,,transcrib]',s ,,notes3 --,obvi\s pr9t & punctuation errors 7 correct$4 --,bold text has be5 r5d]$ z bold text4 --,spac$ out text 7gesp]rt7 has be5 r5d]$ z spac$ text4 --,sup]script lett]s h be5 r5d]$ z ab & abc4 ,a ,,view ,,( ,sir ,,isaac ,,newton's ,,philosophy4 ,illu/ration ,,london3 ,pr9t$ by ,s4 ,,palm]1 #agbh4 ,illu/ration ,to ! ,noble & ,"r ,hon\rable ,,sir ,,rob]t ,,walpole4 ,,sir1 ,i ,take ! lib]ty to s5d y ?is view ( ,sir ,,isaac ,,newton',s philosophy1 :i*1 if x 7 p]=m$ suitable to ! dignity ( ! subject1 might n be a pres5t unwor?y ! acceptance ( ! greate/ p]son4 ,= 8 philosophy op]ations ( nature1 :i* = s _m ages _h imploy$ ! curiosity ( mank9d2 ?\gh no "o be=e him 0 furni%$ ) ! /r5g? ( m9d necess>y to g any dep? 9 ?is difficult se>*4 ,h[ev]1 ,i am enc\rag$ to hope1 t ?is attempt1 imp]fect z x is1 to give our c\ntrym5 9 g5]al "s conception ( ! lab\rs ( a p]son1 :o %all always be ! boa/ ( ?is nation1 may be receiv$ ) indulg5ce by "o1 "u ^: influ5ce ^! k+doms enjoy s mu* happ9ess4 ,inde$ my admiration at ! surpriz+ inv5tions ( ?is great man1 c>ries me to conceive ( him z a p]son1 :o n only mu/ raise ! glory ( ! c\ntry1 :i* gave him bir?2 b t he has ev5 done hon\r to human nature1 by hav+ ext5d$ ! greate/ & mo/ noble ( our faculties1 reason1 to subjects1 :i*1 till he attempt$ !m1 appe>$ to be :olly beyond ! rea* ( our limit$ capacities4 ,& :at c give u a m pleas+ prospect ( our own condition1 ?an to see s exalt$ a pro( ( ! /r5g? ( t faculty1 :]eon ! conduct ( our lives1 & our happ9ess dep5ds2 our passions & all our motives to action be+ 9 su* mann] guid$ by our op9ions1 t :]e ^! are j1 our :ole behavi\r w be praise-wor?y8 ,b :y d ,i presume to deta9 y1 ,,sir1 ) su* reflections z ^!1 :o mu/ h ! fulle/ exp]i5ce )9 y\r own m9d1 ( ! effects ( "r reason8 ,= to :at o!r s\rce c be ascrib$ t amiable frankness & unres]v$ condesc5sion among y\r fri5ds1 or t mascul9e p]spicuity & /r5g? ( argum5t1 :]eby y draw ! admiration ( ! publick1 :ile y are engag$ 9 ! mo/ important ( all causes1 ! lib]ties ( mank9d8 99 99 99 99 99 ,i humbly crave leave to make ! only ackn[l$gem5t )9 my p[]1 = ! b5efits1 :i* ,i receive 9 common ) ! re/ ( my c\ntrym5 f ^! high tal5ts1 by subscrib+ my self ,,sir1 ,y\r mo/ fai?ful1 & ,mo/ humble ,s]vant1 ,,h5ry ,,pemb]ton4 ,,preface4 ,i ,drew up ! foll[+ pap]s _m ye>s ago at ! desire ( "s fri5ds1 :o1 ^u my tak+ c>e ( ! late edition ( ,sir ,,isaac ,,newton',s ,pr9cipia1 p]swad$ me to make !m publick4 ,i laid hold ( t opportunity1 :5 my ?\ghts 7 afre% employ$ on ?is subject1 to revise :at ,i _h =m]ly writt54 ,& ,i n[ s5d x abroad n )\t "s hopes ( answ]+ ^! two ends4 ,my fir/ int5tion 0 to convey to su*1 z are n us$ to ma!matical reason+1 "s idea ( ! philosophy ( a p]son1 :o has acquir$ an univ]sal reputation1 & r5d]$ our nation fam\s = ^! speculations 9 ! le>n$ _w4 ,to :i* purpose ,i h avoid$ us+ t]ms ( art z mu* z possible1 & tak5 c>e to def9e su* z ,i 0 oblig$ to use4 ,?\gh ?is caution 0 ! less necess>y at pres5t1 s9ce _m ( !m are become famili> words to our language1 f ! great numb] ( books wrote 9 x ^u philosophical subjects1 & ! c\rses ( exp]im5ts1 t h ( late ye>s be5 giv5 by sev]al +5i\s m54 ,! o!r view ,i _h1 0 to enc\rage su* "y g5tlem5 z h a turn = ! ma!matical sci5ces1 to pursue ^? /udies ! m *e>fully1 9 ord] to und]/& 9 our au?or himself ! demon/rations ( ! ?+s ,i "h decl>e4 ,& to facilitate _! progress h]e91 ,i int5d to proce$ /ill f>!r 9 ! explanation ( ,sir ,,isaac ,,newton',s philosophy4 ,= z ,i h receiv$ v mu* pleasure f p]us+ 8 writ+s1 ,i hope x is no illaudable ambition to endeav\r ! r5d]+ !m m easily und]/ood1 t great] numb]s may enjoy ! same satisfaction4 ,x w p]haps be expect$1 t ,i %\ld say some?+ p>ticul> ( a p]son1 to :om ,i mu/ always ackn[l$ge my self to be mu* oblig$4 ,:at ,i h to decl>e on ?is head w be b %ort2 = x 0 9 ! v la/ ye>s ( ,sir ,,isaac's life1 t ,i _h ! hon\r ( 8 acqua9tance4 ,?is happ5$ on ! foll[+ occasion4 ,mr4 ,pol5us1 a ,pr(essor 9 ! ,univ]sity ( ,padua1 f a new exp]im5t ( 81 ?\ght ! common op9ion ab\t ! =ce ( mov+ bodies 0 ov]turn$1 & ! tru? ( ,mr4 ,libnitz's notion 9 t matt] fully prov$4 ,! contr>y ( :at ,pol5us _h ass]t$ ,i demon/rat$ 9 a pap]1 :i* ,dr4 ,,mead1 :o takes all opportunities ( oblig+ 8 fri5ds1 0 pleas$ to %ew ,sir ,,isaac ,,newton ,?is 0 s well approv$ ( by him1 t he did me ! hon\r to become a fell[-writ] ) me1 by annex+ to :at ,i _h writt51 a demon/ration ( 8 own drawn f ano!r consid]ation4 ,:5 ,i pr9t$ my disc\rse 9 ! philosophical transactions1 ,i put :at ,sir ,,isaac _h writt5 9 a s*olium by x self1 t ,i might n seem to usurp :at did n belong to me4 ,b ,i conceal$ 8 "n1 n be+ !n suffici5tly acqua9t$ ) him to ask :e!r he 0 will+ ,i might make use ( x or n4 ,9 a little "t aft] he engag$ me to take c>e ( ! new edition he 0 ab\t mak+ if 8 ,pr9cipia4 ,?is oblig$ me to be v frequ5tly ) him1 & z he liv$ at "s di/ance f me1 a great numb] ( lett]s pass$ betwe5 u on ?is acc\nt4 ,:5 ,i _h ! hon\r ( 8 conv]sation1 ,i endeav\r$ to le>n 8 ?\ghts ^u ma!matical subjects1 & some?+ hi/orical conc]n+ 8 inv5tions1 t ,i _h n be5 be=e acqua9t$ )4 ,i f\nd1 he _h read few] ( ! mod]n ma!maticians1 ?an "o c\ld h expect$2 b 8 own prodigi\s inv5tion readily suppli$ him ) :at he might h an occasion = 9 ! pursuit ( any subject he und]took4 ,i h (t5 he>d him c5sure ! h&l+ geometrical subjects by algebraic calculations2 & 8 book ( ,algebra he call$ by ! "n ( ,univ]sal ,ari?metic1 9 opposition to ! injudici\s title ( ,geometry1 :i* ,des ,c>tes _h giv5 to ! treatise1 :]e9 he %ews1 h[ ! geomet] may assi/ 8 inv5tion by su* k9d ( computations4 ,he frequ5tly prais$ ,slusius1 ,b>r[ & ,huyg5s = n be+ influ5c$ by ! false ta/e1 :i* !n began to prevail4 ,he us$ to comm5d ! laudable attempt ( ,hugo de ,om]ique to re/ore ! anci5t analysis1 & v mu* e/eem$ ,apollonius's book ,de sectione rationis = giv+ u a cle>] notion ( t analysis ?an we _h be=e4 ,dr4 ,b>r[ may be e/eem$ z hav+ %ewn a compass ( inv5tion equal1 if n sup]ior to any ( ! mod]ns1 our au?or only except$2 b ,sir ,,isaac ,,newton has sev]al times p>ticul>ly recomm5d$ to me ,huyg5s's /ile & mann]4 ,he ?\ght him ! mo/ elegant ( any ma!matical writ] ( mod]n times1 & ! mo/ j imitator ( ! anti5ts4 ,( _! ta/e1 & =m ( demon/ration ,sir ,,isaac always pr(ess$ himself a great admir]3 ,i h he>d him ev5 c5sure himself = n foll[+ !m yet m closely ?an he did2 & speak ) regret ( 8 mi/ake at ! beg9n+ ( 8 ma!matical /udies1 9 apply+ himself to ! works ( ,des ,c>tes & o!r algebraic writ]s1 be=e he _h consid]$ ! elem5ts ( ,euclide ) t att5tion1 :i* s excell5t a writ] des]ves4 ,z to ! hi/ory ( 8 inv5tions1 :at relates to 8 discov]ies ( ! me?ods ( s]ies & fluxions1 & ( 8 !ory ( light & col\rs1 ! _w has be5 suffici5tly in=m$ ( already4 ,! fir/ ?\ghts1 :i* gave rise to 8 ,pr9cipia1 he _h1 :5 he retir$ f ,cambridge 9 #afff on acc\nt ( ! plague4 ,z he sat alone 9 a g>d51 he fell into a speculation on ! p[] ( gravity3 t z ?is p[] is n f\nd s5sibly dim9i%$ at ! remote/ di/ance f ! c5t] ( ! e>?1 to :i* we c rise1 nei!r at ! tops ( ! l(tie/ build+s1 nor ev5 on ! summits ( ! highe/ m\nta9s2 x appe>$ to him reasonable to conclude1 t ?is p[] mu/ ext5d mu* f>!r ?an 0 usually ?\ght2 :y n z high z ! moon1 said he to himself8 & if s1 h] motion mu/ be influ5c$ by x2 p]haps %e is reta9$ 9 h] orbit !reby4 ,h[ev]1 ?\gh ! p[] ( gravity is n s5sibly weak5$ 9 ! little *ange ( di/ance1 at :i* we c place our selves f ! c5t] ( ! e>?2 yet x is v possible1 t s high z ! moon ?is p[] may diff] mu* 9 /r5g? f :at x is "h4 ,to make an e/imate1 :at might be ! degree ( ?is dim9ution1 he consid]$ ) himself1 t if ! moon be reta9$ 9 h] orbit by ! =ce ( gravity1 no d\bt ! prim>y planets are c>ri$ r\nd ! sun by ! l p[]4 ,& by comp>+ ! p]iods ( ! sev]al planets ) _! di/ances f ! sun1 he f\nd1 t if any p[] l gravity held !m 9 _! c\rses1 its /r5g? mu/ decrease 9 ! duplicate proportion ( ! increase ( di/ance4 ,?is be conclud$ by suppos+ !m to move 9 p]fect circles conc5trical to ! sun1 f :i* ! orbits ( ! greate/ "p ( !m d n mu* diff]4 ,suppos+ !re=e ! p[] ( gravity1 :5 ext5d$ to ! moon1 to decrease 9 ! same mann]1 he comput$ :e!r t =ce w\ld be suffici5t to keep ! moon 9 h] orbit4 ,9 ?is computation1 be+ abs5t f books1 he took ! common e/imate 9 use among geograph]s & our seam51 be=e ,norwood _h measur$ ! e>?1 t #fj ,engli% miles 7 conta9$ 9 "o degree ( latitude on ! surface ( ! e>?4 ,b z ?is is a v faulty supposition1 ea* degree conta9+ ab\t #fi ( our miles1 8 computation did n answ] expectation2 :5ce he conclud$1 t "s o!r cause mu/ at lea/ jo9 ) ! action ( ! p[] ( gravity on ! moon4 ,on ?is acc\nt he laid aside = t "t any f>!r ?