,transcrib]'s ,notes3 ,und]scores 80 be=e & aft] a ^w or phrase indicate italics 9 ! orig9al text4 ,small capitals h be5 conv]t$ to ,,solid capitals4 ,old or antiquat$ spell+s h be5 pres]v$4 ,typographical errors h be5 sil5tly correct$4 ,illu/ration3 ,! ,,great ,,orr]y ,f\r ,feet 9 ,diamet] ,made by ,,?o3 ,,wright ,ma!matical ,in/rum5t-mak] ,,to ,,8 ,,maje/y ,= ! ,royal ,academy at ,,portsm\? ,n[ ,b4 ,cole1 at ! same %op4 ,:o makes ,orr]y's ( diff]5t sorts z may be se5 at 8 ,%op 9 ,,fleet ,,/reet ,:]e is ,sold a ,l>ge ,pr9t ( ! ,orr]y ) ! ,explanation on a ,%eet ( ,imp]ial ,pap]4 ,price #bs4 ,,! ,description & ,use ,,( ,,! ,,globes1 ,,& ,,! ,,orr]y4 ,to :i* is prefix'd1 ,by ,way ( ,,introduction1 ,a brief ,acc\nt ( ! ,,sol> ,,sy/em4 ,by ,,joseph ,,h>ris1 ,,tea*] ( ! ,,ma!matics4 ,,! ,,elev5? ,,edition4 ,,london3 ,pr9t$ = ,b4 ,,cole1 at ! ,orr]y1 ne> ! ,globe ,tav]n1 9 ,fleet /reet1 late ! ,%op ( ,mr4 ,,?omas ,,wright1 ,in/rum5t-mak] to 8 late ,,maje/y2 & ,e4 ,,cu%ee1 ne> ,/4 ,dun/an's ,*ur*1 ,fleet ,/reet4 ,,mdcclxxiii4 ,adv]tisem5t4 ,! great enc\ragem5t ,mr4 ,,wright has _h = _m ye>s pa/ 9 mak+ l>ge ,orr]ies1 ) ! motions ( all ! ,planets & ,satellites1 & ! true motion ( ,saturn's ,r+1 has made him s ready & p]fect1 t ,g5tlem5 may dep5d on hav+ !m made reasonable & s\nd1 n liable to be out ( ,ord]4 ,z may be se5 by "o he made = ,mr4 ,watt's ,academy 9 ,t[]-/reet4 ,ano!r = 8 ,maje/y at ,k5s+ton4 ,ano!r = ! ,new ,royal ,academy at ,portsm\?4 ,ano!r = 8 ,grace ! ,duke ( ,argyle 7late ,"l ,ila47 ,& sev]al o!r l>ge ones = ,noblem5 & ,g5tlem54 ,! above1 & all o!r ,ma!matical1 ,philosophical1 & ,optical ,in/rum5ts1 are n[ made 9 ! mo/ complete mann]1 by ,b4 ,,cole1 ,s]vant to ,mr4 ,,wright1 at ! "t ( ! above be+ made1 & successor to him 9 ! same ,trade & ,bus9ess4 ,,! ,,cont5ts4 ,! ,,introduction3 ,conta9+ a brief ,acc\nt ( ! ,sol> ,sy/em1 & ( ! ,fix$ ,/>s4 ,,sect4 ,i4 ,( ! ,ord] & ,p]iods ( ! ,prim>y ,planets revolv+ ab\t ! ,sun2 & ( ! ,second>y ,planets r\nd _! respective ,prim>ies4 ------ ,( ! ,prim>y ,planets #a ------ ,( ! ,second>y ,planets #e ------ ,( ! ,annual & ,diurnal ,motion ( ! ,planets #g ------ ,t ! ,planets are ,opaque & ,globul> #i ------ ,t ! ,e>? is plac$ betwixt ! ,orbits ( ,m>s & ,v5us ibid4 ------ ,t ! ,planets turn r\nd ! ,sun ibid4 ------ ,t ! ,e>? also turns r\nd ! ,sun #ae ------ ,h[ ! ,annual & ,diurnal ,motion ( ! ,planets are comput$ ibid4 ------ ,h[ ! relative ,di/ance ( ! ,planets f ! ,sun are det]m9$ #ah ------ ,h[ _! absolute ,di/ances f ! ,sun are comput$ #bc ------ ,h[ ! ,magnitudes ( ! ,planets are det]m9$ #bf ------ ,:y ! ,moon appe>s bigg] ?an any ( ! ,planets #bg ------ ,a ,table ( ! ,di/ances1 ,magnitudes1 ,p]iodical1 & ,diurnal ,revolutions ( ! ,planets #bh ------ ,( ,comets #bi ,,sect4 ,,ii4 ,( ! ,fix$ ,/>s #cb ------ ,t ! fix$ ,/>s are lum9\s ,bodies1 at imm5se ,di/ances f u ibid4 ------ ,( ,telescopical ,/>s #ce ------ ,! ,/>s dige/$ into ,con/ellations #cf ------ ,( ! ,galaxy1 or ,milky ,way #ch ,illu/ration ,! ,,description & ,,use ( ! ,,cele/ial & ,,t]re/rial ,,globes4 ,! ,geometrical ,def9ition ( a ,globe1 & ( ! pr9cipal ,use ( ! ,artificial ,globes #db ,t !re w be ! same prospect ( ! ,fix$ ,/>s1 :e!r ! ,spectator be plac$ 9 ! ,sun1 or on ! ,e>? #de ,,sect4 ,i4 ,an ,explanation ( ! ,circles ( ! ,sph]e1 & ( "s ,a/ronomical ,t]ms aris+ !refrom #dg ------ ,( ! ,division ( ,"t #fi ------ ,( ! ,atmosph]e #ha ,,sect4 ,,ii4 ,geographical ,def9itions #hd ------ ,( ! ,situation ( ,places ^u ! ,e>? ibid4 ------ ,( ,zones & ,climates #ij ------ ,( ! ,poetical ,ris+ & ,sett+ ( ! ,/>s #if ------ ,( ! surface ( ! ,e>?1 consid]$ z x is compos$ ( ,l& & ,wat] ibid4 ------ ,( ! appurt5ances ( ! ,globes #aja ,,sect4 ,,iii4 ,! ,use ( ! ,globes #ajd ,,problem ,i4 ,to f9d ! ,latitude & ,longitude ( any giv5 place ^u ! ,globe2 & on ! contr>y1 ! ,latitude & ,longitude be+ giv5 to f9d ! ,place ibid4 ,,prob4 ,,ii4 ,to f9d ! ,diff]5ce ( ,latitude betwixt any two giv5 places #ajf ,,prob4 ,,iii4 ,to f9d ! ,diff]5ce ( ,longitude betwixt any two giv5 places ibid4 ,,prob4 ,,iv4 ,any ,place be+ giv52 to f9d all ^? places t are 9 ! same ,latitude ) ! said place #ajg ,,prob4 ,v4 ,! ,day ( ! ,mon? be+ giv52 to f9d ! ,sun's place 9 ! ,ecliptic1 & 8 ,decl9ation #ajh ,,prob4 ,,vi4 ,to rectify ! ,globe = ! ,latitude1 ,z5i?1 & ,sun's place #aji ,,prob4 ,,vii4 ,to f9d ! ,di/ance betwe5 any two giv5 ,places ^u ! ,globe1 & to f9d all ^? places ^u ! ,globe t are at ! same ,di/ance f a giv5 place #aaj ,,prob4 ,,viii4 ,to f9d ! ,angle ( a ,position ( ,places2 or ! angle =m$ by ! ,m]idian ( "o place1 & a great circle pass+ ?r\gh bo? ! places #aaa ,,prob4 ,,ix4 ,to f9d ! ,antci1 ,p]ici1 & ,antipodes1 to any giv5 place #aac ,,prob4 ,x4 ,! ,h\r ( ! ,day at "o ,place be+ giv52 to f9d ! correspond5t ,h\r 7or :at o',clock x is at t "t7 at any o!r place #aad ,,prob4 ,,xi4 ,! ,day ( ! ,mon? be+ giv52 to f9d ^? places on ! ,globe :]e ! ,sun w be ,v]tical1 or 9 ! ,z5i?1 t ,day #aae ,,prob4 ,,xii4 ,a place be+ giv5 9 ! ,torrid ,zone2 to f9d ^? two ,days 9 :i* ! ,sun w be ,v]tical to ! same #aaf ,,prob4 ,,xiii4 ,to f9d :]e ! ,sun is ,v]tical at any giv5 "t assign$2 or1 ! ,day ( ! ,mon? & ! ,h\r at any place 7suppose ,london7 be+ giv51 to f9d 9 :at place ! ,sun is ,v]tical at t v "t ibid4 ,,prob4 ,,xiv4 ,! ,day1 & ! ,h\r ( ! ,day at "o place1 be+ giv52 to f9d all ^? places ^u ! ,e>? :]e ! ,sun is !n ,ris+1 ,sett+1 ,culm9at+ 7or on ! ,m]idian72 also :]e x is ,day-light1 ,twilight1 ,d>k ,night1 ,midnight2 :]e ! ,twilight !n beg9s1 & :]e x ends2 ! ,height ( ! ,sun 9 any "p ( ! illum9at$ ,hemisph]e2 also 8 ,depression 9 ! obscure ,hemisph]e #aag ,,prob4 ,,xv4 ,! ,day ( ! ,mon? be+ giv51 to %[1 at "o ,view1 ! ,l5g? ( ,days & ,nights 9 all ,places ^u ! ,e>?1 at t "t2 & to expla9 h[ ! ,vicissitudes ( ,day & ,night are really made by ! motion ( ! ,e>? r\nd h] ,axis1 9 #bd ,h\rs1 ! ,sun /&+ /ill #aai ,,prob4 ,,xvi4 ,to ,expla9 9 g5]al ! ,alt]ation ( ,seasons1 or ,l5g? ( ! ,days & ,nights1 made 9 all places ( ! ,_w1 by ! ,sun's1 or ! ,e>?'s ,annual motion 9 ! ,ecliptic #aba ,,prob4 ,,xvii4 ,to %ew by ! ,globe1 at "o ,view1 ! ,l5g? ( ! ,days & ,nights1 at any p>ticul> place1 at all times ( ! ,ye> #abh ,,prob4 ,,xviii4 ,! ,latitude ( any place1 n exce$+ #fi ,degrees1 & ! ,day ( ! ,mon? be+ giv52 to ! "t ( ,sun-ris+ & ,sett+1 & ! l5g? ( ! ,day & ,night #acf ,,prob4 ,,xix4 ,to f9d ! l5g? ( ! longe/ & %orte/ ,day & ,night 9 any giv5 place1 n exce$+ #ff ,degrees ( ,latitude #acg ,,prob4 ,,xx4 ,to f9d 9 :at ,latitude ! longe/ ,day is1 ( any giv5 l5g? less ?an #bd ,h\rs #aci ,,prob4 ,,xxi4 ,a ,place be+ giv5 9 "o ( ! ,frigid ,zones 7suppose ! ,nor!rn7 to f9d :at numb] ( ,days 7( #bd ,h\rs ea*7 ! ,sun do? con/antly %9e ^u ! same1 h[ long he is abs5t1 & also ! fir/ & la/ day ( 8 appe>ance #adj ,,prob4 ,,xxii4 ,to f9d 9 :at ,latitude ! longe/ ,day is1 ( any giv5 l5g?1 less ?an #ahb natural ,days #ada ,,prob4 ,,xxiii4 ,! ,day ( ! ,mon? be+ giv52 to f9d :5 ! ,morn+ & ,ev5+ ,twilight beg9s & ends1 9 any place ^u ! ,globe #adb ,,prob4 ,,xxiv4 ,to f9d ! "t :5 total ,d>kness ceases1 or :5 ! ,twilight cont9ues f ,sun-sett+ to ,sun-ris+1 9 any giv5 place #add ,,prob4 ,,xxv4 ,! ,day ( ! ,mon? be+ giv52 to f9d ^? places ( ! ,frigid ,zones1 :]e ! ,sun beg9s to %9e con/antly )\t sett+2 & also ^? places :]e he beg9s to be totally abs5t #adf ,,prob4 ,,xxvi4 ,! ,latitude1 ! ,sun's ,place1 & 8 ,altitude be+ giv52 to f9d ! ,h\r ( ! ,day1 & ,sun's ,azimu? f ! ,m]idian #adi ,,prob4 ,,xxvii4 ,! ,latitude1 ,h\r ( ! ,day1 & ! ,sun's ,place be+ giv52 to f9d ! ,sun's ,altitude #aej ,,prob4 ,,xxviii4 ,! ,latitude ( ! ,place1 & ! ,day ( ! ,mon? be+ giv52 to f9d ! depression ( ! ,sun bel[ ! ,horizon1 & 8 ,azimu?1 at any ,h\r ( ! ,night #aea ,,prob4 ,,xxix4 ,! ,latitude ( ! ,sun's ,place1 & 8 ,azimu? be+ giv52 to f9d 8 ,altitude1 & ! ,h\r #aeb ,,prob4 ,,xxx4 ,! ,latitude1 ! ,sun's ,altitude1 & 8 ,azimu? be+ giv52 to f9d 8 ,place on ! ,ecliptic1 & ! ,h\r ibid4 ,,prob4 ,,xxxi4 ,! ,decl9ation1 & ,m]idian ,altitude ( ! ,sun1 or ( any ,/> be+ giv52 to f9d ! ,latitude ( ! ,place #aec ,,prob4 ,,xxxii4 ,! ,day & ,h\r ( a ,lun> ,eclipse be+ kn[n2 to f9d all ^? ,places ^u ! ,globe 9 :i* ! same w be visible #aed ,,prob4 ,,xxxiii4 ,! ,day ( ! ,mon?1 & ,h\r ( ! ,day1 accord+ to our way ( reckon+ 9 ,engl&1 be+ giv52 to f9d !reby ! ,babyloni%1 ,italic1 & ,jewi%1 or ,judaical ,h\r #aee ,,prob4 ,,xxxiv4 ,to f9d ! ,"r ,asc5sion & ,decl9ation ( ! ,sun1 or any ,fix$ ,/> #aef ,,prob4 ,,xxxv4 ,to f9d ! ,longitude & ,latitude ( a giv5 ,/> #aeh ,,prob4 ,,xxxvi4 ,! ,latitude ( ! ,place1 ! ,day ( ! ,mon?1 & ! ,h\r be+ giv52 to f9d :at ,/>s are !n ris+ & sett+1 :at ,/>s are culm9at+1 or on ! ,m]idian1 & ! ,altitude & ,azimu? ( any ,/> above ! ,horizon2 & also h[ to di/+ui% ! ,/>s 9 ! ,heav5s "o f ! o!r1 & to "k !m by _! prop] ,names #aei ,,prob4 ,,xxxvii4 ,! ,latitude ( ! ,place be+ giv52 to f9d ! ,amplitude1 ,oblique ,asc5sion1 & ,desc5sion1 ,asc5sional ,diff]5ce1 ,semi-diurnal ,ar*1 & ! "t ( ,cont9uance above ! ,horizon1 ( any giv5 ,po9t 9 ! ,heav5s #afb ,,prob4 ,,xxxviii4 ,! ,latitude & ! ,day ( ! ,mon? be+ giv52 to f9d ! ,h\r :5 any kn[n ,/> w be on ! ,m]idian1 & also ! "t ( its ,ris+ & ,sett+ #afe ,,prob4 ,,xxxix4 ,to f9d at :at "t ( ! ,ye> a giv5 ,/> w be ^u ! ,m]idian1 at a giv5 ,h\r ( ! ,night #aff ,,prob4 ,,xl4 ,! ,day ( ! ,mon? & ! ,azimu?1 ( any kn[n ,/> be+ giv52 to f9d ! ,h\r ( ! ,night #afg ,,prob4 ,,xli4 ,two kn[n ,/>s1 hav+ ! same ,azimu?1 or ! same ,height1 be+ giv52 to f9d ! ,h\r ( ! ,night #afh ,,prob4 ,,xlii4 ,! ,latitude1 ,day ( ! ,mon?1 & ! ,altitude ( any kn[n ,/> be+ giv52 to f9d ! ,h\r ( ! ,night #afi ,,prob4 ,,xliii4 ,hav+ ! ,latitude ( ! ,place1 to f9d ! ,degree ( ! ,ecliptic1 :i* rises or sets ) a giv5 ,/>2 & f !nce to det]m9e ! "t ( its ,cosmical & ,a*ronical ,ris+ & ,sett+ #aga ,,prob4 ,,xliv4 ,hav+ ! ,latitude ( ! ,place2 to f9d ! "t :5 a ,/> rises & sets ,heliacally #agb ,,prob4 ,,xlv4 ,to f9d ! ,place ( any ,planet ^u ! ,globe1 s by t ,means to f9d its ,place 9 ! ,heav5s2 also to f9d at :at ,h\r any ,planet w rise or set1 or be on ! ,m]idian1 at any ,day 9 ! ,ye> #agc ,,prob4 ,,xlvi4 ,to f9d all t space ^u ! ,e>? :]e an ,eclipse ( "o ( ! ,satellites ( ,jupit] w be visible #age ,! ,,description ( ! ,,orr]y #agg ,( ! ,motions ( ! ,planets 9 g5]al #ahc ,( ! ,/ations & ,retrogadations ( ! ,planets #ahf ,( ! ,annual & ,diurnal ,motion ( ! ,e>? #aid ,( ! ,phases ( ! ,moon1 & ( h] ,motion 9 h] ,orbit #bja ,( ! ,eclipses ( ! ,sun & ,moon #bjh ,( ! ,eclipses ( ,jupit]'s ,satellites #bab ,illu/ration ,,! ,,introduction1 ,,conta9+ ,a ,brief ,acc\nt ( ! ,,sol> ,,sy/em1 & ( ! ,,fix$ ,,/>s4 ,,sect4 ,i4 ,( ! ,ord] & ,p]iods ( ! ,prim>y ,planets revolv+ ab\t ! ,sun2 & ( ! ,second>y ,planets r\nd _! respective ,prim>ies4 ,sid5ote3 ,planets4 ,! ,sun is plac$ 9 ! mid/ ( an imm5se space1 :]e9 six opaque sph]ical bodies revolve ab\t him z _! c5t]4 ,^! w&]+ globes are call$ ! ,planets1 :o1 at diff]5t di/ances1 & 9 diff]5t p]iods1 p]=m _! revolutions f ,we/ to ,ea/1 9 ! foll[+ ord]3 #a4 ,m]cury is ne>e/ to ! ,sun ( all ! planets1 & p]=ms its c\rse 9 ab\t ?ree mon?s4 #b4 ,v5us 9 ab\t sev5 mon?s & a half4 #c4 ,! ,e>? 9 a ye>4 #d4 ,m>s 9 ab\t two ye>s4 #e4 ,jupit] 9 twelve4 ,& la/ly1 ,saturn1 ^:#a,orbit includes all ! re/1 sp5ds almo/ #cj ye>s 9 "o revolution r\nd ! ,sun4 ,! di/ances ( ! ,planets f ! ,sun are ne>ly 9 ! same proportion z !y are repres5t$ 9 ,plate #a4 viz4 ,suppos+ ! di/ance ( ! ,e>? f ! ,sun to be divid$ into #aj equal p>ts2 t ( ,m]cury w be ab\t #d ( ^! p>ts2 ( ,v5us #g2 ( ,m>s #ae2 ( ,jupit] #eb2 & t ( ,saturn #ie4 ,! ,*>act]s plac$ be=e ! names ( ! ,planets1 are = brevity's sake commonly made use ( by ,a/ronom]s1 in/ead ( ! words at l5g?1 z 1 = ,v5us1 c4 ,illu/ration3 ,plate #a4 ,,! ,,sol> ,,sy/em ,or ! ,orbits ( ! ,planets accord+ to _! mean di/ances f ! ,sun4 ,sid5ote3 ,nodes4 ,! orbits ( ! ,planets are n all 9 ! same plane1 b v>i\sly incl9$ to "o ano!r2 s t suppos+ "o ( !m to co9cide ) ! above s*eme1 ! o!rs w h "o half above1 & ! o!r half bel[ x2 int]sect+ "o ano!r 9 a l9e pass+ ?r\gh ! ,sun4 ,! plane ( ! ,e>?'s orbit is call$ ! ,ecliptic2 & ?is ! a/ronom]s make ! /&>d to :i* ! planes ( ! o!r orbits are judg$ to incl9e4 ,! "r l9e pass+ ?ro' ! ,sun1 & ! common int]section ( ! plane ( ! orbit ( any planet & ! ,ecliptic1 is call$ ! ,l9e ( ! ,nodes ( t planet2 & ! po9ts !mselves1 :]e9 ! orbit cuts ! ,ecliptic are call$ ! ,nodes4 ,sid5ote3 ,exc5tricity4 ,! incl9ations ( ! orbits ( ! ,planets to ! plane ( ! ecliptic1 are z foll[s1 viz4 ! orbit ( ,m]cury makes an angle ) x ( almo/ #g degrees2 t ( ,v5us some?+ above #c degrees2 ( ,m>s a little less ?an #b degrees2 ( ,jupit]1 #a degree2 & ( ,saturn1 ab\t #b degrees4 ,! orbits ( ! ,planets are n circles1 b ellipses or ovals4 ,:at an ellipsis is1 may be easily und]/ood f ! foll[+ description4 ,imag9e two small pegs fix$ upright on any plane1 & suppose !m ti$ ) ! ends ( a ?read some:at long] ?an _! di/ance f "o ano!r3 ,n[ if a p9 be plac$ 9 ! d\ble ( ! ?read & turn$ q r\nd 7always /ret*+ ! ?read ) ! same =ce7 ! curv$ describ$ by ?is motion is an ,ellipsis4 ,! two po9ts :]e ! pegs /ood1 7ab\t :i* ! ?read 0 turn$7 are call$ ! foci ( t ellipsis2 & if1 )\t *ang+ ! l5g? ( ! ?read1 we alt] ! position ( ! pegs1 we %all !n h an ellipsis ( a diff]5t k9d f ! =m]2 & ! ne>] ! focus's are toge!r1 ! ne>] w ! curve describ$ be to a circle2 until at la/1 ! two focus's co9cide1 & !n ! p9 9 ! d\bl+ ( ! ?read w describe a p]fect circle4 ,! orbits ( all ! ,planets h ! ,sun 9 "o ( _! focus's1 & half ! di/ance betwe5 ! two focus's is call$ ! ,exc5tricity ( ! orbits4 ,?is exc5tricity is diff]5t 9 all ! planets1 b 9 mo/ ( !m s small1 t 9 little s*emes or in/rum5ts1 made to repres5t ! planet>y orbits1 x ne$ n be consid]$4 ,sid5ote3 ,prim>y ,planets4 ,sid5ote3 ,second>y ,planets4 ,! six ,planets above-m5tion$1 are call$ ,prim>ies1 or ,prim>y ,planets2 b besides ^!1 !re are t5 o!r less] ,planets1 :i* are call$ ,second>ies1 ,moons1 or ,satellites4 ,^! moons always accompany _! respective prim>ies1 & p]=m _! ,revolutions r\nd !m1 :il/ bo? toge!r are also c>ri$ r\nd ! ,sun4 ,( ! six ,prim>y ,planets1 !re are b ?ree1 z f> z obs]vation c assure u1 t h ^! att5dants1 viz4 ! ,e>?1 ,jupit]1 & ,saturn4 ,! ,e>? is att5d$ by ! ,moon1 :o p]=ms h] revolution 9 ab\t #bg ,days1 at ! di/ance ( ab\t #cj ,diamet]s ( ! ,e>? f x2 & once a ,ye> is c>ri$ r\nd ! ,sun along ) ! ,e>?4 ,sid5ote3 ,jupit]'s f\r ,moons4 ,jupit] has f\r ,moons1 or ,satellites2 ! fir/1 or inn]mo/1 p]=ms its revolution 9 ab\t "o ,day1 & #ah ,h\rs1 at ! di/ance ( #e ,semidiamet]s ( ,jupit]1 f 8 ,c5t]2 ! second revolves ab\t ,jupit] 9 #c ,days1 #ac ,h\rs1 at ! di/ance ( #i ( 8 ,semidiamet]s2 ! ?ird 9 #g ,days1 & #d ,h\rs1 at ! di/ance ( #ad ,semidiamet]s2 ! f\r?1 & out]mo/1 p]=ms its c\rse 9 ! space ( #af ,days1 #ag ,h\rs2 & is di/ant f ,jupit]'s c5t]1 #be ( 8 ,semidiamet]s4 ,sid5ote3 ,saturn has five ,moons4 ,saturn has no less ?an five ,satellites2 ! fir/1 or inn]mo/1 revolves ab\t him 9 #a ,day1 & #ba ,h\rs1 at ! di/ance ( #d ,semidiamet]s ( 1 f 8 c5t]2 ! second compleats 8 p]iod 9 #b ,days1 at ! di/ance ( #e_/ ( 8 ,semidiamet]s2 ! ?ird1 9 ab\t #d ,days1 at ! di/ance ( #h ,semidiamet]s2 ! f\r? p]=ms its c\rse 9 ab\t #af ,days1 at ! di/ance ( #ah ,semidiamet]s2 ! fif?1 & out]mo/1 takes #gi ,days1 to f9i% 8 c\rse1 & is #ed ,semidiamet]s ( ,saturn di/ant f 8 c5t]4 ,! ,satellites1 z well z _! prim>ies1 p]=m _! revolutions f ,we/ to ,ea/3 ,! planes ( ! ,orbits ( ! ,satellites ( ! same ,planet are v>i\sly incl9$ to "o ano!r1 & consequ5tly are incl9$ to ! plane ( ! ,orbit ( _! prim>y4 ,sid5ote3 ,saturn's ,r+4 ,besides ^! att5dants1 ,saturn is encompass$ ) a ?9 pla9 ,r+1 t does no :]e t\* 8 body2 ,! diamet] ( ?is ,r+ is to ! diamet] ( ,saturn1 z #i to #d2 & ! void space betwe5 ! ,r+ & ! body ( ,saturn is equal to ! bread? ( ! ,r+ itself2 s t 9 "s situations ! ,heav5s may be se5 betwe5 ! ,r+ & 8 body4 ,?is surpriz+ phnom5on ( ,saturn's ,r+1 is a mod]n discov]y2 nei!r 7 ! ,satellites ( ,jupit] & ,saturn kn[n to ! anci5ts4 ,! ,jovial ,planets 7 fir/ discov]$ by ! fam\s ,italian philosoph] ,galilu1 by a telescope :i* he fir/ inv5t$2 & ! celebrat$ ,cass9i1 ! ,fr5* k+'s a/ronom]1 0 ! fir/ t saw all ! ,satellites ( ,saturn2 :i* by reason ( _! great di/ances f ! ,sun1 & ! smallness ( _! own bodies1 _c be se5 by u1 b by ! help ( v good glasses4 ,sid5ote3 ,annual ,motion4 ,sid5ote3 ,diurnal ,motion4 ,! motion ( ! prim>y ,planets r\nd ! ,sun 7z also ( ! ,satellites r\nd _! respective prim>ies7 is call$ _! ,annual ,motion2 because !y h "o ,ye>1 or alt]ation ( ,seasons compleat1 9 "o ( ^! revolutions4 ,besides ?is annual motion1 f\r ( ! ,planets1 viz4 ,v5us1 ! ,e>?1 ,m>s1 & ,jupit] revolve ab\t _! own ,axis1 f ,we/ to ,ea/2 & ?is is call$ _! ,diurnal ,motion4 ,= by ?is rotation1 ea* po9t ( _! surfaces is c>ri$ successively t[>ds or f ! ,sun1 :o always illum9ates ! hemisph]e :i* is next to him1 ! o!r rema9+ obscure2 & :ile any place is 9 ! hemisph]e1 illum9at$ by ! ,sun1 x is ,day1 b :5 x is c>ri$ to ! obscure hemisph]e1 x becomes ,night2 & s cont9ues1 until by ?is rotation ! said place is aga9 enlight5$ by ! ,sun4 ,sid5ote3 ,diurnal ,motion ( ! 1 1 & 4 ,sid5ote3 & likewise turn r\nd _! ,axis4 ,! ,e>? p]=ms its revolution r\nd its axis 9 #bc ,h\rs1 #ef ,m9utes2#b,v5us1 9 #bd ,days1 #h ,h\rs2 ,m>s1 9 #bd ,h\rs1 & #dj ,m9utes2 & ,jupit] moves r\nd 8 own axis 9 #i ,h\rs1 & #ef ,m9utes4 ,! ,sun also is f\nd to turn r\nd 8 axis f ,we/ to ,ea/1 9 #bg ,days3 ,& ! ,moon1 :i* is ne>e/ to u ( all ! ,planets1 revolves ab\t h] axis 9 a ,mon?1 or 9 ! same space ( "t t %e turns r\nd ! ,e>?2 s t ! ,lun>ians h b #a ,day ?r\gh\t ! ,ye>4 ,sid5ote3 ,! ,planets are ,opaque & ,globul>4 ,i4 ,! ,planets are all ,opaque bodies1 hav+ no light b :at !y borr[ f ! ,sun2 = t side ( !m :i* is next t[>ds ! ,sun1 has always be5 obs]v$ to be illum9at$1 9 :at position soev] !y be2 b ! opposite side1 :i* ! ,sol> rays d n rea*1 rema9s d>k & obscure2 :5ce x is evid5t t !y h no light b :at proce$s f ! ,sun2 = if !y _h1 all p>ts ( !m w\ld be lucid1 )\t any d>kness or %ad[4 ,! ,planets are likewise prov$ to be ,globul>2 because let :at "p soev] ( !m be turn$ t[>ds ! ,sun1 its b\nd>y1 or ! l9e sep>at+ t "p f ! opposite1 always appe>s to be circul>2 :i* c\ld n happ51 if !y 7 n globul>4 ,sid5ote3 ,! ,planets turn r\nd ! ,sun4 ,,ii4 ,t ! ,e>? is plac$ betwixt ! ,orbs ( ,m>s & ,v5us1 & t 1 1 1 & 1 d all turn r\nd ! ,sun1 is prov$ f obs]vations z foll[3 ,sid5ote3 ,plate #b4 ,fig4 #a4 #b4 #a4 ,:5ev] ,v5us is 9 conjunction ) ! ,sun1 t is1 :5 %e is 9 ! same direction f ! ,e>?1 or t[>ds ! same "p ( ! ,heav5s ! ,sun is 92 %e ei!r appe>s ) a bright & r\nd face1 l a ,full ,moon1 or else disappe>s3 ,or1 if %e is visible1 %e appe>s horn$1 l a new ,moon2 :i* phnom5a c\ld nev] happ5 if did n turn r\nd ! ,sun1 & 0 n betwixt him & ! ,e>?3 ,= s9ce all ! ,planets borr[ _! light f ! ,sun1 x is necess>y t 's lucid face %\ld be t[>ds ! ,sun2 & :5 %e appe>s fully illum9at$1 %e %ews ! same face to ! ,sun & ,e>?2 & at t "t %e mu/ be above or beyond ! ,sun2 = 9 no o!r position c\ld h] illum9at$ face be se5 f ! ,e>?4 ,f>!r1 :5 %e disappe>s1 or if visible1 appe>s horn$2 t face ( h]'s :i* is t[>ds ! ,sun is ei!r :olly turn$ f ! ,e>?1 or only a small "p ( x c be se5 by ! ,e>?2 & 9 ?is case %e mu/ ( necessity be betwixt u & ! ,sun4 ,let ,s be ! ,sun1 ,t ! ,e>?1 & ,v ,v5us1 hav+ ! same face pres5t$ bo? t[>ds ! ,sun & ,e>?2 "h x is pla9 t ! ,sun is betwixt u & ,v5us & !re=e we mu/ ei!r place ,v5us 9 an ,orbit r\nd ! ,sun1 & likewise betwixt him & u1 z 9 ,fig4 #a4 or else we mu/ make ! ,sun to move r\nd ! ,e>? 9 an ,orbit )9 t ( ,v5us1 z 9 ,fig4 #b4 ,aga91 aft] ,v5us disappe>s1 or becomes horn$1 at h]#c ) ! 1 %e !n mu/ be betwixt u & ! ,sun1 & mu/ move ei!r 9 an ,orbit r\nd ! ,sun & betwixt u & him1 z 9 ,fig4 #a4 or else r\nd ! ,e>?1 & betwixt u & ! ,sun1 z 9 ,fig4 #b4 ,b ,v5us _c move sometimes )9 ! ,sun's ,orbit1 & sometimes )\t x1 z we mu/ suppose if %e moves r\nd ! ,e>?2 !re=e x is pla9 t h] motion is r\nd ! ,sun4 ,sid5ote3 ,:y ,v5us is always ei!r our ,morn+ or ,ev5+ ,/>4 ,besides ! =go+1 !re is ano!r argum5t to prove t ,v5us turns r\nd ! ,sun 9 an ,orbit t is )9 ! ,e>?'s1 because %e is always obs]v$ to keep ne> ! ,sun1 & 9 ! same qu>t] ( ! ,heav5s t he is 91 nev] rec$+ f him m ?an ab\t ( a :ole circle2 & !re=e %e c nev] come 9 opposition to him2 :i* w\ld necess>ily happ51 did %e p]=m h] c\rse r\nd ! ,e>? ei!r 9 a long] or %ort] "t ?an a ,ye>4 ,& ?is is ! reason :y ,v5us is nev] to be se5 ne> midnight1 b always ei!r 9 ! ,morn+ or ,ev5+1 & at mo/ n above ?ree or f\r ,h\rs be=e ,sun-ris+ or aft] ,sun-sett+4 ,f ! "t ( 's sup]ior conjunction 7or :5 %e is above ! ,sun7 %e is m ,ea/]ly ?an ! ,sun1 & !re=e sets lat]1 & is se5 aft] ,sun-sett+2 & !n %e is commonly call$ ! ,ev5+ ,/>4 ,b f ! "t ( h] inf]ior conjunction1 'till %e comes aga9 to ! sup]ior1 %e !n appe>s m ,we/]ly ?an ! ,sun1 & is only to be se5 9 ! morn+ be=e ,sun-ris+1 & is !n call$ ! ,morn+ ,/>4 ,aft] ! same mann] we prove t ,m]cury turns r\nd ! ,sun1 = he always keeps 9 ! ,sun's neighb\rhood1 & nev] rec$es f him s f> z ,v5us does2 & !re=e ! ,orbit ( mu/ lie )9 t ( 2 & on ! acc\nt ( 8 ne>ness to ! ,sun1 he c seldom be se5 )\t a ,telescope4 ,sid5ote3 ,! ,orbit ( ,m>s includes ! ,e>?'s4 ,sid5ote3 ,fig4 #c4 ,m>s is obs]v$ to come 9 opposition1 & likewise to h all o!r aspects ) ! ,sun2 he always pres]ves a r\nd1 full1 & bright face1 except :5 he is ne> 8 quadrate aspect1 :5 he appe>s some:at gibb\s1 l ! ,moon ?ree or f\r ,days be=e or aft] ! full3 ,!re=e ! ,orbit ( mu/ include ! ,e>? )9 x1 & also ! ,sun2 = if he 0 betwixt ! ,sun & u at ! "t ( 8 inf]ior conjunction1 he w\ld ei!r q disappe>1 or appe> horn$1 z ,v5us & ! ,moon d 9 t position4 ,let ,s be ! ,sun1 ,t ! ,e>?1 & ,a ,p ,m>s1 bo? 9 8 conjunction & opposition to ! ,sun1 & 9 bo? positions full2 & ,b ,c ,m>s at 8 quadratures1 :5 he appe>s some:at gibb\s f ! ,e>? at ,t4 ',tis pla9 h5ce1 t ! ,orbit ( ,m>s does include ! ,e>?1 o!rwise he c\ld n come 9 opposition to ! ,sun2 & t x likewise includes ! ,sun1 else he c\ld appe> full at 8 conjunction4 ,m>s :5 he is 9 opposition to ! ,sun1 looks almo/ sev5 times l>g] 9 diamet] ?an :5 he is 9 conjunction ) him1 & !re=e mu/ ne$s be almo/ sev5 times ne>] to u 9 "o position ?an 9 ! o!r2 = ! app>5t magnitudes ( f> di/ant objects increase or decrease 9 proportion to _! di/ances f u3 ,b ,m>s keeps always ne>ly at ! same di/ance f ! ,sun2 !re=e x is pla9 t x is n ! ,e>?1 b ! ,sun1 t is ! c5t] ( 8 motion4 ,x is prov$ 9 ! same way1 t ,jupit] & ,saturn h bo? ! ,sun & ! ,e>? )9 _! ,orbits1 & t ! ,sun1 & n ! ,e>?1 is ! c5t] ( _! motions2 al?o' ! disproportion ( ! di/ances f ! ,e>? is n s great 9 ,jupit]1 z x is 9 ,m>s1 nor s great 9 ,saturn1 z x is 9 ,jupit]1 by reason t !y are at a mu* great] di/ance f ! ,sun4 ,sid5ote3 ,inf]ior & ,sup]ior ,planets4 ,we h n[ %ewn t all ! ,planets turn r\nd ! ,sun1 & t ,m]cury & ,v5us are includ$ betwe5 him & ! ,e>?1 :5ce !y are call$ ! ,inf]ior ,planets1 & t ! ,e>? is plac$ betwe5 ! ,orbits ( ,m>s & ,v5us1 & !re=e includ$ )9 ! ,orbits ( ,m>s1 ,jupit]1 & ,saturn1 :5ce !y are call$ ! ,sup]ior ,planets3 ,& s9ce ! ,e>? is 9 ! middle ( ^! moveable bodies1 & is ( ! same nature ) !m1 we may conclude t %e has ! same sort ( motions2 b t %e turns r\nd ! ,sun is prov$ ?us3 ,sid5ote3 ,! ,e>? does n /& /ill1 b turns r\nd ! ,sun4 ,sid5ote3 ,fig4 #d4 ,all ! ,planets se5 f ! ,e>? appe> to move v unequally1 z sometimes to g fa/]1 at o!r times sl[]2 sometimes to g backw>ds1 & sometimes to be /ation>y1 or n to move at all2 :i* c\ld n happ5 if ! ,e>? /ood /ill4 ,let ,s be ! ,sun1 ,t ! ,e>?1 ! great circle ,a ,b ,c ,d ! ,orbit ( ,m>s1 & ! numb]s #a1 #b1 #c1 c4 its equable motion r\nd ! ,sun2 ! correspond5t numb]s #a1 #b1 #c1 c4 9 ! circle a1 b1 c1 d1 ! motion ( ,m>s1 z x w\ld be se5 f ! ,e>?4 ,x is pla9 f ?is ,figure1 t if ! ,e>? /ood /ill1 ! motion ( ,m>s1 w be always progressive1 7?o' sometimes v unequal27 b s9ce obs]vations prove ! contr>y1 x necess>ily foll[s1 t ! ,e>? turns r\nd ! ,sun4 ,sid5ote3 ,! ,annual & ,diurnal ,motions ( ! ,planets1 h[ comput$4 ,! annual p]iods ( ! ,planets r\nd ! ,sun are det]m9$ by c>efully obs]v+ ! l5g? ( "t s9ce _! dep>ture f a c]ta9 po9t 9 ! ,heav5s1 7or f a fix'd ,/>7 until !y arrive to ! same aga94 ,by ^! sort ( obs]vations ! anci5ts det]m9$ ! p]iodical revolutions ( ! ,planets r\nd ! ,sun1 & 7 s exact 9 _! computations1 z to be capable ( pr$ict+ ,eclipses ( ! ,sun & ,moon4 ,b s9ce ! inv5tion ( telescopes1 a/ronomical obs]vations are made ) great] accuracy2 & ( consequ5ce1 our tables are f> m p]fect ?an ^? ( ! anci5ts4 ,& 9 ord] to be z exact z possible1 a/ronom]s comp>e obs]vations made at a great di/ance ( "t f "o ano!r1 includ+ sev]al p]iods2 by :i* means1 ! error t might be 9 ! :ole1 is 9 ea* p]iod subdivid$ into su* little p>ts z to be inconsid]able4 ,?us ! mean l5g? ( a ,sol> ,ye> is kn[n1 ev5 to ,seconds4 ,! ,diurnal rotation ( ! ,planets r\nd _! axis1 0 discov]$ by c]ta9 spots :i* appe> on ! surfaces4 ,^! spots appe> fir/ 9 ! m>g9 ( ! ,planet's disk1 7or ! edge ( _! surfaces7 & seem by degrees to creep t[>d _! middle1 & s on1 go+ /ill =w>d1 'till !y come to ! opposite side or edge ( ! disk1 :]e !y set or disappe>2 & aft] !y h be5 hid = ! same space ( "t1 t !y 7 visible1 !y aga9 appe> to rise 9 or ne> ! same place1 z !y did at fir/1 !n to creep on progressively1 tak+ ! same c\rse z !y did be=e4 ,^! spots h be5 obs]v$ on ! surfaces ( ! ,sun1 ,v5us1 ,m>s1 & ,jupit]2 by :i* means x has be5 f\nd t ^! bodies turn r\nd _! own axis1 9 ! times be=e-m5tion$4 ,x is v probable t ,m]cury & ,saturn h likewise a motion r\nd _! axis1 t all ! p>ts ( _! surface may alt]nately enjoy ! light & heat ( ! ,sun1 & receive su* *anges z are prop] & conv5i5t = _! nature4 ,b by reason ( ! ne>ness ( to ! ,sun1 & 's imm5se di/ance f him1 no obs]vations h hi!rto be5 made :]eby _! spots 7if !y h any7 c\ld be discov]$1 & !re=e _! ,diurnal motions c\ld n be det]m9$4 ,! ,diurnal motion ( ! ,e>? is comput$ f ! app>5t revolution ( ! ,heav5s1 & ( all ! ,/>s r\nd x1 9 ! space ( a natural ,day4 ,! ,sol> spots d n always rema9 ! same1 b sometimes old ones vani%1 & aft]w>ds o!rs succe$ 9 _! room2 sometimes sev]al small ones ga!r toge!r & make "o l>ge spot1 & sometimes a l>ge spot is se5 to be divid$ into _m small ones4 ,b1 not)/&+ ^! *anges1 !y all turn r\nd ) ! ,sun 9 ! same "t4 ,sid5ote3 ,h[ ! relative di/ances ( ! ,planets f ! ,sun are det]m9$4 ,! relative di/ances ( ! ,planets f ! ,sun1 & likewise f ea* o!r1 are det]m9$ by ! foll[+ me?ods3 ,fir/1 ! di/ance ( ! two inf]ior ,planets & f ! ,sun1 9 respect ( ! ,e>?'s di/ance f him1 is _h by obs]v+ _! greate/ ,elongation f ! ,sun z !y are se5 f ! ,e>?4 ,sid5ote3 ,fig4 #e4 ,elongation4 ,! greate/ ,elongation ( ,v5us is f\nd by obs]vation to be ab\t #dh degrees1 :i* is ! angle ,s ,t 2 :5ce1 by ! kn[n rules ( ,trigonometry1 ! proportion ( ,s 1 ! mean di/ance ( ,v5us f ! ,sun to ,,/1 ! mean di/ance ( ! ,e>? f him may be easily f\nd4 ,aft] ! same mann]1 9 ! "r-angl$ triangle ,s ,t 1 may be f\nd ! di/ance ,s ( ,m]cury f ! ,sun4 ,& if ! mean di/ance ( ! ,e>? f ! ,sun ,s ,t be made #ajjj1 ! mean di/ance ( ,v5us ,s f ! ,sun w be #gbc2 & ( ,m]cury ,s #chg3 ,& if ! ,planets mov$ r\nd ! ,sun 9 circles1 hav+ him = _! c5t]1 ! di/ances "h f\nd w\ld be always _! true di/ances3 ,b z !y move 9 ,ellipses1 _! di/ances f ! ,sun w be sometimes great]1 & sometimes less4 ,_! ,exc5tricities are comput$ to be z foll[s1 viz4 ,m]cury #hj ( ! p>ts ,exc5t4 ( ,v5us #e above-m5tion$4 ,e>? #afi ,sid5ote3 ,helioc5tric & ,geoc5tric ,place1 :at4 ,! di/ances ( ! sup]ior ,planets1 viz4 1 1 & 1 are f\nd by comp>+ _! true places1 z !y are se5 f ! ,sun1 ) _! app>5t places1 z !y are se5 f ! ,e>?4 ,let ,s be ! ,sun1 ! circle ,,abc ! ,e>?'s orbit1 ,,ag a l9e t\*+ ! ,e>?'s orbit1 9 :i* we'll suppose ! sup]ior ,planets are se5 f ! ,e>? 