #bea ,( ! ,conjunctions ( ! h\r & m9ute h&s ( a ,wat*1 #bfd4 ,( ! ,curves describ$ by ! ,satellites1 #bgb4 ,( ! diff]5ce ( "t 9 ! ,moon's ris+ & sett+ on ! p>allel ( ,london e day dur+ h] c\rse r\nd ! ,ecliptic1 #bgg4 ,( ,eclipses1 #cbg4 ,= calculat+ ,new & ,full ,moons & ,eclipses1 foll[+ #cij4 ,( ! ,con/ellations & numb] ( ! ,/>s1 #cii4 ,( ! ,jewi%1 ,egyptian1 ,arabic1 & ,grecian mon?s1 #dae4 ,= ins]t+ ! ,gold5 ,numb]s "r 9 ! ,cal5d>1 #dbc4 ,( ! times ( all ! ,new ,moons = #gf ye>s1 #dbd4 ,( rem>kable ras or ,ev5ts1 #dcc4 ,( ! ,gold5 ,numb]1 ,numb] ( ,direction1 ,dom9ical ,lett] & ,days ( ! ,mon?s1 foll[+ #dcc4 ,,?ales's ,eclipse1 #cbc4 ,,?ucydides's ,eclipse #cbd4 ,tides1 _! ,cause & ,ph5om5a1 #bie-caa4 ,tide-,dial describ$1 #dda4 ,trajectorium ,lun>e describ$1 #ddj4 ,tropics1 #aih4 ,twilight1 none 9 ! ,moon1 #bed4 ,ty*onic ,sy/em absurd1 #ig4 ,u4 ,univ]se1 ! ,"w ( ,almighty ,p[]1 #e1 #afa4 ,up & d[n1 only relative t]ms1 #abb4 ,upp] or "u side ( ! ,e>? no su* ?+1 #abc4 ,v4 ,velocity ( ,light comp>$ ) ! velocity ( ! ,e>? 9 x's annual ,orbit1 #aig4 ,v5us1 h] bulk1 di/ance1 p]iod1 l5g? ( days & nights1 #bf4 ,%9es n by h] own light1 ib4 ,is our morn+ & ev5+ ,/>1 #bh4 ,h] ,axis1 h[ situat$1 #bi4 ,h] surpris+ ,ph5om5a1 #bi-dc4 ,! incl9ation ( h] ,orbit1 #de4 ,:5 %e w be se5 on ! ,sun1 ib4 ,h[ x may probably be soon kn[n if %e has a ,satellite1 #df4 ,appe>s 9 all ! ,%apes ( ! ,moon1 #bc1 #ada4 ,an exp]im5t to %ew h] phases & app>5t motion1 #ada4 ,vision1 h[ caus$1 #afg4 ,w4 ,wea!r1 n hotte/ :5 ! ,sun is ne>e/ to u1 & :y1 #bje4 ,weight1 ! cause ( x1 #abb4 ,_w n et]nal1 #afd4 ,y4 ,ye>1 #djg1 ,great1 #bea1 ,tropical1 #djh1 ,sid]eal1 #djj1 ,lun>1 #daj1 ,civil1 #daa1 ,bissextile1 ib4 ,roman1 #dac1 ,jewi%1 ,egyptian1 ,arabic1 & ,grecian1 #dae1 h[ long x w\ld be if ! ,sun mov$ r\nd ! ,e>?1 #aaa4 ,z4 ,zodiac1 :at1 #cig4 ,h[ divid$ by ! anti5ts1 #cih4 ,zones1 :at1 #aii4 ,,directions to ! ,,bookb9d]4 ,! ,,orr]y ,,plate is to front ! ,title ,page4 ,,plate ,i front+ ,page #e ,,ii #ci ,,iii #di ,,iv #gc ,v #ha ,,vi #ig ,,vii #abe ,,viii #adg ,,ix #adg ,x #aeg ,,xi #agi ,,xii #bjc ,,xiii #bgi ,footnotes ,footnote #a3 ,dr4 ,,"y's ,night ,?\ghts4 ,footnote #b3 ,if a ?read be ti$ loosely r\nd two p9s /uck 9 a table1 & mod]ately /ret*$ by ! po9t ( a black lead p5cil c>ri$ r\nd by an ev5 motion & light pressure ( ! h&1 an oval or ellipsis w be describ$2 ! two po9ts :]e ! p9s are fix$ be+ call$ ! foci or focuses !re(4 ,! ,orbits ( all ! ,planets are elliptical1 & ! ,sun is plac$ 9 or ne> to "o ( ! foci ( ea* ( !m3 & t 9 :i* he is plac$1 is call$ ! l[] focus4 ,footnote #c3 ,a/ronom]s are n f> f ! tru?1 :5 !y reckon ! ,sun's c5t] ! l[] focus ( all ! ,planet>y ,orbits4 ,?