\ghts ^u ?is matt]4 ,b "s ye>s aft]1 a lett] :i* he receiv$ f ,dr4 ,hook1 put him on inquir+ :at 0 ! real figure1 9 :i* a body let fall f any high place desc5ds1 tak+ ! motion ( ! e>? r\nd its axis into consid]ation4 ,su* a body1 hav+ ! same motion1 :i* by ! revolution ( ! e>? ! place has :5ce x falls1 is to be consid]$ z project$ =w>d & at ! same "t drawn d[n to ! c5t] ( ! e>?4 ,?is gave occasion to 8 resum+ 8 =m] ?\ghts conc]n+ ! moon2 & ,pic>t 9 ,france hav+ lately measur$ ! e>?1 by us+ 8 measures ! moon appe>$ to be kept 9 h] orbit purely by ! p[] ( gravity2 & consequ5tly1 t ?is p[] decreases z y rec$e f ! c5t] ( ! e>? 9 ! mann] our au?or _h =m]ly conjectur$4 ,^u ?is pr9ciple he f\nd ! l9e describ$ by a fall+ body to be an ellipsis1 ! c5t] ( ! e>? be+ "o focus4 ,& ! prim>y planets mov+ 9 su* orbits r\nd ! sun1 he _h ! satisfaction to see1 t ?is inquiry1 :i* he _h und]tak5 m]ely out ( curiosity1 c\ld be appli$ to ! greate/ purposes4 ,h]eupon he compos$ ne> a doz5 propositions relat+ to ! motion ( ! prim>y planets ab\t ! sun4 ,sev]al ye>s aft] ?is1 "s disc\rse he _h ) ,dr4 ,halley1 :o at ,cambridge made him a visit1 engag$ ,sir ,,isaac ,,newton to resume aga9 ! consid]ation ( ?is subject2 & gave occasion to 8 writ+ ! treatise :i* he publi%$ "u ! title ( ma!matical pr9ciples ( natural philosophy4 ,?is treatise1 full ( su* a v>iety ( pr(\nd inv5tions1 0 compos$ by him f sc>ce any o!r mat]ials ?an ! few propositions be=e m5tion$1 9 ! space ( "o ye> & an half4 ,?\gh 8 memory 0 mu* decay$1 ,i f\nd he p]fectly und]/ood 8 own writ+s1 contr>y to :at ,i _h frequ5tly he>d 9 disc\rse f _m p]sons4 ,?is op9ion ( !irs might arise p]haps f 8 n be+ always ready at speak+ on ^! subjects1 :5 x might be expect$ he %\ld4 ,b z to ?is1 x may be obs]v$1 t great g5ius's are frequ5tly liable to be abs5t1 n only 9 relation to common life1 b ) reg>d to "s ( ! p>ts ( sci5ce !y are ! be/ in=m$ (4 ,inv5tors seem to treasure up 9 _! m9ds1 :at !y h f\nd out1 aft] ano!r mann] ?an ^? d ! same ?+s1 :o h n ?is inv5tive faculty4 ,! =m]1 :5 !y h occasion to produce _! k1 are 9 "s measure oblig$ imm$iately to inve/igate "p ( :at !y want4 ,= ?is !y are n equally fit at all times3 s x has (t5 happ5$1 t su* z reta9 ?+s *iefly by means ( a v /rong memory1 h appe>$ (f h& m exp]t ?an ! discov]]s !mselves4 ,z to ! moral end[m5ts ( 8 m9d1 !y 7 z mu* to be admir$ z 8 o!r tal5ts4 ,b ?is is a field ,i leave o!rs to exspatiate 94 ,i only t\* ^u :at ,i exp]i5c$ myself dur+ ! few ye>s ,i 0 happy 9 8 fri5d%ip4 ,b ?is ,i imm$iately discov]$ 9 him1 :i* at once bo? surpriz$ & *>m$ me3 ,nei!r 8 extreme great age1 nor 8 univ]sal reputation _h r5dr$ him /iff 9 op9ion1 or 9 any degree elat$4 ,( ?is ,i _h occasion to h almo/ daily exp]i5ce4 ,! ,rem>ks ,i cont9ually s5t him by lett]s on 8 ,pr9cipia 7 receiv$ ) ! utmo/ goodness4 ,^! 7 s f> f be+ any ways displeas+ to him1 t on ! contr>y x occasion$ him to speak _m k9d ?+s ( me to my fri5ds1 & to hon\r me ) a publick te/imony ( 8 good op9ion4 ,he also approv$ ( ! foll[+ treatise1 a great "p ( :i* we read toge!r4 ,z _m alt]ations 7 made 9 ! late edition ( 8 ,pr9cipia1 s !re w\ld h be5 _m m if !re _h be5 a suffici5t "t4 ,b :atev] ( ?is k9d may be ?\ght want+1 ,i %all endeav\r to supply 9 my comm5t on t book4 ,i _h reason to believe he expect$ su* a ?+ f me1 & ,i int5d$ to h publi%$ x 9 8 life "t1 aft] ,i _h pr9t$ ! foll[+ disc\rse1 & a ma!matical treatise ,sir ,,isaac ,,newton _h writt5 a long :ile ago1 conta9+ ! fir/ pr9ciples ( fluxions1 = ,i _h prevail$ on him to let t piece g abroad4 ,i _h exam9$ all ! calculations1 & prep>$ "p ( ! figures2 b z ! latt] "p ( ! treatise _h nev] be5 f9i%$1 he 0 ab\t lett+ me h o!r pap]s1 9 ord] to supply :at 0 want+4 ,b 8 dea? put a /op to t design4 ,z to my comm5t on ! ,pr9cipia1 ,i int5d !re to demon/rate :atev] ,sir ,,isaac ,,newton has set d[n )\t express pro(1 & to expla9 all su* expressions 9 8 book1 z ,i %all judge necess>y4 ,?is comm5t ,i %all =?) put to ! press1 jo9$ to an engli% translation ( 8 ,pr9cipia1 :i* ,i h _h "s "t by me4 ,a m p>ticul> acc\nt ( my :ole design has already be5 publi%$ 9 ! new memoirs ( lit]ature = ! mon? ( m>* #agbg4 ,i h pres5t$ my read]s ) a copy ( v]ses on ,sir ,,isaac ,,newton1 :i* ,i h j receiv$ f a "y ,g5tleman1 :om ,i am pr\d to reckon among ! numb] ( my de>e/ fri5ds4 ,if ,i _h any appreh5sion t ?is piece ( poetry /ood 9 ne$ ( an apology1 ,i %\ld be desir\s ! read] might "k1 t ! au?or is b sixte5 ye>s old1 & 0 oblig$ to f9i% 8 composition 9 a v %ort space ( "t4 ,b ,i %all only take ! lib]ty to obs]ve1 t ! boldness ( ! digressions w be be/ judg$ ( by ^? :o are acqua9t$ ) ,,p9d>4 ,a ,,poem ,,on ,sir ,,isaac ,,newton4 ,,to ,,newton's g5ius1 & immortal fame ,?' adv5t'r\s muse ) trembl+ p9ion so>s4 ,?\1 heav'nly tru?1 f ?y s]aphick ?rone ,look fav\rable d[n1 d ?\ assi/ ,my lab'r+ ?\ght1 d ?\ inspire my song4 ,,newton1 :o fir/ ?' almighty's works display'd1 ,& smoo?'d t mirror1 9 ^: poli%'d face ,! great creator n[ conspicu\s %9es2 ,:o op5'd nature's adamant9e gates1 ,& to our m9ds h] secret p[]s expos'd2 ,,newton dem&s ! muse2 8 sacr$ h& ,%all guide h] infant /eps2 8 sacr$ h& ,%all raise h] to ! ,heliconian height1 ,:]e1 on its l(ty top in?ron'd1 h] head ,%all m+le ) ! ,/>s4 ,hail nature1 hail1 ,o ,goddess1 h&maid ( ?' e!real p[]1 ,n[ lift ?y head1 & to ?' admir+ _w ,%ew ?y long hidd5 beauty4 ,!e ! wise ,( anci5t fame1 immortal ,,plato's self1 ,! ,/agyrite1 & ,syracusian sage1 ,f black obscurity's abyss to raise1 7,droop+ & m\rn+ o'er ?y wondr\s works7 ,) va9 inquiry s\ght4 ,l meteors ^! ,9 _! d>k age bright sons ( wisdom %one3 ,b at ?y ,,newton all _! laurels fade1 ,!y %r9k f all ! hon\rs ( _! names4 ,s glimm'r+ />s contract _! feeble rays1 ,:5 ! swift lu/re ( ,,aurora's face ,fl[s o'er ! skies1 & wraps ! heav'ns 9 light4 ,,! ,deity's omnipot5ce1 ! cause1 ,?' orig9al ( ?+s long lay unkn[n4 ,alone ! beauties prom95t to sight 7,( ! cele/ial p[] ! outw>d =m7 ,drew praise & wond] f ! gaz+ _w4 ,z :5 ! deluge ov]spread ! e>?1 ,:il/ yet ! m\nta9s only re>'d _! heads ,above ! surface ( ! wild expanse1 ,:elm'd deep bel[ ! great f\ndations lay1 ,till "s k9d angel at heav'n's high comm& ,r\l'd back ! ris+ tides1 & haughty floods1 ,& to ! ocean ?und]'d out 8 voice3 ,quick all ! swell+ & imp]i\s waves1 ,! foam+ bill[s & obscur+ surge1 ,back to _! *annels & _! anci5t seats ,recoil affright$3 f ! d>ksome ma9 ,e>? raises smil+1 z new-born1 h] head1 ,& ) fre% *>ms h] lovely face arrays4 ,s 8 ext5sive ?\ght accompli%'d fir/ ,! mighty task to drive ?' ob/ruct+ mi/s ,( ignorance away1 b5ea? ^: gloom ,?' in%r\d$ maje/y ( ,nature lay4 ,he drew ! veil & swell'd ! spread+ sc5e4 ,h[ _h ! moon ar\nd ?' e!real void ,rang'd1 & elud$ lab'r+ mortals c>e1 ,till 8 inv5tion trac'd h] secret /eps1 ,:ile %e incon/ant ) un/eady re9 ,?r\gh endless mazes & me&]s guides ,9 its unequal c\rse h] *ang+ c>r3 ,:e!r beh9d ! sun's sup]ior light ,%e hides ! beauties ( h] radiant face1 ,or1 :5 conspicu\s1 smiles ^u mank9d1 ,unveil+ all h] night-rejoic+ *>ms4 ,:5 ?us ! silv]-tress$ moon dispels ,! fr[n+ horrors f ! br[ ( night1 ,& ) h] spl5dors *e>s ! sull5 gloom1 ,:ile sable-mantl$ d>kness ) 8 veil ,! visage ( ! fair horizon %ades1 ,& ov] nature spreads 8 rav5 w+s2 ,let me ^u "s unfrequ5t$ gre5 ,:ile sleep sits heavy on ! dr[sy _w1 ,seek out "s solit>y peaceful cell1 ,:]e d>ksome woods ar\nd _! gloomy br[s ,b[ l[1 & ev'ry hill's prot5d$ %ade ,obscures ! dusky vale1 !re sil5t dwell1 ,:]e contemplation holds its /ill abode1 ,!re trace ! wide & pa?less void ( heav'n1 ,& c\nt ! />s t sp>kle on its robe4 ,or else 9 fancy's wild'r+ mazes lo/ ,^u ! v]dure see ! fairy elves ,dance o'er _! magick circles1 or behold1 ,9 ?\ght enraptur'd ) ! anci5t b>ds1 ,m$ea's baleful incantations draw ,d[n f h] orb ! paly que5 ( night4 ,b *iefly ,,newton let me so> ) !e1 ,& :ile survey+ all yon />ry vault ,) admiration ,i att5tive gaze1 ,?\ %alt desc5d f ?y cele/ial seat1 ,& waft al(t my high-aspir+ m9d1 ,%alt %ew me !re h[ nature has orda9'd ,h] fundam5tal laws1 %alt lead my ?