9 ! po9ts ( _! orbits 1 1 2 & let ,,defgh be a portion ( a great circle 9 ! ,heav5s1 at an inf9ite di/ance3 ,!n ! place ( ,m>s se5 f ! ,sun is ,d1 :i* is call$ 8 true1 or ,helioc5tric ,place2 b f ! ,e>?1 he w be se5 9 ,g1 :i* is call$ 8 app>5t1 or ,geoc5tric ,place4 ,s likewise ,jupit] & ,saturn w be se5 f ! ,sun 9 ! po9ts ,e & ,f1 _! ,helioc5tric places2 b a spectator f ! ,e>? w see !m 9 ! po9t ( ! ,heav5s ,g1 :i* is _! ,geoc5tric place4 ,! ar*es ,,dg1 ,,eg1 ,,fg1 ! diff]5ces betwe5 ! true & app>5t places ( ! ,sup]ior ,planets1 are call$ ! ,p>allaxes ( ! ,e>?'s annual ,orb1 z se5 f ^! ,planets4 ,if ?ro' ! ,sun we draw ,,% p>allel to ,,ag1 ! angles ,a ,s1 ,a ,s1 ,a ,s1 w be respectively equal to ! angles ,d ,s ,h1 ,e ,s ,h1 & ,f ,s ,h2 & ! angle ,a ,g ,s is equal to ! angle ,,g%1 ^: measure is ! ar* ,,gh2 :i* !re=e w be ! measure ( ! angle ,,ags1 ! angle "u :i* ! semidiamet] ,a ,s ( ! ,e>?'s orbit1 is se5 f ! ,/>ry ,heav5s4 ,b ?is semidiamet] is no?+ 9 respect ( ! imm5se di/ance ( ! ,heav5s or ,fix$ ,/>s2 = f !nce x w\ld appe> "u no s5sible angle1 b look l a po9t4 ,& !re=e 9 ! ,heav5s1 ! angle ,g ,s ,h1 or ! ar* ,g ,h vani%es2 & ! ,po9ts ,g & ,h co9cide2 & ! ar*es ,d ,h1 ,e ,h1 ,f ,h1 may be consid]$ z be+ ( ! same bigness ) ! ar*es ,d ,g1 ,e ,g1 & ,f ,g1 :i* are ! measures ( ! angles ,a ,s1 ,a ,s1 ,a ,s2 :i* angles are ne>ly ! greate/ elongation ( ! ,e>? f ! ,sun1 if ! ,e>? be obs]v$ f ! respective ,planets1 :5 ! l9e ,g ,a1 t\*es ! ,e>?'s orbit 9 ,a4 ,! ne>] any ( ! sup]ior ,planets is to ! ,sun1 ! great] is ! ,p>allax ( ! annual ,orb1 or ! angle "u :i* ! semidiamet] ( ! ,e>?'s orbit is se5 f t ,planet4 ,9 ,m>s ! angle ,s1 7:i* is ! visible elongation ( ! ,e>? se5 f ,m>s1 or ! ,p>allax ( ! annual ,orb se5 f t ,planet7 is ab\t #db degrees1 & !re=e ! ,e>? is always to ! inhabitants ( ,m>s ei!r _! ,morn+ or ,ev5+ ,/>1 & is nev] se5 by !m s f> di/ant f ! ,sun z we see ,v5us4 ,! greate/ elongation ( ! ,e>? se5 f ,jupit]1 be+ ne>ly equal to ! angle ,a ,s1 is ab\t #aa degrees4 ,9 ,saturn ! angle ,a ,s is b #f degrees1 :i* is n mu* above "p ( ! greate/ elongation we obs]ve 9 ,m]cury4 ,& s9ce ,m]cury is s r>ely se5 by u1 probably ! a/ronom]s ( ,saturn 7except !y h bett] ,optics ?an we h7 h n yet discov]$ t !re is su* a body z our ,e>? 9 ! ,univ]se4 ,! ,p>allax ( ! annual ,orb1 or ! greate/ elongation ( ! ,e>?'s orbit se5 f any ( ! sup]ior ,planets1 be+ giv52 ! di/ance ( t ,planet f ! ,sun1 9 respect ( ! ,e>?'s di/ance f him1 may be f\nd by ! same me?ods z ! di/ances ( ! inf]ior ,planets 74 ,?us1 to f9d ! di/ance ( ,m>s f ! ,sun1 x w be z ! ,s9e ( ! angle ,s ,a is to ! ,radius1 s is ! di/ance ,,z 7! di/ance ( ! ,e>? f ! ,sun7 to ,s 1 ! di/ance f ! ,sun to ,m>s4 ,aft] ! same mann] ! di/ances ( ,jupit] & ,saturn are also f\nd4 ,! mean di/ance ( ! ,e>? f ! ,sun be+ made #ajjj1 ! mean di/ances ( ! sup]ior ,planets f ! ,sun are1 viz4 ! mean di/ance f ! ,sun ( #aebd #ada #ebja & ! ,exc5tricity #bej #iech #edg ,to :i*1 if y add or subtract _! mean di/ances1 we %all h ! greate/ or lea/ di/ances ( ^? ,planets f ! ,sun4 ,!re are o!r me?ods by :i* ! relative di/ances ( ! ,planets might be f\nd2 b t :i* ha? be5 "h illu/rat$1 is suffici5t to ev9ce ! c]ta9ty ( t ,problem4 ,sid5ote3 ,h[ ! absolute di/ances ( ! ,planets f ! ,sun are comput$4 ,sid5ote3 ,p>allax ( ! ,e>?'s ,semidiamet]4 ,sid5ote3 ,fig4 #g4 ,hi!rto we h only consid]$ ! di/ances ( ! ,planets 9 relation to "o ano!r1 )\t det]m9+ !m by any kn[n measure2 b 9 ord] to f9d _! absolute di/ances 9 "s det]m9ate measure1 !re mu/ be some?+ giv51 ^: measure is kn[n4 ,n[ ! circumf]5ce ( ! ,e>? is divid$ into #cfj degrees1 & ea* ( ^! degrees into #fj ,geographical miles1 s t ! :ole circumf]5ce conta9s #bafjj2 & by ! kn[n proportion = f9d+ ! diamet] ( a circle f its circumf]5ce1 ! ,e>?'s diamet] w be f\nd to be #fhgb miles1 & its semidiamet] #cdcf miles4 ,! ,p>allax ( ! ,e>?'s semidiamet]1 or ! angle "u :i* x is se5 f a c]ta9 ,planet1 may be f\nd by comp>+ ! true place ( ! ,planet1 z x w\ld be se5 f ! c5t] ( ! ,e>? 7:i* is kn[n by computation7 ) its app>5t place1 z x is se5 f "s po9t on ! ,e>?'s surface4 ,let ,,cza be ! ,e>?1 ,,zc its semidiamet]1 "s ,planet1 & ,,bht ar* ( a great circle 9 ! ,heav5s1 at an inf9ite di/ance4 ,n[ ! ,planet w appe> f ! ,e>?'s c5t] ,c1 9 ! po9t ( ! ,heav5s ,h2 b a spectator f ! po9t ,z ^u ! ,e>?'s surface1 w see ! same object 9 ! po9t ( ! ,heav5s ,b2 & ! ar* ,,bh ! diff]5ce1 is equal to ! angle ,b ,h ,z ,c1 ! ,p>allax2 :i* be+ kn[n1 ! side ,c ! di/ance ( ! ,planet f ! c5t] ( ! ,e>?1 at t "t1 may be easily f\nd4 ,n[ if ?is di/ance ( ! ,planet f ! ,e>? be det]m9$1 :5 ! c5t]s ( ! ,sun1 ! said ,planet1 & ( ! ,e>?1 are 9 ! same "r l9e1 we h ! absolute di/ance ( ! ,planet's orbit f ! ,e>?'s 9 kn[n measure2 !n x w be1 z ! relative di/ance betwixt ! ,e>?'s orbit & t ( ! ,planet is to ! relative di/ance ( ! said ,planet f ! ,sun2 s is ! di/ance ( ! ,planet's orbit f ! ,e>?'s 9 kn[n measure to ! di/ance ( ! said ,planet f ! ,sun 9 ! same measure3 ,:i* be+ kn[n1 ! di/ance ( all ! o!r ,planets f ! ,sun may be f\nd4 ,= x w be1 z ! relative di/ance ( any ,planet f ! ,sun1 is to its di/ance f him 9 a kn[n measure2 s is ! relative di/ance ( any o!r ,planet f him to its di/ance 9 ! same measure4 ,?is may be done by f9d+ ! di/ance ( ! ,planet ,m>s1 :5 he is 9 opposition to ! ,sun1 aft] ! same mann] z we f9d ! di/ance ( a tree1 or ! l1 by two /ations4 ,let be ,m>s1 ,d ! po9t on ! ,e>?'s sup]ficies1 :]e ,m>s is v]tical :5 he is 9 opposition to ! ,sun1 :i* may be f\nd exactly en\gh by calculation1 at :i* "t let an obs]v]1 at ! po9t ,z 7^: situation f ,d mu/ be kn[n7 take ! altitude ( ,m>s1 ^: complem5t w be ! angle ,,zr2 !n 9 ! triangle ,,zc w be giv5 ! angle ,z ,c1 ! angle ,c 7^: measure is ! ar* ,,dz7 & consequ5tly ! angle ,z ,c ! ,p>allax1 & also ! side ,z ,c ! semidiamet] ( ! ,e>?2 by :i* we may f9d ,c ! di/ance ( ,m>s f ! ,e>?4 ,! extreme nicety requir$ 9 ?is obs]vation1 makes x v difficult to det]m9e ! exact di/ances ( ! ,planets f ! ,sun2 b ! celebrat$ ,dr4 ,halley has1 9 ! ,philosophical ,transactions1 %ew$ u a m c]ta9 me?od = f9d+ ! di/ances ( ! ,planets2 :i* is by obs]v+ ! ,transit ( ,v5us ov] ! ,sun4 ,sid5ote3 ,h[ ! ,magnitudes ( ! ,planets are det]m9$4 ,sid5ote3 ,fig4 #h4 ,! eye judge? ( ! magnitudes ( f> di/ant objects1 accord+ to ! quantities ( ! angles "u :i* !y are se5 7:i* are call$ _! app>5t magnitudes27 & ^! angles appe> great] or less 9 a c]ta9 proportion to _! di/ances4 ,:]e=e ! di/ances ( ! ,planets f ! ,e>?1 & _! app>5t diamet]s be+ giv51 _! true diamet]s 7& f !nce _! magnitudes7 may be f\nd4 ,h[ ! di/ances ( ! ,planets may be f\nd has be5 already %ewn2 _! app>5t diamet]s are f\nd by a telescope1 hav+ a ma*9e fix'd to x = measur+ ( angles1 call$ a ,micromet]4 ,let ,,bd1 or ! angle ,,bad be ! app>5t diamet] ( any ,planet1 & ,,ab1 or ,,ad1 7:i* by reason ( ! great di/ance ( ! ,planets 9 respect ( _! magnitudes7 may be consid]$ z be+ ! di/ance ( ! said ,planet f ! obs]v]4 ,n[ 9 ! triangle ,,abd1 hav+ ! sides ,,ab1 ,,ad1 giv51 & ! angle1 ,a1 we h also ! o!r angles ,b & ,d1 7because ! ,side ,,ab1 ,,ad1 are equal7 :5ce ! side ,,bd ! diamet] ( ! ,planet may be easily f\nd by ,trigonometry4 ,sid5ote3 ,:y ! ,moon appe>s bigg] ?an any ( ! ,planets4 ,f h5ce x appe>s1 t ! same body at diff]5t di/ances1 w seem to h v diff]5t magnitudes4 ,?us ! diamet] ,,bd w appe> f ! po9t ,e1 to be twice z l>ge z f ! po9t ,a4 ,x also foll[s1 t a small body1 :5 at no great di/ance f u1 may appe> to be equal1 or ev5 to exce$ ano!r at a great di/ance1 ?o' imm5sely bigg]4 ,?us b d appe>s "u ! same angle1 & consequ5tly ( ! same bigness f ! po9t ,a1 t ! l9e ,b ,d do?1 ?o' "o va/ly exce$s ! o!r4 ,& ?is is ! reason1 :y ! ,moon1 :i* is mu* less ?an any ( ! ,planets1 appe>s to u va/ly bigg] ?an ei!r ( !m1 & ev5 to equal ! ,sun himself1 :i* is _m ?\s& times great] 9 magnitude4 ,! di/ances ( ! ,planets1 & p]iods r\nd ! ,sun1 _! diamet]s & velocities r\nd _! own axis1 accord+ to mod]n computations1 are z foll[s3 ,revolves ab\t ! ,di/ance 9 ,sun 9 ! space ( ,miles ,y4 ,d4 ,h ,saturn #bi3afg3bb #ggg4jjj4jjj ,jupit] #aa3cad3ab #dbd4jjj4jjj ,m>s #a3cba3bc #abc4jjj4jjj ,e>? #j3cfe3 #f #ha4jjj4jjj ,v5us #j3bbd3af #ei4jfj4jjj ,m]cury #j3 #hg3bc #cb4jjj4jjj ,moon ,r\nd ! ,d4 ,h4 ,m4 ,e>?4 #bg3 #g3 #dc #bdj4jjj ,p]iods r\nd ,diamet]s _! own axis4 9 ,miles4 ,d4 ,h4 ,m4 ,sun #be3 #f3 #j #gfc4jjj ,saturn #fa4jjj ,jupit] #j3 #i3 #ef #ha4jjj ,m>s #a3 #j3 #dj #d4ddj ,e>? #j3 #bc3 #ef #g4igj ,v5us #bd3 #h3 #j #g4ijj ,m]cury #d4bdj ,moon #bg3 #g3 #dc #b4agj ,! cause ( ,eclipses & ,phases ( ! ,moon1 & "s o!r phnom5a n "h expla9$1 %all be %ew$ :5 we come to give a ,description ( ! ,orr]y4 ,illu/ration3 ,plate #b4 ,besides ! ,planets already m5tion$1 !re are o!r great bodies t sometimes visit our sy/em1 :i* are a sort ( tempor>y ,planets2 = !y come & abide ) u = a :ile1 & aft]w>ds )draw f u1 = a c]ta9 space ( "t1 aft] :i* !y aga9 return4 ,^! w&]+ bodies are call$ ,comets4 ,sid5ote3 ,( ,comets4 ,! motion ( ,comets 9 ! ,heav5s1 accord+ to ! be/ obs]vations hi!rto made1 seem to be regulat$ by ! same immutable law t rules ! ,planets2 = _! orbits are elliptical1 l ^? ( ! ,planets1 b va/ly n>r[]1 or m exc5tric4 ,yet !y h n all ! same direction ) ! ,planets1 :o move f ,we/ to ,ea/1 = "s ( ! ,comets move f ,ea/ to ,we/2 & _! orbits h diff]5t incl9ations to ! ,e>?'s orbit2 "s incl9+ ,nor?w>dly1 o!rs ,s\?w>dly1 mu* m ?an any ( ! ,planet>y orbits d4 ,al?o' bo? ! ,comets & ! ,planets move 9 elliptic orbits1 yet _! motions seem to be va/ly diff]5t3 ,= ! exc5tricities ( ! ,planet's orbits are s small1 t !y diff] b little f circles2 b ! exc5tricities ( ! ,comets are s v great1 t ! motions ( "s ( !m seem to be almo/ 9 "r l9es1 t5d+ directly t[>ds ! ,sun4 ,n[1 s9ce ! orbits ( ! ,comets are s extremely exc5tric1 _! motions1 :5 !y are 9 _! ,p]ihelia1 or ne>e/ di/ance f ! sun1 mu/ be mu* swift] ?an :5 !y are 9 _! ,aphelia1 or f>!/ di/ance f him2 :i* is ! reason :y ! ,comets make s %ort a /ay 9 our sy/em2 & :5 !y disappe>1 are s long 9 return+4 ,! figures ( ! ,comets are obs]v$ to be v diff]5t2 "s ( !m s5d =? small beams1 l hair1 e way r\nd !m2 o!rs are se5 ) a long fi]y tail1 :i* is always opposite to ! ,sun4 ,_! magnitudes are also v diff]5t1 b 9 :at proportion !y exce$ ea* o!r1 x is z yet unc]ta94 ,nor is x probable1 t _! numb]s are yet kn[n1 = !y h n be5 obs]v$ ) due c>e1 nor _! !ories discov]$1 b ( late ye>s4 ,! anci5ts 7 divid$ 9 _! op9ions conc]n+ !m2 "s imag9$ t !y 7 only a k9d ( ,meteors k9dl$ 9 our atmosph]e1 & 7 !re aga9 dissipat$2 o!rs took !m to be "s om9\s prodigies3 ,b mod]n discov]ies prove1 t !y are ,worlds subject to ! same laws ( motion z ! ,planets are2 & !y mu/ be v h>d & durable bodies1 else !y c\ld n be> ! va/ heat t "s ( !m1 :5 !y are 9 _! ,p]ihelia1 receive f ! ,sun1 )\t be+ utt]ly consum$4 ,! great ,comet :i* appe>$ 9 ! ye> #afhj1 0 )9 _/ "p ( ! ,sun's diamet] f 8 surface2 & !re=e its heat mu/ be prodigi\sly int5se beyond imag9ation4 ,& :5 x is at its greate/ di/ance f ! ,sun1 ! cold mu/ be z rigid4 ,illu/ration ,,sect4 ,,ii4 ,( ! ,,fix$ ,,/>s4 ,sid5ote3 ,! fix$ ,/>s are at imm5se di/ance f u4 ,! fix$ ,/>s are ^? bright & %9+ bodies1 :i* 9 a cle> night appe> to u e :]e disp]s$ ?r\gh ! b\ndless regions ( space4 ,!y are t]m'd fix'd1 because !y are f\nd to keep ! same immutable di/ance "o f ano!r 9 all ages1 )\t hav+ any ( ! motions obs]v$ 9 ! ,planets4 ,! fix$ ,/>s are all plac$ at su* imm5se di/ances f u1 t ! be/ ( telescopes repres5t !m no bigg] ?an po9ts1 )\t hav+ any app>5t diamet]s4 ,sid5ote3 ,! fix$ ,/>s are lum9\s bodies l ! ,sun4 ,x is evid5t f h5ce1 t all ! ,/>s are lum9\s bodies1 & %9e ) _! own prop] & native light1 else !y c\ld n be se5 at su* a great di/ance4 ,= ! ,satellites ( ,jupit] & ,saturn1 ?o' !y appe> "u consid]able angles ?r\gh good telescopes1 yet are altoge!r invisible to ! nak$ eye4 ,sid5ote3 ,! di/ance f u to ! ,sun is no?+ 9 comp>ison ( ! va/ di/ance ( ! fix$ ,/>s4 ,al?\gh ! di/ance betwixt u & ! ,sun is va/ly l>ge1 :5 comp>$ to ! diamet] ( ! ,e>?1 yet x is no?+ :5 comp>$ ) ! prodigi\s di/ance ( ! fix$ ,/>s2 = ! :ole diamet] ( ! ,e>?'s annual orbit1 appe>s f ! ne>e/ fix$ ,/> no bigg] ?an a po9t1 & ! fix$ ,/>s are at lea/ #ajj1jjj times f>!r f u ?an we are f ! ,sun2 z may be demon/rat$ f ! obs]vation ( ^? :o h endeav\r$ to f9d ! ,p>allax ( ! ,e>?'s annual ,orb1 or ! angle "u :i* ! ,e>?'s orbit appe>s f ! fix$ ,/>s4 ,sid5ote3 ,z to appe>ance1 ! ,e>? may be consid]'d z be+ ! c5t] ( ! ,heav5s4 ,h5ce x foll[s1 t ?o' we approa* ne>] to "s fix$ ,/>s at "o "t ( ! ye> ?an we d at ! opposite1 & t by ! :ole l5g? ( ! diamet] ( ! ,e>?'s orbit2 yet ?is di/ance be+ s small 9 comp>ison ) ! di/ance ( ! fix$ ,/>s1 _! magnitudes or positions _c !reby be s5sibly alt]$2 !re=e we may always1 )\t error1 suppose ourselves to be 9 ! same c5t] ( ! ,heav5s1 s9ce we always h ! same visible prospect ( ! ,/>s )\t any alt]ation4 ,sid5ote3 ,! fix$ ,/>s are ,suns4 ,if a spectator 0 plac$ z ne> to any fix$ ,/>1 z we are to ! ,sun1 he w\ld !re obs]ve a body z big1 & e way l1 z ! ,sun appe>s to u3 & our ,sun w\ld appe> to him no bigg] ?an a fix$ ,/>3 & und\bt$ly he w\ld reckon ! ,sun z "o ( !m 9 numb]+ ! ,/>s4 ,:]e=e s9ce ! ,sun diff]e? no?+ f a fix$ ,/>1 ! fix$ ,/>s may be reckon$ s _m ,suns4 ,sid5ote3 ,! fix$ ,/>s are at va/ di/ance f ea* o!r4 ,x is n reasonable to suppose t all ! fix$ ,/>s are plac$ at ! same di/ance f u2 b x is m probable t !y are e :]e int]sp]s$ ?ro' ! va/ indef9ite space ( ! univ]se2 & t !re may be z great a di/ance betwixt any two ( !m1 z !re is betwixt our ,sun & ! ne>e/ fix$ ,/>4 ,h5ce x foll[s1 :y !y appe> to u ( diff]5t magnitudes1 n because !y really are s1 b because !y are at diff]5t di/ances f u2 ^? t are ne>e/ excell+ 9 brightness & lu/re ^? t are mo/ remote1 :o give a fa9t] light1 & appe> small] to ! eye4 ,illu/ration3 ,,new & ,,correct ,,globes accord+ to ! late/ ,obs]vations ,made & ,sold by ,,ri*>d ,,cu%ee at ! ,globe & ,sun betwe5 ,/4 ,dun/ans ,*ur* ,*anc]y ,lane & ,?o3,wright ,in/rum5t-mak] to ,8 ,maje/y at ! ,orr]y & ,globe ne> ,salisbury ,c\rt ,,fleet ,,/reet ,,london ,,e/ates ,survey'd ,,also ,,maps ,,drawn & ,,engrav',d ,sid5ote3 ,! di/ribution ( ! ,/>s into #f classes4 ,sid5ote3 ,( ,telescopical ,/>s4 ,! a/ronom]s di/ribute ! ,/>s into sev]al ord]s or classes2 ^? t are ne>e/ to u1 & appe> brighte/ to ! eye1 are call$ ,/>s ( ! fir/ magnitude2 ^? t are ne>e/ to !m 9 brightness & lu/re1 are call$ ,/>s ( ! second magnitude2 ^? ( ! ?ird class1 are /il$ ,/>s ( ! ?ird magnitude2 & s on1 until we come to ! ,/>s ( ! six? magnitude1 :i* are ! smalle/ t c be disc]n$ by ! nak$ eye4 ,!re are inf9ite numb]s ( small] ,/>s1 t c be se5 ?r\gh telescopes2 b ^! are n r$uc$ to any ( ! six ord]s1 & are only call$ ,telescopical ,/>s4 ,x may be "h obs]v$1 t ?o' ! a/ronom]s h r$uc$ all ! ,/>s t are visible to ! nak$ eye1 into "s "o or o!r ( ^! classes1 yet we are n to conclude f !nce t all ! ,/>s answ] exactly to "s or o!r ( ^! ord]s2 b !re may be 9 reality z _m ord]s ( ! ,/>s1 z !y are 9 numb]1 few ( !m appe>+ exactly ( ! same bigness & lu/re4 ,sid5ote3 ,! ,/>s dige/$ into con/ellations ,! anci5t a/ronom]s1 t !y might di/+ui% ! ,/>s1 9 reg>d to _! situation & position to ea* o!r1 divid$ ! :ole />ry firmam5t into ,sev]al ,a/]isms1 or sy/ems ( ,/>s1 consi/+ ( ^? t are ne> to "o ano!r4 ,^! ,a/]isms are call$ ,con/ellations1 & are dige/$ into ! =ms ( "s animals2 z ,m51 ,lyons1 ,be>s1 ,s]p5ts1 c4 or to ! images ( "s kn[n ?+s2 z1 ( a ,cr[n1 a ,h>p1 a ,triangle1 c4 ,sid5ote3 ,zodiac4 ,! />ry firmam5t 0 divid$ by ! anci5ts into #dh images1 or con/ellations2 twelve ( :i* !y plac$ 9 t "p ( ! ,heav5s :]e9 are ! planes ( ! ,planet>y orbits2 :i* "p is call$ ! ,zodiac1 because mo/ ( ! con/ellations plac$ !re9 resemble "s liv+ creature4 ,! two regions ( ! ,heav5s t are on ea* side ( ! ,zodiac1 are call$ ! ,nor? & ,s\? p>ts ( ! ,heav5s4 ,sid5ote3 ,con/ellations )9 ! ,zodiac4 ,! con/ellations )9 ! ,zodiac are1 #a4 ,aries1 ! ,ram2 #b4 ,taurus1 ! ,bull2 #c4 ,gem9i1 ! ,tw9s2 #d4 ,canc]1 ! ,crab2 #e4 ,leo1 ! ,lion2 #f4 ,virgo1 ! ,virg92 #g4 ,libra1 ! ,balance2 #h4 ,scorpio1 ! ,scorpion2 #i4 ,sagitt>ius1 ! ,ar*]2 #aj4 ,capricornus1 ! ,goat2 #aa4 ,aqu>ius1 ! ,wat]-,be>]2 &1 #ab4 ,pisces1 ! ,fi%es4 ,sid5ote3 ,nor!rn con/ellations4 ,! con/ellations on ! ,nor? side ( ! ,zodiac are ,tw5ty-"o1 viz4 ! ,little ,be>2 ! ,great ,be>2 ! ,dragon2 ,cepheus1 a k+ ( ,e?iopia2 ,bootes1 ! keep] ( ! ,be>2 ! ,nor!rn ,cr[n2 ,h]cules ) 8 ,club1 wat*+ ! ,dragon2 ! ,h>p2 ! ,swan2 ,cassiopeia2 ,p]sius2 ,&rom$a2 ! ,triangle2 ,auriga2 ,pegasus1 or ! ,fly+ ,horse2 ,equuleus2 ! ,dolph92 ! ,arr[2 ! ,eagle2 ,s]p5t>ius2 & ! ,s]p5t4 ,sid5ote3 ,s\!rn con/ellations4 ,! con/ellations not$ by ! anci5ts on ! ,s\? side ( ! ,zodiac1 7 fifte51 viz4 ! ,:ale2 ! riv] ,eridanus2 ! ,h>e2 ,orion2 ! ,great ,dog2 ,little ,dog2 ! ,%ip ,argo2 ,hydra2 ! ,c5taur2 ! ,cup2 ! ,cr[2 ! ,wolf2 ! ,alt>2 ! ,s\!rn ,cr[n2 & ! ,s\!rn ,fi%4 ,to ^! h be5 lately add$ ! foll[+1 viz4 ,! ,phnix2 ! ,crane2 ! ,peacock2 ! ,indian2 ! ,bird ( ,p>adise2 ! ,s\!rn ,triangle2 ! ,fly2 ,cameleon2 ! ,fly+ ,fi%2 ,t\can1 or ! ,am]ican ,goose2 ! ,wat] ,s]p5t1 & ! ,sword ,fi%4 ,! anci5ts plac$ ^? p>ticul> con/ellations or figures 9 ! ,heav5s1 ei!r to commemorate ! de$s ( "s great man1 or "s notable exploit or action2 or else took !m f ! fables ( _! religion1 c4 ,& ! mod]n a/ronom]s d /ill reta9 !m1 to avoid ! confusion t w\ld arise by mak+ new ones1 :5 !y comp>e ! mod]n obs]vations ) ! old ones4 ,sid5ote3 ,un=m$ ,/>s4 ,"s ( ! pr9cipal ,/>s h p>ticul> names giv5 !m1 z ,syrius1 ,arcturus1 c4 ,!re are also sev]al ,/>s t are n r$uc$ into con/ellations1 & ^! are call$ ,un=m$ ,/>s4 ,sid5ote3 ,! ,galaxy1 or ,milky ,way4 ,besides ! ,/>s visible to ! nak$ eye1 !re is a v rem>kable space 9 ! ,heav5s1 call$ ! ,galaxy1 or ,milky ,way4 ,?is is a broad circle ( a :iti% hue1 l milk1 go+ q r\nd ! :ole ,heav5s1 & consi/+ ( an inf9ite numb] ( small ,/>s1 visible ?ro' a telescope1 ?o' n disc]nable by ! nak$ eye1 by reason ( _! exce$+ fa9tness2 yet ) _! light !y comb9e to illu/rate t "p ( ! ,heav5s :]e !y are1 & to cause t %9+ :it5ess4 ,! places ( ! fix$ ,/>s1 or _! relative situations "o f ano!r1 h be5 c>efully obs]v$ by a/ronom]s1 & dige/$ into catalogues4 ,! fir/ among ! ,greeks1 :o r$uc$ ! ,/>s into a catalogue1 0 ,hypp>*us1 :o1 f 8 own obs]vations1 & ( ^? :o liv$ be=e him1 ins]t$ #ajbb ,/>s into 8 catalogue1 ab\t #abj ye>s be=e ! ,*ri/ian ra3 ,?is catalogue has be5 s9ce enl>g$ & improv$ by sev]al le>n$ m51 to ! numb] ( #cjjj1 ( :i* !re are a great _m telescopical1 & n to be disc]n$ by ! nak$ eye2 & ^! are all rank$ 9 ! catalogue z ! ,/>s ( ! sev5? magnitude4 ,x may seem /range to "s1 t !re are no m ?an ?is numb] ( ,/>s visible to ! nak$ eye2 = sometimes 9 a cle> night !y seem to be innum]able3 b ?is is only a deception ( our sight1 aris+ f _! vehem5t sp>kl+1 :ile we look ^u !m confus$ly1 )\t r$uc+ !m into any ord]2 = !re c seldom be se5 above #ajjj ,/>s 9 ! :ole ,heav5s ) ! nak$ eye at ! same "t2 & if we %\ld di/9ctly view !m1 we %all n f9d _m b :at are ins]t$ ^u a good ,cele/ial ,globe4 ,al?o' ! numb] ( ,/>s t c be disc]n$ by ! nak$ eye are s few1 yet x is probable !re are _m m :i* are beyond ! rea* ( our optics1 = ?r\gh telescopes !y appe> 9 va/ multitudes1 e :]e disp]s$ ?r\gh\t ! :ole ,heav52 & ! bett] our glasses are1 ! m ( !m we /ill discov]4 ,! +5i\s ,dr4 ,hook has obs]v$ #gh ,/>s 9 ! ,pleiades1 ( :i* ! nak$ eye is nev] able to disc]n above #g2 & 9 ,orion1 :i* has b #hj ,/>s 9 ! ,briti% catalogue 7& "s ( !m telescopical7 !re has be5 numb]$ #bjjj ,/>s4 ,sid5ote3 ,an idea ( ! ,univ]se4 ,^? :o ?9k t all ^! glori\s bodies 7 creat$ = no o!r purpose ?an to give u a little dim light1 mu/ ent]ta9 a v sl5d] idea ( ! ,div9e ,wisdom2 = we receive m light f ! ,moon itself1 ?an f all ! ,/>s put toge!r4 ,& s9ce ! ,planets are subject to ! same laws ( motion ) our ,e>?1 & "s ( !m n only equal1 b va/ly exce$ x 9 magnitude1 x is n unreasonable to suppose1 t !y are all habitable ,worlds4 ,& s9ce ! ,fix$ ,/>s are no ways beh9d our ,sun1 ei!r 9 bigness or lu/re1 is x n probable1 t ea* ( !m h a sy/em ( ,planet>y ,worlds turn+ r\nd !m1 z we d r\nd our ,sun8 ,& if we asc5d z f> z ! smalle/ ,/> we c see1 %all we n !n discov] innum]able m ( ^! glori\s bodies1 :i* n[ are altoge!r invisible to u8 ,& s ad inf9itum1 ?ro' ! b\ndless space ( ! univ]se4 ,:at a magnifici5t idea mu/ ?is raise 9 u ( ! ,div9e ,be+6 ,:o is e :]e1 & at all times pres5t1 display+ 8 ,div9e ,p[]1 ,wisdom & ,goodness1 among/ all 8 ,creatures6 ,illu/ration ,! ,,description & ,,use ( ! ,,cele/ial & ,,t]re/rial ,,globes4 ,sid5ote3 ,globe or ,sph]e4 ,a ,globe or ,sph]e is a r\nd solid body1 hav+ e "p ( its surface equally di/ant f a po9t )9 x1 call$ its ,c5t]2 & x may be conceiv$ to be =m$ by ! revolution ( a semicircle r\nd its diamet]4 ,sid5ote3 ,great ,circle4 ,sid5ote3 ,hemisph]es4 ,any circle pass+ ?r\gh ! c5t] ( ! sph]e1 !reby divid+ into two equal p>ts or segm5ts1 is call$ a ,great ,circle2 & ! segm5ts ( ! sph]e s divid$1 are call$ ,hemisph]es4 ,e great circle has its ,poles & ,axis4 ,sid5ote3 ,poles4 ,! ,poles ( a great circle are two po9ts on ! surface ( ! sph]e1 diametrically opposite to "o ano!r1 & e :]e equally di/ant f ! said circle4 ,sid5ote3 ,axis4 ,! ,axis ( a circle is a "r l9e pass+ ?r\gh ! c5t] ( ! sph]e1 & ?r\gh ! ,poles ( ! said circle1 & is !re=e p]p5dicul> to ! ,plane3 ,!re=e ,sid5ote3 ,secund>ies4 ,all circles pass+ ?r\gh ! ,poles ( any great circle1 int]sect x 9 two places diametrically opposite1 & also at "r angles2 & ) respect to ! said great circle1 !y may be call$ its ,secund>ies4 ,sid5ote3 ,p>allel or less] ,circles4 ,all circles divid+ ! sph]e into two unequal p>ts1 are call$ less] or p>allel ,circles1 & are usually d5om9at$ by t great circle to :i* !y are p>allel4 ,sid5ote3 ,t]re/rial ,globe4 ,! ,e>? be+ globul>1 its outw>d p>ts1 z ! sev]al ,c\ntries1 ,seas1 c4 are be/1 & mo/ naturally repres5t$ ^u ! surfaces ( a ,globe2 & :5 su* a body has ! outw>d p>ts ( ! ,e>? & ,sea del9eat$ ^u its surface1 & plac$ 9 _! natural ord] & situation1 x is call$ a ,t]re/rial ,globe4 ,sid5ote3 ,cele/ial ,globe4 ,! ,cele/ial ,bodies appe> to u z if !y 7 all plac$ 9 ! same concave sph]e1 !re=e a/ronom]s place ! ,/>s accord+ to _! respective situations & magnitudes1 & also ! images ( ! con/ellations1 ^u ! ext]nal surface ( a ,globe2 = x answ]s ! same purposes z if !y 7 plac$ )9 a concave sph]e1 if we suppose ! ,globe to be transp>5t1 & ! eye plac$ 9 ! c5t]4 ,a ,globe hav+ ! ,/>s plac$ ^u its surface1 z above describ$1 is call$ a ,cele/ial ,globe4 ,^! ,globes are bo? plac$ 9 frames1 ) o!r appurt5ances1 z %all be describ$ 9 a prop] place4 ,sid5ote3 ,! pr9cipal use ( ! ,globes4 ,! pr9cipal uses ( ! ,globes 7besides _! s]v+ z ,maps1 to di/+ui% ! outw>d p>ts ( ! ,e>?1 & ! situations ( ! fix$ ,/>s7 is to expla9 & resolve ! phnom5a aris+ f ! diurnal motion ( ! ,e>? r\nd its ,axis4 ,sid5ote3 ,!re w be ! same prospect ( ! fix$ ,/>s :e!r ! spectator be plac$ on ! ,e>?1 or 9 ! ,sun4 ,x has be5 %ew$ 9 ! ,introduction1 t ! di/ance ( ! ,e>? f ! ,sun1 is no m ?an a po9t1 :5 comp>$ ) ! imm5se di/ance ( ! fix$ ,/>s2 !re=e let ! ,e>? be 9 :at po9t soev] ( h] orbit1 !re w be ! same prospect ( ! ,heav5s1 z a spectator w\ld obs]ve did he reside 9 ! ,sun3 ,& if sev]al circles be imag9$ to pass ?ro' ! c5t] ( ! ,e>?1 & o!rs1 p>allel to !m1 be conceiv$ to pass ?ro' ! c5t] ( ! ,sun1 ^! circles 9 ! ,heav5s w seem to co9cide1 & to pass exactly ?ro' ! same ,/>s4 ,:]e=e z to ! appe>ances ( ! fix$ ,/>s1 x is indiff]5t :e!r ! ,e>? or ! ,sun be made ! c5t] ( ! ,univ]se4 ,b because x is f ! ,e>? t we always obs]ve ! cele/ial bodies1 & _! app>5t motions seem to u to be really made 9 ! ,heav5s1 x is m natural 9 expla9+ ! phnom5a aris+ f ^! motions1 to place ! ,e>? 9 ! c5t]4 ,& aga91 because ! semidiamet] ( ! ,e>?1 :5 comp>$ to h] di/ance f ! ,sun1 is ( no s5sible magnitude1 any po9t1 ^u ! ,e>?'s surface1 let h] be 9 :at "p soev] ( ! orbit1 may be consid]$ z be+ ! c5t] ( ! ,univ]se4 ,^u ^! pr9ciples1 ! diff]5t phnom5a aris+ f ! diurnal motion ( ! ,e>?1 & ! diff]5t situation ( a spectator ^u its surface1 are v naturally illu/rat$ & expla9$ by ! ,globes4 ,z to ! alt]ations ( seasons1 c4 aris+ f ! annual motion ( ! ,e>? r\nd ! ,sun1 x is indiff]5t :i* we suppose to move1 ! ,e>? or ! ,sun1 = 9 bo? cases ! effect w be ! same4 ,:]e=e because x is ! ,sun t appe>s to u to move1 we say ! ,sun is 9 su* a "p ( ! ecliptic1 )\t attribut+ any motion to ! ,e>?1 any m ?an if %e _h actually be5 at re/4 ,= ! same reason we say ! ,sun rises1 or ! ,sun sets2 by :i* we mean t he beg9s to appe> or disappe>1 )\t consid]+ 9 ! lea/ h[ ^! effects are produc$4 ,^! ?