\gh /rictly speak+1 if we consid] ! focus ( ,m]cury's ,orbit to be 9 ! ,sun's c5t]1 ! focus ( ,v5us's ,orbit w be 9 ! common c5t] ( gravity ( ! ,sun & ,m]cury2 ! focus ( ! ,e>?'s ,orbit 9 ! common c5t] ( gravity ( ! ,sun1 ,m]cury1 & ,v5us2 ! focus ( ! ,orbit ( ,m>s 9 ! common c5t] ( gravity ( ! ,sun1 ,m]cury1 ,v5us1 & ! ,e>?2 & s ( ! re/4 ,yet1 ! focuses ( ! ,orbits ( all ! ,planets1 except ,saturn1 w n be s5sibly remov$ f ! c5t] ( ! ,sun2 nor w ! focus ( ,saturn's ,orbit rec$e s5sibly f ! common c5t] ( gravity ( ! ,sun & ,jupit]4 ,footnote #d3 ,z repres5t$ 9 ,plate ,,iii4 ,fig4 ,i4 & describ$ 9 #ach4 ,footnote #e3 ,:5 he is betwe5 ! ,e>? & ! ,sun 9 ! ne>] "p ( 8 ,orbit4 ,footnote #f3 ,! "t betwe5 ! ,sun's ris+ & sett+4 ,footnote #g3 ,"o entire revolution1 or #bd h\rs4 ,footnote #h3 ,^! are less] circles p>allel to ! ,equator1 & z _m degrees f x1 t[>ds ! ,poles1 z ! ,axis ( ! ,planet is incl9$ to ! ,axis ( x's ,orbit4 ,:5 ! ,sun is advanc$ s f> nor? or s\? ( ! ,equator z to be directly ov] ei!r ,tropic1 he goes no f>!r2 b returns t[>ds ! o!r4 ,footnote #i3 ,^! are less] circles r\nd ! ,poles1 & z f> f !m z ! ,tropics are f ! ,equator4 ,! ,poles are ! v nor? & s\? po9ts ( ! ,planet4 ,footnote #aj3 ,a ,degree is a #cfj? "p ( any ,circle4 ,see #ba4 ,footnote #aa3 ,! ,limit ( any inhabitant's view1 :]e ! ,sky seems to t\* ! ,planet all r\nd him4 ,footnote #ab3 ,?is is n /rictly true1 z w appe> :5 we come to treat ( ! ,recession ( ! ,equ9octial ,po9ts 9 ! ,heav5s #bdf2 :i* recession is equal to ! deviation ( ! ,e>?'s ,axis f x's p>allelism3 b ?is is r too small to be s5sible 9 an age1 except to ^? :o make v nice obs]vations4 ,footnote #ac3 ,memoirs d',acad4 ann4 #agbj4 ,footnote #ad3 ,! ,moon's ,orbit crosses ! ,ecliptic 9 two opposite po9ts call$ ! ,moon's ,nodes2 s t "o half ( h] ,orbit is above ! ,ecliptic1 & ! o!r half bel[ x4 ,! ,angle ( x's ,obliquity is #e-a_/c degrees4 ,footnote #ae3 ,,cass9i ,elem5ts d',a/ronomie1 ,liv4 ix4 ,*ap4 #c4 ,footnote #af3 ,optics1 ,art4 #ie4 ,footnote #ag3 ,mr4 ,,:i/on1 9 8 ,a/ronomical ,pr9ciples ( ,religion4 ,footnote #ah3 ,z w be demon/rat$ 9 ! n9? ,*apt]4 ,footnote #ai3 ,optics1 ,b4 ,i4 #aagh4 ,footnote #bj3 ,a/ronomy1 ,b4 ,,ii4 4 #hch4 ,footnote #ba3 ,philosophy1 ,vol4 ,i4 p4 #dja4 ,footnote #bb3 ,acc\nt ( ,sir ,isaac ,newton's ,philosophical ,discov]ies1 ,b4 ,,iii4 c4 #b4 #c4 ,footnote #bc3 ,elem5ts d',a/ronomie1 #cha4 ,footnote #bd3 ,! face ( ! ,sun1 ,moon1 or any ,planet1 z x appe>s to ! eye1 is call$ x's ,disc4 ,footnote #be3 ,! utmo/ limit ( a p]son's view1 :]e ! ,sky seems to t\* ! ,e>? all ar\nd1 is call$ 8 ,horizon2 :i* %ifts z ! p]son *anges 8 place4 ,footnote #bf3 ,! ,plane ( a ,circle1 or a ?9 circul> ,plate1 be+ turn$ edgewise to ! eye appe>s to be a /raight l9e4 ,footnote #bg3 ,a ,degree is ! #cfj? "p ( a ,circle4 ,footnote #bh3 ,"h we d n mean su* a conjunction1 z t ! ne>] ,planet %\ld hide all ! re/ f ! obs]v]'s sight2 7= t w\ld be impossible unless ! int]sections ( all _! ,orbits 7 co9cid5t1 :i* !y are n1 ,see #ba47 b :5 !y 7 all 9 a l9e cross+ ! /&>d ,orbit at "r ,angles4 ,footnote #bi3 ,! ,,orr]y front+ ! ,title-page4 ,footnote #cj3 ,to make ! projectile =ce balance ! gravitat+ p[] s exactly z t ! body may move 9 a ,circle1 ! projectile velocity ( ! body mu/ be su* z x w\ld h acquir$ by gravity alone 9 fall+ ?r\gh half ! radius4 ,footnote #ca3 ,a/ronomical ,pr9ciples ( ,religion1 p4 #ff4 ,footnote #cb3 1 1 i4 e4 ,give me a place to /& on1 & ,i %all move ! ,e>?4 ,footnote #cc3 ,if ! ,sun 0 n agitat$ ab\t ! common c5t] ( gravity ( ! :ole ,sy/em1 & ! ,planets did n act mutually ^u "o ano!r1 _! ,orbits w\ld be elliptical1 & ! areas describ$ by !m w\ld be exactly proportionate to ! times ( description #aec4 ,b obs]vations prove t ^! areas are n 9 su* exact proportion1 & are mo/ v>i$ :5 ! greate/ numb] ( ,planets are 9 any p>ticul> qu>t] ( ! ,heav5s4 ,:5 any two ,planets are 9 conjunction1 _! mutual attractions1 :i* t5d to br+ !m ne>] to "o ano!r1 draws ! inf]ior "o a little f>!r f ! ,sun1 & ! sup]ior "o a little ne>] to him2 by :i* means1 ! figure ( _! ,orbits is some:at alt]$2 b ?is alt]ation is too small to be discov]$ 9 sev]al ages4 ,footnote #cd3 ,religi\s ,philosoph]1 ,vol4 ,,iii4 page #fe4 ,footnote #ce3 ,?is w be demon/rat$ 9 ! elev5? ,*apt]4 ,footnote #cf3 ,a f9e net-"w membrane 9 ! bottom ( ! eye4 ,footnote #cg3 ,book ,i4 ,art4 #eg4 ,footnote #ch3 ,a m$ium1 9 ?is s5se1 is any transp>5t body1 or t ?r\gh :i* ! rays ( light c pass2 z wat]1 glass1 diamond1 air2 & ev5 a vacuum is sometimes call$ a ,m$ium4 ,footnote #ci3 ,,newton's ,sy/em ( ! ,_w1 p4 #abj4 ,footnote #dj3 ,?is is evid5t f pumps1 s9ce none c draw wat] high] ?an #cc foot4 ,footnote #da3 ,namely #ajjjj times ! di/ance ( ,saturn f ! ,sun2 p4 #id4 ,footnote #db3 ,see 8 ,a/ronomy1 p4 #bcb4 ,footnote #dc3 ,z f> z "o c see r\nd him on ! ,e>?4 ,footnote #dd3 ,sid5ote3 ,fig4 ,v4 ,an ,angle is ! incl9ation ( two "r l9es1 z ,,ih & ,,kh1 meet+ 9 a po9t at ,h2 & 9 describ+ an ,angle by ?ree lett]s1 ! middle lett] always d5otes ! angul> po9t3 ?us1 ! above l9es ,,ih & ,,kh meet+ ea* o!r at ,h1 make ! ,angle ,,ihk4 ,& ! po9t ,h is suppos$ to be ! c5t] ( a ,circle1 ! circumf]5ce ( :i* conta9s #cfj equal p>ts call$ degrees4 ,a f\r? "p ( a ,circle1 call$ a ,quadrant1 z ,,ge1 conta9s #ij degrees2 & e ,angle is measur$ by ! numb] ( degrees 9 ! arc x cuts (f2 z ! angle ,,ehp is #de degrees1 ! ,angle ,,ehf #cc1 c3 & s ! ,angle ,,ehf is ! same ) ! angle ,,*n1 & also ) ! ,angle ,,ahm1 because !y all cut (f ! same arc or portion ( ! ,quadrant ,,eg2 & s likewise ! ,angle ,,ehf is great] ?an ! ,angle ,,*d or ,,ahl1 because x cuts (f a great] arc4 ,! ne>] an object is to ! eye ! bigg] x appe>s1 & "u ! great] ,angle is x se54 ,to illu/rate ?is a little1 suppose an ,arr[ 9 ! position ,,ik1 p]p5dicul> to ! "r l9e ,,ha drawn f ! eye at ,h ?r\gh ! middle ( ! ,arr[ at ,o4 ,x is pla9 t ! ,arr[ is se5 "u ! ,angle ,,ihk1 & t ,,ho1 :i* is x's di/ance f ! eye1 divides into halves bo? ! ,arr[ & ! ,angle "u :i* x is se53 viz4 ! ,arr[ into ,,io1 ,,ok1 & ! ,angle into ,,iho & ,,kho3 & ?is w be ! case :atev] di/ance ! ,arr[ is plac$ at4 ,let n[ ?ree ,arr[s1 all ( ! same l5g? ) ,,ik1 be plac$ at ! di/ances ,,ha1 ,,hc1 ,,he1 /ill p]p5dicul> to1 & bisect$ by ! "r l9e ,,ha2 !n w ,,ab1 ,,cd1 ,,ef1 be ea* equal to1 & repres5t ,,io2 & ,,ab 7! same z ,,io7 w be se5 f ,h "u ! ,angle ,,ahb2 b ,,cd 7! same z ,,io7 w be se5 "u ! ,angle ,,*d or ,,ahl2 & ,,ef 7! same z ,,io7 w be se5 "u ! ,angle ,,ehf1 or ,,*n1 or ,,ahm4 ,also1 ,,ef or ,,io at ! di/ance ,,he