\ght ,?r\gh all ! w&'r+s ( ?' unc]ta9 moon1 ,& tea* me all h] op]at+ p[]s4 ,%e & ! sun ) influ5ce conjo9t ,wield ! huge axle ( ! :irl+ e>?1 ,& f _! j direction turn ! poles1 ,sl[ urg+ on ! progress ( ! ye>s4 ,! con/ellations seem to leave _! seats1 ,& o'er ! skies ) solemn pace to move4 ,y1 spl5did rul]s ( ! day & night1 ,! seas obey1 at y\r resi/less sway ,n[ !y contract _! wat]s1 & expose ,! dre>y des>t ( old ocean's reign4 ,! craggy rocks _! horrid sides disclose2 ,trembl+ ! sailor views ! dreadful sc5e1 ,& cauti\sly ! ?reat'n+ ru9 %uns4 ,b :]e ! %all[ wat]s hide ! s&s1 ,!re rav5\s de/ruction lurks conceal'd1 ,!re ! ill-guid$ vessel falls a prey1 ,& all h] numb]s gorge 8 gre$y jaws4 ,b quick return+ see ?' impetu\s tides ,back to ?' ab&on'd %ores impell ! ma94 ,aga9 ! foam+ seas ext5d _! waves1 ,aga9 ! r\l+ floods embrace ! %o>s1 ,& veil ! horr\rs ( ! empty deep4 ,?us ! obsequi\s seas y\r p[] confess1 ,:ile f ! surface heal?ful vap\rs rise ,pl5te\s ?r\gh\t ! atmosph]e diffus'd1 ,or to supply ! m\nta9's heads ) spr+s1 ,or fill ! hang+ cl\ds ) ne$ful ra9s1 ,t fri5dly /reams1 & k9d refre%+ %['rs ,may g5tly lave ! sun-burnt ?ir/y pla9s1 ,or to repl5i% all ! empty air ,) :olsome moi/ure to increase ! fruits ,( e>?1 & bless ! lab\rs ( mank9d4 ,o ,,newton1 :e!r flies ?y mighty s\l1 ,h[ %all ! feeble muse pursue ?r\gh all ,! va/ ext5t ( ?y unb\nd$ ?\ght1 ,t ev5 seeks ?' unse5 recesses d>k ,to p5etrate ( provid5ce imm5se4 ,& ?\ ! great disp5s] ( ! _w ,propiti\s1 :o ) inspiration taught'/ ,our greate/ b>d to s5d ?y praises =?2 ,?\1 :o gav'/ ,,newton ?\ght2 :o smil'd/ s]5e1 ,:5 to its b\nds he /ret*'d 8 swell+ s\l2 ,:o /ill b5ignant ev] ble/ 8 toil1 ,& deign'd to 8 enlight'n$ m9d t' appe> ,confess'd ar\nd ?' int]m9at$ _w3 ,to me ,o ?y div9e infusion grant 7,o ?\ 9 all s inf9itely good7 ,t ,i may s+ ?y ev]la/+ works1 ,?y inexhau/$ /ore ( provid5ce1 ,9 ?\ght effulg5t & res\nd+ v]se4 ,o c\ld ,i spread ! wond'r\s !me ar\nd1 ,:]e ! w9d cools ! ori5tal _w1 ,to ! calm breezes ( ! ,zephir's brea?1 ,to :]e ! froz5 hyp]borean bla/s4 ,to :]e ! boi/'r\s tempe/-lead+ s\? ,f _! deep holl[ caves s5d =? _! /orms4 ,?\ /ill indulg5t p>5t ( mank9d1 ,left humid emanations %\ld no m ,fl[ f ! ocean1 b dissolve away ,?r\gh ! long s]ies ( revolv+ "t2 ,& left ! vital pr9ciple decay1 ,by :i* ! air supplies ! spr+s ( life2 ,?\ ha/ ! fi]y visag'd comets =m'd ,) vivify+ spirits all replete1 ,:i* !y abundant brea! ab\t ! void1 ,r5ew+ ! prolifick s\l ( ?+s4 ,no long] n[ on !e amaz'd we call1 ,no long] tremble at imag9'd ills1 ,:5 comets blaze trem5d\s f on high1 ,or :5 ext5d+ wide _! flam+ tra9s ,) hide\s grasp ! skies engirdle r\nd1 ,& spread ! t]rors ( _! burn+ locks4 ,= ^! ?r\gh orbits 9 ! l5g?'n+ space ,( _m t$i\s r\l+ ye>s compleat ,ar\nd ! sun move regul>ly on2 ,& ) ! planets 9 h>moni\s orbs1 ,& my/ick p]iods _! obeysance pay ,to him maje/ick rul] ( ! skies ,^u 8 ?rone ( circl$ glory fixt4 ,he or "s god conspicu\s to ! view1 ,or else ! sub/itute ( nature seems1 ,guid+ ! c\rses ( revolv+ worlds4 ,he taught great ,,newton ! all-pot5t laws ,( gravitation1 by ^: simple p[] ,! univ]se exi/s4 ,nor "h ! sage ,big ) inv5tion /ill r5ew+ /aid4 ,b ,o bright angel ( ! lamp ( day1 ,h[ %all ! muse display 8 greate/ toil8 ,let h] plunge deep 9 ,aganippe's waves1 ,or 9 ,ca/alia's ev]-fl[+ /ream1 ,t re-inspir$ %e may s+ to !e1 ,h[ ,,newton d>'d adv5t'r\s to unbraid ,! yell[ tresses ( ?y %9+ hair4 ,or did/ ?\ graci\s leave ?y radiant sph]e1 ,& to 8 h& ?y lucid spl5d\rs give1 ,t' unweave ! light-diffus+ wrea?1 & "p ,! bl5d$ glories ( ?y gold5 plumes8 ,he ) labori\s1 & un]r+ c>e1 ,h[ diff]5t & imbodi$ col\rs =m ,?y pi]c+ light1 ) j di/9ction f\nd4 ,he ) quick sight pursu'd ?y d>t+ rays1 ,:5 p5etrat+ to ?' obscure recess ,( solid matt]1 !re p]spicu\s saw1 ,h[ 9 ! texture ( ea* body lay ,! p[] t sep>ates ! diff]5t beams4 ,h5ce ov] nature's unadorn$ face ,?y bright div]sify+ rays dilate ,_! v>i\s hues3 & h5ce :5 v]nal ra9s ,desc5d+ swift h bur/ ! l['r+ cl\ds1 ,?y spl5dors ?r\gh ! dissipat+ mi/s ,9 its fair ve/ure ( unnumb]'d hues ,array ! %['ry b[4 ,at ?y approa* ,! morn+ ris5 f h] pe>ly c\* ,) rosy blu%es decks h] virg9 *eek2 ,! ev'n+ on ! frontispiece ( heav'n ,8 mantle spreads ) _m col\rs gay2 ,! mid-day skies 9 radiant azure clad1 ,! %9+ cl\ds1 & silv] vap\rs rob'd ,9 :ite transp>5t int]mixt ) gold1 ,) bright v>iety ( spl5dor cloa? ,all ! illum9at$ face above4 ,:5 ho>y-head$ w9t] back retires ,to ! *ill'd pole1 !re solit>y sits ,encompass'd r\nd ) w9ds & tempe/s bleak ,9 cav]ns ( imp5etrable ice1 ,& f beh9d ! dissipat$ gloom ,l a new ,v5us f ! p>t+ surge ,! gay-app>ell'd spr+ advances on2 ,:5 ?\ 9 ?y m]idian brightness sitt'/1 ,& f ?y ?rone pure emanations fl[ ,( glory bur/+ o'er ! radiant skies3 ,!n let ! muse ,olympus' top asc5d1 ,& o'er ,!ssalia's pla9 ext5d h] view1 ,& c\nt1 ,o ,tempe1 all ?y beauties o'er4 ,m\nta9s1 ^: summits grasp ! p5dant cl\ds1 ,betwe5 _! wood-invelop'd slopes embrace ,! gre5-attir$ vallies4 ,e fl['r ,"h 9 ! pride ( b\nte\s nature clad ,smiles on ! bosom ( ?' enamell'd meads4 ,ov] ! smil+ lawn ! silv] floods ,( fair ,p5eus g5tly r\l along1 ,:ile ! reflect$ col\rs f ! fl['rs1 ,& v]dant bord]s pi]ce ! lympid waves1 ,& pa9t ) all _! v>iegat$ hue ,! yell[ s&s b5ea?4 ,smoo? glid+ on ,! wat]s ha/5 to ! neighb\r+ sea4 ,/ill ! pleas'd eye ! float+ pla9 pursues2 ,at l5g?1 9 ,neptune's wide dom9ion lo/1 ,surveys ! %9+ bill[s1 t arise ,app>ell'd ea* 9 ,phbus' bright attire3 ,or f a f> "s tall maje/ick %ip1 ,or ! long ho/ile l9es ( ?reat'n+ fleets1 ,:i* o'er ! bright unev5 mirror sweep1 ,9 dazl+ gold & wav+ purple deckt2 ,su* z ( old1 :5 haughty ,a!ns p[] ,_! hide\s front1 & t]rible array ,aga9/ ,pall5e's coa/ ext5d$ wide1 ,& ) trem5d\s w> & battel /]n ,! trembl+ walls ( ,potida %ook4 ,cre/$ ) p5dants curl+ ) ! breeze ,! upright ma/s high bri/le 9 ! air1 ,al(t exalt+ pr\d _! gild$ heads4 ,! silv] waves aga9/ ! pa9t$ pr[s ,raise _! respl5d5t bosoms1 & impe>l ,! fair v]million ) _! gli/'r+ drops3 ,& f on bo>d ! iron-cloa!d ho/ ,ar\nd ! ma9 a gleam+ horr\r ca/s2 ,ea* flam+ buckl] l ! mid-day sun1 ,ea* plum$ helmet l ! silv] moon1 ,ea* mov+ gauntlet l ! light'n+'s blaze1 ,& l a /> ea* braz5 po9t$ spe>4 ,b lo ! sacr$ high-erect$ fanes1 ,fair citadels1 & m>ble-cr[n$ t[]s1 ,& sumptu\s palaces ( /ately t[ns ,magnific5t arise1 ^u _! heads ,be>+ on high a wrea? ( silv] light4 ,b see my muse ! high ,pi]ian hill1 ,behold its %aggy locks & airy top1 ,up to ! skies ?' imp]i\s m\nta9 heaves ,! %9+ v]dure ( ! nodd+ woods4 ,see :]e ! silv] ,hippocr5e fl[s1 ,behold ea* glitt'r+ rivulet1 & rill ,?r\gh mazes w&] d[n ! gre5 desc5t1 ,& sp>kle ?r\gh ! int]wov5 trees4 ,"h re/ a :ile & humble homage pay1 ,"h1 :]e ! sacr$ g5ius1 t inspir'd ,sublime ,m,,onides & ,,p9d>',s brea/1 ,8 habitation once 0 fam'd to hold4 ,"h ?\1 ,o ,,hom]1 (f]'d/ up ?y v[s1 ,!e1 ! k9d muse ,,calliop,a he>d1 ,& l$ !e to ! empyrean feats1 ,!re manife/$ to ?y hall['d eyes ,! de$s ( gods2 !e wise ,,m9]va taught ,! wondr\s art ( kn[+ human k9d2 ,h>moni\s ,,ph,,bus tun'd ?y heav'nly m9d1 ,& swell'd to rapture ea* exalt$ s5se2 ,ev5 ,,m>s ! dreadful battle-rul+ god1 ,,m>s taught !e w>1 & ) 8 bloody h& ,in/ruct$ ?9e1 :5 9 ?y s\nd+ l9es ,we he> ! rattl+ ( ,bellona's c>r1 ,! yell ( discord1 & ! d9 ( arms4 ,,p9d>1 :5 m\nt$ on 8 fi]y /e$1 ,so>s to ! sun1 oppos+ eagle l ,8 eyes undazl$ to ! fi]ce/ rays4 ,he firmly seat$1 n l ,,glaucus' son1 ,/rides 8 swift-w+$ & fire-brea?+ horse1 ,& born al(t /rikes ) 8 r++ ho(s ,! braz5 vault ( heav'n1 sup]ior !re ,looks d[n ^u ! />s1 ^: radiant light ,illum9ates innum]able worlds1 ,t ?r\gh et]nal orbits r\l b5ea?4 ,b ?\ all hail immortaliz$ son ,( h>mony1 all hail ?\ ,?racian b>d1 ,to :om ,,apollo gave 8 tuneful lyre4 ,o might'/ ?\1 ,,orpheus1 n[ aga9 revive1 ,& ,,newton %\ld in=m ?y li/'n+ e> ,h[ ! s(t notes1 & s\l-in*ant+ /ra9s ,( ?y own lyre 7 on ! w9d convey'd4 ,he taught ! muse1 h[ s\nd progressive floats ,^u ! wav+ p>ticles ( air1 ,:5 h>mony 9 ev]-pleas+ /ra9s1 ,melodi\s melt+ at ea* lull+ fall1 ,) s(t allur+ p5etration /eals ,?r\gh ! enraptur'd e> to inmo/ ?