+s are "h m5tion$1 to obviate ! objections t might be made by beg9n]s1 aft] !y h be5 told t ! ,sun /&s /ill4 ,illu/ration ,,sect4 ,i4 ,an ,explanation ( ! ,circles ( ! ,sph]e1 & ( "s ,a/ronomical ,t]ms aris+ !refrom4 ,sid5ote3 ,! ,circles ( ! ,sph]e4 ,9 ord] to det]m9e ! relative situations ( places ^u ! ,e>?1 z well z ! positions ( ! fix$ ,/>s1 & o!r ,cele/ial phnom5a1 ! ,globe ( ! ,e>? is suppos$ to be environ$ by sev]al imag9>y circles1 & ^! are call$ ! ,circles ( ! ,sph]e4 ,^! imag9>y circles are ei!r fix$1 & always obta9 ! same position 9 ! ,heav5s1 or moveable1 accord+ to ! position ( ! obs]v]4 ,^? circles t are fix$1 owe _! orig9 to ! two-fold motion ( ! ,e>?1 & are ! ,equator1 & ! ,ecliptic1 ) _! ,secund>ies & ,p>allels4 ,^! fix$ circles are usually del9eat$ ^u ! surface ( ! ,globes4 ,! moveable circles are only ! ,horizon1 its ,secund>ies & ,p>allels3 ,^! are repres5t$ by ! wood5 frame1 & ! brass r+1 :]e9 ! ,globe is hung1 & a ?9 plate ( brass to be screw$ 9 a prop] place1 ^u ! said r+1 z occasion requires4 ,i4 ,( ! ,equ9octial4 ,sid5ote3 ,! ,equator1 or ,equ9octial4 #a4 ,! ,equator1 or ! ,equ9octial1 is t great circle 9 ! ,heav5s1 9 ^: plane ! ,e>? p]=ms h] diurnal motion r\nd h] axis2 or x is t great circle1 p>allel to :i* ! :ole ,heav5s seem to turn r\nd ! ,e>? f ,ea/ to ,we/ 9 #bd ,h\rs4 ,note1 ,! ,equator & ! ,equ9octial are g5]ally synonym\s t]ms2 b sometimes ! ,equator p>ticul>ly signifies t great circle ^u ! surface ( ! ,e>?1 :i* co9cides ) ! ,equ9octial 9 ! ,heav5s4 ,?is circle is also by ,m>9]s commonly call$ ! ,l9e4 ,sid5ote3 ,nor!rn & ,s\!rn ,hemisph]es4 ,sid5ote3 ,! ,axis ( ! ,_w4 ,sid5ote3 ,poles ( ! ,_w1 or ( ! ,equator4 ,! equ9octial divides ! globe ( ! ,e>?1 & also ! :ole ,heav5s into two equal p>ts1 ,nor? & ,s\?1 :i* are call$ ! ,nor!rn & ,s\!rn ,hemisph]es4 ,! axis ( ?is circle1 is call$ ! ,axis ( ! ,_w1 or ! ,e>?'s ,axis1 because ! ,e>? revolves ab\t x 7f ,we/ to ,ea/7 9 #bd h\rs4 ,! extreme ( ?is axis are call$ ! ,poles ( ! ,_w1 :]e( t :i* lies 9 ! ,nor!rn ,hemisph]e1 is call$ ! ,nor? ,pole1 & ! o!r is call$ ! ,s\? ,pole4 ,! equ9octial circle is always del9eat$ ^u ! surface ( ea* globe1 ) its "n at l5g? express$2 ! axis ( ?is circle1 or ! ,e>?'s axis1 is only an imag9>y l9e 9 ! ,heav5s1 b on ! globes x is express$ by ! wires ab\t :i* !y really turn4 ,! ,poles ( ! _w1 are ! two po9ts ^u ! surface ( ! globe ?r\gh :i* ^! wires pass2 ! ,nor? ,pole is t :i* ha? ! little brass circle1 ) a moveable index plac$ r\nd x2 & ! o!r opposite to x is ! ,s\? ,pole4 ,! ,nor!rn ,hemisph]e is t :]e9 ! ,nor? ,pole is plac$1 & ! opposite "o is ! ,s\!rn ,hemisph]e4 ,! a/ronom]s divide all circles into #cfj equal p>ts1 call$ ,degrees1 ea* degree into #fj equal p>ts1 call$ ,m9utes1 ea* m9ute into #fj ,seconds1 c4 ,b besides ?is division into degrees1 ! equ9octial is also divid$ into #bd equal p>ts1 or ,h\rs1 ea* h\r into #fj ,m9utes1 ea* m9ute into #fj ,seconds1 c4 s t "o h\r is equal to #ae degrees1 ea* m9ute ( "t is equal to #ae m9utes ( a degree1 c4 ,sid5ote3 ,h\r ,circles or ,circles ( ,asc5sion1 also call$ ,m]idians4 #b4 ,all circles conceiv$ to pass ?r\gh ! ,poles ( ! _w1 int]sect+ ! equ9octial at "r angles1 are1 ) respect to any po9t 9 ! ,heav5s1 call$ ,h\r ,circles2 & ! ,circles ( ,asc5sion1 because ! asc5sion ( ! ,heav5ly bodies1 f a c]ta9 po9t1 are by !m det]m9$4 ,^! circles are also1 ) reg>d to places ^u ,e>?1 call$ ,m]idians4 ,sid5ote3 ,! ,brass ,m]idian4 ,! ,m]idians are commonly drawn ^u ! ,t]re/rial ,globe ?ro' e #ae degrees ( ! equ9octial1 !reby mak+ an ,h\r diff]5ce betwixt ! places ?r\gh :i* !y pass4 ,on ! ,cele/ial ,globe !re are commonly drawn b two ( ^! ,m]idians1 cross+ ! equ9octial 9 f\r po9ts equidi/ant f "o ano!r1 !reby divid+ x into f\r quadrants2 b ! int]m$iate ones are "h suppli$1 & also ^u ! ,t]re/rial ,globe1 by ! brass circle on :i* !y are hung1 :i*1 is !re=e call$ ! ,brass ,m]idian1 & sometimes only ! ,m]idian1 x s]v+ = ?is purpose to all ! po9ts ^u ei!r ,globe4 ,sid5ote3 ,! ,h\r ,circle4 ,!re is also a little brass circle fix$ ^u ?is m]idian1 divid$ into #bd ,h\rs1 hav+ an index moveable r\nd ! axis ( ! globe1 to be turn$ to any p>ticul> ,h\r4 ,! use ( ?is circle is to %ew ! diff]5ce ( "t betwixt any two m]idians1 & is !re=e call$ ! ,h\r ,circle4 ,sid5ote3 ,p>allels ( ,decl9ation4 #c4 ,all circles p>allel to ! equ9octial are1 ) respect to any po9t 9 ! ,heav5s1 call$ ,p>allels ( ,decl9ation4 ,s t1 ,sid5ote3 ,decl9ation ,nor? & ,s\?4 #d4 ,! ,decl9ation ( any ,po9t 9 ! ,heav5s 7z ( ! ,sun1 a fix$ ,/>1 or ! l7 is an ar* ( ! m]idian pass+ ?r\gh t po9t1 & int]cept$ betwixt x & ! equator2 & if ! said po9t be to ! 7,nor?w>d_/,s\?w>d7 ( ! equator1 x is call$ 7,nor?_/,s\?7 ,decl9ation4 ,sid5ote3 ,tropics & ,pol> ,circles4 ,( ! p>allels ( decl9ation1 f\r are em95tly di/+ui%$ by p>ticul> names1 viz4 ,! two ,tropics1 & ! two ,pol> ,circles4 ,sid5ote3 ,tropic ( ,canc]2 ( ,capricorn4 ,! tropics are on diff]5t sides ( ! equator ea* #bc degrees & #bi m9utes di/ant f x2 t :i* lies 9 ! ,nor!rn ,hemisph]e1 is call$ ! ,tropic ( ,canc]1 & ! ,s\!rn "o1 ! ,tropic ( ,capricorn4 ,^! circles are ! limits ( ! ,sun's greate/ decl9ation1 & are call$ tropics1 because :5ev] ! ,sun arrives to !m1 he seems to return back aga9 t[>ds ! equator4 ,sid5ote3 ,arctic ,circle4 ,sid5ote3 ,arctic ,pole4 ,sid5ote3 ,ant>ctic ,circle4 ,sid5ote3 ,ant>ctic ,pole4 #f4 ,! ,pol> ,circles are ea* ( !m at ! same di/ance f ! ,poles ( ! _w1 t ! tropics are f ! equator1 viz4 #bc #bi4 ,t :i* lies ne> ! ,nor? ,pole1 is call$ ! ,arctic ,circle1 f ,arctos1 a con/ellation situat$ 9 ! ,heav5s ne> t ,place2 :5ce also ?is ,pole is sometimes call$ ! ,arctic ,pole4 ,! o!r ,pol> circle1 :i* is situat$ ne> ! ,s\? ,pole2 is call$ ! ,ant>ctic ,circle1 because its position is contr>y to ! o!r2 & ! ,s\? ,pole is sometimes call$ ! ,ant>ctic ,pole4 ,! tropics & ! ,pol> circles h ea* _! names express$ ^u ! ,globes4 ,,ii4 ,( ! ,ecliptic4 ,sid5ote3 ,ecliptic4 ,sid5ote3 ,equ9octial4 ,sid5ote3 ,sol/itial ,po9ts4 ,sid5ote3 ,colures4 ,sid5ote3 ,equ9octial ,colure4 ,sid5ote3 ,sol/itial ,colure4 #g4 ,! ,ecliptic is t great circle 9 ^: plane ! ,e>? p]=ms its annual motion r\nd ! ,sun2 or1 9 :i* ! ,sun seems to move r\nd ! ,e>?1 once 9 a ye>4 ,?is circle makes an angle ) ! equ9octial ( #bc degrees #bi m9utes1 & int]sects x 9 two opposite po9ts1 :i* are call$ ! ,equ9octial ,po9ts2 & ! two po9ts 9 ! ecliptic t are at ! greate/ di/ance f ! equ9octial po9ts1 are call$ ! ,sol/itial ,po9ts4 ,! two m]idians pass+ ?r\gh ^? po9ts1 are1 by way ( em95ce1 call$ ,colures2 :]e( t :i* passe? ?ro' ! equ9octial po9ts1 is call$ ! ,equ9octial ,colure2 & t :i* is at "r angles to x1 pass+ ?r\gh ! ,sol/itial ,po9ts1 is call$ ! ,sol/itial ,colure4 ,sid5ote3 ,! ,ecliptic divid$ into signs4 ,! ecliptic is divid$ into #ab equal p>ts1 call$ ,signs1 ea* sign be+ #cj degrees1 beg9n+ f "o ( ! equ9octial po9ts1 & numb]$ f ,we/ to ,ea/2 ! names & *>act]s ( ! twelve signs are z foll[s1 viz4 ,aries1 ,taurus1 ,gem9i1 ,canc]1 ,leo1 ,virgo1 #a4 #b4 #c4 #d4 #e4 #f4 ,libra1 ,scorpio1 ,sagitt>ius1 ,capricornus1 ,aqu>ies1 #g4 #h4 #i4 #aj4 #aa4 ,pisces4 #ab4 ,sid5ote3 ,nor!rn ,signs4 ,! fir/ six ( ^! are call$ ! ,nor!rn ,signs1 & possess t half ( ! ecliptic :i* is to ! ,nor?w>d ( ! equator2 beg9n+ ) ! fir/ po9t ( 1 & end+ ) ! la/ po9t ( 4 ,sid5ote3 ,s\!rn ,signs4 ,! latt] six are call$ ! ,s\!rn ,signs1 because !y possess ! ,s\!rn half ( ! ecliptic2 beg9n+ at ! fir/ po9t ( 1 & end+ ) ! la/ po9t ( 4 ,! division ( ! ecliptic into signs1 & ! names ( ! colures1 are p>ticul>ly express$ ^u ! globes4 ,! signs ( ! ecliptic took _! names f #ab con/ellations m5tion$ 9 ! ,introduction to be situat$ 9 ! ,heav5s ne> ^? places4 ,x is to be obs]v$1 t ! signs are n to be conf\nd$ ) ! con/ellations ( ! same "n3 ,= ! ,sign ( ,aries1 is n ! same ) ! ,con/ellation ,aries2 ! latt] is a sy/em ( ,/>s dige/$ into ! figure ( a ,ram1 b ! sign ( ,aries is only #cj degrees ( ! ecliptic1 c\nt$ f ! equ9octial po9t 1 7:i* is reckon$ ! fir/ po9t 9 ! ecliptic7 to ! beg9n+ ( ,taurus3 ,or1 x is sometimes tak5 = all t space ^u ! ,cele/ial ,globe conta9$ betwe5 ! two circles pass+ ?r\gh ! fir/ po9ts ( & 4 ,:at has be5 "h said ( ,aries1 is to be not$ ( all ! re/ ( ! signs4 ,! con/ellations above-m5tion$ 7 =m]ly situat$ )9 ! signs :i* n[ be> _! names2 b by a sl[ motion ( ! equ9octial po9ts1 be+ "o degree 9 #gb ye>s1 ! con/ellation ,aries has n[ got into ! sign 1 & s ( ! re/4 ,s t ,pisces is n[ got into ! ,sign ( 2 ?is sl[ motion 9 ! ,heav5s is call$ ! ,precession ( ! ,equ9octial ,po9ts4 ,sid5ote3 ,poles ( ! ,ecliptic4 ,! ,poles ( ! ,ecliptic are bo? situat$ 9 ! ,sol/itial ,colure1 at #bc degrees1 #bi m9utes di/ance f ! ,pole ( ! _w2 & !y take _! d5om9ation f ! ,hemisph]e :]e9 !y are plac$1 viz4 t :i* lies 9 ! 7,nor!rn_/,s\!rn7 ,hemisph]e1 is call$ ! 7,nor?_/,s\?7 ,pole ( ! ecliptic4 ,! arctic & ant>ctic circles1 are describ$ by ! ,poles ( ! ecliptic 9 ! diurnal motion ( ! ,e>? r\nd its axis1 :5ce x seems ^! two circles are call$ ,pol>4 ,sid5ote3 ,circles ( ,longitude4 #h4 ,all great circles pass+ ?r\gh ! ,poles ( ! ecliptic1 & consequ5tly int]sect+ x at "r angles1 are call$ ,circles ( ,longitude3 ,s t1 ,sid5ote3 ,longitude ( any ,po9t 9 ! ,heav5s4 ,sid5ote3 ,place ( a ,/>4 #i4 ,! ,longitude ( any ,po9t 9 ! ,heav5s 7z a ,/> or ,planet1 c47 is an ar* ( ! ecliptic conta9$ betwe5 ! circle ( longitude pass+ ?ro' t po9t1 & ! equ9octial po9t 4 ,& t degree ( any sign :i* lies "u ! circle ( longitude1 pass+ ?ro' any ,/> or ,planet1 is call$ ! ,place ( t ,/> or ,planet4 ,note1 ,! ,sun nev] goes out ( ! ecliptic1 & x is n usual to say ! ,sun's longitude1 b we commonly express x ! ,sun's ,place1 :i* is t sign1 degree1 m9ute1 c41 ( ! ecliptic1 :i* he at any "t passes4 #aj4 ,all circles conceiv$ to be drawn p>allel to ! ecliptic1 are call$ ,p>allels ( ,latitude3 ,s t1 ,sid5ote3 ,latitude ( a ,/>1 c4 #aa4 ,! ,latitude ( any po9t 9 ! ,heav5s1 7z a fix$ ,/>1 c47 is an ar* ( ! circle ( longitude1 9 pass+ ?ro' t po9t1 & int]cept$ betwixt x1 & ! ecliptic2 or1 ! latitude is ! di/ance f ! ecliptic2 & if ! said po9t be to ! ,nor?w>d ( ! ecliptic1 x is call$ ,nor? ,latitude2 b if x be to ! ,s\?w>d1 is call$ ,s\? ,latitude4 ,^u ! ,t]re/rial ,globe1 none ( ! circles ( longitude are describ$2 & ^u ! ,cele/ial1 !y are commonly drawn ?ro' ! beg9n+ ( e ,sign2 b !y are all suppli$ ^u bo? ,globes1 by fa/5+ a ?9 plate ( brass ov] "o ( ! ,poles ( ! ecliptic1 & s z to be mov$ to any degree !re( at pleasure4 ,! p>allels ( latitude are also suppli$ by ! graduations ^u ! said plate1 z %all be %ewn 9 a prop] place4 ,we h n[ done ) all ^? circles t are fix$1 & su* z are drawn ^u ! ,globes !mselves2 we next proce$ to ! moveable circles4 ,,iii4 ,( ! ,horizon4 ,sid5ote3 ,horizon4 #ab4 ,! ,horizon is t great circle :i* divides ! upp]1 or visible ,hemisph]e ( ! _w1 f ! l[]1 or invisible3 ,?is circle is di/+ui%$ into two sorts1 ! ,s5sible1 & ! ,rational4 ,sid5ote3 ,s5sible ,horizon4 ,! ,s5sible1 or ,app>5t ,horizon1 is t circle :i* limits or det]m9ates our prospect1 :e!r we are at l& or sea1 rea*+ z f> z we c see1 or x is t circle :]e ! ,sky & ! ,e>?1 or ,wat]1 seem to meet4 ,:5 we are on ,t]ra ,firma1 ?is circle commonly seems rugg$ & irregul>1 occasion$ by ! unev5ness ( ! gr\nd t]m9at+ our prospect2 b at sea !re are no su* irregul>ities2 ! semidiamet] ( ?is circle v>ie? accord+ to ! height ( ! eye ( ! obs]v]2 if a man ( six feet high /ood ^u a l>ge pla91 or ! surface ( ! sea1 he c\ld n see above ?ree miles r\nd4 ,?is circle det]m9es ! ris+ & sett+ ( ! ,heav5ly bodies1 & di/+ui%es ,day & ,night4 ,sid5ote3 ,rational ,horizon4 ,! ,rational1 or true ,horizon1 is a great circle pass+ ?ro' ! c5t] ( ! ,e>?1 p>allel to ! s5sible ,horizon1 be+ di/ant f x by ! ,e>?'s semidiamet]1 :i* is ab\t #cihj miles3 ,?is di/ance is no?+ 9 comp>ison ( ! imm5se di/ance ( ! ,sun & ! fix$ ,/>s1 !re=e a/ronom]s make no di/9ction betwe5 ^! two circles1 b consid] ! app>5t ,horizon1 or t :]e9 ! ,sun appe>s to rise & set1 z pass+ ?ro' ! c5t] ( ! ,e>?4 ,sid5ote3 ,c>d9al ,po9ts ( ! ,horizon4 ,?is circle is divid$ by a/ronom]s into f\r quadrants1 & ea* ( ! quadrants into #ij degrees1 c4 ,! f\r po9ts qu>t]+ ?is circle are call$ ! ,c>d9al ,po9ts1 & are t]m$ ! ,ea/1 ,we/1 ,nor?1 & ,s\?4 ,! ,ea/ is t po9t ( ! ,horizon :]e ! ,sun rises :5 he is 9 ! equ9octial1 or on t day :5 he asc5ds above ! ,horizon exactly at six o'clock2 & ! ,we/ is t po9t ( ! ,horizon :i* is directly opposite to ! ,ea/1 or :]e ! ,sun ,sets :5 he is 9 ! ,equ9octial4 ,! ,s\? is #ij degrees di/ant f ! ,ea/ & ,we/1 & is t[>d t "p ( ! ,heav5s :]e9 ! ,sun always appe>s to u 9 ,great-,brita9 at ,noon2 & ! ,nor? is t "p ( ! ,heav5s :i* is directly opposite to ! ,s\?3 ,or1 ! ,nor? & ,s\? po9ts ( ! ,heav5s may be f\nd by turn+ y\rself ei!r directly t[>ds ! ,ea/ or ! ,we/3 ,if y look t[>ds ! 7,ea/_/,we/7 ! 7,s\?_/,nor?7 w be to ! "r ,h&1 & ! 7,nor?_/,s\?7 to ! left4 ,sid5ote3 ,po9ts ( ! ,compass4 ,besides ! a=em5tion$ divisions ( ! ,horizon into degrees4 ,m>9]s divide x into #cb equal p>ts1 :i* !y call ! ,po9ts ( ! ,compass2 to ea* ( :i* po9ts !y give a p>ticul> "n1 comp\nd$ ( ! f\r ,c>d9als1 accord+ to :at qu>t] ( ! ,compass is int5d$4 ,sid5ote3 ,z5i?4 ,sid5ote3 ,nadir4 ,! c5t] ( ! ,horizon is ! place ( obs]vation1 & ! ,poles ( x are "o exactly ov] our heads1 call$ ! ,z5i?2 & ! o!r exactly "u our feet1 call$ ! ,nadir4 ,sid5ote3 ,v]tical ,circles4 ,sid5ote3 ,m]idian4 ,sid5ote3 ,azimu?4 #ac4 ,all circles conceiv$ to pass ?ro' ! ,z5i? & ,nadir1 are call$ ,v]tical ,circles1 or ,azimu?s4 ,( ^! circles1 t :i* passe? ?ro' ! ,nor? & ,s\? po9ts ( ! ,horizon1 is call$ ! ,m]idian2 s t :5 any object is ^u ! ,m]idian1 x !n be>s ei!r due ,s\?1 or due ,nor? f u2 & ! ,azimu? ( any object is an ar* ( ! ,horizon int]cept$ betwe5 ! v]tical circle pass+ ?r\gh x1 & ei!r ! ,nor? or ,s\? "p ( ! ,m]idian2 :i* "p is commonly specifi$4 ,! m]idian passes ?ro' ! ,poles ( ! _w1 z well z ?r\gh ! ,z5i? & ,nadir1 & !re=e is a secund>y bo? ( ! equ9octial & ! horizon3 ,?is circle divides ! globe into ! ,ea/]n & ,we/]n ,hemisph]es1 & ! ,poles ( x are ! ,ea/ & ,we/ po9ts ( ! ,horizon4 ,all ! heav5ly objects are1 dur+ "o half ( _! cont9uance above ! horizon1 9 ! ,ea/]n ,hemisph]e1 & = ! o!r half 9 ! ,we/]n2 s t :5ev] ! ,sun arrives ^u ! upp] "p ( ! m]idian1 x is !n ,noon1 or ,mid-day1 :i* is ! reason :y ?is circle is call$ ! m]idian2 & :5 he comes to ! l[] "p1 x is !n ,midnight4 ,sid5ote3 ,prime ,v]tical4 ,! v]tical circle pass+ ?ro' ! ,ea/ & ,we/ po9ts ( ! horizon1 is call$ ! ,prime ,v]tical1 or ,circle ( ,ea/ & ,we/1 s t :5 any object is ^u ?is circle 9 ! ,ea/]n hemisph]e1 x appe>s due ,ea/2 & if x be 9 ! ,we/]n hemisph]e1 x appe>s due ,we/4 ,sid5ote3 ,amplitude4 ,t degree 9 ! horizon :]e9 any object rises or sets f ! ,ea/ or ,we/ po9ts1 is call$ ! ,amplitude2 :i* = ris+ is call$ ,amplitude ,ortive1 & ,occasive = sett+2 :i* mu/ be also d5om9at$ :e!r x be ,nor!rly or ,s\!rly4 ,x may be obs]v$1 t ! ,amplitude & ,azimu? are mu* ! same2 ! amplitude %ew+ ! be>+ ( any object :5 he rises or sets1 f ! ,ea/ or ,we/ po9ts ( ! horizon2 & ! azimu?1 ! be>+ ( any object :5 x is above ! horizon1 ei!r f ! ,nor? or ,s\? po9t !re(4 ,z = example1 if an object rises or sets )9 #aj degrees ( ! ,ea/ or ,we/1 suppose t[>ds ! ,s\?1 we accord+ly say1 its ,amplitude is #aj degrees ,s\!rly2 b if an object1 t is ( any height above ! horizon1 %\ld be 9 ! v]tical circle1 pass+ ?ro' ! be=e-m5tion$ po9t1 we !n say1 its ,azimu? is #hj degrees f ! ,s\?1 or #ajj degrees f ! ,nor?1 bo? :i* expressions signify ! same4 ,sid5ote3 ,almacan!rs4 ,sid5ote3 ,altitudes4 ,sid5ote3 ,m]idian ,altitude4 ,sid5ote3 ,z5i? ,di/ance4 #ad4 ,all circles drawn p>allel to ! horizon1 9 ! upp] hemisph]e1 are call$ ,almacan!rs1 or ,p>allels ( ,altitude3 ,s t ! ,altitude ( any po9t 9 ! ,heav5s is an ar* ( ! v]tical circle pass+ ?ro' t po9t1 & int]cept$ betwixt x & ! horizon2 & if ! object be ^u ! m]idian1 x is commonly call$ ! ,m]idian ,altitude4 ,! complem5t ( ! altitude1 or :at x wants ( #ij degrees1 is call$ ! ,z5i? ,di/ance4 ,! horizon 7by :i* we mean ! rational7 is repres5t$ by ! upp] surface ( ! ,wood5 frame1 :]e9 ! globes are plac$2 ^u ?is horizon are describ$ sev]al conc5tric circles1 ! inn]mo/ ( :i* is divid$ into degrees1 :i* ought to be numb]$ bo? ways f ! ,ea/ & ! ,we/1 until !y end at #ij degrees 9 ! ,nor? & ,s\? po9ts4 ,! use ( ^! divisions is to %ew ! amplitudes ( ! ,sun & ,/>s1 at _! ris+ & sett+3 ,also 9 "s conv5i5t place ^u ?is horizon1 !re is commonly not$ ! po9ts ( ! ,compass4 ,)\t ! be=e-m5tion$ circle !re is drawn ! ecliptic ) its divisions1 into signs1 & degrees1 & a circle ( mon?s & days3 ,! use ( ^! two circles is to s]ve z a kal5d> to %ew ! ,sun's place at any "t ( ! ye>1 & by t means to f9d 8 place 9 ! ,ecliptic1 drawn ^u ! globe itself4 ,! ,v]tical ,circles1 & ! ,p>allels ( ,altitude1 are suppli$ by a ?9 plate ( brass1 hav+ a nut & screw at "o end to fa/5 x to ! brass m]idian 9 ! ,z5i? po9t2 :i* be+ done1 ! l[] end ( x may be put betwe5 ! globe x self1 & ! inn] edge ( ! horizon1 & s turn$ r\nd ab\t to any po9t requir$4 ,sid5ote3 ,quadrant ( ,altitude4 ,! fiducial edge !re( repres5t+ ! ,v]tical ,circles1 & ! ,degrees ^u x1 describ+ ! ,p>allels ( ,altitude4 ,?is ?9 plate is call$ ! ,quadrant ( ,altitude4 ,! c5t] ( ! horizon be+ ! place ( obs]vation1 x is evid5t t ?is circle1 & all ! o!rs belong+ to x1 are cont9ually *ang$1 :i* way soev] we move2 :]e=e we may suppose ! horizon1 ) its secund>ies & p>allels1 to inve/ ! globe l a rete or net2 & to be moveable e way r\nd x4 ,?is is v naturally illu/rat$ by ! globes2 if we move directly ,nor?1 or directly ,s\?1 ! *ange made 9 ! horizon1 is repres5t$ by mov+ ! brass m]idian 7keep+ ! globe f turn+ ab\t its axis7 9 ! not*es made 9 ! wood5 horizon1 j s mu* z we travell$4 ,if our c\rse %\ld be due ,ea/1 or due ,we/1 ! alt]ations made !reby are repres5t$ by turn+ ! globe accord+ly ab\t its axis1 ! brass m]idian be+ kept fix$2 & if we /e] betwixt ! m]idian & ! ,ea/ or ,we/ po9ts1 !n we are to turn ! brass m]idian1 & also ! globe ab\t its axis accord+ly2 ! sum ( :i* is1 let ! spectator be at :at po9t soev] ( ! ,e>?'s surface1 he'll !re gravitate1 or t5d exactly t[>ds its c5t]1 & imag9e himself to be on ! highe/ "p !re(1 7! unev5ness ( ! gr\nd n be+ "h consid]$7 :]e=e if we turn ! globe 9 su* a mann] z to br+ ! sev]al progressive /eps ( a travell] successively to ! ,z5i?1 we %all !n h ! successive alt]ations made 9 ! horizon1 9 e "p ( 8 j\rney4 ,?is explication be+ well consid]$1 w be ( help to "y beg9n]s1 to conceive h[ ! ,e>? is e :]e habitable2 & h[ pass5g]s c travel q r\nd x2 = s9ce e ?+ t5ds t[>d ! c5t] ( ! ,e>?1 we are to conceive t po9t z be+ ! l[e/1 & n to c>ry our idea ( d[nw>ds any f>!r4 ,^? t are diametrically opposite to u be+ z mu* ^u ! upp] "p ( ! ,e>? z we are1 !re be+ no su* ?+ 9 nature z "o place be+ high] ?an ano!r1 b z x is at a great] di/ance f ! c5t] ( ! ,e>?1 let x be 9 :at c\ntry soev]4 ,we h n[ done ) all ! circles ( ! sph]e1 & x may be obs]v$1 t ! ,equ9octial1 ! ,ecliptic1 & ! ,horizon1 ) _! ,secund>ies & p>allels1 are all alike2 & alt]+ _! position1 may be made to s]ve = "o ano!r4 ,?us1 if ! ,poles ( ! ,_w be br\ght into ! ,z5i? & ,nadir1 ! ,equ9octial w co9cide ) ! ,horizon1 ! ,m]idians w be ! same ) ! ,v]tical ,circles1 & ! p>allels ( ,decl9ation w be ! p>allels ( ,altitude4 ,aft] ! same mann]1 if %ift+ ! position1 we br+ ! ,ecliptic to co9cide ) ! ,horizon1 ! circles ( ,longitude w be ! ,v]tical ,circles1 & ! p>allels ( ,latitude & ,altitude w co9cide4 ,! horizon & ! equator may be ei!r p>allel1 p]p5dicul>1 or oblique to ea* o!r4 ,sid5ote3 ,p>allel ,sph]e4 #ae4 ,a ,p>allel ,sph]e is t position :]e ! equator co9cides ) ! horizon1 & consequ5tly ! poles ( ! _w are 9 ! ,z5i? & ,nadir3 ,! inhabitants ( ?is sph]e 7if !re be any7 are ^? :o live "u ! poles ( ! _w4 ,sid5ote3 ,"r ,sph]e4 #af4 ,a ,"r or ,direct ,sph]e is t position :]e ! equator is p]p5dicul> to ! horizon1 ! inhabitants :]e( are ^? :o live "u ! equ9octial4 ,sid5ote3 ,oblique ,sph]e4 #ag4 ,an ,oblique ,sph]e is :5 ! equ9octial & ! horizon make oblique angles ) ea* o!r1 :i* e :]e happ5s b "u ! equator & ! poles4 ,sid5ote3 ,diurnal & ,nocturnal ,ar*4 ,! ar* ( any p>allel or decl9ation1 :i* /&s above ! horizon is call$ ! ,diurnal ,ar*2 & ! rema9+ "p ( x1 :i* is bel[ ! horizon1 is call$ ! ,nocturnal ,ar*4 ,t po9t ( ! equ9octial :i* comes to ! 7,ea/]n_/,we/]n7 "p ( ! horizon ) any po9t ( ! ,heav5s1 is call$ ! 7,asc5sion_/,desc5sion7 ( t po9t1 c\nt$ f ! beg9n+ ( 2 & if x be 9 a "r sph]e1 ! asc5sion or desc5sion is call$ "r2 b if x be an oblique sph]e x is call$ an oblique asc5sion or desc5sion4 ,s t1 ,sid5ote3 ,"r ,asc5sion4 #ah4 ,! ,"r ,asc5sion ( ! ,sun1 ,moon1 or any ,/>1 c4 is an ar* ( ! equator conta9$ betwixt ! beg9n+ ( 1 & t po9t ( ! equ9octial :i* rises ) !m 9 a ,"r ,sph]e1 or :i* comes to ! m]idian ) !m 9 an oblique sph]e4 ,sid5ote3 ,oblique ,asc5sion4 #ai4 ,oblique ,asc5sion1 or ,desc5sion1 is an ar* ( ! equ9octial int]cept$ betwe5 ! beg9n+ ( 1 & t ,po9t ( ! ,equator :i* rises or sets ) any po9t 9 ! ,heav5s 9 an oblique sph]e4 ,sid5ote3 ,asc5sional ,diff]5ce4 #bj4 ,asc5sional ,diff]5ce1 is ! diff]5ce betwixt ! "r & oblique asc5sion or desc5sion1 & %ews h[ long ! ,sun rises or sets be=e or aft] ! h\r ( six4 ,,iv4 ,( ! ,division ( ,"t4 ,! p>ts t "t is di/+ui%$ into1 are ,days1 ,h\rs1 ,weeks1 ,mon?s1 & ,ye>s4 ,a ,day is ei!r natural or artificial4 ,sid5ote3 ,natural & ,artificial ,day4 ,a ,natural ,day is ! space ( "t elaps$ :ile ! ,sun goes f any m]idian or hor>y circle1 'till he arrives to ! same aga92 or1 x is ! "t conta9$ f noon1 or any p>ticul> h\r1 to ! next noon1 or ! same h\r aga93 ,an ,artificial ,day is ! "t betwixt ! ,sun's ris+ & sett+2 to :i* is oppos$ ! ,night1 t is1 ! "t ! ,sun is hid "u ! horizon4 ,sid5ote3 ,h\rs1 c4 ,sid5ote3 ,equ9oxes4 ,sid5ote3 ,v]nal & ,autumnal ,equ9ox4 ,sid5ote3 ,sol/ices4 ,sid5ote3 ,summ] & ,w9t] ,sol/ices4 ,! ,natural ,day is divid$ into #bd ,h\rs1 ea* h\r into #fj ,m9utes1 ea* m9ute into #fj ,seconds1 c4 ,! ,artificial ,days are always unequal to all ! inhabitants t are n "u ! equator1 except :5 ! ,sun is 9 ! equ9octial po9ts & 1 :i* happ5s 7accord+ to our way ( reckon+7 ab\t ! #ba/ ( ,m>*1 & ! #bc;d ( ,septemb]2 at ^? times ! ,sun rises at six & sets at six to all ! inhabitants ( ! ,e>?4 ,^! days are call$ ! ,equ9oxes1 or ,equ9octial ,days2 ! fir/ ( :i*1 or :5 ! ,sun is 9 ! fir/ po9t ( ,aries1 is call$ ! ,v]nal ,equ9ox1 & ! latt] is call$ ! ,autumnal ,equ9ox4 ,9 all places :]e ! ,sun desc5ds bel[ ! horizon1 except+ "u ! equator1 ! days cont9ually l5g!n or %ort51 & t fa/] or sl[]1 accord+ z ! ,sun is ne>] to1 or fur!r f ! equ9octial1 until he arrives to ei!r ( ! ,sol/itial ,po9ts or 4 ,at ^? times ! ,sun seems to /& /ill = a few days1 & !n beg9s to return ) a sl[ motion t[>ds ! equ9octial1 /ill ha/5+ 8 pace z he comes ne>] to x3 ,! ,sun ent]s ! tropics ( & 1 ab\t ! #ba/ ( ,june1 & ! #bb;d ( ,decemb]1 :i* days are sometimes call$ ! ,sol/ices2 ! fir/ ( :i* we call ! ,summ] ,sol/ice1 & ! latt] ! ,w9t] ,sol/ice4 ,sid5ote3 ,! diff]5t beg9n+ ( ! day4 ,all nations d n beg9 _! day1 & reckon _! h\rs alike4 ,9 ,great-,brita94 ,france1 & ,spa91 & 9 mo/ places 9 ,europe1 ! days is reckon$ to beg9 at midnight1 f :5ce is c\nt$ twelve h\rs 'till noon1 !n twelve h\rs m 'till next midnight1 :i* makes a compleat day2 yet ! ,a/ronom]s 79 ^! c\ntries7 commonly beg9 _! day at noon1 & s reckon #bd h\rs 'till next noon1 & n twice twelve1 accord+ to ! vulg> computation4 ,sid5ote3 ,babyloni% ,h\rs4 ,sid5ote3 ,italian ,h\rs4 ,! ,babylonians began _! day at ,sun-ris+1 & reckon$ #bd h\rs 'till he rose aga96 ,?is way ( computation we call ! ,babyloni% ,h\rs4 ,9 sev]al p>ts ( ,g]many !y c\nt _! h\rs f ,sun-sett+1 call+ ! fir/ h\r aft] ! ,sun has set1 ! fir/ h\r1 c4 'till he sets ! next day1 :i* !y call ! #bd? h\r3 ,^! are commonly call$ ! ,italian ,h\rs4 ,accord+ to bo? ^! ways ( computation1 _! h\rs are commonly ei!r a little great] or less ?an ! _/ "p ( a natural day1 9 proportion z ! ,sun rises or sets soon] or lat] 9 ! succe$+ days4 ,!y h also ?is inconv5i5ce1 t _! mid-day & midnight happ5 on diff]5t h\rs1 accord+ to ! seasons ( ! ye>4 ,sid5ote3 ,jewi% ,h\rs4 ,sid5ote3 ,planet>y ,h\rs4 ,! ,jews & ! ,romans =m]ly divid$ ! artificial days & nights ea* into #ab equal p>ts2 ^! are t]m$ ! ,jewi% ,h\rs1 & are ( diff]5t l5g?s1 accord+ to ! seasons ( ! ye>2 a ,jewi% ,h\r 9 summ] be+ long] ?an "o 9 w9t]1 & a night-h\r %ort]4 ,?is me?od ( computation is n[ 9 use among ! ,turks1 & ! h\rs are /il$ ! fir/ h\r1 second h\r1 c4 ( ! day or night2 s t ,mid-day always falls on ! six? h\r ( ! day4 ,^! h\rs are also call$ ,planet>y ,h\rs1 because 9 e h\r "o ( ! sev5 ,planets 7 suppose to preside ov] ! ,_w1 & s take x by turns4 ,! fir/ h\r aft] ,sun-ris+ on ,sunday 0 allott$ to ! ,sun2 ! next to ,v5us1 ! ?ird to ,m]cury2 & ! re/ 9 ord] to ! ,moon1 ,saturn1 ,jupit]1 & ,m>s4 ,by ?is means on ! fir/ h\r ( ! next day1 ! ,moon presid$1 & s gave ! "n to t day2 & s sev5 days by ?is me?od _h names giv5 !m f ! ,planets t 7 suppos$ to gov]n on ! fir/ h\r4 ,sid5ote3 ,a ,week4 ,a ,week is a sy/em ( sev5 days1 9 :i* ea* day is di/+ui%$ by a diff]5t "n4 ,9 mo/ c\ntries ^! days are call$ aft] ! names ( ! sev5 ,planets1 z above not$4 ,all nations t h any notion ( religion1 lay ap>t "o day 9 sev5 = public wor%ip2 ! day solemniz$ by ,*ri/ians is ,sunday1 or ! fir/ day ( ! week1 be+ t on :i* our savi\r rose f ! grave1 on :i* ! apo/les aft]w>ds us$ m p>ticul>ly to assemble toge!r to p]=m div9e wor%ip4 ,! ,jews obs]v$ ,saturday1 or ! sev5? day ( ! week1 = _! sabba?1 or day ( re/1 be+ t appo9t$ 9 ! f\r? comm&m5t "u ! ,law4 ,! ,turks p]=m _! religi\s c]emonies on ,friday4 ,sid5ote3 ,a ,mon?4 ,sid5ote3 ,p]iodical & ,synodical ,mon?4 ,a ,mon? is prop]ly a c]ta9 space ( "t measur$ by ! ,moon 9 8 c\rse r\nd ! ,e>?4 ,a ,lun> ,mon? is ei!r ,p]iodical or ,synodical4 ,a ,p]iodical ,mon? is t space ( "t ! ,moon takes to p]=m h] c\rse f "o po9t 9 ! ecliptic 'till %e arrives to ! same aga91 :i* is #bg days1 & "s odd h\rs2 & a ,synodical ,mon? is ! "t betwixt "o new ,moon1 & ! next new ,moon1 :i* is commonly ab\t #bi days4 ,b a ,civil ,mon?1 is diff]5t f ^!1 & consi/s ( a c]ta9 numb] ( days1 few] or m1 accord+ to ! laws & cu/oms ( ! c\ntry :]e !y are obs]v$4 ,sid5ote3 ,a ,ye> ,syd]eal & ,tropical4 ,! compleate/ p]iod ( "t is a ,ye>1 9 :i* all ! v>iety ( seasons return1 & aft]w>ds beg9 anew4 ,a ,ye> is ei!r ,a/ronomical or ,civil4 ,an ,a/ronomical ,ye> is ei!r a ,syd]eal :]e9 ! ,sun dep>t+ f a fix$ ,/>1 returns to x aga92 or ,tropical1 :i* is ! space ( "t ! ,sun takes to p]=m 8 c\rse f any po9t ( ! ecliptic1 'till he returns to x aga94 ,a ,tropical ,ye> consi/s ( #cfe days1 #e h\rs1 & #di m9utes2 ?is is ! "t 9 :i* all ! seasons compleatly returns1 :i* is a small matt] less ?an a ,syd]eal ,ye>4 ,sid5ote3 ,egyptian ,ye>4 ,! ,civil ,ye> is ! same ) ! ,political e/abli%$ ) ! laws ( a c\ntry2 & is ei!r moveable or immoveable4 ,! moveable ye> consi/s ( #cfe days1 be+ less ?an ! tropical ye> by almo/ six h\rs1 & is call$ ! ,egyptian ,ye>1 because obs]v$ 9 t ,c\ntry4 ,! ,romans divid$ ! ye> into #ab kal5d> mon?s1 to :i* !y gave p>ticul> names1 & are /ill reta9$ by mo/ ( ! ,european nations1 viz4 ,janu>y1 ,febru>y1 ,m>*1 ,april1 ,may1 ,june1 ,july1 ,augu/1 ,septemb]1 ,octob]1 ,novemb]1 & ,decemb]4 ,! numb] ( days 9 ea* mon? may be kn[n by ! foll[+ v]ses3 ,?irty ,days ha? ,septemb]1 ,april1 ,june1 & ,novemb]2 ,febru>y ha? ,tw5ty-eight alone1 ,& all ! re/ h ,?irty-"o4 ,! ye> is also divid$ into f\r qu>t]s or seasons1 viz4 ,spr+1 ,summ]1 ,autumn1 & ,w9t]4 ,^! qu>t]s are prop]ly made :5 ! ,sun ent]s into ! equ9octial & sol/itial po9ts ( ! ecliptic2 b 9 civil uses !y are diff]5tly reckon$1 accord+ to ! cu/oms ( sev]al c\ntries4 ,9 ,engl&1 we commonly reckon ! fir/ day ( ,janu>y to be ! fir/ 9 ! ye>1 :i* is !re=e vulg>ly call$ ,new-,ye>'s-,day2 b 9 political & ecclesia/ical affairs1 ! ye> is reckon$ to comm5ce on ,lady-day :i* is ! #be? ( ,m>*2 & f !nce to ,midsumm]-day1 :i* is ! #bd? ( ,june1 is reckon$ ! fir/ qu>t]2 f ,midsumm]-day to ,mi*aelmas-day1 :i* is ! #bi? ( ,septemb]1 is ! second qu>t]2 ! ?ird qu>t] is reckon$ f ,mi*aelmas-day to ,*ri/mas-day1 :i* is ! #be? ( ,decemb]2 & f ,*ri/mas-day to ,lady-day1 is reckon$ ! la/ qu>t] 9 ! ye>4 ,9 common affairs1 a qu>t] is reckon$ f a c]ta9 day to ! same 9 ! f\r? mon? foll[+4 ,sometimes a mon? is reckon$ f\r weeks1 or #bh days1 & s a qu>t] #ab weeks4 ,to all ! inhabitants 9 ! 