w appe> z long z ,,cn w\ld at ! di/ance ,,hc1 or z ,,am w\ld at ! di/ance ,,ha3 & ,,cd or ,,io at ! di/ance ,,hc w appe> z long z ,,al w\ld at ! di/ance ,,ha4 ,s t z an object approa*es ! eye1 bo? x's magnitude & ! ,angle "u :i* x is se5 increase2 & z ! object rec$es1 ! contr>y4 ,footnote #de3 ,! fields :i* are beyond ! gate rise gradually till !y are j se5 ov] x2 & ! arms1 be+ r$1 are (t5 mi/ak5 = a h\se at a consid]able di/ance 9 ^? fields4 ,i once met ) a curi\s deception 9 a g5tleman's g>d5 at ,hackney1 occasion$ by a l>ge pane ( glass 9 ! g>d5-wall at "s di/ance f 8 h\se4 ,! glass 7?r\gh :i* ! fields & sky 7 di/9ctly se57 reflect$ a v fa9t image ( ! h\se2 b ! image seem$ to be 9 ! ,cl\ds ne> ! ,horizon1 & at t di/ance look$ z if x 7 a huge ca/le 9 ! ,air4 ,yet1 ! ,angle "u :i* ! image appe>$1 0 equal to t "u :i* ! h\se 0 se53 b ! image be+ m5tally ref]r$ a mu* great] di/ance ?an ! h\se1 appe>$ mu* bigg] to ! imag9ation4 ,footnote #df3 ,! ,sun & ,moon subt5d a great] ,angle on ! ,m]idian ?an 9 ! ,horizon1 be+ ne>] ! ,e>? 9 ! =m] case ?an ! latt]4 ,footnote #dg3 ,! ,altitude ( any cele/ial ,ph5om5on is an arc ( ! ,sky int]cept$ betwe5 ! ,horizon & ! ,ph5om5on4 ,9 ,fig4 ,,vi4 ( ,plate ,,ii4 let ,,hox be a horizontal l9e1 suppos$ to be ext5d$ f ! eye at ,a to ,x1 :]e ! ,sky & ,e>? seem to meet at ! end ( a long & level pla92 & let ,s be ! ,sun4 ,! arc ,,xy w be ! ,sun's height above ! ,horizon at ,x1 & is f\nd by ! in/rum5t ,,edc1 :i* is a quadrantal bo>d1 or plate ( metal1 divid$ into #ij equal p>ts or degrees on its limb ,,dpc2 & has a c\ple ( little brass plates1 z a & b1 ) a small hole 9 ea* ( !m1 call$ ,sight-,holes1 = look+ ?r\gh1 p>allel to ! edge ( ! ,quadrant :]eon !y /&4 ,to ! c5t] ,e is fix$ "o end ( a ?read ,f1 call$ ! ,plumb-,l9e1 :i* has a small weight or plummet ,p fix$ to x's o!r end4 ,n[1 if an obs]v] holds ! ,quadrant upright1 )\t incl9+ x to ei!r side1 & s t ! ,horizon at ,x is se5 ?r\gh ! sight-holes a & b1 ! plumb-l9e w cut or hang ov] ! beg9n+ ( ! degrees at o1 9 ! edge ,,ec2 b if he elevates ! ,quadrant s z to look ?r\gh ! sight-holes at any "p ( ! ,heav5s1 suppose to ! ,sun at ,s2 j s _m degrees z he elevates ! sight-hole b above ! horizontal l9e ,,hox1 s _m degrees w ! plumb-l9e cut 9 ! limb ,,cp ( ! ,quadrant4 ,=1 let ! obs]v]'s eye at ,a be 9 ! c5t] ( ! cele/ial arc ,,xyv 7& he may be said to be 9 ! c5t] ( ! ,sun's app>5t diurnal ,orbit1 let him be on :at "p ( ! ,e>? he w7 9 :i* arc ! ,sun is at t "t1 suppose #be degrees high1 & let ! obs]v] hold ! ,quadrant s t he may see ! ,sun ?r\gh ! sight-holes2 ! plumb-l9e freely play+ on ! quadrant w cut ! #be? degree 9 ! limb ,,cp equal to ! numb] ( degrees ( ! ,sun's ,altitude at ! "t ( obs]vation4 ,n4 ,b4 ,:oev] looks at ! ,sun1 mu/ h a smoak$ glass be=e 8 eyes to save !m f hurt4 ,! bett] way is n to look at ! ,sun ?r\gh ! sight-holes1 b to hold ! ,quadrant fac+ ! eye1 at a little di/ance1 & s t ! ,sun %9+ ?r\gh "o hole1 ! ray may be se5 to fall on ! o!r4 ,footnote #dh3 ,see ! ,note on #ahe4 ,footnote #di3 ,"h prop] all[ance mu/ be made = ! ,refraction1 :i* be+ ab\t #cd m9utes ( a degree 9 ! ,horizon1 w cause ! ,moon's c5t] to appe> #cd m9utes above ! ,horizon :5 h] c5t] is really 9 x4 ,footnote #ej3 ,by ?is is meant1 t if a l9e be suppos$ to be drawn p>allel to ! ,e>?'s ,axis 9 any "p ( x's ,orbit1 ! ,axis keeps p>allel to t l9e 9 e o!r "p ( x's ,orbit3 z 9 ,fig4 ,i4 ( ,plate ,v2 :]e abcdefgh repres5ts ! ,e>?'s ,orbit 9 an oblique view1 & ,ns ! ,e>?'s ,axis keep+ always p>allel to ! l9e ,,mn4 ,footnote #ea3 ,,smi?'s ,optics1 #aaig4 ,footnote #eb3 ,all ,circles appe> ellipses 9 an oblique view1 z is evid5t by look+ obliquely at ! rim ( a bason4 ,= ! true figure ( a ,circle c only be se5 :5 ! eye is directly ov] x's c5t]4 ,! m obliquely x is view$1 ! m elliptical x appe>s1 until ! eye be 9 ! same plane ) x1 & !n x appe>s l a /raight l9e4 ,footnote #ec3 ,"h we mu/ suppose ! ,sun to be no bigg] ?an an ord9>y po9t 7z 7 because he only cov]s a ,circle half a degree 9 diamet] 9 ! ,heav5s2 :]eas 9 ! figure he hides a :ole sign at once f ! ,e>?4 ,footnote #ed3 ,"h we mu/ suppose ! ,e>? to be a mu* small] po9t ?an t 9 ! prec$+ note m>k$ = ! ,sun4 ,footnote #ee3 ,if ! ,e>? 7 cut along ! ,equator1 q ?r\gh ! c5t]1 ! flat surface ( ?is section w\ld be ! plane ( ! ,equator2 z ! pap] conta9$ )9 any ,circle may be ju/ly t]m$ ! plane ( t ,circle4 ,footnote #ef3 ,! two opposite po9ts 9 :i* ! ,ecliptic crosses ! ,equ9octial1 are call$ ! ,equ9octial ,po9ts3 & ! two po9ts :]e ! ,ecliptic t\*es ! ,tropics 7:i* are likewise opposite1 & #ij degrees f ! =m]7 are call$ ! ,sol/itial ,po9ts4 ,footnote #eg3 ,! ,equ9octial ,circle int]sects ! ,ecliptic 9 two opposite po9ts1 call$ ,aries & ,libra1 f ! ,signs :i* always keep 9 ^! po9ts3 ,!y are call$ ! ,equ9octial ,po9ts1 because :5 ! ,sun is 9 ei!r ( !m1 he is directly ov] ! t]re/rial ,equator2 & !n ! days & nights are equal4 ,footnote #eh3 ,9 ?is disc\rse1 we may consid] ! ,orbits ( all ! ,satellites z circul>1 ) respect to _! prim>y ,planets2 because ! exc5tricities ( _! ,orbits are too small to affect ! ,ph5om5a "h describ$4 ,footnote #ei3 ,if a ,globe be cut q ?r\gh ^u any ,circle1 ! flat surface :]e x is s divid$1 is ! plane ( t circle4 ,footnote #fj3 ,! ,figure %ews ! ,globe z if only elevat$ ab\t #dj degrees1 :i* 0 occasion$ by an ov]sight 9 ! draw+3 b x is /ill suffici5t to expla9 ! ,ph5om5a4 ,footnote #fa3 ,! ,ecliptic1 toge!r ) ! fix$ ,/>s1 make #cff-a_/d app>5t diurnal revolutions ab\t ! ,e>? 9 a ye>2 ! ,sun only #cfe-a_/d4 ,!re=e ! ,/>s ga9 #c m9utes #ef seconds ^u ! ,sun e day3 s t a ,sid]eal day conta9s only #bc h\rs #ef m9utes ( mean ,sol> "t2 & a natural or ,sol> day #bd h\rs4 ,h5ce #ab ,sid]eal h\rs are #a m9ute #eh seconds %ort] ?an #ab ,sol>4 ,footnote #fb3 ,! ,sun advances almo/ a degree 9 ! ,ecliptic 9 #bd h\rs1 ! same way t ! ,moon moves3 & !re=e1 ! ,moon by advanc+ #ac-a_/f degrees 9 t "t goes little m ?an #ab degrees f>!r f ! ,sun ?an %e 0 on ! day be=e4 ,footnote #fc3 ,?is c5t] is z mu* ne>] ! ,e>?'s c5t] ?an ! ,moon's z ! ,e>? is heavi]1 or conta9s a great] quantity ( matt] ?an ! ,moon1 namely ab\t #dj times4 ,if bo? bodies 