\ght1 ,& folds ! s5ses 9 its silk5 b&s4 ,s ! sweet musick1 :i* f ,,orpheus' t\* ,& fam'd ,,amphion',s1 on ! s\nd+ /r+ ,arose h>moni\s1 glid+ on ! air1 ,pi]c'd ! t\gh-b>k'd & knotty-ribb$ woods1 ,into _! saps s(t inspiration brea?'d ,& taught att5tion to ! /ubborn oak4 ,?us :5 great ,,h5ry1 & brave ,,m>lb',,r\gh l$ ,?' imbattl$ numb]s ( ,,britannia',s sons1 ,! trump1 t swells ?' exp&$ *eek ( fame1 ,t adds new vig\r to ! g5'r\s y\?1 ,& r\zes sluggi% c[>dize x self1 ,! trumpet ) its ,m>s-incit+ voice1 ,! w9ds broad brea/ impetu\s sweep+ o'er ,fill'd ! big note ( w>4 ,?' inspir$ ho/ ,) new-born ardor press ! trembl+ ,,gaul2 ,nor great] ?rongs _h rea*'d et]nal night1 ,n if ! fields ( ,ag5c\rt _h yawn'd ,expos+ horrible ! gulf ( fate2 ,or ro>+ ,danube spread 8 arms abroad1 ,& ov]:elm'd _! legions ) 8 floods4 ,b let ! w&'r+ muse at l5g? return2 ,nor yet1 angelick g5ius ( ! sun1 ,9 wor?y lays h] high-attempt+ song ,has blazon'd =? ?y v5]at$ "n4 ,!n let h] sweep ! l\d-res\nd+ lyre ,aga91 aga9 o'er ea* melodi\s /r+ ,tea* h>mony to tremble ) ?y praise4 ,& /ill ?9e e> ,o fav\rable grant1 ,& %e %all tell !e1 t :atev] *>ms1 ,:atev] beauties bloom on nature's face1 ,proce$ f ?y all-influ5c+ light4 ,t :5 aris+ ) tempe/u\s rage1 ,! ,nor? impetu\s rides ^u ! cl\ds ,disp]s+ r\nd ! heav'ns ob/ructive gloom1 ,& ) 8 dread$ prohibition /ays ,! k9d effusion ( ?y g5ial beams2 ,pale are ! rubies on ,,aurora',s lips1 ,no m ! roses blu% ^u h] *eeks1 ,black are ,p5eus' /reams & gold5 s&s ,9 ,tempe's vale dull melan*oly sits1 ,& e fl[] recl9es its languid head4 ,by :at high "n %all ,i invoke !e1 say1 ,?\ life-infus+ deity1 on !e ,i call1 & look propiti\s f on high1 ,:ile n[ to !e ,i (f] up my pray]4 ,o _h great ,,newton1 z he f\nd ! cause1 ,by :i* s\nd r\ls ?ro' ?' undulat+ air1 ,o _h he1 baffl+ times resi/less p[]1 ,discov]'d :at t subtle _s is1 ,or :atsoe'er diffusive else is spread ,ov] ! wide-ext5d$ univ]se1 ,:i* causes bodies to reflect ! light1 ,& f _! /raight direction to div]t ,! rapid beams1 t ?r\gh _! surface pi]ce4 ,b s9ce embrac'd by ?' icy arms ( age1 ,& 8 quick ?\ght by times cold h& congeal'd1 ,ev'n ,,newton left unkn[n ?is hidd5 p[]2 ,?\ f ! race ( human k9d select ,"s o!r wor?y ( an angel's c>e1 ,) inspiration animate 8 brea/1 ,& him in/ruct 9 ^! ?y secret laws4 ,o let n ,,newton1 to ^: spaci\s view1 ,n[ unob/ruct$1 all ?' ext5sive sc5es ,( ! e!real rul]'s works arise2 ,:5 he beholds ?is e>? he late adorn'd1 ,let him n see philosophy 9 te>s1 ,l a fond "m solit>y sit1 ,lam5t+ him h] de>1 & only *ild4 ,b z ! wise ,,py?agoras1 & he1 ,^: bir? ) pride ! fam'd ,abd]a boa/s1 ,) expectation hav+ long survey'd ,?is spot _! anci5t seat1 ) joy beheld ,div9e philosophy at l5g? appe> ,9 all h] *>ms maje/ically fair1 ,conduct$ by immortal ,,newton',s h&4 ,s may he see ano!r sage arise1 ,t %all ma9ta9 h] empire3 !n no m ,imp]i\s ignorance ) haughty sway ,%all /alk rapaci\s o'er ! ravag'd globe3 ,!n ?\1 ,o ,,newton1 %alt protect ^! l9es4 ,! humble tribute ( ! grateful muse2 ,ne'er %all ! sacrilegi\s h& despoil ,h] laurel'd temples1 :om 8 "n pres]ves3 ,& 7 %e equal to ! mighty !me1 ,futurity %\ld wond] at h] song2 ,"t %\ld receive h] ) ext5d$ arms1 ,seat h] conspicu\s 9 8 r\l+ c>r1 ,& be> h] d[n to 8 extreame/ b\nd4 ,,fables ) wond] tell h[ ,t]ra's sons ,) iron =ce unloos'd ! /ubborn n]ves ,( hills1 & on ! cl\d-in%r\d$ top ,( ,pelion ,ossa pil'd4 ,b if ! va/ ,gigantick de$s ( savage /r5g? dem& ,a/oni%m5t f m51 :at !n %alt ?\1 ,o :at expressive rapture ( ! s\l1 ,:5 ?\ be=e u1 ,,newton1 do/ display ,! lab\rs ( ?y great excell+ m9d2 ,:5 ?\ unveile/ all ! wondr\s sc5e1 ,! va/ idea ( ?' et]nal k+1 ,n dreadful be>+ 9 8 angry arm ,! ?und] hang+ o'er our trembl+ heads2 ,b ) ?' effulg5cy ( love replete1 ,& clad ) p[]1 :i* =m'd ?' ext5sive heav5s4 ,o happy he1 ^: ent]priz+ h& ,unb>s ! gold5 & relucid gates ,( ?' empyrean dome1 :]e ?\ en?ron'd ,philosophy art seat$4 ,?\ su/a9'd ,by ! firm h& ( ev]la/+ tru? ,despise/ all ! injuries ( "t2 ,?\ nev] "k'/ decay :5 all ar\nd1 ,antiquity obscures h] head4 ,behold ,?' ,egyptian t[]s1 ! ,babylonian walls1 ,& ,!bes ) all h] hundr$ gates ( brass1 ,behold !m scatt]'d l ! du/ abroad4 ,:atev] n[ is fl\ri%+ & pr\d1 ,:atev] %all1 mu/ "k dev\r+ age4 ,euphrates' /ream1 & sev5-m\!d ,nile1 ,& ,danube1 ?\ t f ,g]mania's soil ,to ! black ,eux9e's f> remot$ %ore1 ,o'er ! wide b\nds ( mighty nations sweep'/ ,9 ?und] l\d ?y rapid floods along4 ,ev'n y %all feel inexorable "t2 ,to y ! fatal day %all come2 no m ,y\r torr5ts !n %all %ake ! trembl+ gr\nd1 ,no long] !n to inundations swol'n ,?' imp]i\s waves ! f]tile pa/ures dr5*1 ,b %runk )9 a n>r[ *annel glide2 ,or ?r\gh ! ye>'s reit]at$ c\rse ,:5 "t himself gr[s old1 y\r wond'r\s /reams ,lo/ ev'n to memory %all lie unkn[n ,b5ea? obscurity1 & ,*aos :elm'd1 ,b /ill ?\ sun illum9ate/ all ,! azure regions r\nd1 ?\ guide/ /ill ,! orbits ( ! planet>y sph]es2 ,! moon /ill w&]s o'er h] *ang+ c\rse1 ,& /ill1 ,o ,,newton1 %all ?y "n survive3 ,z long z nature's h& directs ! _w1 ,:5 ev'ry d>k ob/ruction %all retire1 ,& ev'ry secret yield its hidd5 /ore1 ,:i* !e dim-sight$ age =bad to see ,age t alone c\ld /ay ?y ris+ s\l4 ,& c\ld mank9d among ! fix$ />s1 ,e'en to ?' extreme/ b\nds ( k rea*1 ,to ^? unkn[n innum]able suns1 ,^: light b glimm]s f ^? di/ant worlds1 ,ev'n to ^? utmo/ b\nd>ies1 ^? b>s ,t %ut ! entrance ( ?' illum9'd space ,:]e angels only tread ! va/ unkn[n1 ,?\ ev] %\ld'/ be se5 immortal !re3 ,9 ea* new sph]e1 ea* new-appe>+ sun1 ,9 f>!/ regions at ! v v]ge ,( ! wide univ]se %\ld'/ ?\ be se54 ,& lo1 ?' all-pot5t goddess ,,nature takes ,) h] own h& ?y great1 ?y j rew>d ,( immortality2 al(t 9 air ,see %e displays1 & ) et]nal grasp ,upre>s ! trophies ( great ,,newton's fame4 ,r4 ,,glov]4 ,,! ,,cont5ts4 ,,introduction conc]n+ ,sir ,,isaac ,,newton's me?od ( reason+ 9 philosophy pag4 #a ,,book ,i4 ,,*ap4 #a4 ,( ! laws ( motion ,! fir/ law ( motion prov$ p4 #bi ,! second law ( motion prov$ p4 #bi ,! ?ird law ( motion prov$ p4 #ca ,,*ap4 #b4 ,fur!r pro(s ( ! laws ( motion ,! effects ( p]cussion p4 #di ,! p]p5dicul> desc5t ( bodies p4 #ee ,! oblique desc5t ( bodies 9 a /raight l9e p4 #eg ,! curvil9e> desc5t ( bodies p4 #eh ,! p]p5dicul> asc5t ( bodies ibid4 ,! oblique asc5t ( bodies p4 #ei ,! p[] ( gravity proportional to ! quantity ( matt] 9 ea* body p4 #fj ,! c5tre ( gravity ( bodies p4 #fb ,! me*anical p[]s p4 #fi ,! lev] p4 #ga ,! :eel & axis p4 #gg ,! pulley p4 #hj ,! w$ge p4 #hc ,! screw ibid4 ,! incl9$ pla9 p4 #hd ,! p5dulum p4 #hf ,vibrat+ 9 a circle ibid4 ,vibrat+ 9 a cycloid p4 #ia ,! l9e ( swifte/ desc5t p4 #ic ,! c5tre ( oscillation p4 #id ,exp]im5ts ^u ! p]cussion ( bodies made by p5dulums p4 #ih ,! c5tre ( p]cussion p4 #ajj ,! motion ( projectiles p4 #ajb ,! description ( ! conic sections p4 #ajf ,! diff]5ce betwe5 absolute & relative motion1 z also betwe5 absolute & relative "t p4 #aab ,,*ap4 #c4 ,( c5tripetal =ces p4 #aag ,,*ap4 #d4 ,( ! resi/ance ( fluids p4 #adc ,bodies are resi/$ 9 ! duplicate proportion ( _! velocities p4 #adg ,( ela/ic fluids & _! resi/ance p4 #adi ,h[ fluids may be r5d]$ ela/ic p4 #aej ,! degree ( resi/ance 9 reg>d to ! proportion betwe5 ! d5sity ( ! body & ( ! fluid ,9 r>e & uncompress$ fluids p4 #aec ,9 compress$ fluids p4 #aee ,! degree ( resi/ance z x dep5ds ^u ! figure ( bodies ,9 r>e & uncompress$ fluids p4 #aee ,9 compress$ fluids p4 #aeh ,,book ,,ii4 ,,*ap4 #a4 ,t ! planets move 9 a space empty ( s5sible matt] p4 #afa ,! sy/em ( ! _w describ$ p4 #afb ,! planets suff] no s5sible resi/ance 9 _! motion p4 #aff ,!y are n kept 9 motion by a fluid p4 #afh ,t all space is n full ( matt] )\t vacancies p4 #afi ,,*ap4 #b4 ,conc]n+ ! cause t keeps 9 motion ! prim>y planets p4 #aga ,!y are influ5c$ by a c5tripetal p[] direct$ to ! sun p4 #aga ,! /r5g? ( ?is p[] is reciprocally 9 ! duplicate proportion ( ! di/ance ibid4 ,! cause ( ! irregul>ities 9 ! motions ( ! planets p4 #age ,a correction ( _! motions p4 #agh ,t ! frame ( ! _w is n et]nal p4 #ahj ,,*ap4 #c4 ,( ! motion ( ! moon & ! o!r second>y planets ,t !y are influ5c$ by a c5tripetal =ce direct$ t[>d _! prim>y1 z ! prim>y are influ5c$ by ! sun p4 #ahb ,t ! p[] usually call$ gravity ext5ds to ! moon p4 #ahi ,t ! sun acts on ! second>y planets p4 #aij ,! v>iation ( ! moon p4 #aic ,t ! circuit ( ! moons orbit is increas$ by ! sun 9 ! qu>t]s1 & dim9i%$ 9 ! conjunction & opposition p4 #aih ,! di/ance ( ! moon f ! e>? 