7,nor!rn_/,s\!rn7 ,hemisph]e1 _! ,midsumm] is prop]ly :5 ! ,sun is 9 ! tropic ( 7,canc]1_/,capricorn17 & _! ,midw9t] at ! opposite "t ( ! ye>2 b ^? :o live "u ! equ9octial h two w9t]s1 c4 :5 ! ,sun is 9 ei!r tropic2 ?o' inde$ prop]ly1 !re is no season t may be call$ w9t] 9 ^? p>ts ( ! _w4 ,sid5ote3 ,bissextile1 or ,leap-,ye>4 ,! ,egyptian ye> ( #cfe days be+ less ?an ! true sol> ye>1 by almo/ six h\rs1 x foll[s1 t f\r su* ye>s are less ?an f\r sol> ye>s by a :ole day2 & !re=e 9 #cfe times f\r ye>s1 t is1 9 #adfj ye>s1 ! beg9n+ ( ! ye>s move ?r\gh all ! seasons4 ,to rem$y ?is inconv5i5cy1 ,julius ,cs> 7consid]+ t ! six h\rs1 :i* rema9 at ! end ( e ye>1 w 9 f\r ye>s make a natural day7 ord]$ t e f\r? ye> %\ld h an int]cal>y day1 :i* !re=e consi/s ( #cff days2 ! day add$ 0 put 9 ! mon? ( ,febru>y1 by po/pon+ ,/4 ,mat?ias's day1 :i* 9 common ye>s fall on ! #bd?1 to ! #be? ( ! said mon?1 all ! fix$ fea/s 9 ! ye> f !nce=w>ds fall+ a week-day lat] ?an o!rwise !y w\ld4 ,accord+ to ! ,roman way ( reckon+1 ! #bd? ( ,febru>y 0 ! six? ( ! kal5ds ( ,m>*1 & x 0 ord]$ t = ?is ye> !re %\ld be two six?s1 or t ! six? ( ! kal5ds ( ,m>* %\ld be twice repeat$2 ^u :i* acc\nt ! ye> 0 call$ ,bissextile1 :i* we n[ call ! ,leap-,ye>4 ,to f9d :e!r ! ye> ( our ,"l be leap-ye>1 or ! fir/1 second1 or ?ird aft]2 divide x by f\r1 & ! rema9d]1 if !re be any1 %ews h[ _m ye>s x is aft] leap-ye>2 b if !re be no rema9d]1 !n t ye> is leap-ye>3 ,or1 y may omit ! hundr$s & scores1 & divide ! residue by #d1 ,examp4 #ageg1 omitt+ ! hundr$s & ! tw5ties1 ,i divide ! residue #ag1 by #d1 & ! rema9d] #a1 %ews x to be ! fir/ aft] leap-ye>4 ,sid5ote3 ,julian ,acc\nt or ! ,old ,/yle4 ,?is me?od ( reckon+ ! ye>1 viz4 mak+ ! common ye> to consi/ ( #cfe days1 & e f\r? ye> to h #cff days1 is n[ us$ 9 ,great-,brita9 & ,irel&1 & "s ( ! ,nor!rn p>ts ( ,europe1 & is call$ ! ,julian ,acc\nt1 or ! ,old ,/yle4 ,b ! "t appo9t$ by ,julius ,cs> = ! l5g? ( a sol> ye> is too mu*2 = ! ,sun f9i%es 8 c\rse 9 ! ecliptic1 9 #cfe days1 #e h\rs1 & #di m9utes1 :i* is #aa m9utes less ?an ! civil ye>2 & !re=e he aga9 beg9s 8 circuit #aa m9utes be=e ! civil ye> is end$2 & s mu* be+ ga9$ e ye>1 am\nts 9 #aca ye>s1 to a :ole day4 ,s t if ! ,sun 9 any ye> ent]$ ! equ9ox ^u ! #bj? ( ,m>* at noon1 aft] ! space ( #aca ye>s1 he'll ent] ! same po9t on ! same h\r1 on ! #ai? ( ,m>*4 ,& !re=e ! exqu9oxes w n always fall on ! same day ( ! mon?1 b by degrees w move t[>ds ! beg9n+ ( ! ye>4 ,sid5ote3 ,gregorian ,acc\nt1 or ,new ,/yle4 ,at ! "t ( ! ,c\ncil ( ,nice1 :5 ! t]ms 7 settl$ = obs]v+ ( ,ea/]1 ! ,v]nal ,equ9ox fell ^u ! #ba/ ( ,m>*2 b by its fall+ backw>ds #aa m9utes e ye>1 x 0 f\nd t 9 ,anno #aehb1 :5 ! kal5d> 0 correct$1 ! ,sun ent]$ ! equ9octial circle on ! #aa? ( ,m>*1 hav+ dep>t$ t5 :ole days f its =m] place 9 ! ye>3 & !re=e ,pope ,gregory ! ,x,i,i,ith1 design+ to place ! equ9oxes 9 _! situation ) respect to ! ye>1 took ^! t5 days out ( ! kal5d>1 & ord]$ t ! #aa? ( ,m>* %\ld be reckon$ z ! tw5ty-fir/3 ,& to prev5t ! seasons ( ! ye> f go+ backw>ds = ! future1 he ord]$ e hundr$? ye>1 :i* 9 ,julian =m 0 to be a ,bissextile1 %\ld be a common ye>1 & consi/ only ( #cfe days2 b t be+ too mu*1 e f\r? hundr$ 0 to rema9 ,bissextile4 ,?is =m ( reckon+ be+ e/abli%$ by ! au?ority ( ,pope ,gregory ,,xiii4 is call$ ! ,gregorian ,acc\nt1 or ! ,new ,/yle2 & is obs]v$ 9 all ! c\ntries :]e ! au?ority ( ! ,pope is ackn[l$g$1 & likewise by sev]al nations ( ! re=m$ religion4 ,!re be+ n[ above an hundr$ ye>s pa/1 s9ce ! re=mation 0 made 9 ! kal5d>1 ! ,gregorian acc\nt has accord+ly got be=e ! ,julian "o day m ?an x 0 9 ! "t ( its in/itution1 ! diff]5ce betwe5 ^! two acc\nts be+ n[ elev5 days2 s t ! fir/ day ( any mon?1 accord+ to t way ( reckon+1 is ! #ab? ( ! same mon?1 accord+ to ! ,new ,/yle4 ,i %all conclude ?is section ) a brief acc\nt ( ! ,atmosph]e4 ,sid5ote3 ,atmosph]e4 ,! ,atmosph]e is t ?9 body ( air :i* surr\nds ! ,e>?1 9 :i* ! cl\ds hov]1 & by :i* 9 _! desc5t !y are broke into drops ( ra92 :i* sometimes1 accord+ to ! w>m? or coldness ( air1 are froze into ,sn[1 or ,hail/ones4 ,?und] & ,lightn+ are also made 9 ! ,atmosph]e1 & w9d is no?+ else b a p]cussion ( ! air1 occasion$ by its diff]5t d5sity 9 diff]5t places4 ,! b5efits we receive f ! atmosph]e are innum]able2 )\t air no e>?ly creature c\ld live1 z is pla9ly prov$ by exp]im5ts made by ! ,air-,pump2 & ! :olsom5ess ( a climate *iefly dep5ds ^u t ( its air3 ,if !re 0 no atmosph]e to reflect ! rays ( ! ,sun1 no "p ( ! heav5s w\ld be lucid & bright1 b t :]e9 ! ,sun 0 plac$2 & if a spectator %\ld turn 8 back t[>ds ! ,sun1 he w\ld imm$iately p]ceive x to be q d>k1 & ! lea/ ,/>s w\ld be se5 %9+ z !y d 9 ! cle>e/ night2 & ! ,sun imm$iately be=e 8 sett+ w\ld %9e z brisk z at noon1 b 9 a mom5t1 z soon z he got bel[ ! horizon1 ! :ole hemisph]e ( ! ,e>? w\ld be involv$ 9 z great a d>kness z if x 7 midnight4 ,b by means ( ! atmosph]e x happ5s1 t :ile ! ,sun is above ! horizon1 ! :ole face ( ! heav5s is /rongly illum9at$ by its rays1 s z to obscure ! fa9t light ( ! ,/>s1 & r5d] !m invisible2 & aft] ,sun-sett+1 ?\gh we receive no direct light f him1 yet we enjoy its reflect$ light = "s "t3 ,= ! atmosph]e be+ high] ?an we are1 is a long] "t be=e x is )drawn f ! ,sun 7z if a man 0 to run to ! top ( a /eeple1 he might see ! ,sun aft] x _h be5 set to ^? at ! bottom47 ,! rays :i* ! atmosph]e receives f ! ,sun1 aft] he is )drawn f our sight1 are by refraction fa9tly transmitt$ to u2 until ! ,sun hav+ got ab\t #ah degrees bel[ ! horizon1 he no long] enlight5s our atmosph]e1 & !n all t "p !re( :i* is ov] u becomes d>k4 ,aft] ! same mann] 9 ! morn+1 :5 ! ,sun comes )9 #ah degrees ( our horizon1 he aga9 beg9s to enlight5 ! atmosph]e1 & s m & m by degrees1 until he rises & makes full day4 ,sid5ote3 ,twilight1 or ,crepusculum4 ,?is small illum9ation ( ! atmosph]e1 & ! /ate ( ! ,heav5s betwe5 day & night1 is call$ ! ,twilight1 or ! ,crepusculum4 ,! duration ( twilight is diff]5t 9 diff]5t climates1 & 9 ! same place at diff]5t times ( ! ye>4 ,! beg9n+ or end+ ( twilight be+ accurately giv51 we may f !nce easily f9d ! height ( ! atmosph]e1 :i* is n always ! same4 ,! mean height ( ! atmosph]e is comput$ to be ab\t #dj miles2 b x is probable1 ! air may ext5d itself a great deal fur!r1 !re be+ prop]ly no o!r limits to x1 z we c conceive1 b z x cont9ually decreases 9 d5sity ! f>!r remote x is f ! ,e>?1 9 a c]ta9 ratio2 :i* at la/1 z to our conception1 mu/ 9 a mann] t]m9ate4 ,illu/ration ,,sect4 ,,ii4 ,geographical ,def9itions4 ,( ! ,situations ( ,places ^u ! ,e>?2 ( ! diff]5t ,situations ( its ,inhabitants2 ( ,zones & ,climates4 ,! situations ( places ^u ! ,e>?1 are det]m9$ by _! ,latitude & ,longitude4 ,sid5ote3 ,latitude4 #a4 ,! ,latitude ( any place 7^u ! ,e>?7 is its ne>e/ di/ance1 ei!r ,nor? or ,s\? f ! ,equator2 & if ! place be 9 ! 7,nor!rn_/,s\!rn7 hemisph]e1 x is accord+ly call$ 7,nor?_/,s\?7 ,latitude2 & is measur$ by an ar* ( ! m]idian int]cept$ betwixt ! z5i? ( ! said place1 & ! equator4 ,& all places t lie on ! same side1 & at ! same di/ance f ! equator1 are said to be 9 ! same p>allel ( latitude3 ! p>allels 9 ,geography1 be+ ! same ) ! p>allels ( decl9ation 9 ,a/ronomy4 ,f ?is def9ition arise ! foll[+ ,coroll>ies4 7#a47 ,t no place c h above #ij degrees ( latitude1 ei!r ,nor? or ,s\?4 7#b47 ,^? places t lie "u ! equ9octial 7or ?ro' :i* ! equator passes7 h no latitude1 x be+ f !nce t ! calculation ( latitudes is c\nt$2 & ^? places t lie "u ! ,poles h ! greate/ latitude1 ^? po9ts be+ at ! greate/ di/ance f ! equator4 7#c47 ,! latitude ( any place is always equal to ! elevation ( ! ,pole 9 ! same place above ! horizon2 & is !re=e (t5 express$ by ! ,pole's height1 or elevation ( ! ,pole2 ! reason ( :i* is1 because f ! equator to ! ,pole !re is always ! di/ance ( #ij degrees1 & f ! z5i? to ! horizon ! same numb] ( degrees1 ea* ( ^! includ+ ! di/ance f ! z5i? to ! ,pole3 ,t di/ance !re=e be+ tak5 away f bo?1 w leave ! di/ance f ! z5i? to ! equator1 7:i* is ! latitude7 equal to ! di/ance ( ! ,pole to ! horizon4 7#d47 ,! elevation ( ! equator 9 any place is always equal to ! complem5t ( ! latitude ( ! same place4 7#e47 ,a %ip sail$ directly 7t[>ds_/f7 ! equator 7less5s_/augm5ts7 h] latitude1 7or 7depresses_/raises7 ! ,pole7 j s mu* z is h] di/ance sail$4 ,sid5ote3 ,diff]5ce ( ,latitude4 #b4 ,diff]5ce ( latitude is ! ne>e/ di/ance betwixt any two p>allels ( latitude1 %ew+ h[ f> ! "o is to ! ,nor?w>d or ,s\?w>d ( ! o!r1 :i* c nev] exce$ #ahj degrees4 ,& :5 ! two places are 9 ! same hemisph]e 7or on ! same side ( ! equator7 ! less] latitude subtract$ f ! great]1 & :5 !y are on diff]5t sides ( ! equator1 ! two latitudes add$1 gives ! diff]5ce ( latitude4 ,sid5ote3 ,longitude4 #c4 ,! ,longitude ( any place 7^u ! ,e>?7 is an ar* ( ! equator1 conta9$ betwixt ! m]idian ( ! giv5 place1 & "s fix$ or kn[n m]idian2 or1 x is equal to ! angle =m$ by ! two m]idians1 :i* prop]ly c nev] exce$ #ahj degrees1 ?o' sometimes ! ,longitude is c\nt$ ,ea/]ly q r\nd ! globe4 ,s9ce ! m]idians are all moveable1 & n "o t c be fix$ 9 ! heav5s1 7z ! equ9octial circle is fix$1 f :5ce ! latitudes ( all places are det]m9$ to be s mu* ei!r ,nor? or ,s\?7 ! longitudes ( places _c s well be fix$ f any o!r m]idian1 b e ,geograph] is at 8 lib]ty to make :i* he pleases 8 fir/ m]idian1 f :5ce to calculate ! longitudes ( o!r places4 ,h5ce x is t geograph]s ( diff]5t nations reckon _! longitudes f diff]5t m]idians1 commonly *oos+ ! m]idian pass+ ?r\gh ! metropolis ( _! own c\ntry = _! fir/3 ,?us1 ! ,engli% geograph]s g5]ally make ! m]idian ( ,london to be _! fir/1 ! ,fr5* t ( ,p>is1 & ! ,dut* t ( ,am/]dam1 c4 & m>9]s g5]ally reckon ! longitude f ! la/ kn[n l& !y saw4 ,?is arbitr>y way ( reckon+ ! longitude f diff]5t places1 makes x necess>y1 :5ev] we express ! longitude ( any place1 t ! place f :5ce x is c\nt$ be also express$4 ,f ! prec$+ def9itions arise ! foll[+ coroll>ies3 #a4 ,if a body %\ld /e] directly ,nor?1 or directly ,s\?1 q r\nd ! globe1 he'll cont9ually *ange 8 latitude2 & pass ?r\gh ! two ,poles ( ! _w1 )\t deviat+ ! lea/ f ! m]idian ( ! place he dep>t$ f2 & consequ5tly on 8 return w n diff] 9 8 acc\nt ( "t f ! p resid+ 9 ! said place4 #b4 ,if a body %\ld /e] r\nd ! globe ei!r due ,ea/1 or due ,we/1 he'll cont9ually *ange 8 longitude1 b w g q r\nd )\t alt]+ 8 latitude2 & if 8 c\rse %\ld be due ,ea/1 he'll ga9 a day compleatly 9 8 reckon+1 or reckon "o day m ?an ! inhabitants ( ! place f :5ce he dep>t$2 or if 8 c\rse _h be5 ,we/1 he w\ld h lo/ "o day1 or reckon "o less4 ,! reason ( :i* is evid5t2 = admitt+ our travell] /e]s due ,ea/2 s _m miles 9 "o day z to make 8 diff]5ce ( longitude equival5t to a qu>t] ( an h\r ( "t1 x is evid5t t ! next day ! ,sun w rise to him a qu>t] ( an h\r soon] ?an to ! inhabitants ( ! place f :5ce he dep>t$2 & s daily1 9 proportion to ! rate he travels1 :i* 9 go+ q r\nd1 w make up "o natural day4 ,9 l mann]1 if he /e]s due ,we/ aft] ! same rate1 he'll l5g!n ea* day a qu>t] ( an h\r1 & consequ5tly ! ,sun w rise to him s mu* lat] e day2 by :i* means1 9 go+ q r\nd1 he'll lose "o day compleat 9 8 reckon+4 ,f :5ce x foll[s1 #c4 ,if two bodies %\ld set out f ! same place1 "o /e]+ ,ea/1 & ! o!r ,we/1 & s cont9ue _! c\rses q r\nd1 until !y arrive at ! place f :5ce !y set out1 !y'll diff] two days 9 _! reckon+ at ! "t ( _! return4 #d4 ,if a body %\ld /e] ^u an oblique c\rse 7or any :]e betwixt ! m]idian & ! ,ea/ or ,we/ po9ts7 he'll cont9ually *ange bo? latitude & longitude1 & t m or less1 accord+ to ! c\rse he /e]s2 & if he %\ld g q r\nd ! globe1 he'll diff] 9 8 acc\nt ( "t1 z by ! second ,corol4 #e4 ,! p resid+ 9 ! ,ea/]nmo/ ( any two places1 w reckon _! "t s mu* ! soon] ?an ^? :o live 9 ! o!r place1 accord+ to ! diff]5ce ( longitude betwixt ! two places1 all[+ "o h\r = e #ae degrees1 c4 & ! contr>y4 ,,ii4 ,( ,zones & ,climates1 c4 ,sid5ote3 ,zones1 ,torrid1 ,temp]ate1 & ,frigid4 #d4 ,zones are l>ge tracts ( ! surface ( ! ,e>?1 di/+ui%$ by ! tropics & pol> circles1 be+ five 9 numb]2 viz4 "o ,torrid1 two ,temp]ate & two ,frigid4 ,! ,torrid1 or ,burn+ ,zone1 is all ! space compreh5d$ betwe5 ! two tropics2 ! anci5ts imag9$ ?is tract ( ! ,e>? to be un9habitable1 because ( ! excessive heat1 x be+ s ne> ! ,sun4 ,all ! inhabitants ( ! torrid zone h ! ,sun 9 _! z5i?1 or exactly ov] _! heads twice 9 e ye>2 except+ ^? :o live exactly "u ! two tropics1 :]e ! ,sun comes to _! z5i? only once 9 a ye>4 ,! two ,temp]ate ,zones lie on ei!r side ( ! globe1 betwe5 ! tropics & ! pol> circles4 ,! two ,frigid ,zones are ^? spaces ^u ! globe t are includ$ betwe5 ! two pol> circles4 ,sid5ote3 ,amphiscians4 ,sid5ote3 ,ascians4 ,! inhabitants ( ! ,e>? are also di/+ui%$ by ! div]sity ( _! ,%ad[s4 ,^? :o live 9 ! torrid zone1 are call$ ,amphiscians1 because _! noon-%ad[ is ca/ diff]5t ways1 accord+ z ! ,sun is to ! nor?w>d or s\?w>d ( _! z5i?2 b :5 ! ,sun is 9 _! z5i?1 !y are call$ ,ascians4 ,sid5ote3 ,het]oscians4 ,sid5ote3 ,ascians ,het]oscians4 ,sid5ote3 ,p]iscians4 ,! inhabitants ( ! temp]ate zones1 are call$ ,het]oscians1 because _! noon-%ad[ is always ca/ ! same way3 ,b ^? :o live "u ! tropics are call$ ,ascians ,het]oscians2 ^? :o live 9 ! frigid zones are call$ ,p]iscians1 because sometimes _! %ad[ is ca/ r\nd ab\t !m4 ,^! h>d names are only ,greek words1 import+ h[ ! ,sun ca/s ! %ad[ ( ! sev]al inhabitants ( ! ,e>?2 :i* w\ld be a too trifl+ di/9ction to be made "h1 0 x n = ! sake ( comply+ ) cu/om4 ,! inhabitants ( ! ,e>? are also di/+ui%$ into ?ree sorts1 9 respect to _! relative situation to "o ano!r1 & ^! are call$ ! ,p]ici1 ,antci1 & ,antipodes4 ,sid5ote3 ,p]ici4 #e4 ,! ,p]ici are ^? :o live "u opposite po9ts ( ! same p>allel ( latitude4 ,!y h _! seasons ( ! ye> at ! same "t1 & _! days & nights always ( ! same l5g? ) "o ano!r1 b ! "o's ,noon is ! o!r's ,midnight2 & :5 ! ,sun is 9 ! equ9octial1 he rises ) ! "o1 :5 he sets ) ! o!r4 ,^? :o live "u ! ,poles h no ,p]ici4 ,sid5ote3 ,antci4 #f4 ,! ,antci live "u ! same m]idian1 & 9 ! same latitude1 b on diff]5t sides ( ! equator2 _! ,seasons ( ! ye> are contr>y1 & ! days ( ! "o are equal to ! nights ( ! o!r1 b ! h\r ( ! day & night is ! same ) bo?2 & :5 ! ,sun is 9 ! equ9octial1 he rises & sets to bo? exactly at ! same "t4 ,^? :o live "u ! equator h no ,antci4 ,sid5ote3 ,antipodes4 #g4 ,! ,antipodes are ^? :o live diametrically opposite to "o ano!r1 /&+1 z x 71 exactly feet to feet3 ,_! days & nights1 summ] & w9t]1 are at direct contr>y times4 ,! surface ( ! ,e>? is by "s di/+ui%$ into ,climates4 ,sid5ote3 ,climates4 #h4 ,a ,climate is a tract ( ! surface ( ! ,e>?1 includ$ betwe5 two su* p>allels ( latitude1 t ! l5g? ( ! longe/ day 9 ! "o exce$s t 9 ! o!r by half an h\r4 ,! :ole surface ( ! ,e>? is consid]$1 z be+ divid$ into #fj climates1 viz4 f ! equator to ea* ( ! pol> circles #bd1 aris+ f ! diff]5ce ( h\r 9 ! l5g? ( _! longe/ days2 & f ! pol> circles to ! ,poles !mselves1 are six1 aris+ f ! diff]5ce ( an entire mon?1 ! ,sun be+ se5 9 ! fir/ ( ^! a :ole mon? )\t sett+2 9 ! second two2 & 9 ! ?ird1 ?ree mon?s1 c4 ,^! climates cont9ually decrease 9 bread?1 ! f>!r !y are f ! equator4 ,h[ !y are fram$1 viz4 ! p>allel ( latitude 9 :i* !y end 7t be+ likewise ! beg9n+ ( ! next7 ) ! respective bread? ( ea* ( !m1 is %ew$ 9 ! foll[+ table3 ,a ,,table ( ! ,,climates4 ,,climates betwe5 ! ,equator & ! ,pol> ,circles4 ---------------------------------------- ----- ,climates ,longe/ ,latitude4 ,bread? ,day4 ,d4 ,m4 ,d4 ,m4 ---------------------------------------- ----- #a #ab #h #be #h #be #b #ac #af #be #h #jj #c #ac #bc #ej #g #be #d #ad #cj #be #f #cj ---------------------------------------- ----- #e #ad #cf #bh #f #h #f #ae #da #bb #d #ed #g #ae #de #bi #d #g #h #af #di #a #c #cb ---------------------------------------- ----- #i #af #ea #eh #b #eg #aj #ag #ed #bg #b #bi #aa #ag #ef #cg #b #aj #ab #ah #eh #bi #a #eb ---------------------------------------- ----- #ac #ah #ei #eh #a #bi #ad #ai #fa #ah #a #bj #ae #ai #fb #be #a #g #af #bj #fc #bb #j #eg ---------------------------------------- ----- #ag #bj #fd #f #j #dd #ah #ba #fd #di #j #dc #ai #ba #fe #ba #j #cb #bj #bb #fe #dg #j #bf ---------------------------------------- ----- #ba #bb #ff #f #j #ai #bb #bc #ff #bj #j #ad #bc #bc #ff #bh #j #h #bd #bd #ff #ca #j #c ---------------------------------------- ----- ,,climates betwe5 ! ,pol> ,circles & ! ,poles4 -------------------------------- ,l5g? ( ,days4 ,latitude4 -------------------------------- ,mon?s4 ,d4 ,m4 #a #fg #ba #b #fi #dh #c #gc #cg #d #gh #cj #e #hd #e #f #jj #jj -------------------------------- ,,iii4 ,( ! ,poetical ris+ & sett+ ( ! ,/>s4 ,sid5ote3 ,cosmical1 ,acronical1 & ,heliacal ris+ & sett+4 ,! anci5t ,poets make frequ5t m5tion ( ! ,/>s ris+ & sett+1 ei!r ,cosmically1 ,acronically1 or ,heliacally2 :5ce ^! di/9ctions are call$ ,poetical4 ,a ,/> is said to rise or set ,cosmically1 :5 x rises or sets at ,sun-ris+2 & :5 x rises or sets at ,sun-sett+1 x is said to rise or set ,acronically4 ,a ,/> rises ,heliacally1 :5 fir/ x becomes visible1 aft] x _h be5 s ne> ! ,sun z to be hid by ! spl5dor ( 8 rays3 ,& a ,/> is said to set ,heliacally1 :5 x is fir/ imm]s$1 or hid by ! ,sun's rays4 ,! ,fix$ ,/>s1 & ! ?ree sup]ior ,planets1 ,m>s1 ,jupit]1 & ,saturn1 rise ,heliacally 9 ! morn+2 b ! ,moon rises ,heliacally 9 ! ev5+1 because ! ,sun is swift] ?an ! sup]ior ,planets1 & sl[] ?an ! ,moon4 ,,iv4 ,( ! surface ( ! ,e>?1 consid]$ z x is compos$ ( ,l& & ,wat]4 ,! ,e>? consi/s naturally ( two p>ts1 ,l& & ,wat]1 & !re=e x is call$ ! ,t]raque\s ,globe4 ,ea* ( ^! elem5ts is subdivid$ into v>i\s =ms & p>ts1 :i* accord+ly are di/+ui%$ by diff]5t names4 ,i4 ,( ! ,l&4 ,! l& is di/+ui%$ into ,cont95ts1 ,isl&s1 ,p59sula's1 ,i/hmus's1 ,promontories1 ,m\nta9s1 or ,coa/s4 ,sid5ote3 ,cont95t4 ,sid5ote3 ,ma9 ,l&4 #i4 ,a ,cont95t is a l>ge quantity ( l&1 9 :i* _m great c\ntries are jo9$ toge!r1 )\t be+ sep>at$ f ea* o!r by ! sea3 su* are ,europe1 ,asia1 ,africa1 & ! va/ cont95t ( ,am]ica2 :i* f\r are ! pr9cipal divisions ( ! ,e>?4 ,a cont95t is sometimes call$ ! ,ma9 ,l&4 ,sid5ote3 ,isl&4 #aj4 ,an ,isl& is a c\ntry1 or portion ( l&1 environ$ r\nd ) wat]3 su* are ,great-,brita9 & ,irel&2 ,s>d9ia1 ,sicily1 c4 9 ! ,m$it]ranean ,sea2 ! ,isles ( ,wight1 ,anglesey1 c4 ne> ,engl&4 ,also a small "p ( dry l&1 9 ! mid/ ( a riv]1 is call$ an isl&1 :5 comp>$ to a less]1 is call$ ! cont95t2 z if we comp>e ! ,isle ( ,wight to ,engl&1 ! latt] may be prop]ly call$ ! cont95t4 ,sid5ote3 ,p59sula4 #aa4 ,a ,p59sula is a "p ( l& almo/ environ$ ) wat]1 save "o n>r[ neck adjo9+ x to ! cont95t2 or :i* is almo/ an isl&3 su* is ,d5m>k jo9+ to ,g]many2 also ,africa is prop]ly a l>ge p59sula jo9+ to ,asia4 ,sid5ote3 ,i/hmus4 #ab4 ,an ,i/hmus is a n>r[ neck ( l& jo9+ a p59sula to ! cont95t2 z ! ,i/hmus ( ,sues1 :i* jo9s ,africa to ,asia1 t ( ,panama1 jo9+ ,nor? & ,s\? ,am]ica1 c4 ,sid5ote3 ,promontory4 ,sid5ote3 ,m\nta94 #ac4 ,a ,promontory is a high "p ( l& /ret*+ out into ! sea1 & is (t5 call$ a ,cape or ,headl&3 su* is ! ,cape ( ,good ,hope 9 ! ,s\? ( ,africa2 ,cape ,f9i/re on ! ,we/ ( ,spa92 also ! ,liz>d ,po9t1 & ! ,l&'s ,end1 are two ,capes or ,headl&s on ! ,we/ ( ,engl&4 ,a ,m\nta9 is a high "p ( l& 9 ! mid/ ( a c\ntry1 ov] topp+ ! adjac5t p>ts4 ,sid5ote3 ,a ,coa/ or ,%ore4 ,sid5ote3 ,inl&4 #ad4 ,a ,coa/ or ,%ore is t "p ( l& :i* bord]s ^u ! sea1 :e!r x be 9 isl&s or a cont95t3 ,& t "p ( ! l& :i* is f> di/ant f ! sea1 is call$ ! ,inl& ,c\ntry4 ,^! are ! usual di/9ctions ( ! l&4 ,! ,wat] is di/+ui%$ into ,oceans1 ,seas1 ,lakes1 ,gulfs1 ,/raits1 & ,riv]s4 ,sid5ote3 ,! ,ocean1 or ,ma9 ,sea4 #ae4 ,! ,ocean1 or ,ma9 ,sea1 is a va/ spread+ collection ( wat]1 n divid$ or sep>at$ by l&s runn+ betwe52 su* is ! ,atlantic or ,we/]n ,ocean2 betwe5 ,europe & ,am]ica2 ! ,pacific ,ocean1 or ,s\? ,sea1 c4 ,note1 ,^? p>ts ( ! ocean :i* bord] ^u ! l&1 are call$ by v>i\s names1 accord+ to ^? ( ! adjac5t c\ntries2 z1 ! ,briti% ,sea1 ! ,iri% ,sea1 ! ,fr5* & ,spani% ,sea4 ,sid5ote3 ,a ,lake4 #af4 ,a ,lake is a collection ( deep /&+ wat]1 inclos$ all r\nd ) l&1 & n hav+ any visible & op5 communication ) ! sea3 ,b :5 ?is lake is v l>ge1 x is commonly call$ a sea2 z ! ,caspian ,sea 9 ,asia1 c4 ,sid5ote3 ,a ,gulf4 ,sid5ote3 ,creek or ,hav54 #ag4 ,a ,gulf is a "p ( ! sea almo/ encompass$ ) l&1 or t :i* runs up a great way into ! l&2 z1 ! ,gulf ( ,v5ice1 c4 ,b if x be v l>ge1 'tis r call$ an ,inl& ,sea2 z ! ,baltic ,sea1 ! ,m$it]ranean ,sea1 ! ,r$ ,sea1 or ! ,arabian ,gulf1 c4 ,& a small "p ( sea ?us environ$ ) l& is usually call$ a ,bay4 ,if x be b a v small ,"p1 or1 z x 71 a small arm ( ! sea1 t runs b a few miles betwe5 ! l&1 x is call$ a ,creek or ,hav54 ,sid5ote3 ,a ,/rait4 #ah4 ,a ,/rait is a n>r[ passage ly+ betwe5 two %ores1 :]eby two seas are jo9$ toge!r2 z1 ! ,/raits ( ,dov]1 betwe5 ! ,briti% ,*annel & ! ,g]man ,sea2 ! ,/raits ( ,gibralt]1 betwe5 ! ,atlantic & ! ,m$it]ranean ,sea4 ,! ,m$it]ranean itself is also sometimes call$ ! ,/raits4 ,^! are all ! necess>y t]ms commonly us$ 9 ,geography4 ,! names ( ! sev]al c\ntries & seas1 & all ! pr9cipal divisions ( ! ,e>?1 ! read] w f9d express$ ^u ! ,t]re/rial ,globes4 ,to give a tol]able acc\nt ( ! produce ( ea* c\ntry1 ! g5ius ( ! p1 _! political in/itutions1 c4 is prop]ly a p>ticul> subject ( itself1 & q =eign to our design4 ,we %all next proce$ to ! use ( ! ,globes2 b fir/ x may n be amiss to take a %ort review ( _! appurt5ances4 ,^? circles ( ! sph]e t are fix$1 are 7z has be5 already said7 drawn ^u ! ,globes !mselves2 ^? t are moveable1 are suppli$ by ! ,brass ,m]idian1 ! ,wood5 ,horizon1 & ! ,quadrant ( ,altitude4 ,sid5ote3 ,brass ,m]idian4 #a4 ,t side ( ! ,braz5 ,m]idian1 :i* is divid$ into degrees1 repres5ts ! true ,m]idian2 ?is side is commonly turn$ t[>ds ! ,ea/1 & 'tis usual to place ! globe s be=e y1 t ! ,nor? be to ! "r h&1 & ! ,s\? to ! left4 ,! m]idian is divid$ into #d quadrants1 ea* be+ #ij degrees1 two ( :i* are numb]$ f t "p ( ! equ9octial1 :i* is above ! horizon1 t[>ds ea* ( ! ,poles2 ! o!r two quadrants are numb]$ f ! ,poles t[>ds ! equator4 ,! reason :y two quadrants ( ! m]idian are numb]$ f ! equator1 & ! o!r two f ! ,poles1 is because ! =m] ( ^! two s]ve to %ew ! di/ance ( any po9t on ! globe f ! equator1 & ! o!r to elevate ! globe to ! latitude ( ! place4 ,sid5ote3 ,wood5 ,horizon4 #b4 ,! upp] side ( ! wood5 frame call$ ! ,wood5 ,horizon2 repres5ts ! true horizon2 ! circles drawn ^u ?is plane h be5 already describ$2 we may obs]ve1 t ! fir/ po9t ( is ! ,ea/1 & ! opposite be+ ! fir/ po9t ( is ! ,we/1 ! m]idian pass+ ?r\gh ! ,nor? & ,s\? po9ts4 ,sid5ote3 ,quadrant ( ,altitude4 #c4 ,! ,quadrant ( ,altitude is a flexible plate ( ?9 brass1 hav+ a nut & screw at "o end1 to be fa/5$ to ! m]idian ( ei!r globe1 z occasion requires4 ,! edge ( ?is quadrant :i* has ! graduations ^u x1 call$ ! fiducial edge1 is t :i* is always meant :5ev] we make m5tion ( ! quadrant ( altitude4 ,sid5ote3 ,h\r ,circle4 #d4 ,! ,hor>y or ,h\r ,circle1 is divid$ into twice twelve h\rs1 ! two ,,xii's co9cid+ ) ! m]idian2 ! upp]mo/ ,,xii is t at ,noon1 & ! l[]mo/ t[>ds ! horizon is ,,xii at ,night4 ,! h\rs on ! ,ea/ side ( ! m]idian are ! ,morn+ ,h\rs1 & ^? on ! ,we/ side ! ,h\rs aft] ,noon4 ,! axis ( ! globe c>ries r\nd ! ,h& or ,index :i* po9ts ! h\r1 & passes ?r\gh ! c5t] ( ! h\r circle4 ,! ?+s above describ$ are common to bo? globes2 b !re are "s o!rs :i* are peculi> or prop] to "o sort ( globe4 ,! two ,colures1 & ! ,circles ( ,latitude f ! ecliptic1 belong only to ! ,cele/ial ,globes2 also ! ecliptic itself does prop]ly belong only to ?is globe1 ?o' x is always drawn on ! ,t]re/rial1 = ! sake ( ^? t might n h ! o!r globe by !m4 ,! equ9octial on ! cele/ial globe is always numb]$ into #cfj degrees1 beg9n+ at ! equ9octial po9t 2 b on ! t]re/rial1 x is arbitr>y1 :]e ^! numb]s comm5ce1 accord+ to ! m]idian ( :at place y int5d = y\r fir/2 & ! degrees may be c\nt$ ei!r q r\nd to #cfj1 or bo? ways1 'till !y meet 9 ! opposite "p ( ! m]idian1 at #ahj4 ,illu/ration ,,sect4 ,,iii4 ,! ,,use ( ! ,,globes4 ,,problem ,i4 ,to f9d ! ,latitude & ,longitude ( any giv5 ,place ^u ! ,globe2 & on ! contr>y1 ! ,latitude & ,longitude be+ giv51 to f9d ! ,place4 #a4 ,turn ! globe r\nd its axis1 'till ! giv5 place lies exactly "u ! 