7 susp5d$ on x !y w\ld hang 9 quilibria4 ,s t divid+ #bdj1jjj miles1 ! ,moon's di/ance f ! ,e>?'s c5t]1 by #dj ! excess ( ! ,e>?'s weight above ! ,moon's1 ! quoti5t w be #fjjj miles1 :i* is ! di/ance ( ! common c5t] ( gravity ( ! ,e>? & ,moon f ! ,e>?'s c5t]4 ,footnote #fd3 ,! ,p5umbra is a fa9t k9d ( %ad[ all ar\nd ! p]fect %ad[ ( ! ,planet or ,satellite2 & w be m fully expla9$ by & by4 ,footnote #fe3 ,:i* is ! "t t ! ,eclipse w\ld be at ! greate/ obscuration1 if ! motions ( ! ,sun & ,moon 7 equable1 or ! same 9 all p>ts ( _! ,orbits4 ,footnote #ff3 ,! above p]iod ( #ah ye>s #aa days #g h\rs #dc m9utes1 :i* 0 f\nd out by ! ,*aldeans1 & by !m call$ ,s>os4 ,footnote #fg3 ,a ,digit is a twelf? "p ( ! diamet] ( ! ,sun or ,moon4 ,footnote #fh3 ,!re are two anti5t ,eclipses ( ! ,moon1 record$ by ,ptolemy f ,hipp>*us1 :i* af=d an und5iable pro( ( ! ,moon's accel]ation4 ,! fir/ ( ^! 0 obs]v$ at ,babylon1 ,decemb] ! #bb;d1 9 ! ye> be=e ,,*ri/ #chc3 :5 ! ,moon began to be eclips$ ab\t half an h\r be=e ! ,sun rose1 & ! ,eclipse 0 n ov] be=e ! ,moon set3 b by our be/ ,a/ronomical ,tables1 ! ,moon 0 set at ,babylon half an h\r be=e ! ,eclipse began2 9 :i* case1 !re c\ld h be5 no possibility ( obs]v+ x4 ,! second ,eclipse 0 obs]v$ at ,alex&ria1 ,septemb] ! #bb;d1 ! ye> be=e ,,*ri/ #bja2 :]e ! ,moon rose s mu* eclips$1 t ! ,eclipse mu/ h begun ab\t half an h\r be=e %e rose3 :]eas by our ,tables ! beg9n+ ( ?is ,eclipse 0 n till ab\t #aj m9utes aft] ! ,moon rose at ,alex&ria4 ,_h ^! ,eclipses begun & end$ :ile ! ,sun 0 bel[ ! ,horizon1 we might h imag9$1 t z ! anti5ts _h no c]ta9 way ( measur+ "t1 !y might h be5 s f> mi/ak5 9 ! h\rs1 t we c\ld n h laid any /ress on ! acc\nts giv5 by !m4 ,b1 z 9 ! fir/ ,eclipse ! ,moon 0 set1 & consequ5tly ! ,sun ris51 be=e x 0 ov]2 & 9 ! second ,eclipse ! ,sun 0 set1 & ! ,moon n ris51 till "s "t aft] x began2 ^! are su* circum/ances z ! obs]v]s c\ld n possibly be mi/ak5 94 ,mr4 ,/ruyk 9 ! foll[+ ,catalogue1 not)/&+ ! express words ( ,ptolemy1 puts d[n ^! two ,eclipses z obs]v$ at ,a!ns2 :]e !y might h be5 se5 z above1 )\t any accel]ation ( ! ,moon's motion3 ,a!ns be+ #bj degrees ,we/ ( ,babylon1 & #g degrees ,we/ ( ,alex&ria4 ,footnote #fi3 ,ea* ,olympiad began at ! "t ( ,full ,moon next aft] ! ,summ] ,sol/ice1 & la/$ f\r ye>s1 :i* 7 ( unequal l5g?s because ! "t ( ,full ,moon diff]s #aa days e ye>3 s t !y might sometimes beg9 on ! next day aft] ! ,sol/ice1 & at o!r times n till f\r weeks aft] x4 ,! fir/ ,olympiad began 9 ! ye> ( ! ,julian ,p]iod #cich1 :i* 0 #ggf ye>s be=e ! fir/ ye> ( ,,*ri/1 or #gge be=e ! ye> ( 8 bir?2 & ! la/ ,olympiad1 :i* 0 ! #bic;d1 began ,a4 ,d4 #cic4 ,at ! expiration ( ea* ,olympiad1 ! ,olympic ,games 7 celebrat$ 9 ! ,elean fields1 ne> ! riv] ,alpheus 9 ! ,peloponnesus 7n[ ,morea7 9 hon\r ( ,,jupit] ,,olympus4 ,see ,,/rau*ius's ,brevi>ium ,*ronologium1 p4 #bdg-bea4 ,footnote #gj3 ,! read] may probably f9d x difficult to und]/& :y ,mr4 ,,smi? %\ld reckon ?is ,eclipse to h be5 9 ! #d? ye> ( ! #dh? ,olympiad2 z x 0 only 9 ! end ( ! ?ird ye>3 & also :y ! #bh? ( ,may1 9 ! #ehe? ye> be=e ,,*ri/ %\ld answ] to ! pres5t #aj? ( t mon?4 ,b we hope ! foll[+ explanation w remove ^! difficulties4 ,! mon? ( ,may 7:5 ! ,sun 0 eclips$7 9 ! #ehe? ye> be=e ! fir/ ye> ( ,,*ri/1 :i* 0 a leap-ye>1 fell 9 ! latt] end ( ! ?ird ye> ( ! #dh? ,olympiad2 & ! f\r? ye> ( t ,olympiad began at ! ,summ] ,sol/ice foll[+3 b p]haps ,mr4 ,,smi? beg9s ! ye>s ( ! ,olympiad f ,janu>y1 9 ord] to make !m correspond m readily ) ,julian ye>s2 & s reckons ! mon? ( ,may1 :5 ! ,eclipse happ5$1 to be 9 ! f\r? ye> ( t ,olympiad4 ,! ,place or ,longitude ( ! ,sun at t "t 0 #bi #dc #ag1 to :i* same place ! ,sun return$ 7aft] #bcjj ye>s1 viz47 ,a4 ,d4 #agaf1 on ,may1 #i;d4 #e;h4 #fm4 aft] noon3 s t1 ) respect to ! ,sun's place1 ! #i? ( ,may1 #agaf answ]s to ! #bh? ( ,may 9 ! #ehe? ye> be=e ! fir/ ye> ( ,,*ri/2 t is1 ! ,sun _h ! same ,longitude on bo? ^? days4 ,footnote #ga3 ,be=e ,,*ri/ #dac1 ,augu/ #bg4 ,footnote #gb3 ,be=e ,,*ri/ #afh1 ,june #bj4 ,footnote #gc3 ,,/ruyk's ,eclipses are to ! ,old ,/yle1 all ! re/ to ! ,new4 ,footnote #gd3 ,?is ,eclipse happ5$ 9 ! fir/ ye> ( ! ,peloponnesian w>4 ,footnote #ge3 ,al?\gh ! ,sun & ,moon are sph]ical bodies1 z se5 f ! ,e>? !y appe> to be circul> planes1 & s w\ld ! ,e>? if x 7 se5 f ! ,moon4 ,! app>5tly flat surfaces ( ! ,sun & ,moon are call$ _! ,disks by ,a/ronom]s4 ,footnote #gf3 ,a ,digit is a twelf? "p ( ! diamet] ( ! ,sun & ,moon4 ,footnote #gg3 ,?is is ! same ) ! annual ,argum5t ( ! ,moon4 ,footnote #gh3 ,:5 ! ,romans divid$ ! ,empire1 :i* 0 ab\t #ch ye>s be=e ,,*ri/1 ,spa9 fell to ,augu/us's %>e3 9 memory ( :i*1 ! ,spani>ds dat$ all _! memorable ev5ts ab exordio ,regni ,augu/i2 z ,*ri/ians d f ! bir? ( our ,,savi\r4 ,b 9 process ( "t1 only ! initial lett]s ,,a]a ( ^! words 7 us$ in/ead ( ! words !mselves4 ,& ?us1 accord+ to "s1 came ! ^w ,,ra1 :i* is made use ( to signify a po9t ( "t f :5ce hi/orians beg9 to reckon4 ,footnote #gi3 ,:5 ! ,sun's ,anomaly is #j signs #j degrees1 or #f signs #j degrees1 nei!r ! ,sun nor ! ,moon's ,anomaly h any ,equation2 :i* is ! case 9 ?is ,example4 ,footnote #hj3 ,see ! ,rem>k1 p4 #aie4 ,footnote #ha3 ,babylon is #db deg4 #df m94 ea/ f ! ,m]idian ( ,london1 :i* is equal to #b h\rs #ea m94 ( "t ne>ly4 ,see #bbj4 ,footnote #hb3 ,our ,,savi\r 0 born 9 a leap-ye>1 & !re=e e f\r? ye> bo? be=e & aft] is a leap-ye> 9 ! ,old ,/ile3 b ! ,tables beg9 ) ! ye> next aft] t ( 8 bir?4 ,footnote #hc3 ,:5 only "o ( ! ,nodes is m5tion$1 x is ! ,asc5d+ ,node t is meant1 to :i* ! ,desc5d+ ,node is exactly opposite4 ,footnote #hd3 ,:5 ! ,moon is ,nor? ( ! ,ecliptic & go+ f>!r f x1 h] ,latitude or ,decl9ation f ! ,ecliptic is call$ ,nor? ,asc5d+3 :5 %e is ,nor? ( ! ,ecliptic & go+ t[>d x1 h] ,latitude is ,nor? ,desc5d+3 :5 %e is ,s\? ( ! ,ecliptic & go+ f>!r f x1 h] ,latitude is ,s\? ,desc5d+3 & la/ly1 :5 %e is ,s\? ( ! ,ecliptic & go+ t[>d x1 h] ,latitude is ,s\? ,asc5d+4 ,footnote #he3 ,see ,page #aic1 ,example ,,ii4 ,footnote #hf3 ,m4 ,maup]tuis1 9 8 diss]tation on ! figures ( ! ,cele/ial ,bodies 7p4 #fa-fc7 is ( op9ion t "s ,/>s1 by _! prodigi\s quick rotations on _! ,axes1 may