9 ! qu>t]s & 9 ! conjunction & opposition is alt]$ by ! sun p4 #bjj ,^! irregul>ities 9 ! moon's motion v>i$ by ! *ange ( di/ance betwe5 ! e>? & sun p4 #bja ,! p]iod ( ! moon r\nd ! e>? & h] di/ance v>i$ by ! same means ibid4 ,! motion ( ! nodes & ! incl9ation ( ! moons orbit p4 #bjb ,! motion ( ! apogeon & *ange ( ! ecc5tricity p4 #bah ,! inequalities ( ! o!r second>y planets d$ucible f ^! ( ! moon p4 #bbi ,,*ap4 #d4 ,( comets ,!y are n meteors1 nor plac$ totally )\t ! planet>y sy/em p4 #bcj ,! sun acts on !m 9 ! same mann] z on ! planets p4 #bca ,_! orbits are ne> to p>abola's p4 #bcc ,! comet t appe>$ at ! end ( ! ye> #afhj1 probably p]=ms its p]iod 9 #ege ye>s1 & ano!r comet 9 #ge ye>s p4 #bcd ,:y ! comets move 9 planes m diff]5t f "o ano!r ?an ! planets p4 #bce ,! tails ( comets p4 #bch ,! use ( !m p4 #bdc #bdd ,! possible use ( ! comet x self p4 #bde #bdf ,,*ap4 #e4 ,( ! bodies ( ! sun & planets ,t ea* ( ! heav5ly bodies is endu$ ) an attractive p[]1 & t ! =ce ( ! same body on o!rs is proportional to ! quantity ( matt] 9 ! body attract$ p4 #bdg ,?is prov$ 9 ! e>? p4 #bdh ,9 ! sun p4 #bej ,9 ! re/ ( ! planets p4 #bea ,t ! attractive p[] is ( ! same nature 9 ! sun & 9 all ! planets1 & !re=e is ! same ) gravity p4 #beb ,t ! attractive p[] 9 ea* ( ^! bodies is proportional to ! quantity ( matt] 9 ! body attract+ ibid4 ,t ea* p>ticle ( :i* ! sun & planets are compos$ is endu$ ) an attract+ p[]1 ! /r5g? ( :i* is reciprocally 9 ! duplicate proportion ( ! di/ance p4 #beg ,! p[] ( gravity univ]sally belongs to all matt] p4 #bei ,! diff]5t weight ( ! same body ^u ! surface ( ! sun1 ! e>?1 ,jupit] & ,saturn2 ! respective d5sities ( ^! bodies1 & ! proportion betwe5 _! diamet]s p4 #bfa ,,*ap4 #f4 ,( ! fluid p>ts ( ! planets ,! mann] 9 :i* fluids press p4 #bfd ,! motion ( waves on ! surface ( wat] p4 #bfi ,! motion ( s\nd ?r\gh ! air p4 #bgj ,! velocity ( s\nd p4 #bhb ,conc]n+ ! tides p4 #bhc ,! figure ( ! e>? p4 #bif ,! effect ( ?is figure ^u ! p[] ( gravity p4 #cjj ,! effect x has ^u p5dulums p4 #cjb ,bodies desc5d p]p5dicul>ly to ! surface ( ! e>? p4 #cjd ,! axis ( ! e>? *anges its direction twice a ye>1 & twice a mon? p4 #cac ,! figure ( ! second>y planets ibid4 ,,book ,,iii4 ,,*ap4 #a4 ,conc]n+ ! cause ( col\rs inh]5t 9 ! light ,! sun's light is compos$ ( rays ( diff]5t col\rs p4 #cah ,! refraction ( light p4 #cai #cbj ,bodies appe> ( diff]5t col\r by day-light1 because "s reflect "o k9d ( light m copi\sly ?an ! re/1 & o!r bodies o!r k9ds ( light p4 #cbi ,! effect ( mix+ rays ( diff]5t col\rs p4 #ccd ,,*ap4 #b4 ,( ! prop]ties ( bodies :]eon _! col\rs dep5d4 ,light is n reflect$ by imp++ aga9/ ! solid p>ts ( bodies p4 #cci ,! p>ticles :i* compose bodies are transp>5t p4 #cda ,cause ( opacity p4 #cdb ,:y bodies 9 ! op5 day-light h diff]5t col\rs p4 #cdd ,! great porosity ( bodies consid]$ p4 #cee ,,*ap4 #c4 ,( ! refraction1 reflection1 & inflection ( light4 ,rays ( diff]5t col\rs are diff]5tly refract$ p4 #ceg ,! s9e ( ! angle ( incid5ce 9 ea* k9d ( rays be>s a giv5 proportion to ! s9e ( refraction p4 #cfa ,! proportion betwe5 ! refractive p[]s 9 diff]5t bodies p4 #cff ,unctu\s bodies refract mo/ 9 proportion to _! d5sity p4 #cfh ,! action betwe5 light & bodies is mutual p4 #cfi ,light has alt]nate fits ( easy transmission & reflection p4 #cga ,! fits f\nd to return alt]nately _m ?\s& times p4 #cge ,:y bodies reflect "p ( ! light incid5t ^u !m & transmit ano!r "p ibid4 ,sir ,,isaac ,,newton's conjecture conc]n+ ! cause ( ?is alt]nate reflection & transmission ( light p4 #cgf ,! inflection ( light p4 #cgg ,,*ap4 #d4 ,( optic glasses4 ,h[ ! rays ( light are refract$ by a sph]ical surface ( glass p4 #cgh ,h[ !y are refract$ by two su* surfaces p4 #chj ,h[ ! image ( objects is =m$ by a convex glass p4 #cha ,:y convex glasses help ! sight 9 old age1 & concave glasses assi/ %ort-sight$ p p4 #chc ,! mann] 9 :i* vision is p]=m$ by ! eye p4 #che ,( telescopes ) two convex glasses p4 #chf ,( telescopes ) f\r convex glasses p4 #chh ,( telescopes ) "o convex & "o concave glass ibid4 ,( microscopes p4 #chi ,( ! imp]fection ( telescopes aris+ f ! diff]5t refrangibility ( ! light p4 #cij ,( ! reflect+ telescope p4 #cic ,,*ap4 #e4 ,( ! ra9b[ ,( ! inn] ra9b[ p4 #cid #cie #cih #cii ,( ! outt] b[ p4 #cif #cig #djj ,( a p>ticul> appe>ance 9 ! inn] ra9b[ p4 #dja ,conclusion p4 #dje ,,errata4 ,,page #be4 l9e #d4 read ,9 ^! ,precepts4 p4 #dj4 l4 #bd4 = ,i read ,k4 p4 #ec4 l4 p5ult4 f4 4 r4 ,f4 p4 #hb4 l4 ult4 f4 #dj4 r4 #da4 p4 #hc l4 ult4 f4 #dc4 r4 #de4 p4 #ia4 l4 #c4 f4 #dh4 r4 #ej4 ibid4 l4 #be4 = #di4 r4 #ea4 p4 #ib4 l4 #ah4 f4 ,a ,g ,f ,e4 r4 ,h ,g ,f ,c4 p4 #if4 l4 #bc4 dele ! comma aft] 4 p4 #adj4 l4 #ab4 dele &4 p4 #add4 l4 #ae4 f4 ?reefold4 r4 two-fold4 p4 #afb4 l4 #be4 f4 4 r4 4 p4 #aic4 #a4 #b4 r4 always4 p4 #aii4 l4 p5ult4 & p4 #bjj4 l4 #c4 #e4 f4 ,f4 r4 ,c4 p4 #bja4 l4 #h4 f4 asc5ds4 r4 mu/ asc5d4 ibid4 l4 #aj4 f4 x desc5ds4 r4 desc5d4 p4 #bjh4 l4 #ad4 f4 ,w ,t ,o4 r4 ,n ,t ,o4 ,9 fig4 #aaj4 draw a l9e f ,i ?r\gh ,t1 till x meets ! circle ,a ,d ,c ,b1 :]e place ,w4 p4 #baf4 l4 p5ult4 f4 action4 r4 motion4 p4 #bba4 l4 #bc4 f4 ,a ,f4 r4 ,a ,h4 p4 #bcb4 l4 #bc4 aft] inv5tion put a full po9t4 p4 #bec4 l4 p5ult4 delete ! comma aft] rem>kable4 p4 #bee4 l4 ult4 f4 ,d ,e4 r4 ,b ,e4 p4 #bgh4 l4 #ag4 f4 4 r4 4 p4 #bii4 l4 #ai r4 !4 p4 #cfa4 l4 #ab4 f4 ,i4 r4 t4 p4 #cfi4 l4 #b1 #c4 r4 ,pseudo-topaz4 p4 #cgh4 l4 #ab4 f4 t4 r4 ?an4 p4 #cgi4 l4 #ae4 f4 conv]ge4 r4 div]ge4 p4 #chd4 l4 #g4 f4 optic-glass4 r4 optic-n]ve4 p4 #cia4 l4 #ah4 r4 z #ej to #gh4 p4 #cib4 l4 #ah4 aft] telescope add be ab\t #ajj feet long & !4 9 fig4 #afa4 f4 put 4 p4 #cii4 l4 #h4 r4 ,a n1 ,a x4 c4 p4 #djj4 #a4 #ai4 r4 ,a 1 ,a 4 ,a 1 ,a 4 ,a 4 p4 #dja4 l4 #ad4 r4 fig4 #afc4 ,! pages #cgd1 #cge1 #cgf are errone\sly numb]$ #cge1 #cgf1 #cgg2 & ! pages #chb1 #chc are numb]$ #cha1 #chb4 ,a ,,li/ ( su* ( ! ,,subscrib]s ,,names ,z are come to ! ,,h& ( ! ,,au?or4 ,a ,m,onseigneur d',aguesseau1 ,*anceli] de ,france ,rev]5d ,mr ,abbot1 ( ,emanuel ,coll4 ,camb4 ,capt4 ,george ,abell ,! ,hon4 ,sir ,john ,an/ru!r1 ,b>4 ,?omas ,abney1 ,esq2 ,mr4 ,na?an ,abraham ,sir ,ar?ur ,a*eson1 ,b>t4 ,mr ,william ,adair ,rev4 ,mr ,john ,adams1 ,fell[ ( ,sidney ,coll4 ,cambridge ,mr ,william ,adams ,mr ,george ,adams ,mr ,william ,adamson1 ,s*ol> ( ,caius ,coll4 ,camb4 ,mr ,samuel ,adee1 ,fell4 ( ,corp4 ,*r4 ,coll4 ,oxon ,mr ,&rew ,adlam ,mr ,john ,adlam ,mr ,/eph5 ,a9swor? ,mrs ,aiscot ,mr ,rob]t ,ak5head1 ,booksell] at ,newca/le ^u ,tyne ,s4 ,b4 ,alb9us1 ,m4 ,d4 ,anatom4 & ,*irurg 9 ,acad4 ,l4 ,b4 ,pr(4 ,george ,aldridge1 ,m4 ,d4 ,mr ,george ,algood ,mr ,aliffe ,rob]t ,all51 ,esq2 ,mr ,za*4 ,all5 ,rev4 ,mr ,all]ton1 ,fell[ ( ,sidney ,coll4 ,cambridge ,mr ,/4 ,am& ,mr ,john ,anns ,?omas ,anson1 ,esq2 ,rev4 ,dr4 ,*ri/oph] ,an/ey ,mr ,isaac ,antrabus ,mr ,jo%ua ,appleby ,john ,arbu?not1 ,m4 ,d4 ,william ,ar*]1 ,esq2 ,mr ,john ,ar*]1 ,m]*ant ( ,am/]dam ,?omas ,ar*]1 ,esq2 ,coll4 ,john ,arm/rong1 ,surveyor-,g5]al ( ,8 ,maje/y's ,ordnance ,mr ,armytage ,mr ,/reet ,arnold1 ,surgeon ,mr ,ri*>d ,arnold ,mr ,asc\gh ,mr ,*>les ,asgill ,ri*>d ,a%1 ,esq2 ( ,antigua ,mr ,a%1 ,fell[-,common] ( ,jesus ,coll4 ,cambridge ,william ,a%ur/1 ,esq2 ( ,ca/le ,h5n+ham1 ,essex ,mr ,?omas ,a%ur/ ,mr ,samuel ,a%ur/ ,mr ,john ,askew1 ,m]*ant ,mr ,edw>d ,a?awes1 ,m]*ant ,mr ,abraham ,atk9s ,mr ,edw>d ,k5sey ,atk9s ,mr ,ay]/ ,mr ,jona?an ,aylewor?1 ,jun4 ,r[l& ,aynswor?1 ,esq2 ,b ,8 ,grace ! ,duke ( ,b$=d ,"r ,hon\rable ! ,m>quis ( ,b[mont ,"r ,hon4 ! ,e>l ( ,burl+ton ,"r ,hon\rable ,"l ,visc\nt ,bateman ,rt4 ,rev4 ,ld4 ,bp4 ( ,ba? & ,wells ,rt4 ,rev4 ,"l ,bi%op ( ,bri/ol ,"r ,hon4 ,"l ,ba?ur/ ,ri*>d ,backwell1 ,esq2 ,mr ,william ,back%ell1 ,m]*4 ,edmund ,backwell1 ,g5t4 ,sir ,edmund ,bacon ,ri*>d ,bag%aw1 ( ,oakes1 ,esq2 ,?o4 ,bag%aw1 ( ,bakewell1 ,esq2 ,rev4 ,mr4 ,bag%aw ,sir ,rob]t ,baylis ,hon\rable ,george ,baillie1 ,esq2 ,giles ,bailly1 ,m4 ,d4 ( ,bri/ol ,mr ,s]jeant ,ba9es ,rev4 ,mr4 ,samuel ,bak]1 ,resid54 ( ,/4 ,paul's4 ,mr ,george ,bak] ,mr ,francis ,bak] ,mr ,rob]t ,bak] ,mr ,john ,bakewell ,an?ony ,balam1 ,esq2 ,*>les ,bale1 ,m4 ,d4 ,mr ,atwell1 ,fell[ ( ,exet] ,coll4 ,oxon ,mr ,savage ,atwood ,mr ,john ,atwood ,mr ,james ,audley ,sir ,rob]t ,au/51 ,b>t4 ,sir ,john ,au/5 ,b5jam9 ,av]y1 ,l4 ,l4 ,d4 ,mr ,balgay ,rev4 ,mr ,?o4 ,ball1 ,preb5d>y ( ,*i*e/] ,mr ,pappillon ,ball1 ,m]*ant ,mr ,levy ,ball ,rev4 ,mr ,jacob ,ball1 ( ,&ov] ,rev4 ,mr ,edw>d ,ballad1 ( ,tr94 ,coll4 ,cambridge ,mr ,ball] ,john ,bamb]1 ,m4 ,d4 ,rev4 ,mr ,bany]1 ,fell[ ( ,emanuel ,coll4 ,cambridge ,mr ,h5ry ,bany]1 ( ,wisbe*1 ,surgeon ,mr ,john ,b>b]1 ,apo!c>y 9 ,cov5try ,h5ry ,/eu>t ,b>clay1 ( ,colairny1 ,esq2 ,rev4 ,mr ,b>clay1 ,canon ( ,w9dsor ,mr ,david ,b>clay ,mr ,b5jam9 ,b>k]1 ,booksell] 9 ,london ---- ,b>k]1 ,esq2 ,mr ,francis ,b>k/ead ,rev4 ,mr ,b>n>d ,?omas ,b>rett1 ,esq2 ,mr ,b>rett ,ri*>d ,b>ret1 ,m4 ,d4 ,mr ,b>r[1 ,apo!c>y ,william ,b>r[by1 ,m4 ,d4 ,edw>d ,b>ry1 ,m4 ,d4 ( ,corke ,mr ,humphrey ,b>?olomew1 ( ,univ]sity ,college1 ,oxon ,mr ,b5jam9 ,b>tlett ,mr ,h5ry ,b>tlett ,mr ,james ,b>tlett ,mr ,newton ,b>ton1 ( ,tr9ity ,college1 ,cambridge ,rev4 ,mr4 ,b>ton ,william ,b>nsley1 ,esq2 ,mr ,samuel ,bateman ,mr ,?omas ,bates ,pet] ,b>hur/1 ,esq2 ,m>k ,b>r1 ,esq2 ,?omas ,ba/1 ,esq2 ,mr ,batley1 ,booksell] 9 ,london ,mr ,*ri/oph] ,batt1 jun4 ,mr ,william ,batt1 ,apo!c>y ,rev4 ,mr ,battely1 ,m4 ,a4 ,/ud5t ( ,*ri/ ,*ur*1 ,oxon ,mr ,edmund ,baugh ,rev4 ,mr4 ,?omas ,bayes ,edw>d ,bayley1 ,m4 ,d4 ( ,havant ,john ,bayley1 ,m4 ,d4 ( ,*i*e/] ,mr4 ,alex&] ,baynes1 ,pr(essor ( ,law 9 ! ,univ]sity ( ,ed9burgh ,mr ,b5jam9 ,bea* ,?omas ,beacon1 ,esq2 ,rev4 ,mr ,philip ,be>cr(t ,mr ,?omas ,be>cr(t ,mr ,william ,bea*cr(t ,ri*>d ,be>d1 ,m4 ,d4 ( ,worce/] ,mr ,joseph ,beasley ,rev4 ,mr ,beats1 ,m4 ,a4 ,fell[ ( ,magdal5 ,college1 ,cambridge ,sir ,george ,beaumont ,john ,beaumont1 ,esq2 ( ,clapham ,william ,bee*]1 ( ,h[b]ry1 ,esq2 ,mr ,mi*ael ,bee*] ,mr ,f9ney ,beifield1 ( ! ,inn]-,temple ,mr ,b5jam9 ,bell ,mr ,humphrey ,bell ,mr ,ph9eas ,bell ,leon>d ,belt1 ,g5t4 ,william ,b5b[1 ,esq2 ,mr ,m>t9 ,b5dall ,mr ,george ,b5net1 ( ,cork1 ,booksell] ,rev4 ,mr ,m>t9 ,b5son1 ,ar*deacon ( ,b]ks ,samuel ,b5son1 ,esq2 ,william ,b5son1 ,esq2 ,rev4 ,ri*>d ,b5tly1 ,d4 ,d4 ,ma/] ( ,tr9ity ,coll4 ,cambridge ,?omas ,b]e1 ,esq2 ,! ,hon4 ,john ,b]kley1 ,esq2 ,mr ,maurice ,b]kley1 s54 ,surgeon ,john ,b]n>d1 ,esq2 ,mr ,*>les ,b]n>d ,hugh ,be!ll1 ( ,rise 9 ,york%ire1 ,esq2 ,hugh ,be!ll1 ( ,sw9don 9 ,york%ire1 ,esq2 ,mr ,silvanus ,bevan1 ,apo!c>y ,mr ,calv]ly ,bewick1 jun4 ,h5ry ,bigg1 ,b4 ,d4 ,w>d5 ( ,new ,college1 ,oxon ,sir ,william ,bill]s ---- ,bill]s1 ,esq2 ,mr ,john ,bill+sley ,mr ,george ,b9ckes ,rev4 ,mr ,bir*9%a1 ( ,exet] ,college1 ,oxon ,rev4 ,mr ,ri*>d ,biscoe ,mr ,hawley ,bi%op1 ,fell[ ( ,/4 ,john's ,college1 ,oxon ,dr ,bird1 ( ,read+ ,h5ry ,blaake1 ,esq2 ,mr ,h5ry ,blaake ,rev4 ,mr ,george ,black ,/ew>d ,black]1 ,esq2 ,william ,black]1 ,esq2 ,r[l& ,blackman1 ,esq2 ,rev4 ,mr ,*>les ,blackmore1 ( ,worce/] ,rev ,mr ,blackwall1 ( ,emanuel ,college1 ,cambridge ,jona?an ,blackwel1 ,esq2 ,james ,blackwood1 ,esq2 ,mr ,?omas ,bl&=d ,ar?ur ,blaney1 ,esq2 ,mr ,james ,blew ,mr ,william ,bliz>d ,dr ,blom] ,mr ,h5ry ,blunt ,mr ,elias ,bocket ,mr ,?omas ,bock+ ,mr ,*>les ,boehm1 ,m]*ant ,mr ,william ,bogdani ,mr ,john ,du ,bois1 ,m]*ant ,mr ,samuel ,du ,bois ,mr ,joseph ,bolton1 ( ,londond]ry1 ,esq2 ,mr ,john ,bond ,john ,boni?on1 ,m4 ,a4 ,mr ,james ,bonwick1 ,booksell] 9 ,london ,?omas ,boone1 ,esq2 ,rev4 ,mr ,p5ny/one1 ,m4 ,a4 ,mrs ,judi? ,boo? ,?omas ,bootle1 ,esq2 ,?omas ,borret1 ,esq2 ,mr ,b5jam9 ,boss ,dr ,bo/ock ,h5ry ,bosville1 ,esq2 ,mr ,john ,boswor? ,dr ,george ,b\lton ,hon4 ,b\rn ,m4 ,d4 ( ,*e/]field ,mrs ,ca!r9e ,bovey ,mr ,humphrey ,b[5 ,mr ,b[] ,john ,b[es1 ,esq2 ,william ,b[les1 ,esq2 ,mr ,john ,b[les ,mr ,?omas ,b[les ,mr ,duv]eux ,b[ly ,dudd+ton ,bradeel1 ,esq2 ,rev4 ,mr ,james ,bradley1 ,pr(essor ( ,a/ronomy1 9 ,ox=d ,mr ,job ,bradley1 ,booksell] 9 ,*e/]field ,rev4 ,mr ,john ,bradley ,rev4 ,mr ,brad%aw1 ,fell[ ( ,jesus ,college1 ,cambridge ,mr ,joseph ,brad%aw ,mr ,?omas ,black%aw ,mr ,rob]t ,bragge ,*ampion ,bramfield1 ,esq2 ,joseph ,br&1 ,esq2 ,mr ,?omas ,branck] ,mr ,?omas ,br& ,mr ,braxton ,capt4 ,david ,braym] ,rev ,mr ,*>les ,br5t1 ( ,bri/ol ,mr ,william ,br5t ,mr ,edmund ,bret ,john ,brickdale1 ,esq2 ,rev4 ,mr ,john ,bridg5 ,a4 ,m4 ,abraham ,bridges1 ,esq2 ,george ,briggs1 ,esq2 ,john ,bridges1 ,esq2 ,brook ,bridges1 ,esq2 ,orl&o ,bridgman1 ,esq2 ,mr ,*>les ,bridgman ,mr ,william ,bridgman1 ( ,tr9ity ,college1 ,cambridge ,sir ,humphrey ,briggs1 ,b>t4 ,rob]t ,bri/ol1 ,esq2 ,mr ,joseph ,broad ,pet] ,brooke1 ( ,me]1 ,esq2 ,mr ,jacob ,brook ,mr ,brooke1 ( ,oriel ,coll4 ,oxon ,mr ,?omas ,brookes ,mr ,james ,brooks ,william ,brooks1 ,esq2 ,rev4 ,mr ,william ,brooks ,/amp ,brooksbank1 ,esq2 ,mr ,murdock ,broom] ,william ,br[n1 ,esq2 ,mr ,ri*>d ,br[n1 ( ,norwi* ,mr ,william ,br[n1 ( ,hull ,mrs ,s>ah ,br[n ,mr ,john ,br[ne ,mr ,john ,br[n+1 ( ,bri/ol ,mr ,john ,br[n+ ,noel ,broxholme1 ,m4 ,d4 ,william ,bryan1 ,esq2 ,rev4 ,mr ,brydam ,*ri/oph] ,buckle1 ,esq2 ,samuel ,buckley1 ,esq2 ,mr ,budg5 ,sir ,john ,bull ,josiah ,bullock1 ( ,faulkb\rn-,hall1 ,essex1 ,esq2 ,rev4 ,mr ,ri*>d ,bullock ,rev4 ,mr ,ri*>d ,bundy ,mr ,alex&] ,bunyan ,rev4 ,mr ,d4 ,burges ,eb5ez] ,burgess1 ,esq2 ,rob]t ,burle/on1 ,m4 ,b4 ,gilb]t ,burnet1 ,esq2 ,?omas ,burnet1 ,esq2 ,rev4 ,mr ,gilb]t ,burnet ,8 ,excell5cy ,w4 ,burnet1 ,esq2 ,gov]n\r ( ,new-,york ,mr ,traf=d ,burn/on1 ( ,tr94 ,college1 ,cambridge ,pet] ,burrel ,esq2 ,john ,burridge1 ,esq2 ,james ,burr\gh1 ,esq2 ,beadle & ,fell[ ( ,caius ,coll4 ,cambr4 ,mr ,b5jam9 ,burr\ghs ,j]emiah ,burr\ghs1 ,esq2 ,rev4 ,mr ,joseph ,burr\ghs ,*ri/oph] ,burr[1 ,esq2 ,james ,burr[1 ,esq2 ,william ,burr[1 ,a4 ,m4 ,francis ,burton1 ,esq2 ,john ,burton1 ,esq2 ,samuel ,burton1 ( ,dubl91 ,esq2 ,william ,burton1 ,esq2 ,mr ,burton4 ,ri*>d ,burton1 ,esq2 ,dr ,simon ,burton ,rev4 ,mr ,?omas ,burton1 ,m4,a4 ,fell[ ( ,caius ,college1 ,cambridge ,john ,bury1 jun4 ,esq2 ,rev4 ,mr ,samuel ,bury ,mr ,william ,bu% ,rev4 ,mr ,samuel ,butl] ,mr ,joseph ,button1 ( ,newca/le ^u ,tyne ,hon4 ,edw>d ,byam1 ,gov]n\r ( ,antigua ,mr ,edw>d ,byam1 ,m]*ant ,mr ,john ,byrom ,mr ,duncumb ,bri/[1 ,m]*4 ,mr ,william ,bradgate ,c ,8 ,grace ! ,ar*bi%op ( ,cant]bury ,"r ,hon4 ! ,"l ,*ancellor ,8 ,grace ! ,duke ( ,*&ois ,! ,"r ,hon4 ! ,e>l ( ,c>lisle ,"r ,hon4 ,e>l ,c[p] ,rt4 ,rev4 ,"l ,bi%op ( ,c>lisle ,rt4 ,rev4 ,"l ,bi%op ( ,*i*e/] ,rt4 ,rev4 ,"l ,bi%4 ( ,cl\s]t 9 ,irel& ,rt4 ,rev1 ,"l ,bi%op ( ,cloyne ,rt4 ,hon4 ,"l ,cl9ton ,rt4 ,hon4 ,"l ,*etwynd ,rt4 ,hon4 ,"l ,james ,cav5di% ,! ,hon4 ,"l ,c>dross ,rt4 ,hon4 ,"l ,ca/lema9 ,"r ,hon4 ,"l ,/4 ,cl>e ,cornelius ,callaghan1 ,esq2 ,mr ,*>les ,callaghan ,felix ,calv]t1 ( ,allbury1 ,esq2 ,pet] ,calv]t1 ( ,hunsd[n 9 ,h]t=d%ire1 ,esq2 ,mr ,william ,calv]t ( ,emanuel ,college1 ,cambridge ,rev]5d ,mr ,john ,cambd5 ,john ,campbell1 ( ,/ackpole-,c\rt1 9 ! ,c\nty ( ,pembroke1 ,esq2 ,mrs ,campbell1 ( ,/ackpole-,c\rt ,mrs4 ,elizabe? ,cap] ,mr ,dellill]s ,c>bonel ,mr ,john ,c>leton ,mr ,ri*>d ,c>lton1 ( ,*e/]field ,mr ,na?aniel ,c>p5t] ,h5ry ,c>r1 ,esq2 ,john ,c>r1 ,esq2 ,john ,c>ru!rs1 ,esq2 ,rev4 ,dr4 ,george ,c>t]1 ,provo/ ( ,oriel ,college ,mr ,samuel ,c>t] ,hon\rable ,edw>d ,c>t]et1 ,esq2 ,rob]t ,c>tes1 jun4 9 ,virg9ia1 ,esq2 ,mr ,william ,c>tli* ,james ,macc>tney1 ,esq2 ,mr ,c>twright1 ( ,a9ho ,mr ,william ,c>twright1 ( ,tr9ity ,college1 ,cambridge ,rev]5d ,mr ,william ,c>y1 ( ,bri/ol ,mr ,lynd=d ,c>yl ,mr ,john ,case ,mr ,john ,ca/le ,rev]5d ,mr ,cattle ,hon4 ,william ,cayley1 ,consul at ,cadiz1 ,esq2 ,william ,*amb]s1 ,esq2 ,mr ,nehemiah ,*ampion ,mr ,ri*>d ,*ampion ,mat!w ,*&l]1 ,esq2 ,mr ,george ,*annel ,mr ,*ann+ ,mr ,joseph ,*appell1 ,attorney at ,bri/ol ,mr ,rice ,*>lton1 ,apo!c>y at ,bri/ol ,/4 ,john ,*>elton1 ,esq2 ,mr ,ri*>d ,*>elton ,mr ,?omas ,*ase1 ( ,lisbon1 ,m]*ant ,rob]t ,*auncey1 ,m4 ,d4 ,mr ,pet] ,*auvel ,patricius ,*awor?1 ( ,ansley1 ,esq2 ,pole ,*awor? ( ! ,inn] ,temple1 ,esq2 ,mr ,william ,*eseld51 ,surgeon to h] ,maje/y ,james ,*e?am1 ,esq2 ,mr ,james ,*e?am ,*>les ,*ild1 ,a4 ,b4 ( ,cl>e-,hall1 9 ,cambridge1 ,esq2 ,mr ,*olmely1 ,g5tleman ,common] ( ,new-,college1 ,oxon ,?omas ,*ur*1 ,esq2 ,rev]5d ,mr ,/4 ,clair ,rev]5d ,mr ,mat!w ,cl>ke ,mr ,william ,cl>k ,b>?olomew ,cl>ke1 ,esq2 ,*>les ,cl>ke1 ( ,l9colns-,inn1 ,esq2 ,george ,cl>ke1 ,esq2 ,samuel ,cl>ke1 ( ! ,inn]-,temple1 ,esq2 ,rev]5d ,mr ,alur$ ,cl>ke1 ,preb5d>y ( ,w9*e/] ,rev4 ,john ,cl>ke1 ,d4 ,d4 ,dean ( ,s>um ,mr ,john ,cl>k1 ,a4 ,b4 ( ,tr9ity ,college1 ,cambridge ,mat!w ,cl>ke1 ,m4 ,d4 ,rev4 ,mr ,r5b4 ,cl>ke1 ,rector ( ,norton1 ,leice/]%ire ,rev4 ,mr ,rob]t ,cl>ke1 ( ,bri/ol ,rev4 ,samuel ,cl>ke1 ,d4 ,d4 ,mr ,?omas ,cl>ke1 ,m]*ant ,mr ,?omas ,cl>ke ,rev4 ,mr ,cl>kson1 ( ,pet]-,h\se1 ,cambridge ,mr ,ri*>d ,clay ,william ,clayton1 ( ,m>d51 ,esq2 ,samuel ,clayton1 ,esq2 ,mr ,william ,clayton ,mr ,john ,clayton ,mr ,?omas ,clegg ,mr ,ri*>d ,clem5ts1 ( ,ox=d1 ,booksell] ,!ophilus ,clem5ts1 ,esq2 ,mr ,george ,clif=d1 jun4 ( ,am/]dam ,george ,cli!r[1 ,esq2 ,george ,clive1 ,esq2 ,dr4 ,clopton1 ( ,bury ,/eph5 ,clutt]buck1 ,esq2 ,h5ry ,coape1 ,esq2 ,mr ,na?aniel ,coatswor? ,rev4 ,dr4 ,cobd51 ,*apla9 to ! ,bi%op ( ,london ,hon4 ,col4 ,john ,codr+ton1 ( ,wraxall1 ,som]set%ire ,"r ,hon4 ,m>maduke ,coghill1 ,esq2 ,francis ,coghlan1 ,esq2 ,sir ,?omas ,coke ,mr ,*>les ,colborn ,b5jam9 ,cole1 ,g5t4 ,dr ,edw>d ,cole ,mr ,*ri/ian ,colebr&t ,james ,colebrooke1 ,esq2 ,mr ,william ,coleman1 ,m]*ant ,mr ,edw>d ,collet ,mrs ,h5rietta ,collet ,mr ,john ,collet ,mrs ,m>y ,collett ,mr ,samuel ,collet ,mr ,na?aniel ,colli] ,an?ony ,coll9s1 ,esq2 ,?omas ,coll9s1 ( ,gre5wi*1 ,m4 ,d4 ,mr ,pet] ,coll9son ,edw>d ,colmore1 ,fell[ ( ,magdal5 ,college1 ,oxon ,rev4 ,mr ,john ,colson ,mrs ,m>g>et ,col/ock1 ( ,*i*e/] ,capt4 ,john ,colvil ,r5 de la ,combe1 ,esq2 ,rev4 ,mr ,john ,condor ,john ,conduit1 ,esq2 ,john ,con+ham1 ,m4 ,d4 ,8 ,excell5cy ,william ,conolly1 "o ( ! ,lords ,ju/ices ( ,irel& ,mr ,edw>d ,con/able1 ( ,read+ ,rev4 ,mr ,conybe>e1 ,m4 ,a4 ,rev4 ,mr ,james ,cook ,mr ,john ,cooke ,mr ,b5jam9 ,cook ,william ,cook1 ,b ,l4 ( ,/4 ,john's ,college1 ,oxon ,james ,cooke1 ,esq2 ,john ,cooke1 ,esq2 ,mr ,?omas ,cooke ,mr ,william ,cooke1 ,fell[ ( ,/4 ,john's ,college1 ,oxon ,rev4 ,mr ,coop]1 ( ,nor?