7,ea/]n side ( ! brass7 m]idian1 !n t degree ^u ! m]idian1 :i* is directly ov] x1 is ! ,latitude2 :i* is accord+ly ,nor? or ,s\?1 z x lies 9 ! ,nor!rn or ,s\!rn hemisph]e1 ! globe rema9+ 9 ! same position4 ,t degree ^u ! equator :i* is cut by ! braz5 m]idian1 is ! ,longitude requir$ f ! fir/ m]idian ^u ! globe4 ,if ! longitude is c\nt$ bo? ways f ! fir/ m]idian ^u ! globe1 !n we are to consid]1 :e!r ! giv5 place lies ,ea/]ly or ,we/]ly f ! fir/ m]idian1 & ! longitude mu/ be express$ accord+ly4 ,! ,latitudes ( ! foll[+ places3 & ^u a globe :]e ! longitude is reckon$ bo? ways f ! m]idian ( ,london1 _! longitudes w be f\nd z foll[3 ,latitude4 ,longitude4 ,deg4 ,deg4 ,rome #da ,nor?4 #ac ,ea/4 ,p>is #dh ,n4 #b ,e4 ,mexico #bj ,n4 #ajb ,w4 ,cape ,horn #eh ,s4 #hj ,w4 #b4 ,! ,latitude & ,longitude be+ giv5 to f9d ! ,place4 ,seek = ! giv5 longitude 9 ! equator1 & br+ t po9t to ! m]idian2 !n c\nt f ! equator on ! m]idian ! degree ( latitude giv51 t[>ds ! arctic & ant>ctic ,pole1 accord+ z ! latitude is ,nor!rly or ,s\!rly1 & "u t degree ( latitude lies ! ,place requir$4 ,,prob4 ,,ii4 ,to f9d ! ,diff]5ce ( ,latitude betwixt any two giv5 ,places4 ,br+ ea* ( ! places propos$ successively to ! m]idian1 & obs]ve :]e !y int]sect x1 !n ! numb] ( degrees ^u ! m]idian1 conta9$ betwe5 ! two int]sections1 w be ! ,diff]5ce ( ,latitude requir$4 ,or1 if ! places propos$ are on ! same side ( ! equator1 hav+ fir/ f\nd _! latitudes1 subtract ! less] f ! great]2 b if !y are on contr>y sides ( ! equator1 add !m bo? toge!r1 & ! diff]5ce 9 ! fir/ case1 & ! sum 9 ! latt]1 w be ! diff]5ce ( latitude requir$4 ,?us ! diff]5ce ( latitude betwixt ,london & ,rome w be f\nd to be #i degrees2 betwixt ,p>is & ,cape ,bona ,esp]ance #hc degrees4 ,,prob4 ,,iii4 ,to f9d ! ,diff]5ce ( ,longitude betwixt any two giv5 ,places4 ,br+ ea* ( ! giv5 places successively to ! m]idian1 & see :]e ! m]idian cuts ! equator ea* "t2 ! numb] ( degrees conta9$ betwixt ^? two po9ts1 if x be less ?an #ahj degrees1 o!rwise ! rema9d] to #cfj degrees1 w be ! diff]5ce ( longitude requir$4 ,or1 ,hav+ br\ght "o ( ! giv5 places to ! m]idian1 br+ ! index ( ! h\r circle to #ab o'clock2 !n hav+ br\ght ! o!r place to ! m]idian1 ! numb] ( h\rs conta9$ betwe5 ! place ! index 0 fir/ set at1 & ! place :]e x n[ po9ts1 is ! diff]5ce ( longitude 9 "t betwixt ! two places4 ,?us ! diff]5ce ( longitude betwixt ,rome & ,con/ant9ople w be f\nd to be #ai degrees1 or #a h\r & a qu>t]2 betwixt ,mexico & ,pek9 9 ,*9a1 #bdj degrees1 or #i h\rs4 ,,prob4 ,,iv4 ,any ,place be+ giv5 to f9d all ^? ,places t are 9 ! same ,latitude ) ! same ,place4 ,! latitude ( any giv5 place be+ m>k$ ^u ! m]idian1 turn ! globe r\nd its axis1 & all ^? places t pass "u ! same m>k are 9 ! same latitude ) ! giv5 place1 & h _! days & nights ( equal l5g?s4 ,& :5 any place is br\ght to ! m]idian1 all ! inhabitants t lie "u ! upp] semicircle ( x1 h _! ,noon or mid-day at ! same po9t ( absolute "t exactly4 ,,prob4 ,v4 ,! day ( ! ,mon? be+ giv52 to f9d ! ,sun's ,place 9 ! ,ecliptic1 & 8 ,decl9ation4 #a4 ,to f9d ! ,sun's ,place3 ,look = ! day ( ! mon? giv5 9 ! kal5d> ( mon?s ^u ! horizon1 & "r aga9/ x y'll f9d t sign & degree ( ! ecliptic :i* ! ,sun is 94 ,! ,sun's place be+ ?us f\nd1 look = ! same 9 ! ecliptic l9e :i* is drawn ^u ! globe1 & br+ t po9t to ! m]idian1 !n t degree ( ! m]idian1 :i* is directly ov] ! ,sun's place1 is ! ,decl9ation requir$2 :i* is accord+ly ei!r ,nor? or ,s\?1 z ! ,sun is 9 ! ,nor!rn or ,s\!rn signs4 ,?us1 ,sun's ,place4 ,decl9ation4 ,deg4 ,m94 ,deg4 ,m94 ,april #bc #c #jj #ab #cb ,n4 ,july #ca #g #ea #ah #bj ,n4 ,octob] #bf #b #di #ab #bh ,s4 ,janu>y #bj #j #di #bj #jg ,s4 ,,prob4 ,,vi4 ,to rectify ! ,globe = ! ,latitude1 ,z5i?1 & ! ,sun's ,place4 #a4 ,= ! ,latitude3 ,if ! place be 9 ! ,nor!rn hemisph]e1 raise ! arctic ,pole above ! horizon2 b = ! ,s\? latitude y mu/ raise ! ant>ctic2 !n move ! m]idian up & d[n 9 ! not*es1 until ! degrees ( ! latitude c\nt$ ^u ! m]idian bel[ ! ,pole1 cuts ! horizon1 & ! globe is adju/$ to ! latitude4 #b4 ,to rectify ! ,globe = ! ,z5i?3 ,hav+ elevat$ ! globe accord+ to ! latitude1 c\nt ! degrees !re( ^u ! m]idian f ! equator1 t[>ds ! elevat$ ,pole1 & t po9t w be ! z5i? or ! v]tex ( ! place2 to ?is po9t ( ! m]idian fa/5 ! quadrant ( altitude1 s t ! graduat$ edge !re( may be jo9$ to ! said po9t4 #c4 ,br+ ! ,sun's place 9 ! ecliptic to ! m]idian1 & !n set ! h\r index to ,,xii at ,noon1 & ! globe w be rectifi$ to ! ,sun's ,place4 ,if y h a little m>9]'s compass1 ! m]idian ( ! globe may be easily set to ! m]idian ( ! place4 ,,prob4 ,,vii4 ,to f9d ! ,di/ance betwe5 any two giv5 places ^u ! ,globe1 & to f9d all ^? places ^u ! globe t are at ! same di/ance f a giv5 place4 ,lay ! quadrant ( altitude ov] bo? ! places1 & ! numb] ( degrees int]cept$ betwe5 !m be+ r$uc$ into miles1 w be ! di/ance requir$3 ,or1 y may take ! di/ance betwixt ! two places ) a pair ( compasses1 & apply+ t ext5t to ! equator1 y'll h ! degrees ( di/ance z be=e4 ,note1 ,a geographical mile is ! _/? "p ( a degree2 :]e( if y multiply ! numb] ( degrees by #fj1 ! product w be ! numb] ( geographical miles ( di/ance s\ght2 b to r$uce ! same into ,engli% miles1 y mu/ multiply by #gj1 because ab\t #gj ,engli% miles make a degree ( a great circle ^u ! sup]ficies ( ! ,e>?4 ,?us1 ! di/ance betwixt ,london & ,rome w be f\nd to be ab\t #ac degrees1 :i* is #ghj geographical miles4 ,if y rectify ! globe = ! latitude & z5i? ( any giv5 place1 & br+ ! said place to ! m]idian2 !n turn+ ! quadrant ( altitude ab\t1 all ^? places t are cut by ! same po9t ( x1 are at ! same di/ance f ! giv5 place4 ,,prob4 ,,viii4 ,to f9d ! angle ( position ( ,places1 or ! angle =m$ by ! m]idian ( "o ,place1 & a great circle pass+ ?r\gh bo? ! ,places4 ,hav+ rectifi$ ! globe = ! latitude & z5i? ( "o ( ! giv5 places1 br+ ! said place to ! m]idian1 !n turn ! quadrant ( altitude ab\t1 until ! fiducial edge !re( cuts ! o!r place1 & ! numb] ( degrees ^u ! horizon1 conta9$ betwe5 ! said edge & ! m]idian1 w be ! angle ( position s\ght4 ,?us1 ! angle ( position at ! ,liz>d1 betwe5 ! m]idian ( ! ,liz>d & ! great circle1 pass+ f !nce to ,b>badoes is #fi degrees ,s\?-,we/]ly2 b ! angle ( position betwe5 ! same places at ,b>badoes1 is b #ch degrees ,nor?-,ea/]ly4 ,,s*olium ,! angle ( position betwe5 two places is a diff]5t ?+ f :at is meant by ! be>+s ( places2 ! ,be>+s ( two places is det]m9$ by a sort ( spiral l9e1 call$ a ,rhumb ,l9e1 pass+ betwe5 !m 9 su* a mann]1 z to make ! same or equal angles ) all ! m]idians ?r\gh :i* x passe?2 b ! angle or position is ! v same ?+ ) :at we call ! azimu? 9 a/ronomy1 bo? be+ =m$ by ! m]idian & a great circle pass+ ?ro' ! z5i? ( a giv5 place 9 ! heav5s1 !n call$ ! azimu?1 or ^u ! ,e>?1 !n call$ ! angle ( position4 ,f h5ce may be %ew$ ! error ( t geographical p>adox1 viz4 ,if a place ,a be>s f ano!r ,b due ,we/1 ,b %all n be> f ,a due ,ea/4 ,i f9d ?is p>adox v9dicat$ by an au?or1 :o at ! same "t gives a true def9ition ( a rhumb l9e3 ,b 8 argum5ts are ungeometrical2 = if x be admitt$ t ! ,ea/ & ,we/ l9es make ! same angles ) all ! m]idians ?r\gh :i* !y pass1 x w foll[ t ^! l9es are ! p>allels ( latitude3 ,= any p>allel ( latitude is ! cont9uation ( ! surface ( a ,cone1 ^: sides are ! radii ( ! sph]e1 & circumf]5ce ( its base ! said p>allel2 & x is evid5t1 t all ! m]idians cut ! said surface at "r 7& !re=e at equal7 angles2 :5ce x foll[s1 t ! rhumbs ( ,ea/ & ,we/ are ! p>allels ( latitude1 ?\gh ! case may seem diff]5t1 :5 we draw incl9+ l9es 7l m]idians7 ^u pap]1 )\t c>ry+ our ideas any f>!r4 ,,prob4 ,,ix4 ,to f9d ! ,antci1 ,p]ici1 & ,antipodes to any giv5 place4 ,br+ ! giv5 place to ! m]idian2 & hav+ f\nd its latitude1 c\nt ! same numb] ( degrees on ! m]idian f ! equator t[>ds ! contr>y ,pole1 & t w give ! place ( ! ,antci4 ,! globe be+ /ill 9 ! same position1 set ! h\r index to ,,xii at noon1 !n turn ! globe ab\t 'till ! index po9ts to ! l[] ,,xii2 ! place :i* !n lies "u ! m]idian1 hav+ ! same latitude ) ! giv5 place1 is ! ,p]ici requir$4 ,z ! globe n[ /&s1 ! ,antipodes ( ! giv5 place are "u ! same po9t ( ! m]idian1 t its ,antci /ood be=e3 ,or1 if y reckon #ahj degrees ^u ! m]idian f ! giv5 place1 t po9t w be ! ,antipodes4 ,let ! giv5 place be ,london1 9 ! latitude ( #ea degrees ,nor?1 t place :i* lies "u ! same m]idian & ! latitude #ea degrees ,s\?1 is ! ,antci2 t :i* lies 9 ! same p>allel ) ,london1 & #ahj degrees ( longitude f x1 is ! ,p]ici1 & ! ,antipodes is ! place ^: longitude f ,london is #ahj degrees1 & latitude #ea degrees ,s\?4 ,,prob4 ,x4 ,! ,h\r ( ! ,day at "o place be+ giv52 to f9d ! correspond5t ,h\r 7or :at o',clock x is at t "t7 9 any o!r place4 ,! diff]5ce ( "t betwixt two places is ! same ) _! diff]5ce ( longitude2 :]e=e hav+ f\nd _! diff]5ce ( longitude1 r$uc$ into "t 7by all[+ "o h\r = e #ae degrees1 c47 & if ! place :]e ! h\r is requir$ lies 7,ea/]ly_/,we/]ly7 f ! place :]e ! h\r is giv51 7add_/subtract7 ! diff]5ce ( longitude r$uc$ into "t 7to_/f7 ! h\r giv52 & ! sum or rema9d] w accord+ly be ! h\r requir$4 ,or1 ,hav+ br\ght ! place at :i* ! h\r is giv5 to ! m]idian1 set ! h\r index to ! giv5 h\r2 !n turn ! globe ab\t until ! place :]e ! h\r is requir$ comes to ! m]idian1 & ! index w po9t out ! h\r at ! said place4 ,?us :5 x is ,noon at ,london1 x is ,h4 ,m4 ,rome #j #eb ,p4 ,m4 ,at ,con/ant9ople #b #jg ,p4 ,m4 ,v]a-,cruz #e #cj ,a4 ,m4 ,pek9 9 ,*9a #g #ej ,p4 ,m4 ,,prob4 ,,xi4 ,! ,day ( ! ,mon? be+ giv51 to f9d ^? places on ! globe :]e ! ,sun w be ,v]tical1 or 9 ! ,z5i?1 t day4 ,hav+ f\nd ! ,sun's place 9 ! ecliptic1 br+ ! same to ! m]idian1 & note ! degree ov] x2 !n turn+ ! globe r\nd1 all places t pass "u t degree w h ! ,sun v]tical t day4 ,,prob4 ,,xii4 ,a place be+ giv5 9 ! ,torrid ,zone1 to f9d ^? two ,days 9 :i* ! ,sun %all be ,v]tical to ! same4 ,br+ ! giv5 place to ! m]idian1 & m>k :at degree ( latitude is exactly ov] x2 !n turn+ ! globe ab\t its axis1 ^? two po9ts ( ! ecliptic1 :i* pass exactly "u ! said m>k1 are ! ,sun's place2 aga9/ :i*1 ^u ! wood5 horizon1 y'll h ! days requir$4 ,,prob4 ,,xiii4 ,to f9d :]e ! ,sun is ,v]tical at any giv5 "t assign$2 or ! ,day ( ! ,mon? & ! ,h\r at any ,place 7suppose ,london7 be+ giv51 to f9d 9 :at place ! ,sun is ,v]tical at t v "t4 ,hav+ f\nd ! ,sun's decl9ation1 & br\ght ! fir/ place 7,london7 to ! m]idian1 set ! index to ! giv5 h\r1 !n turn ! globe ab\t until ! index po9ts to ,,xii at noon2 :i* be+ done1 t place ^u ! globe :i* /&s "u ! po9t ( ! ,sun's decl9ation ^u ! m]idian1 has ! ,sun t mom5t 9 ! ,z5i?4 ,,prob4 ,,xiv4 ,! ,day1 & ! ,h\r ( ! ,day at "o place1 be+ giv52 to f9d all ^? places ^u ! ,e>?1 :]e ! ,sun is !n ,ris+1 ,sett+1 ,culm9at+ 7or on ! m]idian7 also :]e x is ,day-light1 ,twilight1 ,d>k ,night1 ,midnight2 :]e ! ,twilight !n beg9s1 & :]e x ends2 ! height ( ! ,sun 9 any "p ( ! illum9at$ hemisph]e2 also 8 depression 9 ! obscure hemisph]e4 ,hav+ f\nd ! place :]e ! ,sun is v]tical at ! giv5 h\r1 rectify ! globe = t latitude1 & br+ ! said place to ! m]idian4 ,!n all ^? places t are 9 ! ,we/]n semicircle ( ! horizon1 h ! ,sun ris+ at t "t4 ,^? 9 ! ,ea/]n semicircle h x sett+4 ,to ^? :o live "u ! upp] semicircle ( ! m]idian1 x is #ab o'clock at noon4 ,&1 ,^? :o live "u ! l[] semicircle ( ! m]idian1 h x at midnight4 ,all ^? places t are above ! horizon1 h ! ,sun above !m1 j s mu* z ! places !mselves are di/ant f ! horizon2 :i* height may be kn[n by fix+ ! quadrant ( altitude 9 ! z5i?1 & lay+ x ov] any p>ticul> place4 ,9 all ^? places t are #ah degrees bel[ ! ,we/]n side ( ! horizon1 ! twilight is j beg9n+ 9 ! morn+1 or ! day breaks4 ,& 9 all ^? places t are #ah degrees bel[ ! ,ea/]n side ( ! horizon1 ! twilight is end+1 & ! total d>kness beg9n+4 ,! twilight is 9 all ^? places ^: depression bel[ ! horizon does n exce$ #ah degrees4 ,&1 ,all ^? places t are l[] ?an #ah degrees1 h d>k night4 ,! depression ( any place bel[ ! horizon is equal to ! altitude ( its ,antipodes1 :i* may be easily f\nd by ! quadrant ( altitude4 ,,prob4 ,,xv4 ,! ,day ( ! ,mon? be+ giv52 to %[1 at "o view1 ! l5g? ( ,days & ,nights 9 all places ^u ! ,e>? at t "t2 & to expla9 h[ ! vicissitudes ( ,day & ,night are really made by ! motion ( ! ,e>? r\nd h] axis 9 #bd h\rs1 ! ,sun /&+ /ill4 ,! ,sun always illum9ates "o half ( ! globe1 or t hemisph]e :i* is next t[>ds him1 :ile ! o!r rema9s 9 d>kness3 ,& if 7z by ! la/ problem7 we elevate ! globe accord+ to ! ,sun's place 9 ! ecliptic1 x is evid5t1 t ! ,sun 7he be+ at an imm5se di/ance f ! ,e>?7 illum9ates all t hemisph]e1 :i* is above ! horizon2 ! wood5 horizon itself1 w be ! circle t]m9at+ light & d>kness2 & all ^? places t are bel[ x1 are :olly depriv$ ( ! sol> light4 ,! globe /&+ 9 ?is position1 ^? ar*es ( ! p>allels ( latitude :i* /& above ! horizon1 are ! ,diurnal ,ar*es1 or ! l5g? ( ! day 9 all ^? latitudes at t "t ( ! ye>2 & ! rema9+ p>ts ( ^? p>allels1 :i* are bel[ ! horizon1 are ! ,nocturnal ,ar*es1 or ! l5g? ( ! night 9 ^? places4 ,! l5g? ( ! diurnal ar*es may be f\nd by c\nt+ h[ _m h\rs are conta9$ betwe5 ! two m]idians1 cutt+ any p>allel ( latitude1 9 ! ,ea/]n & ,we/]n p>ts ( ! horizon4 ,9 all ^? places t are 9 ! ,we/]n semicircle ( ! horizon1 ! ,sun appe>s ris+3 ,= ! ,sun1 /&+ /ill 9 ! v]tex 7or above ! brass m]idian7 appe>s ,ea/]ly1 & #ij degrees di/ant f all ^? places t are 9 ! ,we/]n semicircle ( ! horizon2 & !re=e 9 ^? places he is !n ris+4 ,n[1 if we pit* ^u any p>ticul> place ^u ! globe1 & br+ x to ! m]idian1 & !n br+ ! h\r index to ! l[] #ab1 :i* 9 ?is case1 we'll suppose to be #ab at noon2 7because o!rwise ! numb]s ^u ! h\r circle w n answ] our purpose7 & aft]w>ds turn ! globe ab\t1 until ! a=esaid place be br\ght to ! ,we/]n side ( ! horizon2 ! index w !n %ew ! "t ( ! ,sun ris+ 9 t place4 ,!n turn ! globe gradually ab\t f ,we/ to ,ea/1 & m9d+ ! h\r index1 we %all see ! progress made 9 ! day e h\r1 9 all latitudes ^u ! globe1 by ! real motion ( ! ,e>? r\nd its axis2 until1 by _! cont9ual approa* to ! brass m]idian 7ov] :i* ! ,sun /&s /ill all ! :ile7 !y at la/ h noon day1 & ! ,sun appe>s at ! highe/2 & !n by degrees1 z !y move ,ea/]ly ! ,sun seems to decl9e ,we/w>d1 until1 z ! places successively arrive 9 ! ,ea/]n "p ( ! horizon1 ! ,sun appe>s to set 9 ! ,we/]n3 ,= ! places t are 9 ! horizon1 are #ij degrees di/ant f ! ,sun4 ,we may obs]ve1 t all places ^u ! ,e>?1 t diff] 9 latitude1 h _! days ( diff]5t l5g? 7except :5 ! ,sun is 9 ! equ9octial7 be+ long] or %ort]1 9 proportion to :at "p ( ! p>allels /&s above ! horizon4 ,^? t are 9 ! same latitude1 h _! days ( ! same l5g?2 b h !m comm5ce soon] or lat]1 accord+ z ! places diff] 9 longitude4 ,,prob4 ,,xvi4 ,to expla9 9 g5]al ! alt]ation ( ,seasons1 or l5g? ( ! ,days & ,nights made 9 all places ( ! ,_w1 by ! ,sun's 7or ! ,e>?'s7 annual motion 9 ! ,ecliptic4 ,x has be5 %ew$ 9 ! la/ problem1 h[ to place ! globe 9 su* a position z to exhibit ! l5g? ( ! diurnal & nocturnal ar*es 9 all places ( ! ,e>?1 at a p>ticul> "t3 ,if ! globe be cont9ually rectifi$1 accord+ z ! ,sun alt]s 8 decl9ation1 7:i* may be kn[n by br++ ea* degree ( ! ecliptic successively to ! m]idian7 y'll see ! gradual increase or decrease made 9 ! days1 9 all places ( ! ,_w1 accord+ z a great] or less] portion ( ! p>allels ( latitude1 /&s above ! horizon4 ,we %all illu/rate ?is problem by examples tak5 at diff]5t times ( ! ye>4 #a4 ,let ! ,sun be 9 ! fir/ po9t ( 7:i* happ5s on ! #ba/ ( ,june7 t po9t be+ br\ght to ! m]idian1 w %ew ! ,sun's decl9ation to be #bc degrees ,nor?2 !n ! globe mu/ be rectifi$ to ! latitude ( #bc degrees2 & = ! bett] illu/ration ( ! problem1 let ! fir/ m]idian ^u ! globe be br\ght "u ! brass m]idian4 ,! globe be+ 9 ?is position1 y'll see at "o view ! l5g? ( ! days 9 all latitudes1 by c\nt+ ! numb] ( h\rs conta9$ betwe5 ! two extreme m]idians1 cutt+ any p>ticul> p>allel y pit* ^u1 9 ! ,ea/]n & ,we/]n "p ( ! horizon4 ,& y may obs]ve t ! l[] "p ( ! arctic circle j t\*es ! horizon1 & consequ5tly all ! p :o live 9 t latitude h ! ,sun above _! horizon = ! space ( #bd h\rs1 )\t sett+2 only :5 he is 9 ! l[] "p ( ! m]idian 7:i* !y w\ld call #ab at night7 he j t\*es ! horizon4 ,to all ^? :o live betwe5 ! arctic circle & ! ,pole1 ! ,sun does n set1 & its height above ! horizon1 :5 he is 9 ! l[] "p ( ! m]idian1 is equal to _! di/ance f ! arctic circle3 ,= example1 ,^? :o live 9 ! #hc;d p>allel h ! ,sun :5 he is l[e/ at ?is "t #ac degrees high4 ,if we ca/ our eye ,s\?w>d1 t[>ds ! equator1 we %all f9d1 t ! diurnal ar*es1 or ! l5g? ( days 9 ! sev]al latitudes1 gradually less53 ,! diurnal ar* ( ! p>allel ( ,london at ?is "t is #af h\rs2 t ( ! ,equator 7is always7 #ab h\rs2 & s cont9ually less1 'till we come to ! ,ant>ctic ,circle1 ! upp] "p ( :i* j t\*es ! horizon2 j ^? :o live 9 ?is latitude h j "o sight ( ! ,sun1 peep+ z x 7 9 ! horizon3 ,& all t space betwe5 ! ant>ctic circle & ! ,s\? ,pole1 lies 9 total d>kness4 ,if f ?is position we gradually move ! m]idian ( ! globe accord+ to ! progressive alt]ations made 9 ! ,sun's decl9ation1 by 8 motion 9 ! ecliptic1 we %all f9d ! diurnal ar*es ( all ^? p>allels1 t are on ! ,nor!rn side ( ! equator1 cont9ually decrease2 & ^? on ! ,s\!rn side cont9ually increase1 9 ! same mann] z ! days 9 ^? places %ort5 & l5g!n4 ,let u aga9 obs]ve ! globe :5 ! ,sun has got )9 #aj degrees ( ! equ9octial2 n[ ! l[] "p ( ! #hj? p>allel ( ,nor? latitude j t\*es ! horizon1 & all ! space betwixt ?is & ! pole1 falls 9 ! illum9at$ hemisph]e3 b all ^? p>allels t lie betwixt ?is & ! arctic circle1 :i* be=e 7 :olly above ! horizon1 d n[ int]sect x1 & ! ,sun appe>s to !m to rise & set4 ,f h5ce to ! equator1 we %all f9d t ! days h gradually %ort5$2 & f ! equator ,s\?w>d1 !y h gradually l5g!n$1 until we come to ! #hj? p>allel ( ! ,s\? latitude2 ! upp] "p ( :i* j t\*es ! horizon2 & all places betwixt ?is & ! ,s\? ,pole are 9 total d>kness2 b ^? p>allels betwixt ?is & ! ant>ctic circle1 :i* be=e 7 :olly ^u ! horizon1 are n[ p>tly above x2 ! l5g? ( _! days be+ exactly equal to t ( ! nights 9 ! same latitude 9 ! contr>y hemisph]e4 ,?is also holds univ]sally1 t ! l5g? ( "o day 9 "o latitude ,nor?1 is exactly equal to ! l5g? ( ! night 9 ! same latitude ,s\?2 & vice v]sa4 ,let u aga9 foll[ ! motion ( ! ,sun1 until he has got into ! equ9octial1 & take a view ( ! globe :ile x is 9 ?is position4 ,n[ all ! p>allels ( latitude are cut into two equal p>ts by ! horizon1 & consequ5tly ! days & nights are ( equal l5g?s1 viz4 #ab h\rs ea*1 9 all places ( ! _w2 ! ,sun ris+ & sett+ at six o'clock1 except+ "u ! two ,poles1 :i* n[ lie exactly 9 ! horizon3 ,"h ! ,sun seems to /& /ill 9 ! same po9t ( ! heav5s = "s "t1 until by degrees1 by 8 motion 9 ! ecliptic1 he asc5ds high] to "o & disappe>s to ! o!r1 !re be+ prop]ly no days & nights "u ! ,poles2 = !re ! motion ( ! ,e>? r\nd its axis _c be obs]v$4 ,if we foll[ ! motion ( ! ,sun t[>ds ! ,s\!rn tropic1 we %all see ! diurnal ar*es ( ! ,nor!rn p>allels cont9ually decrease1 & ! ,s\!rn ones increase 9 ! same proportion1 accord+ to _! respective latitudes2 ! ,nor? ,pole cont9ually desc5d+1 & ! ,s\? ,pole asc5d+1 above ! horizon1 until ! ,sun arrives into 1 at :i* "t all ! space )9 ! ant>ctic circle is above ! horizon2 :ile ! space betwe5 ! arctic circle1 & its neighb\r+ ,pole1 is 9 total d>kness4 ,& we %all n[ f9d all o!r circum/ances q rev]se to :at !y 7 :5 ! ,sun 0 9 2 ! nights n[ all ov] ! _w be+ ( ! same l5g? t ! days 7 ( be=e4 ,we h n[ got to ! extremity ( ! ,sun's decl9ation2 & if we foll[ him ?r\gh ! o!r half ( ! ecliptic1 & rectify ! globe accord+ly1 we %all f9d ! seasons return 9 _! ord]1 until at l5g? we br+ ! globe into its fir/ position4 ,! two =ego+ problems 7 n1 z ,i "k (1 publi%$ 9 any book on ?is subject be=e2 & ,i h dwelt ! long] ^u !m1 because !y v well illu/rate h[ ! vicissitudes ( days & nights are made all ov] ! _w1 by ! motion ( ! ,e>? r\nd h] axis2 ! horizon ( ! globe be+ made ! circle1 sep>at+ light & d>kness1 & s ! ,sun to /& /ill 9 ! v]tex4 ,& if we really c\ld move ! m]idian1 accord+ to ! *ange ( ! ,sun's decl9ation1 we %\ld see at "o view1 ! cont9ual *ange made 9 ! l5g? ( days & nights1 9 all places on ! ,e>?2 b z globes are fitt$ up1 ?is _c be done2 nei!r are !y adapt$ = ! common purposes1 9 places ne> ! equator1 or any :]e 9 ! ,s\!rn hemisph]e4 ,b ?is inconv5i5ce is n[ rem$i$ 7at a small additional exp5ce7 by ! h\r circle be+ made to %ift to ei!r ,pole2 & "s globes are n[ made ) an h\r circle fix$ to ! globe at ea* ,pole betwe5 ! globe & m]idian1 s z to h none )\t side to int]rupt ! m]idian f mov+ q r\nd ! wood5 horizon4 ,,prob4 ,,xvii4 ,to %ew by ! globe1 at "o view1 ! longe/ ( ! ,days & ,nights 9 any p>ticul> places1 at all times ( ! ,ye>4 ,because ! ,sun1 by 8 motion 9 ! ecliptic1 alt]s 8 decl9ation a small matt] e day2 if we suppose all ! torrid zone to be fill$ up ) a spiral l9e1 hav+ s _m turn+s2 or a screw hav+ s _m ?reads1 z ! ,sun is days 9 go+ f "o tropic to ! o!r3 ,& ^! ?reads at ! same di/ance f "o ano!r 9 all places1 z ! ,sun alt]s 8 decl9ation 9 "o day 9 all ^? places respectively3 ,?is spiral l9e or screw w repres5t ! app>5t pa?s describ$ by ! ,sun r\nd ! ,e>? e day2 & by foll[+ ! ?read f "o tropic to ! o!r1 & back aga91 we %all h ! pa? ! ,sun seems to describe r\nd ! ,e>? 9 a ye>4 ,b because ! incl9ations ( ^! ?reads to "o ano!r are b small1 we may suppose ea* diurnal pa? to be "o ( ! p>allels ( latitude1 drawn1 or suppos$ to be drawn ^u ! globe4 ,?us mu* be+ premis$1 we %all expla9 ?is ,problem1 by plac+ ! globe accord+ to "s ( ! mo/ rem>kable positions ( x1 z be=e we did = ! mo/ rem>kable seasons ( ! ye>4 ,9 ! prec$+ problem1 ! globe be+ rectifi$ accord+ to ! ,sun's decl9ation1 ! upp] p>ts ( ! p>allels ( latitude1 repres5t$ ! ,diurnal ,ar*es1 or ! l5g? ( ! days all ov] ! _w1 at t p>ticul> "t3 ,"h we are to rectify ! globe accord+ to ! latitude ( ! place1 & !n ! upp] p>ts ( ! p>allels ( decl9ation are ! diurnal ar*es2 & ! l5g? ( ! days at all times ( ! ye>1 may be "h det]m9$ by f9d+ ! numb] ( h\rs conta9$ betwe5 ! two extreme m]idians1 :i* cut any p>allel ( decl9ation 9 ! ,ea/]n & ,we/]n po9ts ( ! horizon2 aft] ! same mann]1 z be=e we f\nd ! l5g? ( ! day 9 ! sev]al latitudes at a p>ticul> "t ( ! ye>4 #a4 ,let ! place propos$ be "u ! equ9octial1 & let ! globe be accord+ly rectifi$ = #jj degrees ( latitude1 :i* is call$ a direct position ( ! sph]e4 ,"h all ! p>allels ( latitude1 :i* 9 ?is case we w call ! p>allels ( decl9ation1 are cut by ! horizon into two equal p>ts2 & consequ5tly ^? :o live "u ! equ9octial1 h ! days & nights ( ! same l5g? at all times ( ! ye>2 & also 9 ?is "p ( ! ,e>?1 all ! ,/>s rise & set1 & _! cont9uance above ! horizon1 is equal to _! /ay bel[ x1 viz4 #ab h\rs4 ,if f ?is position we gradually move ! globe accord+ to ! sev]al alt]ations ( latitudes1 :i* we w suppose to be ,nor!rly2 ! l5g?s ( ! ,diurnal ,ar*es w cont9ually increase1 until we come to a p>allel ( decl9ation1 z f> di/ant f ! equ9octial1 z ! place itself is f ! ,pole4 ,?is p>allel w j t\* ! horizon1 & all ! heav5ly bodies t are betwixt x & ! ,pole nev] desc5d bel[ ! horizon4 ,9 ! mean "t1 :ile we are mov+ ! globe1 ! l5g?s ( ! diurnal ar*es ( ! ,s\!rn p>allels ( decl9ation1 cont9ually dim9i% 9 ! same proportion t ! ,nor!rn ones increas$2 until we come to t p>allel ( decl9ation :i* is s f> di/ant f ! equ9octial ,s\!rly1 z ! place itself is f ! ,nor? ,pole4 ,! upp] "p ( ?is ,p>allel j t\*es ! horizon1 & all ! ,/>s t are betwixt x & ! ,s\? ,pole nev] appe> above ! horizon4 ,& all ! nocturnal ar*es ( ! ,s\!rn p>allels ( decl9ation1 are exactly ( ! same l5g? ) ! diurnal ar*es ( ! correspond5t p>allels ( ,nor? decl9ation4 #b4 ,let u take a view ( ! globe :5 x is rectifi$ = ! latitude ( ,london1 or #ea degrees ,nor?4 ,:5 ! ,sun is 9 ! tropic ( 1 ! day is ab\t #af h\rs2 z he rec$es f ?is tropic1 ! days proportionably %ort51 until1 he arrives into 1 & !n ! days are at ! %orte/1 be+ n[ ( ! same l5g? ) ! night1 :5 ! ,sun 0 9 1 viz4 #g h\rs4 ,! l[] "p ( t p>allel ( decl9ation1 :i* is #ch degrees f ! equ9octial ,nor!rly1 j t\*es ! horizon2 & ! ,/>s t are betwixt ?is p>allel & ! ,nor? ,pole1 nev] set to u at ,london4 ,9 l mann] ! upp] "p ( ! ,s\!rn p>allel ( #ch degrees j t\*es ! horizon1 & ! ,/>s t lie betwixt ?is p>allel & ! ,s\!rn ,pole1 are nev] visible 9 ?is latitude4 ,aga91 let u rectify ! globe = ! latitude ( ! ,arctic ,circle1 we %all !n f9d1 t :5 ! ,sun is 9 1 he t\*es ! horizon on t day )\t sett+1 be+ #bd h\rs compleat above ! horizon2 & :5 he is 9 ,capricorn1 he once appe>s 9 ! horizon1 b does n rise 9 ! space ( #bd h\rs3 ,:5 he is 9 any o!r po9t ( ! ecliptic1 ! days are long] or %ort]1 accord+ to 8 di/ance f ! tropics4 ,all ! ,/>s t lie betwe5 ! tropic ( ,canc]1 & ! ,nor? ,pole1 nev] set 9 ?is latitude2 & ^? t are betwe5 ! tropic ( ,capricorn1 & ! ,s\? ,pole1 are always hid bel[ ! horizon4 ,if we elevate ! globe /ill high]1 ! circle ( p]petual ,app>ition w be ne>] ! equator1 z w t ( p]petual ,occultation on ! o!r side4 ,= example1 ,let u rectify ! globe = ! latitude ( #hj degrees ,nor?3 :5 ! ,sun's decl9ation is #aj degrees ,nor?2 he beg9s to turn above ! horizon )\t sett+2 & all ! :ile he is mak+ 8 progress f ?is po9t to ! tropic ( 1 & back aga91 he nev] sets4 ,aft] ! same mann]1 :5 8 decl9ation is #aj degrees ,s\?1 he is j se5 at noon 9 ! horizon2 & all ! :ile he is go+ ,s\?w>d1 & back aga91 he disappe>s1 be+ hid j s long z be=e1 at ! opposite "t ( ! ye> he appe>$ visible4 ,let u n[ br+ ! ,nor? ,pole into ! ,z5i?1 !n w ! equ9octial co9cide ) ! horizon2 & consequ5tly all ! ,nor!rn p>allels are above ! horizon1 & all ! ,s\!rn ones bel[ x4 ,"h is b "o day & "o night ?r\gh\t ! ye>1 x be+ day all ! :ile ! ,sun is to ! ,nor?w>d ( ! equ9octial1 & night = ! o!r half ye>4 ,all ! ,/>s t h ,nor? decl9ation1 always appe> above ! horizon1 & at ! same height2 & all ^? t are on ! o!r side1 are nev] se54 ,:at has be5 "h said ( rectify+ ! globe to ,nor? latitude1 holds = ! same latitude ,s\?2 only t be=e ! longe/ days 71 :5 ! ,sun 0 9 1 ! same happ5+ n[ :5 ! ,sun is 9 2 & s ( ! re/ ( ! p>allels1 ! seasons be+ directly opposite to ^? :o live 9 diff]5t hemisph]es4 ,i %all aga9 expla9 "s ?+s deliv]$ above 9 g5]al t]ms1 by p>ticul> problems4 ,b f :at has be5 already said1 we may fir/ make ! foll[+ obs]vations3 #a4 ,all places ( ! ,e>? d equally enjoy ! b5efit ( ! ,sun1 9 respect ( "t1 & are equally depriv$ ( x1 ! ,days at "o "t ( ! ,ye>1 be+ exactly equal to ! ,nights at ! opposite season4 #b4 ,9 all places ( ! ,e>?1 save exactly "u ! ,poles1 ! ,days & ,nights are ( equal l5g? 7viz4 #ab h\rs ea*7 :5 ! ,sun is 9 ! equ9octial4 #c4 ,^? :o live "u ! equ9octial1 h ! days & nights ( equal l5g?s at all times ( ! ye>4 #d4 ,9 all places betwe5 ! equ9octial & ! ,poles1 ! days & nights are nev] equal1 b :5 ! ,sun is 9 ! equ9octial po9ts & 4 #e4 ,! ne>] any place is to ! equator1 ! less is ! diff]5ce betwe5 ! l5g? ( ! artificial days & nights 9 ! said place2 & ! m remote ! great]4 #f4 ,to all ! inhabitants ly+ "u ! same p>allel ( latitudes ! days & nights are ( equal l5g?s1 & t at all times ( ! ye>4 #g4 ,! ,sun is v]tical twice a ye> to all places betwe5 ! tropics2 to ^? "u ! tropics1 once a ye>2 b nev] any :]e else4 #h4 ,9 all places betwe5 ! ,pol> ,circles1 & ! ,poles1 ! ,sun appe>s "s numb] ( days )\t sett+2 & at ! opposite "t ( ! ye> he is = ! same l5g? ( "t )\t ris+2 & ! ne>] unto1 or fur!r remote f ! ,pole1 ^? places are1 ! long] or %ort] is ! ,sun's cont9u$ pres5ce or abs5ce f ! ,pole4 #i4 ,9 all places ly+ exactly "u ! ,pol> ,circles1 ! ,sun1 :5 he is 9 ! ne>e/ tropic1 appe>s #bd h\rs )\t sett+2 & :5 he is 9 ! contr>y tropic1 he is = ! same l5g? ( "t1 )\t ris+2 b at all o!r times ( ! ye>1 he rises & sets !re1 z 9 o!r places4 #aj4 ,9 all places ly+ 9 ! 