n only assume ! figures ( oblate sph]oids1 b t by ! great c5trifugal =ce1 aris+ f su* rotations1 !y may become ( ! figures ( mill-/ones2 or be r$uc$ to flat circul> planes1 s ?9 z to be q invisible :5 _! edges are turn$ t[>ds u2 z ,saturn's ,r+ is 9 su* positions4 ,b :5 v exc5tric ,planets or ,comets g r\nd any flat ,/>1 9 ,orbits mu* incl9$ to x's ,equator1 ! attraction ( ! ,planets or ,comets 9 _! p]ihelions mu/ alt] ! incl9ation ( ! ,/>2 on :i* acc\nt x w appe> m or less l>ge & lum9\s z x's broad side is m or less turn$ t[>ds u4 ,& ?us he imag9es we may acc\nt = ! app>5t *anges ( magnitude & lu/re 9 ^? ,/>s1 & likewise = _! appe>+ & disappe>+4 ,footnote #hg3 ,see ?is ^w expla9$ 9 ! note at ! foot ( page #aid4 ,footnote #hh3 ,see ! note on #cbc4 ,footnote #hi3 ,matt4 xxvii4 #de4 ,m>k xv4 #dc4 ,luke xxiii4 #dd4 ,transcrib]'s ,note ,?is book uses inconsi/5t spell+ & hyph5ation1 :i* 7 reta9$ 9 ! ebook v]sion4 ,"s corrections h be5 made to ! text1 includ+ correct+ ! errata & normaliz+ punctuation4 ,fur!r corrections are not$ bel[3 ,errata3 l4 #ae f botton - l4 #ae f bottom p4 #i3 =w>d 9 ! ,eliptic - =w>d 9 ! ,ecliptic p4 #ca3 is at x 7 - is z x 7 p4 #cf1 ,footnote #bb mov$ f ref]r+ to ,ru!rfur? to ,maclaur91 additionally #8,isacc ,newton' *ang$ to #8,isaac ,newton'4 ,footnote m>k] on ,ru!rfur? remov$ z !re 0 no footnote associat$ ) x4 p4 #ch3 on ! ! same ,axis - on ! same ,axis ,footnote #cb - p4 #fi3 :o 7 supris$ to f9d - :o 7 surpris$ to f9d p4 #fi3 ?an ^? :* - ?an ^? :i* p4 #gb3 ?an tie a ?read - !n tie a ?read p4 #gd3 is is equal to - is equal to p4 #gd3 ! graduad$ limb - ! graduat$ limb ,footnote #di3 bove ! horizon - above ! horizon p4 #gh3 diff]5t l5ghts - diff]5t l5g?s p4 #gh3 f ! ! ,equator - f ! ,equator p4 #ij3 is n in/antaneons - is n in/antane\s p4 #ib3 ,degreees & ,p>ts ( ! ,equtor- ,degrees & ,p>ts ( ! ,equator p4 #acb3 appe> suppris+ - appe> surpris+ p4 #acc3 ,:5 ,jupit] at - ,:5 ,jupit] is at ,sid5ote p4 #acf3 ,! reason ( ( ?is - ! reason ( ?is p4 #adj ! opposite po9ts rises - ! opposite po9t rises ,sid5ote p4 #ada3 ,h>ve/ aad ,hunt]'s - ,h>ve/ & ,hunt]'s p4 #aed3 espeically z to ! - especially z to ! ,sid5ote p4 #aee3 a]eal ,tides - a]ial ,tides p4 #aeh3 ! ! ,e>? - ! ,e>? p4 #afj3 goes r\nd him #hg days - goes r\nd him 9 #hg days p4 #afa3 ,eclipses & revolulution - ,eclipses & revolution p4 #afg3 ,jacobus ,ptlaum5 - ,jacobus ,pflaum5 p4 #afh3 set set d[n - set d[n p4 #agb ,table #b1 #a/ column1 #f? r[3 #achh - #adhh p4 #agd3 duplicate entry = #afjf ,sept #b4 remov$ p4 #agg3 =etold by ,?alls - =etold by ,?ales p4 #ahj3 ! ,eclipse is annual> - ! ,eclipse is annul> p4 #aic3 ,,eaample ,,ii4 - ,,example ,,ii p4 #bjb3 ^! two ,fquations - ^! two ,equations p4 #bjc3 _! ,sun w be - _! ,sum w be p4 #baj3 ! page numb] 0 pr9t$ z #aaj & has be5 correct$ p4 #baj3 ,motion & ,semi diamet] - ,motion & ,semi-diamet] p4 #bcb3 - p4 #bcb3 - p4 #bch3 oblate sph]iod - oblate sph]oid p4 #bfa #ah ,degres - #ah ,degrees ,index ,m]cury 7,quicksiv]7 - ,m]cury 7,quicksilv]7 ,li/ ( ,plates ,page numb] = ,plate ,,iv correct$ f #ae to #ig