7,nor!rn_/,s\!rn7 hemisph]e1 ! longe/ day & %orte/ night1 is :5 ! ,sun is 9 ! 7,nor!rn_/,s\!rn7 tropic1 & on ! contr>y4 ,,prob4 ,,xviii4 ,! ,latitude ( any place1 n exce$+ #ff degrees1 & ! day ( ! ,mon? be+ giv52 to f9d ! "t ( ,sun-ris+ & sett+1 & ! l5g? ( ! ,day & ,night4 ,hav+ rectifi$ ! globe accord+ to ! latitude1 br+ ! ,sun's place to ! m]idian1 & put ! h\r index to #ab at noon2 !n br+ ! ,sun's place ! ,ea/]n "p ( ! horizon1 & ! index w %ew ! "t :5 ! ,sun rises4 ,aga91 turn ! globe until ! ,sun's place be br\ght to ! ,we/]n side ( ! horizon1 & ! index w %ew ! "t ( ,sun-sett+4 ,! h\r ( ,sun-sett+ d\bl$1 gives ! l5g? ( ! day2 & ! h\r ( ,sun-ris+ d\bl$1 gives ! l5g? ( ! night4 ,let x be requir$ to f9d :5 ! ,sun rises & sets at ,london on ! #bj? ( ,april4 ,rectify ! globe = ! latitude ( ,london1 & hav+ f\nd ! ,sun's place correspond+ to ,may ! #a/1 viz4 #aj degrees1 br+ to #aj degrees to ! m]idian1 & set ! index to #ab at noon2 !n turn ! globe ab\t 'till #aj degrees be br\ght to ! ,ea/]n "p ( ! horizon1 & y'll f9d ! index po9t #d h\rs1 ?is be+ d\bl$1 gives ! l5g? ( ! night #i h\rs4 ,aga91 br+ ! ,sun's place to ! ,we/]n "p ( ! horizon1 & ! index w po9t #g h\rs1 :i* is ! "t ( ,sun-sett+2 ?is be+ d\bl$1 gives ! l5g? ( ! day #ad h\rs4 ,,prob4 ,,xix4 ,to f9d ! l5g? ( ! longe/ & %orte/ ,day & ,night 9 any giv5 place1 n exce$+ #ff degrees ( ,latitude4 ,note1 ,! longe/ day at all places on ! 7,nor?_/,s\?7 side ( ! equator1 is :5 ! ,sun is 9 ! fir/ po9t ( 7,canc]_/,capricorn7 ,:]e=e hav+ rectifi$ ! globe = ! latitude1 f9d ! "t ( ,sun-ris+ & sett+1 & !nce ! l5g? ( ! day & night1 z 9 ! la/ problem1 accord+ to ! place ( ! ,sun3 ,or1 hav+ rectifi$ ! globe = ! latitude1 br+ ! sol/itial po9t ( t hemisph]e1 to ! ,ea/ "p ( ! horizon1 & set ! index to #ab at noon2 !n turn+ ! globe ab\t 'till ! said sol/itial po9t t\*es ! ,we/]n side ( ! horizon1 ! numb] ( h\rs f noon to ! place :]e ! index po9ts 7be+ c\nt$ accord+ to ! motion ( ! index7 is ! l5g? ( ! longe/ day2 ! complem5t :]e( to #bd h\rs1 is ! l5g? ( ! %orte/ night1 & ! rev]se gives ! %orte/ day & ! longe/ night4 ,longe/ ,day4 ,%or4 ,n4 ,deg4 ,h\rs4 ,h\rs4 #de #ae #h ,?us 9 ,lat4 #ea #af #g #fj #ah #e ,if f ! l5g? ( ! longe/ day1 y subtract #ab h\rs1 ! numb] ( half h\rs rema9+1 w be ! ,climate3 ,?us t place :]e ! longe/ day is #af h\rs1 lies 9 ! #i? ,climate4 ,& by ! rev]se1 hav+ ! ,climate1 y h !reby ! l5g? ( ! longe/ day4 ,,prob4 ,,xx4 ,to f9d 9 :at ,latitude ! longe/ ,day is1 ( any giv5 l5g?1 less ?an #bd h\rs4 ,br+ ! sol/itial po9t to ! m]idian1 & set ! index to #ab at noon2 !n turn ! globe ,we/w>d1 'till ! index po9ts at half ! numb] ( h\rs giv52 :i* be+ done1 keep ! globe f turn+ r\nd its axis1 & slide ! m]idian up or d[n 9 ! not*es1 'till ! sol/itial po9t comes to ! horizon1 !n t elevation ( ! ,pole w be ! latitude4 ,if ! h\rs giv5 be #af1 ! latitude is #di degrees2 if #bj h\rs1 ! latitude is #fc degrees4 ,,prob4 ,,xxi4 ,a place be+ giv5 9 "o ( ! ,frigid ,zones 7suppose ! ,nor!rn7 to f9d :at numb] ( ,days 7( #bd h\rs ea*7 ! ,sun do? con/antly %9e ^u ! same1 h[ long he is abs5t1 & also ! fir/ & la/ ,day ( 8 appe>ance4 ,hav+ rectifi$ ! globe accord+ to ! latitude1 turn x ab\t until "s po9t 9 ! fir/ quadrant ( ! ecliptic 7because ! latitude is ,nor?7 int]sects ! m]idian 9 ! ,nor? po9t ( ! horizon2 & "r aga9/ t po9t ( ! ecliptic on ! horizon1 /&s ! day ( ! mon? :5 ! longe/ day beg9s4 ,& if ! globe be turn$ ab\t 'till "s po9t 9 ! second quadrant ( ! ecliptic cuts ! m]idian 9 ! same po9t ( ! horizon1 x w %ew ! ,sun's place :5 ! longe/ day ends1 :5ce ! day ( ! mon? may be f\nd1 z be=e3 ,!n ! numb] ( natural days conta9$ betwe5 ! times ! longe/ day beg9s & ends is ! l5g? ( ! longe/ day requir$4 ,aga91 turn ! globe ab\t1 until "s po9t 9 ! ?ird quadrant ( ! ecliptic cuts ! m]idian 9 ! ,s\? "p ( ! horizon2 t po9t ( ! ecliptic w give ! "t :5 ! longe/ night beg9s4 ,la/ly1 turn ! globe ab\t1 until "s po9t 9 ! f\r? quadrant ( ! ecliptic cuts ! m]idian 9 ! ,s\? po9t ( ! horizon2 & t po9t ( ! ecliptic w be ! place ( ! ,sun :5 ! longe/ night ends4 ,or1 ! "t :5 ! longe/ day or night beg9s1 be+ kn[n1 _! end may be f\nd by c\nt+ ! numb] ( days f t "t to ! succe$+ sol/ice2 !n c\nt+ ! same numb] ( days f ! sol/itial day1 w give ! "t :5 x ends4 ,,prob4 ,,xxii4 ,to f9d 9 :at ,latitude ! longe/ ,day is1 ( any giv5 l5g? less ?an #ahb ,natural ,days4 ,f9d a po9t 9 ! ecliptic half s _m degrees di/ant f ! sol/itial po9t1 z !re are days giv51 & br+ t po9t to ! m]idian2 !n keep ! globe f turn+ r\nd its axis1 & move ! m]idian up or d[n until ! a=esaid po9t ( ! ecliptic comes to ! horizon2 t elevation ( ! ,pole w be ! latitude requir$4 ,if ! days giv5 7 #gh1 ! latitude is #ga degrees4 ,?is me?od is n accurate1 because ! degrees 9 ! ecliptic d n correspond to natural days2 & also because ! ,sun does n always move 9 ! ecliptic at ! same rate2 h[ev]1 su* problems z ^! may s]ve = amusem5ts4 ,,prob4 ,,xxiii4 ,! day ( ! ,mon? be+ giv51 to f9d :5 ! ,morn+ & ,ev5+ ,twilight beg9s & ends1 9 any place ^u ! ,globe4 ,9 ! =ego+ problem1 by ! l5g? ( ! day1 we mean ! "t f ,sun-ris+ to ,sun-set2 & ! night we reckon$ f ,sun-set1 'till he rose next morn+4 ,b x is f\nd by exp]i5ce1 t ,total ,d>kness does n comm5ce 9 ! ev5+1 'till ! ,sun has got #ah degrees bel[ ! horizon2 & :5 he comes )9 ! same di/ance ( ! horizon next morn+1 we h ! fir/ ,dawn ( ,day4 ,?is fa9t light :i* we h 9 ! morn+ & ev5+1 be=e & aft] ! ,sun's ris+ & sett+1 is :at we call ! ,twilight4 #d ,hav+ rectifi$ ! globe = ! latitude1 ! z5i?1 & ! ,sun's place1 turn ! globe & ! quadrant ( altitude until ! ,sun's place cuts #ah degrees bel[ ! horizon 7if ! quadrant rea*es s f>7 !n ! index ^u ! h\r circle w %ew ! beg9n+ or end+ ( twilight aft] ! same mann] z be=e we f\nd ! "t ( ! ,sun-ris+ & sett+1 9 ,prob4 #ah4 ,b by reason ( ! ?ickness ( ! wood5 horizon1 we c't conv5i5tly see1 or compute :5 ! ,sun's place is br\ght to ! po9t a=esaid4 ,:]e=e ! globe be+ rectifi$ z above direct$1 turn ! globe1 & also ! quadrant ( altitude1 ,we/w>d1 until t po9t 9 ! ecliptic1 :i* is opposite to ! ,sun's place1 cuts ! quadrant 9 ! #ah? degree above ! horizon2 !n ! h\r index w %ew ! "t :5 day breaks 9 ! morn+4 ,& if y turn ! globe & ! quadrant ( altitude1 until ! po9t opposite to ! ,sun's place cuts ! quadrant 9 ! ,ea/]n hemisph]e1 ! h\r h& w %ew :5 twilight ends 9 ! ev5+4 ,or1 hav+ f\nd ! "t f midnight :5 ! morn+ twilight beg9s1 if y reckon s _m h\rs be=e midnight1 x w give ! "t :5 ! ev5+ twilight ends4 ,hav+ f\nd ! "t :5 twilight beg9s 9 ! morn+1 f9d ! "t ( ,sun-ris+1 by ,prob4 #ah1 & ! diff]5ce w be ! duration ( twilight4 ,?us at ,london on ! #ab? ( ,may twilight beg9s at ?ree qu>t]s pa/ "o o'clock3 ,! ,sun rises at ab\t half an h\r pa/ f\r3 ,:5ce ! duration ( twilight n[ is #b h\rs1 bo? 9 ! morn+ & ev5+4 ,on ! #ab? ( ,novemb]1 ! twilight beg9s at half an h\r pa/ six1 be+ some:at above an h\r be=e ,sun-ris+4 ,,prob4 ,,xxiv4 ,to f9d ! "t :5 total ,d>kness ceases1 or :5 ! ,twilight cont9ues f ,sun-sett+ to ,sun-sett+1 9 any giv5 place4 ,let ! place be 9 ! ,nor!rn hemisph]e2 !n if ! complem5t ( ! latitude be great] ?an 7! depression7 #ah degrees1 subtract #ah degrees f x1 & ! rema9d] w be ! ,sun's decl9ation ,nor?1 :5 total d>kness ceases4 ,b if ! complem5t ( ! latitude is less ?an #ah degrees1 _! diff]5ce w be ! ,sun's decl9ation ,s\?1 :5 ! twilight beg9s to cont9ue all night4 ,if ! latitude is ,s\?1 ! only diff]5ce w be1 t ! ,sun's decl9ation w be on ! contr>y side4 ,?us at ,london1 :5 ! ,sun's decl9ation ,nor? is great] ?an #bj degrees1 !re is no total d>kness1 b con/ant twilight1 :i* happ5s f ! #bf? ( ,may to ! #ah? ( ,july1 be+ ne> two mon?s4 ,"u ! ,nor? ,pole ! twilight ceases1 :5 ! ,sun's decl9ation is great] ?an #ah degrees ,s\?1 :i* is f ! #ac? ( ,novemb]1 'till ! #bi? ( ,janu>y3 ,s t not)/&+ ! ,sun is abs5t 9 ?is "p ( ! _w = half a ye> toge!r1 yet total d>kness does n cont9ue above #aa weeks2 & besides1 ! ,moon is above ! horizon = a :ole =tnight ( e mon? ?r\gh\t ! ye>4 ,,prob4 ,,xxv4 ,! day ( ! ,mon? be giv52 to f9d ^? places ( ! ,frigid ,zones1 :]e ! ,sun beg9s to %9e cont9ually )\t sett+2 & also ^? places :]e he beg9s to be totally abs5t4 ,br+ ! ,sun's place to ! m]idian1 & m>k ! numb] ( degrees conta9$ betwixt t po9t & ! equator2 !n c\nt ! same numb] ( degrees f ! ne>e/ ,pole 7viz4 ! ,nor? ,pole1 if ! ,sun's decl9ation is ,nor!rly1 o!rwise ! ,s\? ,pole7 t[>ds ! equator1 & note t po9t ^u ! m]idian2 !n turn ! globe ab\t1 & all ! places :i* pass "u ! said po9t1 are ^? :]e ! ,sun beg9s to %9e con/antly1 )\t sett+ on ! giv5 day4 ,if y lay ! same di/ance f ! opposite ,pole t[>ds ! equator1 & turn ! globe ab\t1 all ! places :i* pass "u t po9t1 w be ^? :]e ! longe/ night beg9s4 ,! ,latitude ( ! place be+ giv51 to f9d ! h\r ( ! day :5 ! ,sun %9es4 ,if x be 9 ! summ]1 elevate ! ,pole accord+ to ! latitude1 & set ! m]idian due ,nor? & ,s\?2 !n ! %ad[ ( ! axis w cut ! h\r on ! ,dial plate3 ,= ! globe be+ rectifi$ 9 ?is mann]1 ! h\r circle is a true ,equ9octial ,dial2 ! axis ( ! globe be+ ! ,gnomon4 ,?is holds true 9 ,!ory1 b x might n be v accurate 9 practice1 because ( ! difficulty 9 plac+ ! horizon ( ! globe truly horizontal1 & its m]idian due ,nor? & ,s\?4 ,if x be 9 ! w9t] half ye>1 elevate ! ,s\? ,pole accord+ to ! latitude ,nor?1 & let ! ,nor? "p ( ! horizon be 9 ! ,s\? "p ( ! m]idian2 !n ! %ade ( ! axis w %[ ! h\r ( ! day z be=e3 ,b ?is _c be s conv5i5tly p]=m$1 ?o' ! reason is ! same z 9 ! =m] case4 ,to f9d ! ,sun's altitude1 :5 x %9es1 by ! ,globe4 ,hav+ set ! frame ( ! globe truly horizontal or level1 turn ! ,nor? ,pole t[>ds ! ,sun1 & move ! m]idian up or d[n 9 ! not*es1 until ! axis ca/s no %ad[2 !n ! ar* ( ! m]idian1 conta9$ betwixt ! ,pole & ! horizon1 is ! ,sun's altitude4 ,note1 ,! be/ way to f9d ! ,sun's altitude1 is by a little quadrant graduat$ into degrees1 & hav+ sights & a plummet to x3 ,?us1 hold ! quadrant 9 y\r h&1 s z ! rays ( ! ,sun may pass ?r\gh bo? ! sights1 ! plummet !n hang+ freely by ! side ( ! in/rum5t1 w cut 9 ! limb ! altitude requir$4 ,^! quadrants are to be _h at ! in/rum5t-mak]s1 ) l9es drawn ^u !m1 = f9d+ ! h\r ( ! day1 & ! azimu?2 ) sev]al o!r pretty conclusions1 v ent]ta9+ = beg9n]s4 ,! ,latitude & ! ,day ( ! ,mon? be+ giv51 to f9d ! h\r ( ! day :5 ! ,sun %9es4 ,hav+ plac$ ! wood5 frame ^u a level1 & ! m]idian due ,nor? & ,s\?1 rectify ! globe = ! latitude1 & fix a ne$le p]p5dicul>ly ov] ! ,sun's place3 ,! ,sun's place be+ br\ght to ! m]idian1 set ! h\r index at #ab at noon1 !n turn ! globe ab\t until ! ne$le po9ts exactly to ! ,sun1 & ca/s no %ad[1 & !n ! index w %ew ! h\r ( ! day4 ,,prob4 ,,xxvi4 ,! ,latitude1 ! ,sun's ,place1 & 8 ,altitude1 be+ giv52 to f9d ! h\r ( ! ,day1 & ! ,sun's ,azimu? f ! ,m]idian4 ,hav+ rectifi$ ! globe = ! latitude1 ! z5i?1 & ! ,sun's place1 turn ! globe & ! quadrant ( altitude1 s t ! ,sun's place may cut ! giv5 degree ( altitude3 !n ! index w %[ ! h\r1 & ! quadrant w cut ! azimu? 9 ! horizon4 ,?us1 if at ,london1 on ! #ba/ ( ,augu/1 ! ,suns altitude1 be #cf degrees 9 ! =5oon1 ! h\r ( ! day w be ,,ix1 & ! ,sun's azimu? ab\t #eh degrees f ! ,s\? "p ( ! m]idian4 ,! ,sun's ,azimu? be+ giv51 to place ! ,m]idian ( ! ,globe due ,nor? & ,s\?1 or to f9d a ,m]idian ,l9e :5 ! ,sun %9es4 ,let ! ,sun's azimu? be #cj degrees ,s\?-,ea/]ly1 set ! horizon ( ! globe ^u a level1 & br+ ! ,nor? ,pole into ! z5i?2 !n turn ! horizon ab\t until ! %ade ( ! axis cuts z _m h\rs z is equival5t to ! azimu? 7all[+ #ae degrees to an h\r7 9 ! ,nor?-,we/ "p ( ! h\r circle1 viz4 ,x at night1 :i* be+ done1 ! m]idian ( ! globe /&s 9 ! true m]idian ( ! place4 ,! globe /&+ 9 ?is position1 if y hang two plummets at ! ,nor? & ,s\? po9ts ( ! wood5 horizon1 & draw a l9e betwixt !m1 y w h a m]idian l9e2 :i* if x be on a fix$ plane 7z a floor or w9d[7 x w be a guide = plac+ ! globe due ,nor? & ,s\?1 at any o!r "t4 ,,prob4 ,,xxvii4 ,! ,latitude1 ,h\r ( ! ,day1 & ! ,sun's place be+ giv51 to f9d ! ,sun's ,altitude & ,azimu?4 ,rectify ! globe = ! latitude1 ! z5i?1 & ! ,sun's place1 !n ! numb] ( degrees conta9$ betwixt ! ,sun's place & ! v]tex1 is ! ,sun's m]idional z5i? di/ance2 ! complem5t ( :i* to #ij degrees1 is ! ,sun's m]idian altitude4 ,if y turn ! globe ab\t until ! index po9ts to any o!r giv5 h\r1 !n br++ ! quadrant ( altitude to cut ! ,sun's place1 y w h ! ,sun's altitude at t h\r2 & :]e ! quadrant cuts ! horizon1 is ! ,sun's azimu? at ! same "t4 ,?us ,may ! #a/ at ,london1 ! ,sun's m]idian altitude w be #fa degrees2 & at #aj o'clock 9 ! morn+1 ! ,sun's altitude w be #eb degrees1 & 8 azimu? ab\t #ej degrees f ! ,s\? "p ( ! m]idian4 ,,prob4 ,,xxviii4 ,! ,latitude ( ! place1 & ! day ( ! ,mon? be+ giv52 to f9d ! depression ( ! ,sun bel[ ! ,horizon1 & ! ,azimu? at any ,h\r ( ! ,night4 ,hav+ rectifi$ ! globe = ! latitude1 ! z5i?1 & ! ,sun's place1 take a po9t 9 ! ecliptic exactly opposite to ! ,sun's place1 & f9d ! ,sun's altitude & azimu?1 z by ! la/ problem1 & ^! w be ! depression & ! altitude requir$4 ,?us1 if ! "t giv5 be ! #a/ ( ,decemb]1 at #aj o'clock at night1 ! depression & azimu? w be ! same z 0 f\nd 9 ! la/ problem4 ,,prob4 ,,xxix4 ,! ,latitude1 ! ,sun's ,place1 & 8 ,azimu? be+ giv51 to f9d 8 ,altitude1 & ! ,h\r4 ,rectify ! globe = ! latitude1 ! z5i?1 & ! ,sun's place1 !n put ! quadrant ( altitude to ! ,sun's azimu? 9 ! horizon1 & turn ! globe 'till ! ,sun's place meet ! edge ( ! quadrant1 !n ! said edge w %ew ! altitude1 & ! index po9t to ! h\r4 ,?us1 ,may ! #ba/ at ,london :5 ! ,sun is due ,ea/1 8 altitude w be ab\t #bd degrees1 & ! h\r ab\t ,,vii 9 ! morn+2 & :5 8 azimu? is #fj degrees ,s\?-,we/]ly1 ! altitude w be ab\t #dd degrees1 & ! h\r ab\t #b 9 ! aft]noon4 ,?us1 ! latitude & ! day be+ kn[n1 & hav+ besides ei!r ! altitude1 ! azimu?1 or ! h\r2 ! o!r two may be easily f\nd4 ,,prob4 ,,xxx4 ,! ,latitude1 ! ,sun's ,altitude1 & 8 ,azimu? be+ giv52 to f9d 8 ,place 9 ! ,ecliptic & ! ,h\r4 ,rectify ! globe = ! latitude & z5i?1 & set ! edge ( ! quadrant to ! giv5 azimu?2 !n turn+ ! globe ab\t1 t po9t ( ! ecliptic :i* cuts ! altitude1 w be ! ,sun's place4 ,keep ! quadrant ( ! altitude 9 ! same position1 & hav+ br\ght ! ,sun's place to ! m]idian1 & ! h\r index to #ab at noon1 turn ! globe ab\t 'till ! ,sun's place cuts ! quadrant ( altitude1 & !n ! index w po9t ! h\r ( ! day4 ,,prob4 ,,xxxi4 ,! ,decl9ation & ,m]idian ,altitude ( ! ,sun1 or ( any ,/> be+ giv52 to f9d ! ,latitude ( ! ,place4 ,m>k ! po9t ( decl9ation ^u ! m]idian1 accord+ z x is ei!r ,nor? or ,s\? f ! equator2 !n slide ! m]idian up or d[n 9 ! not*es1 'till ! po9t ( decl9ation be s f> di/ant f ! horizon1 z is ! giv5 m]idian altitude2 t elevation ( ! ,pole w be ! latitude4 ,?us1 if ! ,sun's1 or any ,/>'s m]idian altitude be #ej degrees1 & its decl9ation #aa degrees ,nor?1 ! latitude w be #ea degrees ,nor?4 ,,prob4 ,,xxxii4 ,! ,day & ,h\r ( a ,lun> ,eclipse be+ kn[n2 to f9d all ^? ,places ^u ! ,globe :]e ! same w be visible4 #e ,f9d :]e ! ,sun is v]tical at ! giv5 h\r1 & br+ t po9t to ! z5i?2 !n ! ,eclipse w be visible 9 all ^? places t are "u ! horizon2 ,or1 if y br+ ! ,antipodes to ! place :]e ! ,sun is v]tical1 into ! z5i?1 y w h ! places :]e ! ,eclipse w be visible above ! horizon4 ,note1 ,because ,lun> eclipses cont9ue sometimes = a long :ile toge!r1 !y may be se5 9 m places ?an "o hemisph]e ( ! ,e>?2 = by ! ,e>?'s motion r\nd its axis1 dur+ ! "t ( ! eclipse1 ! ,moon w rise 9 sev]al places aft] ! eclipse began4 ,note1 ,:5 an eclipse ( ! ,sun is c5tral1 if y br+ ! place :]e ! ,sun is v]tical at t "t1 into ! z5i?1 "s "p ( ! eclipse w be visible 9 mo/ places )9 ! upp] hemisph]e2 b by reason ( ! %ort duration ( ,sol> eclipses1 & ! latitude :i* ! ,moon commonly has at t "t 7?o' b small7 !re is no c]ta9ty 9 det]m9+ ! places :]e ^? eclipses w be visible by ! globe2 b rec\rse mu/ be _h to calculations4 ,,prob4 ,,xxxiii4 ,! ,day ( ! ,mon?1 & ,h\r ( ! ,day1 accord+ to our way ( reckon+ 9 ,engl&1 be+ giv52 to f9d !reby ! ,babylonic1 ,italic1 & ! ,jewi%1 or ,judaical ,h\r4 #a4 ,to f9d ! ,babylonic ,h\r 7:i* is ! numb] ( h\rs f ,sun-ris+47 ,hav+ f\nd ! "t ( ,sun-ris+ 9 ! giv5 place1 ! diff]5ce betwixt ?is & ! h\r giv51 is ! ,babylonic ,h\r4 #b4 ,to f9d ! ,italic ,h\r 7:i* is ! numb] ( h\rs f ,sun-sett+47 ,subtract ! h\r ( ,sun-sett+ f ! giv5 h\r1 & ! rema9d] w be ! ,italic ,h\r requir$4 #c4 ,to f9d ! ,jewi% ,h\r 7:i* is _/ "p ( an ,artificial ,day47 ,f9d h[ _m h\rs ! day consi/s (2 !n say1 z ! numb] ( h\rs ! day consi/s ( is to #ab h\rs1 s is ! h\r s9ce ,sun-ris+ to ! ,judaical h\r requir$4 ,?us1 if ! ,sun rises at #d o'clock 7consequ5tly sets at #h7 & ! h\r giv5 be #e 9 ! ev5+1 ! ,babyloni% h\r w be ! #ac?1 ! ,italic ! #ba/ & ! ,jewi% h\r w be n9e & ?ree qu>t]s4 ,! conv]se be+ giv51 ! h\r ( ! day1 accord+ to our way ( reckon+ 9 ,engl&1 may be easily f\nd4 ,! foll[+ ,problems are peculi> to ! ,cele/ial ,globe4 ,,prob4 ,,xxxiv4 ,to f9d ! ,"r ,asc5sion & ,decl9ation ( ! ,sun1 or any ,fix$ ,/>4 ,br+ ! ,sun's place 9 ! ecliptic to ! m]idian2 !n t degree ( ! equator1 :i* is cut by ! m]idian1 w be ! ,sun's ,"r ,asc5sion2 & t degree ( ! m]idian1 :i* is exactly ov] ! ,sun's place1 is ! ,sun's ,decl9ation4 ,aft] ! same mann]1 br+ ! place ( any ,fix$ ,/> to ! m]idian1 & y w f9d its ,"r ,asc5sion 9 ! equ9octial1 & ,decl9ation ( ! m]idian4 ,?us1 ! "r asc5sion & decl9ation is f\nd1 aft] ! same mann] z ! longitude & latitude ( a place ^u ! ,t]re/rial ,globe4 ,note1 ,! "r asc5sion & decl9ation ( ! ,sun v>y e day2 b ! "r asc5sion1 c4 ( ! ,fix$ ,/>s is ! same ?r\gh\t ! ye>#f4 ,! ,sun's ,"r ,asc5sion4 ,decl94 ,deg4 ,deg4 ,janu>y #ca #cad #ag ,s4 ,april #e #ad #f ,n4 ,?us on ,july #ba #abj #bj ,n4 ,novemb] #bf #bdb #ba ,s4 ,r4 ,asc4 ,dcl4 ,deg4 ,deg4 ,aldeb>an #fe #af ,n4 ,spica ,virg9is #aig #i ,s4 ,capella #gd #de ,n4 ,syrius1 or ! ,dog-,/> #ih #af ,s4 ,note1 ,! decl9ation ( ! ,sun may be f\nd aft] ! same mann] by ! ,t]re/rial ,globe1 & also 8 "r asc5sion1 :5 ! equ9octial is numb]$ into #cfj degrees1 comm5c+ at ! equ9octial po9t 3 ,b z ! equ9octial is n always numb]$ s1 & ?is be+ prop]ly a ,problem 9 ,a/ronomy1 we *oose r to place x "h4 ,by ! conv]se ( ?is problem1 hav+ ! "r asc5sion & decl9ation ( any po9t giv51 t po9t itself may be easily f\nd ^u ! globe4 ,,prob4 ,,xxxv4 ,to f9d ! ,longitude & ,latitude ( a giv5 ,/>4 ,hav+ br\ght ! sol/itial colure to ! m]idian1 fix ! quadrant ( altitude ov] ! prop] ,pole ( ! ecliptic1 :e!r x be ,nor? or ,s\?2 !n turn ! quadrant ov] ! giv5 ,/>1 & ! ar* conta9$ betwixt ! ,/> & ! ecliptic1 w be ! latitude1 & ! degree cut on ! ecliptic w be ! ,/>'s longitude4 ,?us ! latitude ( ,arcturus w be f\nd to be #ca degrees ,nor?1 & ! longitude #bjj degrees f 1 or #bj degrees f 3 ,! latitude ( ,fomalhaut 9 ! ,s\!rn ,fi%1 #ba degrees ,s\?1 & longitude #bii degrees1 or #bi degrees4 ,by ! conv]se ( ?is me?od1 hav+ ! latitude & longitude ( a ,/> giv51 x w be easy to f9d ! ,/> ^u ! globe4 ,! di/ance betwixt two ,/>s1 or ! numb] ( degrees conta9$ betwixt !m1 may be f\nd by lay+ ! quadrant ( altitude ov] ea* ( !m1 & c\nt+ ! numb] ( degrees int]cept$2 aft] ! same mann] z we f\nd ! di/ance betwixt two places on ! ,t]re/rial ,globe1 9 ,prob4 ,,vii4 ,,prob4 ,,xxxvi4 ,! ,latitude ( ! ,place1 ! ,day ( ! ,mon?1 & ! ,h\r be+ giv52 to f9d :at ,/>s are !n ris+ or sett+1 :at ,/>s are culm9at+1 or on ! m]idian1 & ! ,altitude & ,azimu? ( any ,/> above ! ,horizon2 & also h[ to di/+ui% ! ,/>s 9 ! ,heav5s "o f ! o!r1 & to "k !m by _! prop] ,names4 ,hav+ rectifi$ ! globe = ! latitude1 ! z5i?1 & ! ,sun's place1 turn ! globe ab\t until ! index po9ts to ! giv5 h\r1 ! globe be+ kept 9 ?is position4 ,all ^? ,/>s t are 9 7,ea/]n_/,we/]n7 side ( ! horizon1 are !n 7,ris+_/,sett+74 ,all ^? ,/>s t are "u ! m]idian1 are !n culm9at+4 ,& if ! quadrant ( altitude be laid ov] ! c5t] ( any p>ticul> ,/>1 x w %[ t ,/>'s altitude at t "t2 & :]e x cuts ! horizon1 w be ! ,/>'s azimu? f ! ,nor? or ,s\? "p ( ! m]idian4 ,! globe be+ kept 9 ! same elevation1 & f turn+ r\nd its axis1 move ! wood5 frame ab\t until ! ,nor? & ,s\? po9ts ( ! horizon lie exactly 9 ! m]idian2 !n "r l9es imag9$ to pass f ! c5t] ?ro' ea* ,/> ^u ! surface ( ! globe1 w po9t out ! real ,/> 9 ! heav5s1 :i* ^? on ! globe are made to repres5t4 ,& if y are by ! side ( "s wall ^: be>+ y "k1 lay ! quadrant ( altitude to t be>+ 9 ! horizon1 & x w cut all ^? ,/>s :i* at t v "t are to be se5 9 ! same direction1 or close by ! side ( ! said wall4 ,?us kn[+ "s ( ! rem>kable ,/>s 9 any "p ( ! heav5s1 ! neighb\r+ ,/>s may be di/+ui%$ by obs]v+ _! situations ) respect to ^? t are already kn[n1 & comp>+ !m ) ! ,/>s drawn ^u ! globe4 ,?us1 if y turn y\r face t[>ds ! ,nor?1 y w f9d ! ,nor? ,pole ( ! globe po9ts to ! ,pole-,/>2 !n y may obs]ve two ,/>s some:at less bright ?an ! ,pole-,/>1 almo/ 9 a "r l9e ) x1 & f\r m :i* =m a sort ( quadrangle2 ^! sev5 ,/>s make ! con/ellation call$ ! ,little ,be>2 ! ,pole ,/> be+ 9 ! tip ( ! tail4 ,9 ?is neighb\rhood y w obs]ve sev5 bright ,/>s1 :i* are commonly call$ ,*>les's ,wane2 ^! are ! bright ,/>s 9 ! ,great ,be>1 & =m mu* su* ano!r figure ) ^? be=e-m5tion$ 9 ! little ,be>3 ,! two =emo/ ( ! squ>e lie almo/ 9 a "r l9e ) ! ,pole ,/>1 & are call$ ! ,po9t]s1 s t kn[+ ! ,po9t]s1 y may easily f9d ! ,pole-,/>4 ,?us ! re/ ( ! ,/>s 9 ?is con/ellation1 & all ! ,/>s 9 ! neighb\r+ con/ellations may be easily f\nd1 by obs]v+ h[ ! unkn[n ,/>s lie ei!r 9 quadrangles1 triangles1 or /rait l9es f ^? t are already kn[n ^u ! globe4 ,aft] ! same mann] ! globe be+ rectifi$1 y may di/+ui% ^? ,/>s t are to ! ,s\?w>d ( y1 & be soon acqua9t$ ) all ! ,/>s t are visible 9 our hemisph]e4 ,,s*olium4 ,! globe be+ rectifi$ to ! latitude ( any place1 if y turn x r\nd its axis1 all ^? ,/>s t d n g bel[ ! horizon dur+ a :ole revolution ( ! globe1 nev] set 9 t place2 & ^? t d n come above ! horizon nev] rise4 ,,prob4 ,,xxxvii4 ,! latitude ( ! place be+ giv52 to f9d ! ,amplitude1 ,oblique ,asc5sion & ,desc5sion1 ,asc5sional ,diff]5ce1 ,semi-diurnal ,ar*1 & ! "t ( cont9uance above ! horizon1 ( any giv5 po9t 9 ! heav5s4 ,hav+ rectifi$ ! globe = ! latitude1 & br\ght ! giv5 po9t to ! m]idian1 set ! index to ! h\r ( #ab2 !n turn ! globe until ! giv5 po9t be br\ght to ! ,ea/]n side ( ! horizon1 & t degree ( ! equ9octial :i* is cut by ! horizon at t "t1 w be ! ,oblique ,asc5sion2 & :]e ! giv5 po9t cuts ! horizon1 is ! ,amplitude ,ortive3 ,if ! globe be turn$ ab\t until ! giv5 po9t be br\ght to ! ,we/]n side ( ! horizon1 x w !re %[ ! ,amplitude ,occasive2 & :]e ! horizon cuts ! equ9octial at t "t1 is ! ,oblique ,desc5sion4 ,! "t betwe5 ! index at ei!r ( ^! two positions1 & ! h\r ( #f2 or half ! diff]5ce betwe5 ! oblique asc5sion & desc5sion is ! ,asc5sional ,diff]5ce4 ,if ! place be 9 ,nor? latitude & ! decl9ation ( ! giv5 po9t be 7,nor?_/,s\?7 ! asc5sional diff]5ce r$uc$ into "t1 & 7add$ to_/subtract$ f7 #f o',clock1 gives ! ,semi-diurnal ,ar*2 ! complem5t :]e( to a semicircle1 is ! ,semi-nocturnal ,ar*4 ,if ! place be 9 ,s\? latitude1 !n ! contr>y is to be obs]v$ ) respect to ! decl9ation4 ,! semi-7diurnal_/nocturnal7 ar* be+ d\bl$1 gives ! "t ( cont9uance 7above_/bel[7 ! horizon4 ,or ! "t ( cont9uance above ! horizon1 may be f\nd by c\nt+ ! numb] ( h\rs conta9$ 9 ! upp] "p ( ! hor>y circle1 betwixt ! place :]e ! index po9t$ :5 ! giv5 po9t 0 9 ! ,ea/]n or ,we/]n p>ts ( ! horizon4 ,if ! giv5 po9t 0 ! ,sun's place1 ! index po9t$ ! "t ( 8 ris+ & sett+1 :5 ! said place 0 9 ! ,ea/]n & ,we/]n p>ts ( ! horizon1 z 9 ,prob4 #ah4 ,or ! "t ( ,sun-ris+ may be f\nd by add+ or subtract+ 8 asc5sional diff]5ce1 to or f ! h\r ( six1 accord+ z ! latitude & decl9ation are ei!r contr>y or ! same way4 ,?us1 at ,london1 on ! #ca/ ( ,may1 ! ,sun's ,amplitude is #bd degrees ,nor!rly4 ,oblique ,asc5sion1 #bj4 ,oblique ,desc5sion1 #eh4 ,asc5sional ,diff]5ce1 #ai4 ,semi-diurnal ,ar*1 #aji4 ,8 cont9uance above ! horizon1 #ad h\rs4 ,sun rises at ?ree qu>t]s pa/ f\r4 ,sun sets a qu>t] pa/ sev54 ,^! ?+s = ! ,sun v>y e day2 b = a ,fix$ ,/> ! day ( ! mon? ne$ n be giv51 = !y are ! same all ! ye> r\nd4 ,9 ! latitude ( #ea ,nor?1 ,syrus's ,amplitude is ab\t #bh degrees ,s\!rly4 ,oblique ,asc5sion1 #aba4 ,oblique ,desc5sion1 #ge4 ,asc5sional ,diff]5ce1 #bc4 ,semi-diurnal ,ar*1 #fg4 ,cont9uance above ! horizon1 #i h\rs4 ,,prob4 ,,xxxviii4 ,! ,latitude & ! ,day ( ! ,mon? be+ giv52 to f9d ! ,h\r :5 any kn[n ,/> w be ^u ! m]idian1 & also ! "t ( its ris+ & sett+4 ,hav+ rectifi$ ! globe = ! latitude ( ! ,sun's place1 br+ ! giv5 ,/> to ! m]idian1 & also to ! ,ea/ or ,we/ side ( ! horizon1 & ! index w %ew accord+ly :5 ! ,/> culm9ates1 or ! "t ( ! ris+ or sett+4 ,?us at ,london1 on ! #ba/ ( ,janu>y1 ,syrius w be ^u ! m]idian1 at a qu>t] pa/ t5 9 ! ev5+2 rises at #e h\rs1 & sets at ?ree qu>t]s pa/ two 9 ! morn+4 ,by ! conv]se ( ?is problem1 kn[+ ! "t :5 any ,/> is ^u ! m]idian1 y may easily f9d ! ,sun's place4 ,?us1 br+ ! giv5 ,/> to ! m]idian1 & set ! index to ! giv5 h\r2 !n turn ! globe 'till ! index po9ts to #ab at noon1 & ! m]idian w cut ! ,sun's place 9 ! ecliptic4 ,?us :5 ,syrius comes to ! m]idian at #aj h\rs aft] noon1 ! ,sun's place w be deg4 ,,prob4 ,,xxxix4 ,to f9d at :at "t ( ! ,ye> a giv5 ,/> w be ^u ! ,m]idian1 at a giv5 ,h\r ( ! ,night4 ,br+ ! ,/> to ! m]idian1 & set ! index to ! giv5 h\r1 !n turn he globe 'till ! index po9ts to #ab at noon1 & ! m]idian w cut ! ecliptic 9 ! ,sun's place2 :5ce ! day ( ! mon? may be easily f\nd 9 ! kal5d> ^u ! horizon4 ,,prob4 ,,xl4 ,! ,day ( ! ,mon?1 & ! ,azimu? ( any kn[n ,/> be+ giv52 to f9d ! ,h\r ( ! ,night4 ,hav+ rectifi$ ! globe = ! latitude & ! ,sun's place1 if ! giv5 ,/> be due ,nor? or ,s\?1 br+ x to ! m]idian1 & ! index w %[ ! h\r ( ! night4 ,if ! ,/> be 9 any o!r direction1 fix ! quadrant ( altitude 9 ! z5i?1 & set x to ! ,/>'s azimu? 9 ! horizon2 !n turn ! globe ab\t until ! quadrant cuts ! c5t] ( ! ,/>1 & ! index w %ew ! h\r ( ! night4 ,! be>+ ( any po9t 9 ! heav5s may be f\nd by ! foll[+ me?ods4 ,hav+ a m]idian l9e drawn 9 two w9d[s1 t are opposite to "o ano!r1 y may cross x at "r angles ) ano!r l9e repres5t+ ! ,ea/ & ,we/2 f ! po9t ( ! int]section describe a circle1 & divide ea* quadrant into #ij degrees2 !n get a smoo? bo>d1 ( ab\t #b feet long1 & foot broad 7m or less1 z y judge conv5i5t7 & on ! back "p ( x fix ano!r small bo>d crossways1 s t x may s]ve z a foot to support ! bigge/ bo>d upright1 :5 x is set ^u a level1 or an horizontal plane4 ,! bo>d be+ ?us prep>$1 set ! l[] edge ( ! smoo?1 or =e side ( x1 close to ! c5t] ( ! circle1 !n turn x ab\t to ! m]idian1 or to any azimu? po9t requir$ 7keep+ ! edge ( x always close to ! c5t]7 & ca/+ y\r eye along ! flat side ( x1 y w easily p]ceive :at ,/>s are ^u ! m]idian1 or any o!r be>+ t ! bo>d is set to4 ,,prob4 ,,xli4 ,two kn[n ,/>s hav+ ! same ,azimu?1 or ! same ,height1 be+ giv52 to f9d ! ,h\r ( ! ,night4 ,rectify ! globe = ! latitude1 ! z5i?1 & ! ,sun's place4 #a4 ,:5 ! two ,/>s are 9 ! same azimu?1 turn ! globe1 & also ! quadrant ab\t1 until bo? ,/>s co9cide ) ! edge !re(2 !n w ! index %ew ! h\r ( ! night2 & :]e ! quadrant cuts ! horizon1 is ! common azimu? ( bo? ,/>s4 #b4 ,if ! two ,/>s are ( ! same altitude1 move ! globe s t ! same degree on ! quadrant w cut bo? ,/>s1 !n ! index w %ew ! h\r4 ,?is problem is useful :5 ! quantity ( ! azimu? ( ! two ,/>s 9 ! fir/ case1 or ( _! altitude 9 ! latt] case1 is n kn[n4 ,if two ,/>s 7 giv51 "o on ! m]idian1 & ! o!r 9 ! ,ea/ or ,we/ "p ( ! horizon2 to f9d ! ,latitude4 ,br+ t ,/> :i* 0 obs]v$ on ! m]idian1 to ! m]idian ( ! globe1 & keep ! globe f turn+ r\nd its axis2 !n slide ! m]idian up or d[n 9 ! not*es1 'till ! o!r ,/> is br\ght to ! ,ea/ or ,we/ "p ( ! horizon1 & t elevation ( ! ,pole w be ! ,latitude s\ght4 ,,prob4 ,,xlii4 ,! ,latitude1 ,day ( ! ,mon?1 & ! ,altitude ( any kn[n ,/> be+ giv52 to f9d ! ,h\r ( ! ,night4 ,rectify ! globe = ! latitude1 z5i?1 & ,sun's place3 ,turn ! globe1 & ! quadrant ( altitude1 backw>d or =w>d1 'till ! c5t] ( t ,/> meets ! quadrant 9 ! degree ( altitude giv52 !n ! index w po9t ! true h\r ( ! night2 & also :]e ! quadrant cuts ! horizon1 w be ! azimu? ( ! ,/> at t "t4 ,if ! ,latitude1 ! ,sun's ,altitude1 & 8 ,decl9ation 7in/ead ( 8 ,place 9 ! ,ecliptic7 are giv52 to f9d ! ,h\r ( ! ,day & ,azimu?4 ,rectify ! globe = ! latitude & z5i?1 & hav+ br\ght ! equ9octial colure to ! m]idian1 set ! index to #ab at noon2 :i* be+ done1 turn ! globe & ! quadrant1 until ! giv5 decl9ation 9 ! equ9octial colure1 cuts ! altitude on ! quadrant2 !n ! index w %ew ! ,h\r ( ! day1 & ! quadrant cut ! ,azimu? 9 ! horizon4 ,if ! ,altitude ( two ,/>s on ! same ,azimu? 7 giv52 to f9d ! ,latitude ( ! ,place4 ,set ! quadrant ov] bo? ,/>s at ! obs]v$ degrees ( altitude1 & keep x fa/ ^u ! globe ) y\r f+]s2 !n slide ! m]idian up or d[n 9 ! not*es1 'till ! quadrant cuts ! giv5 azimu? 9 ! horizon2 t elevation ( ! ,pole w be ! latitude requir$4 ,,prob4 ,,xliii4 ,hav+ ! ,latitude ( ! place1 to f9d ! degree ( ! ,ecliptic1 :i* rises or sets ) a giv5 ,/>2 & f !nce to det]m9e ! "t ( its ,cosmical & ,a*ronical ris+ & sett+4 ,hav+ rectifi$ ! globe = ! latitude1 br+ ! giv5 ,/> to ! ,ea/]n side ( ! horizon1 & m>k :at degree ( ! ecliptic rises ) x3 ,look = t degree 9 ! wood5 horizon1 & "r aga9/ x1 9 ! kal5d>1 y w f9d ! mon? & day :5 ! ,/> rises ,cosmically4 ,if y br+ ! ,/> to ! ,we/]n side ( ! horizon1 t degree ( ! ecliptic :i* rises at t "t1 w give ! day ( ! mon? :5 ! said ,/> sets ,cosmically4 ,s likewise aga9/ ! degree :i* sets ) ! ,/>1 y w f9d ! day ( ! mon? ( ! ,a*ronical sett+2 & if y br+ x to ! ,ea/]n "p ( ! horizon1 t degree :i* sets at t "t w be ! ,sun's place :5 ! ,/> rises ,a*ronically4 ,?us1 9 ! latitude ( ,london1 ,syrius1 or ! ,dog-,/>1 rises ,cosmically ! #aj? ( ,augu/1 & sets ,cosmically ! #aj? ( ,octob]4 ,aldeb>an1 or ! ,bull's ,eye1 rises ,a*ronically on ! #bb;d ( ,may1 & sets ,a*ronically on ! #ai? ( ,decemb]4 ,,prob4 ,,xliv4 ,hav+ ! ,latitude ( ! place1 to f9d ! "t :5 a ,/> rises & sets ,heliacally4 ,hav+ rectifi$ ! globe = ! latitude1 br+ ! ,/> to ! ,ea/]n side ( ! horizon1 & turn ! quadrant r\nd to ! ,we/]n side1 'till x cuts ! ecliptic 9 #ab degrees ( altitude above ! horizon1 if ! ,/> be ( ! fir/ magnitude2 !n t po9t ( ! ecliptic :i* is cut by ! quadrant1 is #ab degrees high above ! ,we/]n "p ( ! horizon1 :5 ! ,/> rises2 b at ! same "t ! opposite po9t 9 ! ecliptic is #ab degrees bel[ ! ,ea/]n "p ( ! horizon1 :i* is ! depression ( a ,/> ( ! fir/ magnitude1 :5 %e rises ,heliacally2 or has got s f> f ! ,sun's beams1 t %e may be se5 9 ! morn+ be=e ,sun-ris+4 ,:]e=e look = ! said po9t ( ! ecliptic on ! horizon1 & "r aga9/ x w be ! day ( ! mon? :5 ! ,/> rises ,heliacally4 ,to f9d ! ,heliacal sett+1 br+ ! ,/> to ! ,we/ side ( ! horizon1 & turn ! quadrant ab\t to ! ,ea/]n side1 'till ! #ab? degree ( x above ! horizon1 cuts ! ecliptic2 !n t degree ( ! ecliptic :i* is opposite to ?is po9t1 is ! ,sun's place :5 ! ,/> sets ,heliacally4 ,?us y w f9d t ,arcturus rises ,heliacally ! #bh? ( ,septemb]1 & sets ,heliacally ,decemb] ! #b;d4 ,,prob4 ,,xlv4 ,to f9d ! place ( any ,planet ^u ! globe2 & s by t means1 to f9d its place 9 ! ,heav5s3 ,also to f9d at :at ,h\r any ,planet w rise or set1 or be on ! m]idian at any "o ,day 9 ! ,ye>4 ,y mu/ fir/ seek 9 an ,ephem]is 7,:ite's ,ephem]is w d well en\gh7 = ! place ( ! ,planet propos$ on t day2 !n m>k t po9t ( ! ecliptic1 ei!r ) *alk1 or by /ick+ on a little black pat*2 & !n = t night y may p]=m any problem1 z be=e1 by a ,fix$ ,/>4 ,let x be requir$ to f9d ! situation ( ,jupit] among ! ,fix$ ,/>s 9 ! heav5s1 & also :at "t he rises & sets1 & comes to ! m]idian on ! #ai? ( ,may1 #ageg1 ,n4 ,s4 at ,london4 ,look+ = ! #ai? ( ,may1 #ageg1 9 ,:ite's ,ephem]is1 ,i f9d t ,jupit]'s place at t "t is 9 ab\t #ab degrees ( 2 latitude ab\t #a degree ,nor?4 ,!n look+ = t po9t ^u ! ,cele/ial globe1 ,i f9d t is !n ne>ly 9 conjunction ) ! bright ,/> 9 ! ,s\!rn ,balance1 & ab\t #a degree ,nor? ( x4 ,to f9d :5 he rises & sets1 & comes to ! m]idian3 ,hav+ put a little black pat* on ! place ( ,jupit]1 elevate ! globe accord+ to ! latitude1 & hav+ br\ght ! ,sun's place to ! m]idian1 set ! h\r index to #ab at noon2 !n turn ! m>k :i* 0 made = ,jupit]1 to ! ,ea/]n "p ( ! horizon1 ,i f9d w rise some:at m ?an half an h\r aft] ?ree 9 ! aft]noon2 & turn+ ! globe ab\t1 ,i f9d x comes to ! m]idian a little be=e elev5 at night2 & sets almo/ a qu>t] pa/ six next morn+4 ,?is example be+ und]/ood1 x w be easy to f9d :5 ei!r ( ! o!r two sup]ior ,planets1 viz4 ,m>s & ,saturn1 rise1 set1 & come to ! m]idian4 ,i %all conclude ?is subject ab\t ! ,globes ) ! foll[+ problems4 ,,prob4 ,,xlvi4 ,to f9d all t space ^u ! ,e>?1 :]e an ,eclipse ( "o ( ! ,satellites ( ,jupit] w be visible4 ,hav+ f\nd t place ^u ! ,e>?1 9 :i* ! ,sun is v]tical at ! "t ( ! eclipse1 by ,prob4 #ac1 elevate ! globe accord+ to ! latitude ( ! said place2 !n br+ ! place to ! m]idian1 & set ! h\r index to #ab at noon4 ,if ,jupit] be 9 consequ5ce ( ! ,sun1 draw a l9e ) black lead1 or ! l1 along ! ,ea/]n side ( ! horizon1 :i* l9e1 w pass ov] all ^? places :]e ! ,sun is sett+ at t "t2 !n c\nt ! diff]5ce betwixt ! "r asc5sion ( ! ,sun1 & t ( ,jupit]1 & turn ! globe ,we/w>d1 'till ! h\r index po9ts to ?is diff]5ce2 !n keep ! globe f turn+ r\nd its axis1 & elevate ! m]idian1 accord+ to ! decl9ation ( ,jupit]4 ,! globe be+ 9 ?is position1 draw a l9e along ! ,ea/]n side ( ! horizon2 !n ! space betwe5 ?is l9e1 & ! l9e be=e drawn1 w compreh5d all ^? places ( ! ,e>? :]e ,jupit] w be visible1 f ! sett+ ( ! ,sun1 to ! sett+ ( ,jupit]4 ,b if ,jupit] be 9 antec$5ce ( ! ,sun 7i4 e4 rises be=e him7 hav+ br\ght ! place :]e ! ,sun is v]tical1 to ! z5i?1 & put ! h\r index to #ab at noon1 draw a l9e on ! ,we/]n side ( ! horizon2 !n elevate ! globe accord+ to ! decl9ation ( ,jupit]1 & turn x ab\t ,ea/w>d1 until ! index po9ts to s _m h\rs di/ant f noon1 z is ! diff]5ce ( "r asc5sion ( ! ,sun & ,jupit]4 ,! globe be+ 9 ?is position1 draw a l9e along ! ,we/]n side ( ! horizon2 !n ! space conta9$ betwe5 ?is l9e1 & ! o!r la/ drawn1 w compreh5d all ^? places ^u ! ,e>? :]e ! ,eclipse is visible1 betwe5 ! ris+ ( ! ,sun1 & t ( ,jupit]4 ,illu/ration ,! ,,description ( ! ,great ,,orr]y1 lately made by ,mr4 ,,?omas ,,wright1 ,ma!matical ,in/rum5t-,mak] to 8 late ,,maje/y1 & n[ by ,,b5jam9 ,,cole1 8 ,successor4 ,! ,,orr]y is an ,a/ronomical ,ma*9e1 made to repres5t ! motions ( ! ,planets4 ,^! ma*9es are made ( v>i\s sizes1 "s hav+ m ,planets ?an o!rs2 b ,i %all "h conf9e myself to ! description ( t above-m5tion$4 ,9 ! ,introduction we gave a %ort acc\nt ( ! ,ord]1 ,p]iods1 ,di/ances1 & ,magnitudes ( ! ,prim>y ,planets2 & ( ! ,di/ances & ,p]iodical ,resolutions ( ! ,second>y ,planets r\nd _! respective ,prim>ies4 ,we %all "h expla9 _! ,/ations1 ,regradations1 ,eclipses1 ,phases1 c4 b fir/ let u take a g5]al view ( ! ,orr]y4 ,sid5ote3 ,! ,description ( ! ,orr]y4 ,sid5ote3 ,vide ,frontispiece4 ,! frame :i* conta9s ! :eel-"w1 c4 t regulates ! :ole ,ma*9e1 is made ( f9e ebony1 & is ne> f\r feet 9 diamet]2 ! outside !re( is adorn$ ) twelve pila/]s1 curi\sly wr\ght & gilt3 ,betwe5 ^! pila/]s ! twelve ,signs ( ! ,zodiac are neatly pa9t$1 ) gild$ frames4 ,above ! frame is a broad r+1 support$ ) twelve pill>s3 ,?is r+ repres5ts ! ,plane ( ! ,ecliptic1 ^u :i* !re are two scales ( degrees1 & betwe5 ^? ! names & *>act]s ( ! twelve ,signs4 ,ne> ! outside is a scale ( mon?s & days1 exactly correspond+ to ! ,sun's place at noon1 ea* day ?r\gh\t ! ye>4 ,above ! ecliptic /&s "s ( ! pr9cipal circles ( ! sph]e1 accord+ to _! respective situations 9 ! heav5s1 viz4 ,n #aj1 are ! two ,colures1 divid$ into degrees1 & half degrees2 ,n #aa1 is "o half ( ! ,equ9octial ,circle1 mak+ an angle ) ! ecliptic ( #bc degrees4 ,! ,tropic ( ,canc]1 & ! ,arctic ,circle1 are ea* fix$ p>allel1 & at _! prop] di/ance f ! equ9octial4 ,on ! ,nor!rn half ( ! ecliptic is a brass semicircle1 moveable ^u two po9ts fix$ 9 & 3 ,?is semicircle s]ves z a moveable horizon1 to be put to any degree ( latitude ^u ! ,nor? "p ( ! m]idian4 ,! :ole ma*9e is also s contriv$1 z to be set to any latitude1 )\t 9 ! lea/ affect+ any ( ! inside motions3 ,= ?is purpose !re are two /rong h+es 7,n #ac17 fix$ to ! bottom frame1 ^u :i* ! in/rum5t moves1 & a /rong brass ar*1 hav+ holes at e degree1 ?ro' :i* a /rong p9 is to be put1 accord+ to ! elevation4 ,?is ar* & ! two h+es1 support ! :ole ma*9e1 :5 x is lift$ up accord+ to any latitude2 & ! ar* at o!r times lies conv5i5tly "u ! bottom frame4 ,:5 ! ma*9e is set to any latitude 7:i* is easily done by two m51 ea* tak+ hold ( two h&les1 conv5i5tly fix$ = t purpose7 set ! moveable horizon to ! same degree ^u ! m]idian1 & y may =m an idea ( ! respective altitude1 or depressions ( ! ,planets1 above or bel[ ! horizon1 accord+ to _! respective positions1 ) reg>d to ! m]idian4 ,)9 ! ecliptic1 & ne>ly 9 ! same place !re(1 /&s ! ,sun1 & all ! ,planets1 bo? ,prim>y & ,second>y4 ,! ,sun 7,n #a47 /&s 9 ! middle ( ! :ole sy/em1 ^u a wire1 mak+ an angle ) ! plane ( ! ecliptic1 ( ab\t #hb degrees2 :i* is ! incl9ation ( ! ,sun's axis1 to ! axis ( ! ecliptic4 ,next to ! ,sun is a ,small ball 7,n #b47 repres5t+ ,m]cury3 ,next to ,m]cury is ,v5us 7,n #c47 repres5t$ by a l>g] ball 7& bo? ^! /& ^u wires17 s t ! balls !mselves may be m visibly p]ceiv$ by ! eye4 ,! ,e>? is repres5t$ 7,n #d47 by an ivory ball1 hav+ "s ( ! pr9cipal m]idians & p>allels1 & a little sket* ( a map describ$ ^u x4 ,! wire :i* supports ! ,e>?1 makes an angle ) ! plane ( ! ecliptic #ff degrees1 :i* is ! incl9ation ( ! ,e>?'s axis to t ( ! ecliptic4 ,ne> ! bottom ( ! ,e>?'s axis is a ,dial ,plate 7,n #i47 hav+ an index po9t+ to ! h\rs ( ! day1 z ! ,e>? turns r\nd its axis4 ,r\nd ! ,e>? is a r+1 support$ by two small pill>s1 :i* r+ repres5ts ! ,orbit ( ! ,moon1 & ! division ^u x answ]s to ! ,moon's latitude2 ! motion ( ?is r+ repres5ts ! motion ( ! ,moon's ,orbit1 accord+ to t ( ! ,nodes4 ,)9 ?is r+ is ! ,moon 7,n #e47 hav+ a black cap or case1 :i* by its motion1 repres5ts ! ,phases ( ! ,moon accord+ to h] age4 ,)\t ! ,orbits ( ! ,e>? & ,moon is ,m>s 7,n #f47 ,! next 9 ord] to ,m>s is ,jupit]1 & 8 f\r ,moons 7,n #g72 ea* ( ^! moons is support$ by a crook$ wire fix$ 9 a socket1 :i* turns ab\t ! pill> t supports ,jupit]4 ,^! satellites may be turn$ by ! h& to any position2 & yet :5 ! ma*9e is put 9 motion1 !y w all move 9 _! prop] times4 ,! out]mo/ ( all is ,saturn1 & 8 five ,moons 7,n #h47 ,^! moons are support$ & contriv$ aft] ! same mann] ) ^? ( ,jupit]4 ,! :ole ma*9e is put into motion by turn+ a small w9* 7l ! key ( a clock1 ,n #ad47 & all ! inside "w is s truly wr\ght1 t x requires b v small /r5g? to put ! :ole motion4 ,above ! h&le !re is a cyl9drical p91 :i* may be drawn a little out1 or pu%$ 91 at pleasure3 :5 x is pu%$ 91 all ! ,planets1 bo? prim>y & ,second>y1 w move accord+ to _! respective p]iods1 by turn+ ! h&le3 ,:5 x is drawn out1 ! motions ( ! ,satellites ( ,jupit] & ,saturn w be /opp$1 :ile all ! re/ move )\t int]ruption4 ,?is is a v good contrivance to pres]ve ! in/rum5t f be+ clogg$ by ! swift motions ( ! :eels belong+ to ! ,satellites ( ,jupit] & ,saturn1 :5 ! motions ( ! re/ ( ! ,planets are only consid]$4 ,!re is also a brass lamp hav+ two convex glasses1 to be put 9 ! room ( ! ,sun2 & also a small] ,e>? & ,moon1 made some:at 9 proportion to _! di/ance f ea* o!r1 :i* may be put on at pleasure4 ,! lamp turns r\nd 9 ! same "t ) ! ,e>?1 & by means ( ! glasses ca/ a /rong light ^u h]2 & :5 ! small] ,e>? & ,moon are plac$ on1 x w be easy to %ew :5 ei!r ( !m may be eclips$4 ,hav+ ?us giv5 a brief description ( ! outw>d "p ( ?is ma*9e1 ,i %all next give an acc\nt ( ! phnom5a expla9$ by x1 :5 x is put into motion4 ,( ! ,motions ( ! ,planets 9 g5]al4 ,hav+ put on ! h&le1 pu% 9 ! p9 :i* is j above x1 & place a small black pat* 7or bit ( waf]7 ^u ! middle ( ! ,sun 7= in/ance7 "r aga9/ ! fir/ degree ( 2 y may also place pat*es ^u ,v5us1 ,m>s1 & ,jupit]1 "r aga9/ "s not$ po9t 9 ! ecliptic4 ,if y lay a ?read f ! ,sun to ! fir/ degree ( 1 y may set a m>k :]e x int]sects ! orbit ( ea* ,planet1 & t w be a help to note ! "t ( _! revolutions4 ,"o entire turn ( ! h&le answ]s to ! diurnal motion ( ! ,e>? r\nd h] axis1 z may be se5 by ! motion ( ! h\r index1 :i* is plac$ at ! foot ( ! wire on :i* ! t]ella is fix$4 ,:5 ! index has mov$ ! space ( t5 h\rs1 y may obs]ve t ,jupit] has made "o revolution compleat r\nd its axis2 ! h&le be+ turn$ until ! h\r index has pass$ ov] #bd days1 #h h\rs1 w br+ ! pat* ^u ,v5us to its =m] situation ) respect to ! ecliptic1 :i* %ews t has made "o entire revolution r\nd h] axis4 ,m>s makes "o compleat revolution r\nd its axis 9 #bd h\rs & ab\t #dj m9utes4 ,:5 ! h&le is turn$ #be times r\nd1 ! spot ^u ! ,sun w po9t to ! same degree ( ! ecliptic1 z x did :5 ! in/rum5t 0 fir/ put into motion4 ,by obs]v+ ! motions ( ! spots ^u ! surface ( ! ,sun1 & ( ! ,planets 9 ! heav5s1 _! diurnal motion 0 discov]$2 aft] ! same mann] z we d "h obs]ve ! motions ( _! repres5tatives1 by t ( ! m>ks plac$ ^u !m4 ,if :ile y turn ! h&le y obs]ve ! ,planets1 y w see !m p]=m _! motions 9 ! same relative times z !y really d 9 ! heav5s1 ea* mak+ its p]iod 9 ! times m5tion$ 9 ! ,tables1 ,page1 #bh1 #bg turns ( ! h&le w br+ ! ,moon r\nd ! ,e>?1 :i* is call$ a ,p]iodic ,mon?2 & all ! :ile %e keeps ! same face t[>ds ! ,e>?2 = ! ,moon's annual & diurnal motion are p]=m$ bo? 9 ! same "t ne>ly1 s t we always see ! same face or side ( ! ,moon4 ,if be=e ! in/rum5t is put into motion1 ! satellites ( ,jupit] & ,saturn be br\ght into ! same "r l9e f _! respective prim>ies1 y w see !m1 z y turn ! h&le1 imm$iately disp]s$ f "o ano!r1 accord+ to _! diff]5t cel]ities4 ,?us "o turn ( ! h&le w br+ ! fir/ ( ,jupit]'s ,moons ab\t _/ "p r\nd ,jupit]1 :ile ! second has describ$ b _/ "p1 ! ?ird b above _/1 & ! f\r? n q _/ "p1 ea* ( its respective orbits4 ,if y turn ! h&le until ! h\r index has mov$ #ah h\rs m1 ! fir/ satellite w !n be br\ght into its =m] position1 & s has made "o entire revolution2 ! second at ! same "t w be almo/ diametrically opposite to ! fir/1 & s has made a little m ?an half ( "o revolution2 ! o!rs w be 9 diff]5t aspects1 accord+ to ! l5g? ( _! p]iods1 z w be pla9ly exhibit$ by ! in/rum5t4 ,! same obs]vations may be made ) respect to ! satellites ( ,saturn4 ,! ma*9e is s contriv$1 t ! h&le may be turn$ ei!r way2 &1 if be=e y put x into motion1 y obs]ve ! aspect 7or situation ) respect to ea* o!r7 ( ! ,planets1 & !n turn ! h&le r\nd any numb] ( times2 ! same numb] ( revolutions be+ made backw>ds1 w br+ all ! ,planets to _! =m] situations4 ,i %all next proce$ to p>ticul>s4 ,( ! ,/ations & ,retrogradations ( ! ,planets4 ,sid5ote3 ,retrograde ,motion ( ! ,planets4 ,! prim>y ,planets1 z !y all turn r\nd ! ,sun1 at diff]5t di/ances1 & 9 diff]5t times1 appe> to u f ! ,e>? to h diff]5t motions2 z sometimes !y appe> to move f ,we/ to ,ea/1 accord+ to ! ord] ( ! signs1 :i* is call$ _! ,direct ,motion2 !n by degrees !y slack5 _! pace1 until at la/ !y lose all _! motion1 & become ,/ation>y1 or n to move at all2 t is1 !y appe> 9 ! same place ) respect to ! fix$ ,/>s = "s "t toge!r2 aft] :i* !y aga9 beg9 to move1 b ) a contr>y direction1 z f ,ea/ to ,we/1 :i* is call$ _! ,retrograde ,motion2 !n aga9 !y become /ation>y1 & aft]w>ds reassume _! direct motion4 ,! reason ( all ^! appe>ances is v evid5tly %ewn by ! ,orr]y4 ,( ! ,/ations1 c4 ( ! ,inf]ior ,planets4 ,we %all in/ance 9 ! ,planet ,m]cury1 because 8 motion r\nd ! ,sun diff]s m f ! ,e>?'s ?an t ( ,v5us does4 ,:5 ,m]cury is 9 8 sup]ior conjunction 7or :5 he is 9 a direct l9e f ! ,e>? beyond ! ,sun7 fa/5 a /r+ ab\t ! axis ( ! ,e>?1 & ext5d x ov] ,m]cury to ! ecliptic2 !n turn+ ! h&le1 keep ! ?read all ! :ile ext5d$ ov] 1 & y w f9d x move ) a direct motion 9 ! ecliptic1 b cont9ually sl[]1 until ,m]cury has ! greate/ elongation f ! ,e>?4 ,ne> ?is position1 ! ?read = "s "t w lay ov] ,m]cury )\t be+ mov$ 9 ! ecliptic1 ?o' ! ,e>? & ,m]cury bo? cont9ue _! progressive motion 9 _! respective orbits4 ,:5 ,m]cury has got a little pa/ ?is place1 y w f9d ! ?read mu/ be mov$ backw>d 9 ! ecliptic1 beg9n+ fir/ ) a sl[ motion1 & !n fa/] by degrees1 until ,m]cury is 9 8 inf]ior conjunction1 or directly betwe5 ! ,e>? & ! ,sun4 ,next ?is position ( 1 8 retrograde motion w be ! swifte/2 b he /ill moves ! same way1 ?o' cont9ually sl[]1 'till he has aga9 come to 8 greate/ elongation1 :]e he w appe> ! second "t to be /ation>y2 aft] :i* he beg9s to move =w>d1 & t fa/] by degrees1 until he is come to ! same position ) respect to ! ,e>?1 t he 0 9 at fir/4 ,! same obs]vations may be made relat+ to ! motions ( ,v5us4 ,9 l mann] ! diff]5t motions obs]v$ 9 ! sup]ior ,planets may be also expla9$ by ! ,orr]y4 ,if y ext5d ! ?read ov] ,jupit]1 & proce$ aft] ! same mann] z be=e we did 9 reg>d to ,m]cury1 y w f9d t f ! "t ,jupit] is 9 conjunction ) ! ,sun1 8 motion is direct1 b cont9ually sl[]1 until ! ,e>? is ne>ly 9 a quadrate aspect ) ,jupit]1 ne> :i* position ,jupit] seems to be /ation>y3 ,aft] :i* he beg9s to move1 & cont9ually m5ds 8 pace1 until he comes 9 opposition to ! ,sun1 at :i* "t 8 retrograde motion is swifte/4 ,he /ill seems to g backw>d1 b ) a sl[] pace1 'till ! ,e>? & he are aga9 9 a quadrate aspect1 :]e ,jupit] seems to h lo/ all 8 motion2 aft] :i* he aga9 resumes 8 direct motion1 & s proce$s fa/] by degrees1 'till ! ,e>? & he are aga9 9 opposition to ea* ano!r4 ,sid5ote3 ,plate #c4 ,fig4 #a4 ,^! diff]5t motions obs]v$ 9 ! ,planets1 are easily illu/rat$1 z foll[e?3 ,! less] circle r\nd ! ,sun is ! orbit ( ,m]cury1 9 :i* he p]=ms 8 revolution r\nd ! ,sun1 9 ab\t ?ree mon?s1 or :ile ! ,e>? is go+ ?ro' "p ( h] orbit1 or f ,a to ,n4 ,! numb]s #a1 #b1 #c1 c4 9 ! orbit ( ,m]cury1 %[ ! spaces he describes 9 a week ne>ly1 & ! di/ance ,,ab1 ,,bc1 ,,dc1 c4 9 ! ,e>?'s orbit1 d likewise %[ h] motion 9 ! same "t4 ,! lett]s ,a1 ,b1 ,c1 c4 9 ! great orb1 are ! motions ( ,m]cury 9 ! ,heav5s1 z !y appe> f ! ,e>?4 ,n[ if ! ,e>? be suppos$ 9 ,a1 & ,m]cury 9 #ab1 ne> 8 sup]ior conjunction ) ! ,sun2 a spectator on ! ,e>? w see 1 z if he 7 9 ! po9t ( ! ,heav5s ,a1 & :ile is mov+ f #ab to #a1 & f #a to #b1 c4 ! ,e>? 9 ! same "t also moves f ,a to ,b1 & f ,b to ,c1 c4 ,all :i* "t appe>s 9 ! ,heav5s to move 9 a direct motion f ,a to ,b1 & f ,b to ,c1 c4 b gradually sl[]1 until he arrives ne> ! po9t ,g2 ne> ?is place he appe>s /ation>y1 or to /& /ill2 & aft]w>ds 7?o' he /ill cont9ues to move uni=mly 9 8 own orbit1 ) a progressive motion7 yet 9 ! sph]e ( ! fix$ ,/>s he w appe> to be retrograde1 or to g backw>ds1 z f ,g to ,h1 f ,h to ,i1 c4 until he has arriv$ ne> ! po9t ,l1 :]e aga9 he w appe> to be /ation>y2 & aft]w>ds to move 9 a direct motion f ,l to ,m1 & f ,m to ,n1 c4 ,:at has be5 "h %ew$ conc]n+ ! motions ( ,m]cury1 is also to be und]/ood ( ! motions ( ,v5us2 b ! conjunctions ( ,v5us ) ! ,sun d n happ5 s (t5 z 9 ,m]cury2 = ,v5us mov+ 9 a l>g] orbit1 & mu* sl[] ?an ,m]cury1 does n s (t5 ov]take ! ,e>?4 ,b ! retrogradations are mu* great] 9 ,v5us ?an !y are 9 ,m]cury1 = ! same reasons4 ,sid5ote3 ,fig4 #b4 ,! inn]mo/ circle repres5ts ! ,e>?'s orbit1 divid$ into #ab p>ts1 answ]+ to h] mon?ly motion2 ! greate/ circle is 9 ! orbit ( ,jupit]1 :i* he describes 9 ab\t #ab ye>s2 & !re=e ! _/ !re(1 f ,a to ,n1 def9es 8 motion1 9 "o ( our ye>s ne>ly2 & ! int]m$iate divisions1 ,a1 ,b1 ,c1 c4 8 mon?ly motion4 ,let u suppose ! ,e>? to be 9 ! po9t ( h] orbit #ab1 & ,jupit] 9 ,a1 9 8 conjunction ) ! ,sun2 x is evid5t t f ! ,e>? ,jupit] w be se5 9 ! great orb1 or 9 ! po9t ( ! ,heav5s ,a1 & :ile ! ,e>? is mov+ f #ab to #a1 #b1 c4 also moves f ,a to ,b1 c4 all :i* "t he appe>s 9 ! ,heav5s to move ) a direct motion f ,a to ,b1 ,c1 c41 until he comes 9 opposition to ! ,e>? ne> ! po9t ( ! ,heav5s ,e1 :]e he appe>s to be /ation>y2 aft] :i* aga9 beg9s to move 7?o' at fir/ ) a sl[ pace7 f ,e ?r\gh ,f1 ,h1 ,i to ,k1 :]e aga9 he appe>s to /& /ill1 b aft]w>ds he reassumes 8 direct motion f ,i ?ro' ,k1 to ,m1 c4 ,f ! con/ruction ( ! prec$+ figure x appe>s1 t :5 ! sup]ior ,planets are 9 conjunction ) ! ,sun1 _! direct motion is mu* quick] ?an at o!r times2 & t because !y really move f ,we/ to ,ea/1 :ile ! ,e>? 9 ! opposite "p ( ! ,heav5s is c>ri$ ! same way1 & r\nd ! same c5t]4 ,?is motion aft]w>ds cont9ually slack5s until ! ,planet comes almo/ 9 opposition to ! ,sun1 :5 ! l9e jo9+ ! ,e>? & ,planet1 w cont9ue = "s "t ne>ly p>allel to itself1 & s ! ,planet seems f ! ,e>? to /& /ill2 aft] :i*1 x beg9s to move ) a sl[ motion backw>d1 until x comes into a qu>tile aspect ) ! ,sun1 :5 aga9 x w appe> to be /ation>y1 = ! above reasons2 aft] t x w resume its direct motion1 until x comes into a conjunction ) ! ,sun1 !n x w proce$ z above expla9$4 ,h5ce x also appe>s1 t ! retrogradations ( ! sup]ior ,planets are mu* sl[] ?an _! direct motions1 & _! cont9uance mu* %ort]2 = ! ,planet1 f its la/ qu>t]1 until x comes 9 opposition to ! ,sun1 appe>s to move ! same way ) ! ,e>?1 by :om x is !n ov]tak53 ,aft] :i* x beg9s to g backw>ds1 b ) a sl[ motion1 because ! ,e>? be+ 9 ! same "p ( ! ,heav5s1 & mov+ ! same way t ! ,planet really does1 ! app>5t motion ( ! ,planet backw>ds1 mu/ !reby be less5$4 ,:at has be5 "h said conc]n+ ! motions ( ,jupit]1 is also to be und]/ood ( ,m>s & ,saturn4 ,b ! retrogradations ( ,saturn d (t5] happ5 ?an ^? ( ,jupit]1 because ! ,e>? (t5] ov]takes ,saturn2 & = ! same reason1 ! regressions ( ,jupit] d (t5] happ5 ?an ^? ( ,m>s4 ,b ! retrogradations ( ,m>s are mu* great] ?an ^? ( ,jupit]1 ^: are also mu* great] ?an ^? ( ,saturn4 ,9 ei!r ( ! satellites ( ,jupit] or ,saturn1 ^! diff]5t appe>ances 9 ! neighb\r+ ,worlds are mu* (t5] se5 ?an !y are by u 9 ! prim>y ,planets4 ,we nev] obs]ve ^! diff]5t motions 9 ! ,moon1 because %e turns r\nd ! ,e>? z h] c5t]2 nei!r d we obs]ve !m 9 ! ,sun1 because he is ! c5t] ( ! ,e>?'s motion2 :5ce ! app>5t motion ( ! ,sun always appe>s ! same way r\nd ! ,e>?4 ,( ! ,annual & ,diurnal ,motion ( ! ,e>?1 & ( ! increase & decrease ( ,days & ,nights4 ,! ,e>? 9 h] annual motion r\nd ! ,sun1 has h] axis always 9 ! same direction1 or p>allel to itself2 t is1 if a l9e be drawn p>allel to ! axis1 :ile ! ,e>? is 9 any po9t ( h] orbit1 ! axis 9 all o!r positions ( ! ,e>? w be p>allel to ! said l9e4 ,?is p>allelism ( ! axis1 & ! simple motion ( ! ,e>? 9 ! ecliptic1 solves all ! phnom5a ( diff]5t seasons4 ,^! ?+s are v well illu/rat$ by ! ,orr]y4 ,illu/ration3 ,plate #c4 ,if y put on ! lamp 9 ! place ( ! ,sun1 y w see h[ "o half ( our globe is always illum9at$ by ! ,sun1 :ile ! o!r hemisph]e rema9s 9 d>kness2 h[ ,day & ,night are =m$ by ! revolution ( ! ,e>? r\nd h] axis2 = z %e turns f ,we/ to ,ea/1 ! ,sun appe>s to move f ,ea/ to ,we/4 ,& :ile ! ,e>? turns 9 h] orbit1 y may obs]ve t h] axis always po9ts ! same way1 & ! sev]al seasons ( ! ye> cont9ually *ange4 ,to make ^! ?+s pla9]1 we w take a view ( ! ,e>? 9 diff]5t p>ts ( h] orbit4 ,:5 ! ,e>? is 9 ! fir/ po9t ( ,libra 7:i* is f\nd by ext5d+ a ?read f ! ,sun1 & ov] ! ,e>?1 to ! ecliptic7 we h ! ,v]nal ,equ9ox1 & ! ,sun at t "t appe>s 9 ! fir/ po9t ( 4 ,9 ?is position ( ! ,e>?1 two ,poles ( ! _w are 9 ! l9e sep>at+ light & d>kness2 & z ! ,e>? turns r\nd h] axis1 j "o half ( ! equator1 & all its p>allels1 w be 9 ! light1 & ! o!r half 9 ! d>k2 & !re=e ! days & nights mu/ be e :]e equal4 ,z ! ,e>? moves along 9 h] orbit1 y w p]ceive ! ,nor? ,pole advances by degrees into ! illum9at$ hemisph]e1 & at ! same "t ! ,s\? ,pole rec$es into d>kness2 & 9 all places to ! ,nor?w>d ( ! equator1 ! days cont9ually l5g!n1 :ile ! contr>y happ5s 9 ! ,s\!rn p>ts1 until at l5g? ! ,e>? is arriv$ 9 ,capricorn4 ,9 ?is position ( ! ,e>? all ! space includ$ )9 ! arctic circle falls :olly )9 ! light1 & all ! opposite "p ly+ )9 ! ant>ctic circle1 is q involv$ 9 d>kness4 ,9 all places betwe5 ! equator & ! arctic circle1 ! days are n[ at ! longe/1 & are gradually long]1 z ! place are m remote f ! equator4 ,9 ! ,s\!rn hemisph]e !re is a contr>y effect4 ,all ! :ile ! ,e>? is travell+ f ,capricorn t[>ds ,aries1 ! ,nor? ,pole gradually rec$es f ! light1 & ! ,s\? ,pole approa*es ne>] to x2 ! days 9 ! ,nor!rn hemisph]e gradually decrease1 & 9 ! ,s\!rn hemisph]e !y increase 9 ! same proportion1 until ! ,e>? be arriv$ 9 2 !n ! two ,poles ( ! _w lie exactly 9 ! l9e sep>at+ light & d>kness1 & ! days are equal to ! nights 9 all places ( ! _w4 ,z ! ,e>? advances t[>ds ,canc]1 ! ,nor? ,pole gradually rec$es f ! light1 :ile ! ,s\!rn "o advances into x1 at ! same rate4 ,9 ! ,nor!rn hemisph]e ! days decrease1 & 9 ! ,s\!rn "o !y gradually l5g!n1 until ! ,e>? be+ arriv$ 9 ,canc]1 ! ,nor? frigid ,zone is all involv$ 9 d>kness1 & ! ,s\? frigid ,zone falls intirely )9 ! light2 ! days e :]e 9 ! ,nor!rn hemisph]e are n[ at ! %orte/1 & to ! ,s\?w>d !y are at ! longe/4 ,z ! ,e>? moves f h5ce t[>ds ,libra1 ! ,nor? ,pole gradually approa*es ! light1 & ! o!r rec$es f x2 & 9 all places to ! ,nor?w>d ( ! equator1 ! days n[ l5g!n1 :ile 9 ! opposite hemisph]e !y gradually %ort51 until ! ,e>? has gott5 into 2 9 :i* position ! days & nights w aga9 be ( equal l5g? 9 all p>ts ( ! _w4 ,y might h obs]v$ t 9 all positions ( ! ,e>?1 "o half ( ! equator 0 9 ! light1 & ! o!r half 9 d>kness2 :5ce "u ! equator1 ! days & nights are always ( ! same l5g?3 ,& all ! :ile ! ,e>? 0 go+ f t[>ds 1 ! ,nor? ,pole 0 con/antly illum9at$1 & ! ,s\? ,pole all ! :ile 9 d>kness2 & = ! o!r half ye>1 ! contr>y4 ,sometimes !re is a semicircle exactly fac+ ! ,sun1 fix$ ov] ! middle ( ! ,e>?1 :i* may be call$ ! horizon ( ! disk3 ,?is w d in/ead ( ! lamp1 if t half ( ! ,e>? :i* is next ! ,sun be consid]$1 z be+ ! illum9at$ hemisph]e1 & ! o!r half1 to be t :i* lies 9 d>kness4 ,sid5ote3 ,plate #d4 ,! great circle 1 1 c4 repres5t ! ,e>?'s annual orbit2 & ! f\r less] circles ,,esqc1 ! ecliptic1 ^u ! surface ( ! ,e>?1 co9cid+ ) ! great ecliptic 9 ! ,heav5s4 ,^! f\r less] figures repres5t ! ,e>? 9 ! f\r c>d9al po9ts ( ! ecliptic1 ,p be+ ! ,nor? ,pole ( ! equator1 & p ! ,nor? ,pole ( ! ecliptic2 ,,spc1 ! sol/itial colure :i* is always p>allel to ! great sol/itial colure 9 ! ,heav5s2 ,,epq ! equ9octial colure4 ,! o!r circles pass+ ?ro' ,p1 are m]idians at two h\rs di/ance f "o ano!r2 ! semicircle ,e,q is ! ,nor!rn half ( ! equator2 ! p>allel circle t\*+ ! ecliptic 9 ,s1 is ! tropic ( ,canc]2 ! dott$ circle1 ! p>allel ( ,london1 & ! small circle1 t\*+ ! ,pole ( ! ecliptic1 is ! ,arctic ,circle4 ,! %ad$ "p1 :i* is always opposite to ! ,sun1 is ! obscure hemisph]e1 or t :i* lies 9 d>kness2 & t :i* is next ! ,sun1 is ! illum9at$ hemisph]e4 ,if we suppose ! ,e>? 9 1 %e w !n see ! ,sun 9 7:i* makes our v]nal equ9ox7 & 9 ?is position ! circle b\nd+ light & d>kness1 :i* "h is ,,sc1 passes ?ro' ! ,poles ( ! ,_w1 & bisects all ! p>allels ( ! equator2 & !re=e ! diurnal & nocturnal ar*es1 or ! l5g? ( ! days & nights1 are equal 9 all places ( ! _w4 ,b :ile ! ,e>? 9 h] annual c\rse1 moves ?r\gh 1 1 to 1 ! l9e ,,sc1 keep+ /ill p>allel to itself1 or to ! place :]e x 0 at fir/1 ! ,pole ,p w1 by ?is motion1 gradually advance into ! illum9at$ hemisph]e2 & also ! diurnal ar*es ( ! p>allels gradually increase1 & consequ5tly ! nocturnal ones decrease 9 ! same proportion1 until ! ,e>? has arriv$ into 2 9 :i* position ! ,pole ,p1 & all ! space )9 ! arctic circle1 fall :olly )9 ! illum9at$ hemisph]e1 & ! diurnal ar*es ( all ! p>allels t are )\t ?is circle1 w exce$ ! nocturnal ar*es m or less1 z ! places are ne>] to1 or f>!r (f f x1 until ! di/ance f ! ,pole is z f> z ! equator1 :]e bo? ^! ar*es are always equal4 ,aga91 :ile ! ,e>? is mov+ f ?r\gh 1 1 to 1 ! ,pole ,p beg9s to incl9e to ! l9e1 di/+ui%+ light & d>kness1 9 ! same proportion t be=e x rec$$ f x2 & consequ5tly ! diurnal ar*es gradually less51 until ! ,e>? has arriv$ into :]e ! ,pole ,p w aga9 fall on ! horizon1 & s cause ! days & nights to be e :]e equal4 ,b :5 ! ,e>? has pass$ 1 :ile %e is go+ ?ro' 1 & 1 c4 ! ,pole ,p w beg9 to fall 9 ! obscure hemisph]e1 & s rec$e gradually f ! light1 until ! ,e>? is arriv$ 9 2 9 :i* position n only ! ,pole1 b all ! space )9 ! arctic circle1 are involv$ 9 d>kness1 & ! diurnal ar*es ( all ! p>allels1 )\t ! arctic circle1 are equal to ! nocturnal ar*es ( ! same p>allels1 :5 ! ,e>? 0 9 ! opposite po9t 2 & x is evid5t t ! days are n[ at ! %orte/1 & ! nights ! longe/4 ,b :5 ! ,e>? has pa/ ?is po9t1 :ile %e is go+ ?r\gh & 1 ! ,pole ,p w aga9 gradually approa* ! light1 & s ! diurnal ar*es ( ! p>allels gradually l5g!n1 until ! ,e>? is arriv$ 9 2 at :i* "t ! days & nights w aga9 be equal 9 all places ( ! ,_w1 & ! ,pole itself j see ! ,sun4 ,illu/ration3 ,plate #d4 ,"h we only consid]$ ! phnom5a belong+ to ! ,nor!rn p>allels2 b if ! ,pole ,p be made ! ,s\? ,pole1 !n all ! p>allels ( latitude w be p>allels ( ,s\? latitude1 & ! days1 e :]e1 9 any position ( ! ,e>?1 w be equal to ! nights ( ^? :o liv$ 9 ! opposite hemisph]e1 "u ! same p>allels4 ,( ! ,phases ( ! ,moon1 & ( h] ,motion 9 h] ,orbit4 ,sid5ote3 ,nodes4 ,sid5ote3 ,dragon's ,head4 ,sid5ote3 ,dragon's ,tail4 ,sid5ote3 ,retrograde ,motion ( ! ,nodes4 ,! orbit ( ! ,moon makes an angle ) ! plane ( ! ecliptic1 ( above #e degrees1 & cuts x into two po9ts1 diametrically opposite 7aft] ! same mann] z ! equator & ! ecliptic cut ea* o!r ^u ! globe1 9 & 7 :i* po9ts are call$ ! ,nodes2 & a "r l9e jo9+ ^! po9ts1 & pass+ ?r\gh ! c5t] ( ! ,e>?1 is call$ ! ,l9e ( ! ,nodes4 ,t node :]e ! ,moon beg9s to asc5d ,nor?w>d above ! plane ( ! ecliptic1 is call$ ! ,asc5d+ ,node1 & ! ,head ( ! ,dragon1 & is ?us commonly m>k$ ,symbol4 ,! o!r node f :5ce ! ,moon1 desc5ds to ! ,s\?w>d ( ! ecliptic1 is call$ ! ,desc5d+ ,node1 & ! ,dragon's ,tail1 & is ?us m>k$ ,symbol4 ,! l9e ( nodes cont9ually %ifts itself f ,ea/ to ,we/1 contr>y to ! ord] ( ! signs2 & ) ?is retrograde motion1 makes "o revolution r\nd ! ,e>?1 9 ! space ( ab\t #ai ye>s4 ,sid5ote3 ,p]iodical ,mon?4 ,sid5ote3 ,synodical ,mon?4 ,! ,moon describes its orbit r\nd ! ,e>? 9 ! ,space ( #bg days & #g h\rs1 :i* space ( "t is call$ a ,p]iodical ,mon?2 yet f "o conjunction to ! next1 ! ,moon sp5ds #bi days & a half1 :i* is call$ a ,synodical ,mon?2 because :ile ! ,moon 9 h] prop] ,orbit f9i%es h] c\rse1 ! ,e>? advances ne> a :ole sign 9 ! ecliptic2 :i* space ! ,moon has /ill to describe1 be=e %e w be se5 9 conjunction ) ! ,sun4 ,:5 ! ,moon is 9 conjunction ) ! ,sun1 note h] place 9 ! ecliptic2 !n turn+ ! h&le1 y w f9d t #bg days & #g h\rs w br+ ! ,moon to ! same place2 & aft] y h made #b revolutions m1 ! ,moon w be exactly betwixt ! ,sun & ! ,e>?4 ,sid5ote3 ,phases ( ! ,moon4 ,! ,moon all ! :ile keeps 9 h] orbit1 & s ! wire t ,supports h] cont9ually rises or falls 9 a socket1 z %e *anges h] latitude2 ! black cap %ifts itself1 & s %ews ! phases ( ! ,moon1 accord+ to h] age1 or h[ mu* ( h] enlight5$ "p is se5 f ! ,e>?4 ,9 "o synodical mon?1 ! l9e ( ! nodes moves ab\t #a degree f ,we/ to ,ea/1 & s makes "o entire revolution 9 #ai ye>s4 ,let ,,ab be an ar* ( ! ,e>?'s orbit1 & :5 ! ,e>? is 9 ,t1 let ! ,moon be 9 ,n1 9 conjunction ) ! ,sun 9 ,s1 :ile ! ,moon is describ+ h] orbit ,,nafd1 ! ,e>? w describe ! ar* ( h] orbit ,t t2 & :5 ! ,e>? has got into ! po9t t1 ! ,moon w be 9 ! po9t ( h] orbit n1 hav+ made "o compleat revolution r\nd ! ,e>?4 ,b ! ,moon1 be=e %e comes 9 conjunction ) ! ,sun1 mu/ aga9 describe ! ar* n o2 :i* ar* is simil> to ,t t1 because ! l9es ,,fn1 f n1 are p>allel2 & because1 :ile ! ,moon describes ! ar* n o1 ! ,e>? advances =w>d 9 ! ecliptic2 ! ar* describ$ by ! ,moon1 aft] %e has f9i%$ h] p]iodical mon?1 be=e %e makes a synodical mon?1 mu/ be some:at great] ?an n o4 ,to det]m9e ! mean l5g? ( a synodical mon?1 f9d ! diurnal motion ( ! ,moon 7or ! space %e describes r\nd ! ,e>? 9 "o day7 & likewise ! diurnal motion ( ! ,e>?2 !n ! diff]5ce betwixt ! two motions1 is ! app>5t motion ( ! ,moon r\nd ! ,e>? 9 "o day2 !n x w be1 z ?is diff]5tial ar* is to a :ole circle2 s is "o day to t space ( "t :]e9 ! ,moon appe>s to describe a compleat circle r\nd ! ,e>?1 :i* is ab\t #bi days4 ,b ?is is n always a true ,lunation1 = ! motion ( ! ,moon is sometimes fa/]1 & sometimes sl[]1 accord+ to ! position ( ! ,e>? 9 h] orbit4 ,9 "o synodical mon? ! ,moon has all mann] ( aspects ) ! ,sun & ,e>?1 & because %e is opaque1 t face ( h]s w only appe> bright :i* is t[>ds ! ,sun1 :ile ! opposite rema9s 9 d>kness4 ,b ! inhabitants ( ! ,e>? c only see t face ( ! ,moon :i* is turn$ t[>ds ! ,e>?2 & !re=e1 accord+ to ! v>i\s positions ( ! ,moon1 9 respect ( ! ,sun & ,e>?1 we obs]ve diff]5t portions ( h] illum9at$ face1 & s a cont9ual *ange 9 h]#g,phases4 ,let ,s be ! ,sun1 ,,rtv an ar* ( ! ,e>?'s orbit1 ,t ! ,e>?1 & ! circle ,,abcd1 c4 ! ,moon's orbit1 9 :i* %e turns r\nd ! ,e>? 9 ! space ( a mon?2 & let ,a1 ,b1 ,c1 c4 be ! c5t]s ( ! ,moon 9 diff]5t p>ts ( h] orbit4 ,n[ if ) ! l9es ,s ,a1 ,s ,b1 c4 we jo9 ! c5t]s ( ! ,sun & ,moon1 & at "r angles to ^! draw ! l9es ,h ,o2 ! said l9es ,h ,o w be ! circles t sep>ate ! illum9at$ "p ( ! ,moon f ! d>k & obscure4 ,aga91 if we conceive ano!r l9e ,i ,l to be drawn at "r angles to ! l9es ,,ta1 ,,tb1 c4 pass+ f ! c5t] ( ! ,e>? to ! ,moon1 ! said l9e ,i ,l w divide ! visible hemisph]e ( ! ,moon1 or t :i* is turn$ t[>ds u1 f ! invisible1 or t :i* is turn$ f u2 & ?is circle may be call$ ! ,circle ( ,vision4 ,sid5ote3 ,full ,moon4 ,sid5ote3 ,half ,moon4 ,sid5ote3 ,new ,moon4 ,n[ x is manife/1 t :5ev] ! ,moon is 9 ! position ,a1 or 9 t po9t ( h] orbit :i* is opposite to ! ,sun1 ! circle ( vision1 & ! circle b\nd+ light & d>kness1 d co9cide1 & all ! illum9at$ face ( ! ,moon is turn$ t[>ds ! ,e>?1 & is visible to u2 & 9 ?is position ! ,moon is said to be full4 ,b :5 ! ,moon arrives to ,b1 all h] illum9at$ face is !n n t[>ds ! ,e>?1 !re be+ a "p ( x1 ,,hbi1 n to be se5 by u2 & !n h] visible face is defici5t f a circle1 & appe>s ( a gibb\s =m1 z 9 ,b4 ,fig4 #c4 ,aga9 :5 %e arrives to ,c1 ! two =em5tion$ circles cut ea* o!r at "r angles1 & !n we obs]ve a half ,moon1 z 9 ,c1 ,fig4 #c4 ,& aga9 ! illum9at$ face ( ! ,moon is m & m turn$ f ! ,e>?1 until %e comes to ! ,po9t ,e1 :]e ! circle ( vision1 & t b\nd+ light & d>kness1 d aga9 co9cide4 ,"h ! ,moon disappe>s1 ! illum9at$ "p be+ :olly turn$ f ! ,e>?2 & %e is n[ said to be 9 ,conjunction ) ! ,sun1 because %e is 9 ! same direction f ! ,e>? t ! ,sun is 91 :i* position we call a ,new ,moon4 ,:5 ! ,moon is arriv$ to ,f1 %e aga9 assumes a horn$ figure1 b h] horns 7:i* be=e ! *ange 7 turn$ ,we/w>d7 h n[ *ang$ _! position1 & look ,ea/w>d4 ,:5 %e has arriv$ to a quadrate aspect at ,g1 %e w appe> bissect$1 l a half ,moon1 aft]w>ds %e w /ill gr[ bigg]1 until at la/ %e comes to ,a1 :]e aga9 %e w appe> 9 h] full spl5dor4 ,! same appe>ances :i* we obs]ve 9 ! ,moon are likewise obs]v$ by ! ,lun>ians 9 ! ,e>?1 our ,e>? see+ a ,moon to !m1 z _! ,moon is to u2 & we are obs]v$ by !m to be c>ri$ r\nd 9 ! space ( "t t !y are really c>ri$ r\nd ! ,e>?4 ,b ! same phases ( ! ,e>? & ,moon happ5 :5 !y are 9 contr>y position2 = :5 ! ,moon is 9 conjunction to u1 ! ,e>? is !n 9 opposition to ! ,moon1 & ! ,lun>ians h !n a full ,e>?1 z we 9 a simil> position h a full ,moon4 ,:5 ! ,moon comes 9 opposition to ! ,sun1 ! ,e>?1 se5 f ! ,moon1 w appe> 9 conjunction ) h]1 & 9 t position ! ,e>? w disappe>2 aft]w>ds %e w assume a horn$ figure1 & s %ew ! same phases to ! inhabitants ( ! ,moon z %e does to u4 ,( ! ,eclipses ( ! ,sun & ,moon4 ,sid5ote3 ,eclipse4 ,an ,eclipse is t deprivation ( light 9 a ,planet1 :5 ano!r is int]pos$ betwixt x & ! ,sun4 ,?us1 an eclipse ( ! ,sun is made by ! int]position ( ! ,moon at h] conjunction1 & an eclipse ( ! ,moon is occasion$ by ! %ad[ ( ! ,e>? fall+ ^u ! ,moon1 :5 %e is 9 opposition to ! ,sun4 ,sid5ote3 ,fig4 #d4 ,sid5ote3 ,lun> ,eclipse4 ,let ,s be ! ,sun1 ,t ! ,e>?1 & ,,abc its %ad[2 n[ if ! ,moon1 :5 %e is 9 opposition to ! ,sun1 %\ld come into ! conical space ,,abc1 %e w !n be depriv$ ( ! sol> light1 & s und]go an eclipse4 ,sid5ote3 ,sol> ,eclipse4 ,sid5ote3 ,fig4 #e4 ,9 ! same mann]1 :5 ! %ad[ ( ! ,moon falls ^u ! ,e>? 7:i* c nev] happ5 b :5 ! ,moon is 9 conjunction ) ! ,sun7 t "p ^u :i* ! %ad[ falls w be involv$ 9 d>kness1 & ! ,sun eclips$4 ,b because ! ,moon is mu* less ?an ! ,e>?1 ! %ad[ ( ! _c cov] ! :ole ,e>?1 b only a "p ( x4 ,let ,s be ! ,sun1 ,t ! ,e>?1 ,,abc ! ,moon's orbit1 & ,l ! ,moon 9 conjunction ) ! ,sun3 ,"h ! %ad[ ( ! ,moon falls only ^u ! "p ,,de ( ! ,e>?'s surface1 & !re only ! ,sun is intirely hid3 b !re are o!r p>ts ,,ef1 ,,dg1 on ea* side ( ! %ad[1 :]e ! inhabitants are depriv$ ( "p ( ! ,sol> rays1 & t m or less1 accord+ to _! di/ance f ! %ad[4 ,^? :o live at ,h & ,i w see half ( ! ,sun eclips$1 b 9 ! spaces ,,fm1 ,,gn1 all ! ,sun's body w be visible1 )\t any eclipse4 ,f ! prec$+ figure x appe>s1 t an eclipse ( ! ,sun does n rea* a great way ^u ! sup]ficies ( ! ,e>?2 b ! :ole body ( ! ,moon may sometimes be involv$ 9 ! ,e>?'s %ad[4 ,sid5ote3 ,fig4 #f4 ,al?\gh ! ,moon se5 f ! ,e>?1 & ! ,e>? se5 f ! ,moon1 are ea* alt]nately1 once a mon?1 9 conjunction ) ! ,sun2 yet1 by reason ( ! incl9ation ( ! ,moon's orbit to ! ecliptic1 ! ,sun is n eclips$ e new ,moon1 nor ! ,moon at e full4 ,let ,t be ! ,e>?1 ,,dte an ar* ( ! ecliptic1 ,,albf1 ! ,moon's orbit1 hav+ ! ,e>? ,t1 9 its c5t]2 & let ,,agbg be ano!r circle co9cid+ ) ! ecliptic1 & ,a1 ,b1 ! nodes1 or ! two po9ts :]e ! ,moon's orbit & ! ecliptic cut ea* o!r4 ,a ! asc5d+ node1 & ,b ! desc5d+ node4 ,! angle ,,gal equal to ,,gbl is ! incl9ation ( ! ,moon's orbit to ! ecliptic1 be+ ab\t #e degrees4 ,n[ a spectator f ! ,e>? at ,t1 w obs]ve ! ,sun to move 9 ! circle ,,agbc1 & ! ,moon 9 h] orbit ,,albf2 :5ce x is evid5t1 t ! ,sun & ,moon c nev] be se5 9 a direct l9e1 f ! c5t] ( ! ,e>?1 b :5 ! ,moon is 9 "o ( ! nodes ,a or ,b2 & !n only w ! ,sun appe> c5trally eclips$4 ,b if ! conjunction ( ! ,moon happ5s :5 %e is any :]e )9 ! di/ance ,a c ( ! nodes1 ei!r ,nor? or ,s\?1 ! ,sun w !n be eclips$1 m or less1 accord+ to ! di/ance f ! node ,a1 or ,b4 ,if ! conjunction happ5s :5 ! ,moon is 9 b1 ! ,sun w be !n "o half eclips$2 & if x happ5s :5 %e is 9 c1 ! ,moon's limb w j t\* ! ,sun's disk1 )\t hid+ any "p ( x4 ,! %ad[ ( ! ,e>? at ! place :]e ! ,moon's orbit int]sects x1 is ?ree times z l>ge z ! ,moon's diamet]1 z 9 ,fig4 #d4 & !re=e x (t5 happ5s t eclipses ( ! ,moon are total1 :5 !y are n c5tral3 ,& = ! same reason ! ,moon may sometimes be totally eclips$ = ?ree h\rs toge!r2 :]eas total eclipses ( ! ,sun c sc>cely ev] exce$ f\r m9utes4 ,! eclipses ( ! ,sun & ,moon are v well expla9$ by ! ,orr]y3 ,?us hav+ put ! lamp 9 ! place ( ! ,sun1 & ! little ,e>? & ! little ,moon 9 _! prop] places1 in/ead ( ! l>g] ones1 let ! room :]e9 ! in/rum5t /&s be d>k5$2 !n turn+ ! h&le ab\t1 y w see :5 ! conjunction ( ! ,moon happ5s4 ,:5 %e is 9 or ne> "o ( ! nodes1 h] %ad[ w fall ^u ! ,e>?1 & s deprive t "p ^u :i* x falls ( ! light ( ! ,sun3 ,if ! conjunction happ5s :5 ! ,moon is n ne> "o ( ! nodes1 ! light ( ! lamp w fall ^u ! ,e>?1 ei!r above or bel[ ! ,moon1 accord+ to h] latitude at t "t4 ,9 l mann]1 :5 ! full ,moon happ5s ne> "o ( ! nodes1 ! %ad[ ( ! ,e>? w fall ^u ! ,moon2 & if ! ,moon's latitude be b small1 h] :ole face w be involv$ 9 d>kness4 ,at o!r times1 :5 ! full ,moon happ5s :5 %e is n ne> "o ( h] nodes1 ! %ad[ ( ! ,e>? w pass ei!r above or bel[ ! ,moon1 & s by t means ! ,moon w escape be+ eclips$4 ,( ! ,eclipses ( ! ,satellites ( ,jupit]4 ,! app>5t diamet]s ( ! inf]ior ,planets are s small1 t :5 !y pass betwixt u & ! ,sun1 !y only appe> l small spots ^u ! ,sun's surface1 )\t depriv+ u ( any s5sible quantity ( 8 light4 ,! %ad[ ( ! ,e>? likewise t]m9ates be=e x rea*es any ( ! sup]ior ,planets1 s t !y are nev] eclips$ by u2 & ! ,e>? :5 %e is 9 conjunction ) ! ,sun1 only appe>s l a black spot ^u 8 surface4 ,b ,jupit] & 8 ,moons mutually eclipse ea* o!r1 z our ,e>? & ,moon d2 z also do? ,saturn & 8 ,moons4 ,! satellites ( ,jupit] become twice hid f u1 9 "o circulation r\nd 2 viz4 once beh9d ! body ( ,jupit]1 i4 e4 :5 !y are 9 ! "r l9e jo9+ ! c5t]s ( ! ,e>? & 2 & aga9 !y become invisible :5 !y ent] ! %ad[ ( ,jupit]1 :i* happ5s :5 !y are at _! ,full1 z se5 f 1 at :i* times !y also suff] eclipses2 :i* eclipses happ5 to !m aft] ! same mann] z !y d to our ,moon1 by ! int]position ( ! ,e>? betwixt h] & ! ,sun4 ,sid5ote3 ,fig4 #g4 ,let ,s be ! ,sun1 ,,abt ! ,e>?'s orbit2 & ,c ,d1 an ar* ( ,jupit]'s orbit1 9 :i* let ,jupit] be 9 ! po9t 2 & let ,,cfdh be ! orbit ( "o ( ,jupit]'s satellites1 :i* we w "h suppose to be ! f>!/ f him4 ,^! satellites1 :ile !y move ?ro' ! inf]ior p>ts ( _! orbs1 viz4 f ,d ?ro' ,h1 ,i1 to ,c1 seem f ! ,e>? & ! ,sun to h a retrograde motion2 b :5 !y are 9 ! sup]ior "p ( _! orbit1 !y are !n se5 to move f ,we/ to ,ea/1 accord+ to _! true motion4 ,n[ :ile !y describe ! sup]ior "p ( _! orbits1 !y w be twice hid f ! ,e>?1 once 9 ! %ad[ ( 1 & once beh9d 8 body4 ,if ,jupit] be m ,we/]ly ?an ! ,sun1 t is1 :5 ! ,e>? is 9 ,a1 !y w be fir/ hid 9 ! %ad[ ,f1 & aft]w>ds beh9d ! body ( 9 ,g3 ,b :5 ! ,e>? is 9 ,b1 !n !y are fir/ hid beh9d 's body 9 ,e1 & aft]w>ds fall into ! %ad[ ,f4 ,:ile ! satellites describe ! inf]ior p>ts ( _! orbit1 !y only once disappe>1 :i* may be ei!r 9 ,i or ,h1 accord+ to ! position ( ! ,e>?1 9 :i* places !y _c be di/+ui%$ f ! body ( ,jupit]4 ,illu/ration3 ,plate #e ,fig4 ,i ,fig4 ,,ii ,fig4 ,,iii ,fig4 ,,iv ,fig4 ,v ,fig4 ,,vi ,fig4 ,,vii ,:5 ! satellites se5 f are 9 conjunction ) ! ,sun1 _! %ad[s w !n fall ^u 1 & "s "p ( 8 body be involv$ 9 d>kness1 to :i* "p ! ,sun w be totally eclips$4 ,by obs]v+ ! eclipses ( ,jupit]'s satellites1 x 0 fir/ discov]$ t light is n propogat$ in/antane\sly1 ?\gh x moves ) an incr$ible swiftness3 ,= if light came to u 9 an in/ant1 an obs]v] 9 ,t w see an eclipse ( "o ( ! satellites1 at ! same "t t ano!r 9 ,k w\ld4 ,b x has be5 f\nd by obs]vations1 t :5 ! ,e>? is 9 ,k1 at h] ne>e/ di/ance f ,jupit]1 ^! eclipses happ5 mu* soon] ?an :5 %e is 9 ,t4 ,n[ hav+ ! diff]5ce ( "t betwixt ^! appe>ances 9 ,k & ,t1 we may f9d ! l5g? ( "t ! light takes 9 pass+ f ,k to ,t1 :i* space is equal to ! diamet] ( ! ,e>?'s annual orb4 ,by ^! k9ds ( obs]vations x has be5 f\nd1 t light rea*es f ! ,sun to u 9 ! space ( elev5 m9utes ( "t1 :i* is at lea/ at ! rate ( #ajj1jjj miles 9 a second4 ,,f9is4 ,illu/ration ,,an ,,index ,,( ,,! ,,a/ronomical ,,t]ms ,made ,use ( 9 ?is ,,book4 ,acronical ,ris+ & ,sett+ ( ! ,/>s ,page #if ,almacan!rs #fc ,altitudes ib4 ------ ,m]idian ,altitude #fc ,amplitude #fb ,amphiscians #ia ,annual ,motion #g ,antci #ib ,ant>ctic ,circle #ec ------ ,pole ib4 ,antipodes #ic ,arctic ,circle #eb ,arctic ,pole #ec ,asc5sion #fh ------ ,"r ib4 ------ ,oblique #fi ,asc5sional ,diff]5ce ib4 ,ascians #ia ------ ,het]oscians ib4 ,a/]isms #cf ,atmosph]e #ha ,axis #dc ------ ( ! ,_w #di ,azimu? #fa ,babyloni% ,h\rs #ga ,bissextile #gh ,circle #db ------ ,great ,circles ib4 ------ ,p>allel1 or less] ,circles #dc ------ ,second>y ,circles ib4 ,circles ( ! ,sph]e #dg ,climates #ic ,colures #ec ------ ,equ9octial ,colure ib4 ------ ,sol/itial ,colure #ed ,comets #bi ,conjunction #aa1 #bjg ,con/ellations #cf ,cosmical ris+ & sett+ ( ! ,/>s #if ,crepusculum #hc ,day1 ,natural & ,artificial #fi ,decl9ation #eb ,diurnal ,motion #g ,diurnal ,ar* #fh ,eclipses #bjh ------ ,sol> ib4 ------ ,lun> ib4 ,eclipses ( ,jupit]'s ,satellites #bab ,ecliptic #ec ,egyptian ,ye> #ge ,elongation #ah ,equator1 or ,equ9octial #dh ,equ9octial ,po9ts #ec ------ ,precession ( #ee ------ ,v]nal & ,autumnal #gj ,exc5tricity #d ,galaxy1 or ,milky ,way #ch ,geoc5tric ,place #ai ,globe #db ------ ,t]re/rial #dc ------ ,cele/ial #dd ,gregorian ,acc\nt #hj ,heliacal ris+ & sett+ ( ! ,/>s #if ,helioc5tric ,place #ai ,hemisph]e #db ------ ,nor!rn & ,s\!rn #di ,het]oscians #ia ,horizon #eh ------ ,s5sible ib4 ------ ,rational #ei ,h\r ,circles #ej ,italian ,h\rs #gb ,jewi% ,h\rs ib4 ,julian ,acc\nt #gi ,latitude1 9 ,a/ronomy #ef ------ 9 ,geography #hd ,longitude 9 ,a/ronomy #ef ------ 9 ,geography #hg ,m]idian #ej1 #fa ,nadir #fa ,nodes #c1 #bjb ,nocturnal ,ar* #fh ,orbit #c ,p>allel ( ! ,e>?'s ,semidiamet] #bc ------ ( ! ,e>?'s ,annual ,orb #bj ,p]ici #ib ,p]iscians #ia ,p]iodical ,mon? #gd1 #bjb ,phases ( ! ,moon #bja ,planets #a ------ ,inf]ior & ,sup]ior #ad ,planet>y ,h\rs #gb ,poles #db ------ ( ! ,_w #di ------ ( ! ,ecliptic #ef ,pol> ,circles #eb ,po9ts ( ! ,compass #fj ------ ,c>d9al ,po9ts #ei ,prim>y ,planets #e ,retrograde ,motion ( ! ,planets #ahg ------ ( ! ,nodes #bjb ,second>y ,planets #e ,sid]eal ,ye> #gd ,signs ( ! ,zodiac #ed ------ ,nor!rn & ,s\!rn ib4 ,sol/ices #ga ------ ,summ] & ,w9t] ,sol/ices ib4 ,sol/itial ,po9ts #ec ,sph]e #db ------ ,p>allel & ,"r #fg ------ ,oblique #fh ,/ation>y #ahf ,/yle ,old #gi ------ ,new ,/yle #hj ,synodical ,mon? #gd1 #bjb ,tropics 7( ,canc] & ,capricorn7 #eb ,twilights #hc ,v]tical ,circles #fa ------ ,prime ,v]tical #fb ,z5i? #fa ,z5i? ,di/ance #fc ,zones1 ,torrid1 ,temp]ate1 & ,frigid #ij ,,! ,,end ,directions to ! ,b9d]4 ,! great ,,orr]y to face ! ,title4 ,plate ,i4 ,page #b ,plate ,,ii4 #bh ,! ,globes #ce ,plate ,,iii4 #aid ,plate ,,iv4 #bjj ,plate ,v4 #bad ,a ,,catalogue ,( ,ma!matical1 ,philosophical1 & ,optical ,in/rum5ts1 ,,made & ,,sold by ,,b5jam9 ,,cole1 ,at 8 ,%op1 ! ,sign ( ! ,orr]y1 ,no4 #acf1 9 ,fleet /reet1 ,london4 l4 s4 d4 ,v>iety ( pocket cases ( ,draw+ ,in/rum5ts1 9 ,silv]1 f #cl4 #cs4 to #bj #j #j ,ditto1 9 ,brass1 f #es4 to #e #e #j ,magaz9e ,cases1 9 ,silv]1 f #abl4 to #aej #j #j ,ditto1 9 ,brass1 f #el4 to #ej #j #j ,circul> ,compasses to describe a ,circle z small z a p9's head1 f #cs4 to #j #g #f ,long ,h& ,draw+-p5s1 f #as4 to #j #e #j ,compasses 9 ,brass1 ) %ift+ po9ts1 z ! ,ink & ,black ,lead po9ts1 f #bs4 #f;d4 to #a #a #j ,pla9 ,compasses1 f #f;d4 to #j #e #j ,beam ,compasses1 = draw+ l>ge circles1 f #ab4 to #c #j #j ,proportionable ,compasses1 f #al4 #as4 to #e #e #j ,triangul> ,compasses1 f #ads4 to #j #ah #j ,elliptical ,compasses1 = ,ovals1 f #al4 #aas4 #f;d4 to #e #e #j ,hair ,compasses #j #g #f ,b[s = draw+ curv$ l9es1 f #ds4 to #j #aj #f ,sets ( ,fea!r-edge ,scales1 9 ,brass1 ,ivory1 or ,wood1 f #abs4 to #a #af #j ,pla9 ditto1 or ,plott+ ditto1 9 ditto1 f #h;d4 to #j #ah #j ,gunt]'s #b feet1 & #a foot ,scales1 9 ,brass or ,wood1 f #bs4 to #b #b #j ,protractors ( all sorts1 f #as4 #f;d4 to #a #af #j ,p>allel ,rules1 f #f to #cf in*es1 f #bs4 #f;d4 to #a #af #j ,cross-b> ditto1 9 ,brass1 ,ivory1 or ,wood1 f #d in*es1 to #c feet1 f #ajs4 #f;d4 to #c #j #j ,sectors1 9 ditto1 f #bs4 #f;d4 to #d #ad #f ,!odolites1 f #cl4 #cs4 to #f #f #j ,ditto1 ) ,v]tical ar*1 ,_s ,levels1 ,telescope1 c4 f #ajl4 #ajs4 to #ba #j #j ,pla9 ,tables1 f #cl4 #cs4 to #e #e #j ,circumf]5tors1 ! pr9cipal ,in/rum5t = ,survey+ 9 ! ,we/-,indies1 f #al4 #afs4 to #c #ac #f ,gunt]'s f\r pole *a9s1 f #fs4 to #j #ab #j ,_s ,levels ( all sorts1 f #es4 to #ab #ab #j ,p5tographia1 = ! ready & exact r$uction or copy+ ( ,s*emes1 ,draw+s1 ,pr9ts1 c4 #d #ad #f ,measur+ ,:eels = ,survey+1 f #dl4 #ads4 #f;d4 to #f #f #j ,hadley's ,quadrants1 ) ,diagonal ,divisions #a #ad #j ,ditto1 ) a ,nonius1 f #bl4 #bs4 to #c #ac #f ,ditto1 all 9 ,brass1 f #cl4 #acs4 #f;d4 to #f #f #j ,davies's ,quadrant1 f #abs4 to #a #a #j ,cole's ditto1 f #ahs4 to #a #e #j ,sutton's ditto #j #f #j ,gunt]'s ditto1 f #cs4 #f;d4 to #a #a #j ,horizontal ,sun ,dials1 = all ,latitudes1 f #es4 to #aj #j #j ,r+ ,dials1 f #ajs4 #f;d4 to #ba #j #j ,azimu? ,compasses1 f #el4 #es4 to #aj #j #j ,amplitude ditto1 f #al4 #gs4 to #e #e #j ,m>9]'s ,compasses1 ei!r = ! ,cab91 or ,b9acle1 f #gs4 #f;d4 to #c #ac #j ,pocket ,compasses1 f #as4 to #a #aa #f ,l>ge ,orr]ies1 f #ejl4 to #bej #j #j ,armill>y ,sph]es1 f #abl4 to #ej #j #j ,sev5te5 in* ,globes #f #f #j ,fifte5 in* ditto #e #e #j ,twelve in* ditto #c #c #j ,n9e in* ditto #b #b #j ,six in* ditto #a #af #j ,?ree in* ditto1 9 a case1 f #hs4 to #j #aj #j ,l>ge d\ble ,b>rell'd /&+ air pumps #be #j #j ,app>atus to ditto1 f #cl4 #cs4 to #ab #ab #j ,d\ble ,b>rell'd table air pumps1 ) _! app>atus1 f #el4 #aes4 #f;d4 to #bj #j #j ,s+le ,b>rell'd ditto #b #ab #f ,app>atus to ditto #b #b #j ,electrical ,ma*9es1 9 ,brass1 ) app>atus1 box1 c4 f #el4 #es4 to #ac #ac #j ,b>omet]s1 f #al4 #as4 to #a #af #j ,ditto ,!rmomet]1 9 "o frame1 f #a4 #aas4 #f;d4 to #b #ab #f ,b>omet]1 ,!rmomet]1 & ,hydromet]1 all 9 "o frame1 f #bl #abs4 #f;d4 to #c #ac #f ,f>5heit's ,!rmomet]s1 9 mahogany cases1 f #al4 #es4 to #a #aa #f ,pocket ditto1 9 black cases1 f #abs4 to #a #a #j ,_s ,!rmomet]s1 on box scales1 = hot-h\ses #j #aj #f ,hydromet]s1 9 ,ivory1 f #ds4 to #j #e #f ,ditto1 9 copp]1 ) weights1 c4 = prov+ ,spirits1 f #al4 #as4 to #a #e #j ,hydro/atic ,balance1 ) app>atus1 c4 #a #ae #j ,speak+ ,trumpets1 f #ajs4 to #a #aa #f ,he>+ ditto1 f #gs4 #f;d4 to #a #a #j ,reflect+ ,telescopes1 f #al4 #afs4 to #ej #j #j ,refract+ ditto1 ( v>i\s l5g?s1 ) f\r or six glasses1 f #gs4 #f;d4 to #f #f #j ,d\ble reflect+ ,microscopes1 f #cl4 #acs4 #f;d4 to #g #g #j ,sol> ditto1 9 ,brass1 f #dl4 #ds4 to #f #f #j ,wilson's pocket ditto1 f #al4 #es4 to #b #ab #f ,opake ditto1 f #bl4 #abs4 #f;d4 to #c #ac #f ,clo? ditto1 f #cs4 #f;d4 to #j #g #f ,fl[] ditto1 f #cs4 #f;d4 to #j #e #j ,diagonal ,ma*9es = view+ pr9ts1 f #afs4 to #a #aa #f ,l>ge ,book ,cam]a ,obscura1 f #dl4 #ds4 to #e #e #j ,box ,cam]a ,obscura1 f #ajs4 #f;d4 to #b #b #j ,scioptric ,ball & ,socket1 9 ,wood #j #g #f ,op]a ,glasses1 f #es4 to #b #ab #f ,prospect ditto1 f #h;d4 to #j #aj #f ,magic ,lan?orn1 )\t objects1 f #al4 #as4 to #a #g #j ,magic ,lan?orn slid]s1 ) objects1 f #es4 to #j #aj #f ,mirrors1 convex or concave1 ( all sizes1 9 black frames1 f #ajs4 #f;d4 to #af #af #j ,prisms1 f #fs4 to #a #a #j ,read+ ,glasses set 9 a v>iety ( curi\s frames1 f #bs4 #f;d4 to #b #ab #f ,wat*mak]'s ,glasses1 9 frames1 f #as4 to #j #aj #f ,concave ditto1 = %ort sight$ p]sons1 f #as4#f;d4 to #b #b #j ,spectacles gr\nd on brass tools1 & set 9 silv]1 tortoise %ell1 horn1 c4 f #as4 to #a #g #j ,a*romatic1 ,op]a1 & ,prospect glasses1 f #al4 #as4 to #a #af #j ,a*romatic ,telescopes ( any l5g?1 at #al4 #as4 ea* foot4 ,gaug+ ,rules1 ,c>p5t]'s ,rules1 & all o!r k9d ( ,rules1 at ! usual ,prices4 ,! ,elev5? ,edition ( ,,h>ris on ! ,globes1 ) ! ,description & ,use ( ! ,orr]y1 #cs4 #f;d4 ,! ,use ( ! ,sector & pla9 ,scale expla9$1 #as4 ,! ,use ( ,,hadley's ,quadrant expla9$1 #f;d4 ,a f9e ,pr9t ( ! ,orr]y1 on imp]ial pap]1 #bs4 ,a small] ditto1 #f;d4 ,v>iety ( o!r ,in/rum5ts too t$i\s to m5tion1 are made & sold at ! above place3 ,:]e any ,g5tleman1 by ,lett]1 or o!r ,directions1 may dep5d on be+ z fai?fully s]v$ z if pres5t4 ,& z ,i h be5 long 9 ! ,:olesale "p ( ! ,bus9ess1 ,m]*ants1 c4 may be sure ( be+ suppli$ on ! ,be/ ,t]ms4 ,z also by ,m4 ,,allison1 at ,falm\?4 ,illu/ration ,,footnotes3 #a ,by ! ,orbit ( a ,planet is commonly und]/ood ! ,tract or ,r+1 describ$ by its ,c5t] r\nd ! ,sun1 b by ! ,plane ( ! ,orbit is meant a flat ,surface ext5d$ e way ?ro' ! ,orbit inf9itely4 #b ,n4 ,b4 ,accord+ to ,bia*9i's ,obs]vations1 ,v5us's axis incl9es #ge degrees f ! p]p5dicul> to ! plane ( ! ,ecliptic 7:i* is #ea deg4 m ?an ! axis ( our ,e>?7 h] ,tropics are only #ae deg4 f h] ,poles1 & h] ,pol> ,circles at ! same di/ance f h] ,equator2 s t ! ,sun's greate/ ,decl9ation on ea* side ( h] ,equator is #ge deg4 by :i* %e mu/ und]go a mu* great] v>iety ( seasons ?an we d on our ,e>?4 #c ,is a m>k commonly us$ = conjunction2 ?us ) ! 1 is to be read conjunction ) ! ,sun4 #d ,prob4 ,,vi4 #e ,prob4 ,,xiii4 #f ,! ins5sible *ange 9 ! ,longitude1 ,"r ,asc5sion1 & ,decl9ation ( ! ,fix$ ,/>s1 made by _! sl[ motion1 p>allel to ! ecliptic 7be+ b #a degree 9 #gb ye>s7 is n wor? notice 9 ?is place4 #g ,phases ( ! ,moon are ^? diff]5t appe>ances we obs]ve 9 h]1 accord+ to h] position 9 respect to ! ,sun & ,e>?4