-,hall ,*>les ,cope1 ,esq2 ,rev4 ,mr ,b>clay ,cope ,mr ,john ,copel& ,john ,copl&1 ,m4 ,b4 ,godfrey ,copley1 ,esq2 ,sir ,ri*>d ,corbet1 ,b>4 ,rev4 ,mr ,francis ,corbett ,mr ,paul ,corbett ,mr ,?omas ,corbet ,h5ry ,cornelis51 ,esq2 ,rev4 ,mr ,john ,corni% ,mrs ,elizabe? ,cornwall ,libr>y ( ,corpus ,*ri/i ,college1 ,cambridge ,mr ,william ,cossley1 ( ,bri/ol1 ,booksell] ,mr ,solomon du ,co/a ,dr4 ,h5ry ,co/>d ,dr4 ,cotes1 ( ,pomfret ,caleb ,coteswor?1 ,m4 ,d4 ,pet] ,cott+ham1 ,esq2 ,mr ,john ,cott+ton ,sir ,john ,h9de ,cotton ,mr ,james ,c\lt] ,george ,c\r?op1 ( ,:iligh 9 ,sussex1 ,esq2 ,mr ,pet] ,c\r?ope ,mr ,john ,c\ssmak]1 jun4 ,mr ,h5ry ,c[>d1 ,m]*ant ,an?ony ,a%ley ,c[p]1 ,esq2 ,! 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,inn]-,temple1 ,esq2 ,mr ,james ,f]ne1 ,surgeon ,mr ,john ,f]r&1 ( ,tr9ity ,college1 ,cambridge ,mr ,daniel ,mussaphia ,fidalgo ,mr ,fidl] ,hon4 ,mrs ,celia ,fi5nes ,hon4 & ,rev4 ,mr4 ,f9*1 ,dean ( ,york ,hon4 ,edw>d ,f9*1 ,esq2 ,mr ,john ,f9* ,philip ,f9*] ,esq2 ,mr ,mi*ael ,fit*1 ( ,tr9ity ,college1 ,cambridge ,hon4 ,john ,fitz-,morris1 ,esq2 ,mr ,flet*] ,m>t9 ,folkes1 ,esq2 ,dr ,foot ,mr ,francis ,=e/] ,john ,=e/]1 ,esq2 ,mrs ,alice ,=? ,mr ,john ,=! ,mr ,joseph ,foskett ,mr ,edw>d ,fo/] ,mr ,pet] ,fo/] ,pet] ,f\lkes1 ,d4 ,d4 ,canon ( ,*ri/-,*ur*1 ,oxon ,rev4 ,dr4 ,rob]t ,f\lkes ,rev4 ,mr ,rob]t ,f\lks1 ,m4 ,a4 ,fell[ ( ,magdal5 ,college1 ,cambridge ,mr ,abel ,f\n]eau1 ,m]*ant ,mr ,*ri/oph] ,f[l] ,mr ,john ,f[l]1 ( ,nor?amp4 ,mr ,joseph ,f[l] ,hon4 ,sir ,william ,f[nes1 ,b>4 ,george ,fox1 ,esq2 ,edw>d ,foy1 ,esq2 ,rev4 ,dr4 ,frankl&1 ,dean ( ,gl\ce/] ,fr$]ick ,frankl&1 ,esq2 ,mr ,joseph ,frankl9 ,mr ,abraham ,franks ,?omas ,fr$]ick1 ,esq2 ,g5tleman ,common] ( ,new ,college1 ,oxon ,?omas ,freeke1 ,esq2 ,mr ,joseph ,freame ,ri*>d ,freeman1 ,esq2 ,mr ,francis ,freeman1 ( ,bri/ol ,ralph ,freke1 ,esq2 ,patrick ,fr5*1 ,esq2 ,edw>d ,fr5*1 ,m4 ,d4 ,dr4 ,frew9 ,john ,fre9d1 ,m4 ,d4 ,mr ,?omas ,fro/ ,?omas ,fry1 ( ,hanham1 ,gl\ce/]%ire1 ,esq2 ,mr ,r[l& ,fry1 ,m]*ant ,francis ,fuljam1 ,esq2 ,rev4 ,mr ,full]1 ,fell[ ( ,emanuel ,college1 ,cambridge ,mr ,john ,full] ,?omas ,full]1 ,m4 ,d4 ,mr ,william ,fullwood1 ( ,hunt+don ,rev4 ,james ,fynney1 ,d4 ,d4 ,preb5d>y ( ,durham ,capt4 ,fy%e ,mr ,francis ,fayram1 ,booksell] 9 ,london ,g ,8 ,grace ! ,duke ( ,grafton ,"r ,hon4 ,e>l ( ,godolph9 ,"r ,hon4 ,lady ,betty ,g]ma9 ,"r ,hon4 ,"l ,g>let ,"r ,rev4 ,bi%op ( ,gl\ce/] ,"r ,hon4 ,"l ,/4 ,george ,rt4 ,hon4 ,"l ,*ief ,b>on ,gilb]t ,mr ,jona?an ,gale1 ( ,jamaica ,rog] ,gale1 ,esq2 ,8 ,excell5cy ,monsieur ,galvao1 ,envoy ( ,portugal ,james ,gambi]1 ,esq2 ,mr ,joseph ,gambol1 ( ,b>badoes ,mr ,joseph ,gamonson ,mr ,h5ry ,g>br& ,rev4 ,mr ,g>d9] ,mr ,na?aniel ,g>l& ,mr ,na?aniel ,g>l&1 jun4 ,mr ,joas ,g>l& ,mr ,james ,g>l& ,mrs ,anne ,g>l& ,mr ,edw>d ,g>lick ,mr ,alex&] ,g>rett ,mr ,john ,gascoygne1 ,m]*ant ,rev4 ,dr ,gaske? ,mr ,h5ry ,ga?am ,mr ,john ,gay ,?omas ,ge>+1 ,esq2 ,coll4 ,gee ,mr ,edw>d ,gee1 ( ,que5's ,college1 ,cambridge ,mr ,jo%ua ,gee1 s54 ,mr ,jo%ua ,gee1 jun4 ,ri*>d ,fitz-,g]ald1 ( ,gray's-,inn1 ,esq ,mr ,?omas ,g]r>d ,edw>d ,gibbon1 ,esq2 ,john ,gibbon1 ,esq2 ,mr ,h>ry ,gibbs ,rev4 ,mr ,philip ,gibbs ,?omas ,gibson1 ,esq2 ,mr ,john ,gibson ,mr ,samuel ,gideon ,rev4 ,dr ,cl&i% ,gilb]t1 ( ,tr9ity ,college1 ,dubl9 ,mr ,john ,gilb]t ,john ,gir>dos1 ,esq2 ,mr ,john ,girl1 ,surgeon ,rev4 ,dr4 ,gilb]t1 ,dean ( ,exet]1 #d ,books ,mr ,gisby1 ,apo!c>y ,mr ,ri*>d ,glanville ,john ,glov]1 ,esq2 ,mr ,john ,glov]1 ,m]*ant ,mr ,?omas ,glov]1 ,m]*ant ,john ,godd>d1 ,m]*ant1 9 ,rott]dam ,pet] ,godfrey1 ,esq2 ,mr ,joseph ,godfrey ,capt4 ,john ,godlee ,joseph ,godman1 ,esq2 ,capt4 ,h>ry ,g(f ,mr ,?omas ,goldney ,jona?an ,goldsmy?1 ,m4 ,d4 ,rev4 ,mr ,william ,goldw9 ---- ,gooday1 ,esq2 ,john ,goodrick1 ,esq2 ,fell[ ,common] ( ,tr9ity ,coll4 ,cambridge ,sir ,h5ry ,goodrick1 ,b>t4 ,mr ,?omas ,goodw9 ,sir ,william ,gordon1 ,b>4 ,"r ,hon4 ,sir ,ralph ,gore1 ,b>t4 ,ar?ur ,gore1 ,esq2 ,mr ,francis ,gore ,mr ,john ,*>les ,goris ,rev4 ,mr ,william ,gosl+1 ,m4 ,a4 ,william ,gosl91 ,esq2 ,mr ,william ,gossip1 ,a4 ,b4 ( ,tr94 ,coll4 ,cambridge ,john ,g\ld1 jun4 ,esq2 ,na?aniel ,g\ld1 ,esq2 ,mr ,?omas ,g\ld ,rev4 ,mr ,g[an1 ( ,leyd5 ,ri*>d ,graham1 jun4 ,esq2 ,mr ,george ,graham ,mr ,?omas ,gra+] ,mr ,walt] ,gra+] ,mr ,john ,grant ,monsieur ,s' ,graves&e1 ,pr(essor ( ,a/ronomy & ,exp]im4 ,philosophy 9 ,leyd5 ,dr ,gray ,mr ,*>les ,gray ( ,col*e/] ,mr ,john ,greaves ,mr ,francis ,gre5 ,dr ,gre51 ,pr(essor ( ,physick 9 ,cambridge ,samuel ,gre51 ,g5t4 ,mr ,george ,gre51 ,b4 ,d4 ,mr ,pet] ,gre5 ,mr ,mat!w ,gre5 ,mr ,na?aniel ,gre51 ,apo!c>y ,mr ,/eph5 ,gre5hill1 ( ,jesus ,college1 ,cambridge ,mr ,ar?ur ,gre5hill ,mr ,joseph ,gre5up ,mr ,r&olph ,gre5way1 ( ,?avies ,inn ,mr ,?omas ,gregg1 ( ! 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,univ]sity ( ,ed9burgh ,mr ,john ,hamilton ,mr ,?omas ,hammond1 ,booksell] 9 ,york ,mrs ,m>?a ,hammond ,mr ,john ,h& ,rev4 ,mr ,h&1 ,fell[ ( ,emanuel ,college1 ,cambridge ,mr ,samuel ,h&ly ,gabriel ,hang]1 ,esq2 ,james ,hannott1 ( ,spittle-,fields1 ,esq2 ,mr ,han ,hankey ,h>bord ,h>bord1 ( ,gunton 9 ,norfolk1 ,esq2 ,ri*>d ,h>c\rt1 ,esq2 ,mr ,?omas ,h>dey ,john ,h>d+1 ,esq2 ,sir ,william ,h>dress1 ,b>4 ,pet] ,h>dwick1 ,m4 ,d4 ( ,bri/ol ,mr ,?omas ,h>dwick1 ,attorney ,rev4 ,mr ,jona?an ,h>dey ,h5ry ,h>e1 ,esq2 ,mr ,h>e1 ( ,beck+ham 9 ,k5t ,mr ,m>k ,h>=d ,mr ,trueman ,h>=d ,hon4 ,edw>d ,h>ley1 ,esq2 ,capt4 ,h>l[e ,mr ,h5ry ,h>mage ,mr ,j]emiah ,h>man ,h5ry ,h>r+ton1 ,esq2 ,b>r[s ,h>ris1 ,esq2 ,james ,h>ris1 ,esq2 ,william ,h>ris1 ( ,s>um1 ,esq2 ,rev4 ,mr ,dean ,h>ris ,mr ,?omas ,h>ris ,rev4 ,mr ,h>ris1 ,pr(essor ( ,mod]n ,hi/ory 9 ,cambridge ,mr ,ri*>d ,h>ris ,mrs ,b>b>a ,h>rison ,mr ,william ,h>rison ,rev4 ,mr ,h5ry ,h>t ,mr ,moses ,h>t ,sir ,john ,h>top1 ,b>t4 ,mr ,pet] ,h>vey ,h5ry ,h>wood1 ,esq2 ,john ,h>wood1 ,l4 ,d4 ,rob]t ,prose ,hassel1 ,esq2 ,george ,hatley1 ,esq2 ,mr ,william ,hav5s ,capt4 ,john ,hawk9s ,mr ,m>k ,hawk9s1 ,surgeon ,mr ,walt] ,hawkswor?1 ,m]*4 ,mr ,francis ,hawl+ ,mr ,john ,huxley1 ( ,%effield ,mr ,ri*>d ,hayd51 ,m]*ant ,*]ry ,hayes1 ,m4 ,a4 ,mr ,?ompson ,hayne ,mr ,samuel ,haynes ,mr ,?omas ,haynes ,mr ,john ,hayw>d1 ,surgeon ,mr ,joseph ,hayw>d1 ( ,mad]a1 ,m]*ant ,rev4 ,sir ,francis ,head1 ,b>t4 ,james ,head1 ,esq2 ,?omas ,heames1 ,esq2 ,edmund ,hea?1 ,esq2 ,?omas ,hea?1 ,esq2 ,mr ,b5jam9 ,hea? ,cornelius ,hea?cote1 ( ,cut?oy1 ,m4 ,d4 ,mr ,james ,hamilton1 ,m]*ant ,mr ,?omas ,hasl$5 ,sir ,gilb]t ,hea?cote ,john ,hea?cote1 ,esq2 ,william ,hea?cote1 ,esq2 ,mr ,abraham ,heaton ,an?ony ,heck1 ,esq2 ,john ,h$ges1 ,esq2 ,mr ,paul ,heeg]1 jun4 ,m]*4 ,dr ,ri*>d ,hei%am ,mr ,jacob ,h5riques ,mr ,john ,h]b]t1 ,apo!c>y 9 ,cov5try ,george ,hepburn1 ,m4 ,d4 ( ,lynn-,regis ,mr ,samuel ,h]r+ ,mr ,john ,he!r+ton ,mr ,ri*>d ,hett1 ,booksell] ,fitz ,heugh1 ,esq2 ,hew] ,edgley ,hew]1 ,esq2 ,rob]t ,hey%am1 ,esq2 ,mr ,ri*>d ,heywood ,mr ,john ,heywood ,mr ,samuel ,hibb]d9e ,na?aniel ,hickman1 ,m4 ,a4 ,mr ,samuel ,hickman ,rev4 ,mr ,hiffe1 ,s*oolma/] at ,k5s+ton ,mr ,bang] ,higg5s ,mr ,samuel ,highl& ,mr ,joseph ,highmore ,rev4 ,mr ,john ,hildrop4 ,m4 ,a4 ,ma/] ( ! ,free-,s*ool 9 ,m>lbor\gh ,mr ,francis ,hildy>d1 ,booksell] 9 ,york ,mr ,hilgrove ,mr ,james ,hilh\se ,john ,hill1 ,esq2 ,mr ,john ,hill ,mr ,r[l& ,hill1 ( ,/4 ,john's ,college1 ,cambridge ,samuel ,hill1 ,esq2 ,mr ,humphrey ,hill ,rev4 ,mr ,ri*>d ,hill ,mr ,pet] ,/4 ,hill1 ,surgeon ,mr ,william ,h9*liff1 ,booksell] ,mr ,pet] ,h9d ,b5jam9 ,h9de1 ( ! ,inn]-,temple1 ,esq2 ,rob]t ,h9de1 ,esq2 ,mr ,pet] ,h9de1 jun4 ,rev4 ,mr ,dean ,h9ton ,mr ,rob]t ,hirt ,capt4 ,joseph ,hiscox1 ,m]*ant ,mr ,william ,ho>e ,mr ,william ,hobman ,sir ,na?aniel ,hodges ,mr ,hodges1 ,m4 ,a4 ( ,jesus ,college1 ,oxon ,mr ,joseph ,jory ,hodges ,mr ,hodgson1 ,ma/] ( ! ,ma!maticks 9 ,*ri/'s ,hospital ,mr ,hodson ,edw>d ,hody1 ,m4 ,d4 ,mr ,?omas ,hook ,samuel ,hold51 ,esq2 ,mr ,adam ,hold51 ( ,gre5wi* ,rog]s ,holl&1 ,esq2 ,mr ,james ,holl&1 ,m]*ant ,ri*>d ,holl& ,m4 ,d4 ,john ,holl+s1 ,m4 ,d4 ,mr ,?omas ,hollis ,mr ,john ,holli/] ,mr ,edw>d ,holl[ay ,mr ,?omas ,holmes ,rev4 ,mr ,holmes1 ,fell[ ( ,emanuel ,college1 ,cambridge ,rev4 ,mr ,samuel ,holt ,mat!w ,holwor?y1 ,esq2 ,mr ,john ,hook ,mr ,le ,hook ,mrs ,elizabe? ,hooke ,john ,hook]1 ,esq2 ,mr ,john ,hoole ,mr ,samuel ,hoole ,mr ,?omas ,hope ,?omas ,hopgood1 ,g5t4 ,sir ,ri*>d ,hopk9s ,ri*>d ,hopwood1 ,m4 ,d4 ,mr ,h5ry ,horne ,rev4 ,mr ,john ,horseley ,samuel ,horseman1 ,m4 ,d4 ,mr ,/eph5 ,horseman ,mr ,?omas ,h\ghton ,mr ,?omas ,h\ld+ ,james ,h[1 ,esq2 ,john ,h[1 ( ,hans ,cope1 ,esq2 ,mr ,john ,h[e ,mr ,ri*>d ,h[ ,hon4 ,edw>d ,h[>d1 ,esq2 ,william ,h[>d1 ,esq2 ,rev4 ,dean ,rob]t ,h[>d ,?omas ,hucks1 ,esq2 ,mr ,huds=d1 ( ,tr9ity ,coll4 ,oxon ,capt4 ,rob]t ,hudson1 jun4 ,mr ,john ,hughes ,edw>d ,hulse1 ,m4 ,d4 ,sir ,gu/avus ,humes ,rev4 ,mr ,david ,humphreys1 ,s4 ,t4 ,b4 ,fell[ ( ,tr94 ,coll4 ,cambridge ,maurice ,hunt1 ,esq2 ,mr ,hunt1 ( ,h>t-,hall1 ,oxon ,mr ,john ,hunt ,james ,hunt]1 ,esq2 ,mr ,william ,hunt] ,mr ,john ,hussey1 ( ,%effield ,ignatius ,hussey1 ,esq2 ,rev4 ,mr ,*ri/oph] ,hussey1 ,m4 ,a4 ,rector ( ,we/-,wickham 9 ,k5t ,?omas ,hut*9son1 ,esq2 ,fell[ ,common] ( ,sidney-,college1 ,cambridge ,rev4 ,mr ,hut*9son1 ( ,h>t-,hall1 ,oxon ,mr ,s&ys ,hut*9son1 ( ,tr9ity ,college1 ,cambridge ,mr ,huxley1 ,m4 ,a4 ( ,braz5 ,nose ,college1 ,oxon ,mr ,?omas ,hyam1 ,m]*ant ,mr ,john ,hyde ,mr ,hyett1 ,g5t4 ,common] ( ,pembroke ,college1 ,oxon ,i ,"r ,hon4 ! ,e>l ( ,ilay ,edw>d ,jackson1 ,esq2 ,mr ,/eph5 ,jackson1 ,m]*ant ,mr ,cu?b]t ,jackson ,rev4 ,mr4 ,pet] ,jackson ,mr ,jo%ua ,jackson ,john ,jacob1 ,esq2 ,mr ,jacob5s ,joseph ,jackson1 ( ,london1 ,goldsmi? ,rev4 ,sir ,george ,jacobs1 ( ,h\ghton 9 ,norfolk ,mr ,h5ry ,jacomb ,mr ,john ,jacques1 ,apo!c>y 9 ,cov5try ,mr ,samuel ,jacques1 ,surgeon at ,uxbridge ,william ,james1 ,esq2 ,rev4 ,mr ,david ,james1 ,rector ( ,wr\ghton1 ,bucks ,mr ,b5jam9 ,james ,mr ,rob]t ,james1 ( ,/4 ,john's1 ,oxon ,sir ,!odore ,janss51 ,b>t4 ,mr ,john ,j>vis1 ,surgeon at ,d>t=d 9 ,k5t ,mr ,edw>d ,jasp] ,edw>d ,jauncy1 ( ! ,middle-,temple ,esq2 ,rev4 ,dr ,ri*>d ,ibbetson ,john ,idle1 ( ! ,middle ,temple1 ,esq2 ,mr ,samuel ,jeake ,mr ,samuel ,jebb ,mr ,david ,jeff]ies ,rev4 ,mr ,joseph ,jeff]ies ,b>?olomew ,jeffrey1 ( ! ,middle ,temple1 ,esq2 ,edw>d ,jeffries1 ,esq2 ,lady ,jekyll ,ralph ,j5ison1 ,esq2 #b ,books ,david ,j5k9s1 ,l4 ,l4 ,d4 ,*ancellor ( ,d]ry ,mr ,j5k9s ,mr ,samuel ,j5n+s1 ( ,hull ,libr>y ( ,jesus ,coll4 ,cambridge ,john ,+ilby1 ,esq2 ,m>t9 ,innys1 ( ,bri/ol1 ,g5t4 ,messieurs ,william & ,john ,innys ( ,london1 ,booksell]s ,?omas ,jobb]1 ,esq2 ,rob]t ,jocelyn1 ,esq2 ,rev4 ,mr ,samuel ,jo*am ,oliv] ,/4 ,john1 ,esq2 ,george ,johnson1 ,esq2 ,hon4 ,james ,johnson1 ,esq2 ,james ,jur91 ,m4 ,d4 ,rev4 ,mr ,rob4 ,johnson4 ,s4 ,t4 ,b4 ,fell[ ( ,tr9ity ,college1 ,cambridge ,mr ,isaac ,johnson ,mr ,mi*ael ,johnson1 ,m]*ant 9 ,rott]dam ,edw>d ,jones1 ,esq2 ,*ancellor ( ! ,diocese ( ,/4 ,david's ,mr ,jones1 ,m4 ,a4 ( ,jesus ,college1 ,oxon ,mr ,jacob ,jones ,rev4 ,mr ,james ,jones1 ,rector ( ,c\nd1 ,salop ,mr ,som]set ,jones1 ,a4 ,b4 ( ,*ri/-,*ur*1 ,oxon ,mr ,john ,jones1 ,surgeon ,mr ,john ,jope1 ,fell[ ( ,new ,college1 ,oxon ,*>les ,joy1 ,esq2 ,daniel ,ivie1 ,esq2 ( ,*elsea ,hospital ,k ,8 ,grace ! ,duke ( ,k+/on ,"r ,hon\rable ,g]r>d1 ,"l ,visc\nt ,k+sale ,"r ,rev]5d ,"l ,bi%op ( ,killale ,rt4 ,rev4 ,"l ,bi%op ( ,killd>e ,"r ,rev]5d ,"l ,bi%op ( ,killmore ,rev4 ,mr ,william ,kay1 ,rector ( ,wigg9ton1 ,york%ire ,b5jam9 ,ke5e1 ,esq2 ,hon4 ,major ,g5]al ,kellum ,mr ,?omas ,kemp1 ,m4 ,a ( ,/4 ,john's ,college1 ,oxon ,mr ,rob]t ,k5dall ,mr ,clayton ,k5drick ,john ,k5drick1 ,esq2 ,john ,kemp1 ( ! ,middle ,temple1 ,esq2 ,mr ,*idrock ,k5t ,samuel ,k5t1 ,esq2 ,rev ,mr ,samuel ,k]rick1 ,fell[ ( ,*ri/ ,*ur* ,college1 ,cambridge4 ,mr ,kidbey ,mr ,rob]t ,kidd ,libr>y ( ,k+'s ,college1 ,cambridge ,b5jam9 ,k+1 ( ,antigua1 ,esq2 ,mr ,mat?ias ,k+ ,mrs ,jane ,k+ ,hon4 ,colonel ,pe>cy ,kirke ,mr ,?omas ,knap ,rev4 ,samuel ,knight1 ,d4 ,d4 ,preb5d>y ( ,ely ,mr ,rob]t ,knight1 jun4 ,francis ,kn[llyes1 ,esq2 ,mr ,ralph ,knox ,l ,rt4 ,hon4 ,"l ,visc\nt ,lonsdale ,rt4 ,hon4 ,ld4 ,visc\nt ,lym+ton ,rt4 ,rev4 ,"l ,bi%op ( ,london ,"r ,rev4 ,"l ,bi%op ( ,l&aff ,"r ,hon\rable ,"l ,lyn ,john ,lade1 ,esq2 ,mr ,hugh ,langh>ne ,mr ,john ,lang=d ,mr ,william ,l>kman ,mr ,william ,lambe1 ( ,exet] ,college1 ,oxon ,ri*>d ,langley1 ,esq2 ,mr ,rob]t ,lacy ,james ,lamb1 ,esq2 ,rev4 ,mr ,?omas ,lamb]t1 ,m4 ,a4 ,vic> ( ,l$burgh1 ,york%ire ,mr ,daniel ,lamb]t ,mr ,john ,lampe ,dr4 ,lane1 ( ,hit*9 9 ,h]t=d%ire ,mr ,timo?y ,lane ,rev4 ,dr4 ,laney1 ,ma/] ( ,pembroke ,hall1 ,cambr4 #b ,books ,mr ,pet] de ,langley ,rev4 ,mr ,na?aniel ,l>dn] ,mr ,l>n\l ,mr ,h5ry ,lascelles1 ( ,b>badoes1 ,m]*ant ,rev4 ,mr ,john ,laur5ce1 ,rector ( ,bi%op's ,w>em\? ,mr ,rog] ,laur5ce1 ,m4 ,a4 ,mr ,lav+ton ,mr ,william ,law1 ,pr(essor ( ,moral ,philosophy 9 ! ,univ]sity ( ,ed9burgh ,mr ,john ,lawton1 ( ! ,excise-,(fice ,mr ,godfrey ,laycock1 ( ,hallifax ,mr ,*>les ,leadbett]1 ,tea*] ( ! ,ma!maticks ,mr ,james ,leake1 ,booksell] 9 ,ba? ,/eph5 ,m>t9 ,leak1 ,esq2 ,rev4 ,mr ,le*m]e ,william ,lee1 ,esq2 ,mr ,lee1 ( ,*ri/ ,*ur*1 ,oxon ,rev4 ,mr ,john ,lee ,mr ,william ,leek ,rev4 ,mr ,leeson ,pet] ,legh1 ( ,lyme 9 ,*e%ire1 ,esq2 ,rob]t ,legu>re1 ( ,gray's-,inn1 ,esq2 ,mr ,lehunt ,mr ,john ,lehunt1 ( ,cant]bury ,francis ,leigh1 ,esq2 ,mr ,john ,leigh ,mr ,p]cival ,lewis ,mr ,?omas ,lewis ,new ,college ,libr>y ,sir ,h5ry ,liddell1 ,b>4 ( ,/4 ,pet]'s ,college1 ,cambridge ,h5ry ,liddell1 ,esq2 ,mr ,william ,limb]y ,rob]t ,l9dsay1 ,esq2 ,c\ntess ( ,lippe ,rev4 ,dr4 ,james ,lisle ,rev4 ,mr ,li/] ,mr ,george ,liv+/one1 ,"o ( ! ,cl]ks ( ,session ,salisbury ,lloyd1 ,esq2 ,rev4 ,mr ,john ,lloyd1 ,a4 ,b4 ( ,jesus ,college ,mr ,na?aniel ,lloyd1 ,m]*ant ,mr ,samuel ,lobb1 ,booksell] at ,*elms=d ,william ,lock1 ,esq2 ,mr ,james ,lock1 #b ,books ,mr ,jo%ua ,locke ,*>les ,locki]1 ,esq2 ,ri*>d ,lockwood1 ,esq2 ,mr ,b>?olom4 ,l(tus1 #i ,books ,william ,logan1 ,m4 ,d4 ,mr ,moses ,loman1 jun4 ,mr ,longley ,mr ,b5jam9 ,longuet ,mr ,grey ,longueville ,mr ,rob]t ,"l ,mrs ,m>y ,"l ,mr ,b5jam9 ,lork9 ,mr ,william ,l\p ,ri*>d ,love1 ( ,bas+ 9 ,hants1 ,esq2 ,mrs ,love1 9 ,laur5ce-,lane ,mr ,jo%ua ,lov]1 ( ,*i*e/] ,william ,l[ndes1 ,esq2 ,*>les ,l[ndes1 ,esq2 ,mr ,cornelius ,lloyd ,rob]t ,lucas1 ,esq2 ,coll4 ,ri*>d ,lucas ,sir ,b>tlet ,lucy ,edw>d ,luck91 ,esq2 ,mr ,john ,ludbey ,mr ,lud]s1 ,m]*ant ,lamb]t ,ludl[1 ,esq2 ,william ,ludl[1 ,esq2 ,pet] ,ludl[1 ,esq2 ,john ,lupton1 ,esq2 ,ni*olas ,luke1 ,esq2 ,lyonel ,lyde1 ,esq2 ,dr4 ,george ,lyn* ,mr ,jo%ua ,lyons ,m4 ,8 ,grace ! ,duke ( ,montague ,8 ,grace ! ,duke ( ,montrosse ,8 ,grace ! ,duke ( ,man*e/] ,! ,rt4 ,hon4 ,"l ,visc\nt ,moleswor? ,! ,rt4 ,hon4 ,"l ,mansel ,! ,rt4 ,hon4 ,ld4 ,mickle?wait ,! ,rt4 ,rev4 ,ld4 ,bi%op ( ,mea? ,mr ,mace ,mr ,joseph ,ma*am1 ,m]*ant ,mr ,john ,ma*91 ,pr(essor ( ,a/ronomy 9 ,gre%am ,college ,mr ,mackay ,mr ,mackelcan ,william ,mack951 ( ,antigua1 ,esq2 ,mr ,col9 ,mac ,laur91 ,pr(essor ( ! ,ma!maticks 9 ! ,univ]sity ( ,ed9burgh ,galatius ,macmahon1 ,esq2 ,mr ,madox1 ,apo!c>y ,rev4 ,mr ,isaac ,madox1 ,preb5d>y ( ,*i*e/] ,h5ry ,ma9w>+1 ( ,ov]-,peov] 9 ,*e%ire1 ,esq2 ,mr ,rob]t ,ma9w>+1 ( ,london1 ,m]*ant ,capt4 ,john ,maitl& ,mr ,cecil ,mal*] ,syd5ham ,mallhu/1 ,esq2 ,ri*>d ,malone1 ,esq2 ,mr ,?omas ,malyn ,mr ,john ,mann ,mr ,william ,man ,dr4 ,manaton ,mr ,john ,m&e ,dr4 ,b]n>d ,m&eville ,mr ,james ,m&y ,rev4 ,mr ,bell+ham ,manlev]or1 ,m4 ,a4 ,rector ( ,mah]a ,isaac ,manley1 ,esq2 ,?omas ,manley1 ( ! ,inn]-,temple1 ,esq2 ,mr ,john ,manley ,mr ,william ,manley ,mr ,b5jam9 ,mann+ ,rawleigh ,mansel1 ,esq2 ,h5ry ,m>*1 ,esq2 ,mr ,john ,m>ke ,sir ,george ,m>kham ,mr ,john ,m>kham1 ,apo!c>y ,mr ,william ,m>kes ,mr ,james ,m>kwick ,hon4 ,?omas ,m>ley1 ,esq2 "o ( 8 ,maje/y's ,sollicitors g5]al ( ,irel& ,rev4 ,mr ,george ,m>ley ,mr ,b5jam9 ,m>riot1 ( ! ,ex*equ] ,john ,m>%1 ,esq2 ,mr ,samuel ,m>% ,rob]t ,m>%all1 ,esq2 ,record] ( ,clonmell ,rev4 ,mr ,h5ry ,m>%all ,rev4 ,na?aniel ,m>%all1 ,d4 ,d4 ,canon ( ,w9dsor ,mat!w ,m>t91 ,esq2 ,?omas ,m>t91 ,esq2 ,mr ,john ,m>t9 ,mr ,james ,m>t9 ,mr ,josiah ,m>t9 ,coll4 ,samuel ,m>t91 ( ,antigua ,john ,mason1 ,esq2 ,mr ,john ,mason1 ( ,gre5wi* ,mr ,*>les ,mason1 ,m4 ,a4 ,fell4 ( ,tr94 ,coll4 ,cambridge ,mr ,cornelius ,mason ,dr4 ,ri*>d ,middleton ,massey ,mr ,ma/]man ,rob]t ,ma!r1 ( ! ,middle-,temple1 ,esq2 ,mr ,william ,ma!ws ,rev4 ,mr ,ma!w ,mr ,john ,mat!ws ,mrs ,he/] ,lumbroso de ,mattos ,rev4 ,dr4 ,pet] ,matur91 ,dean ( ,killala ,william ,maubry1 ,esq2 ,mr ,gamaliel ,maud ,rev4 ,mr ,pet] ,maurice1 ,treasur] ( ! ,*4 ( ,bangor ,h5ry ,maxwell1 ,esq2 ,john ,maxwell1 jun4 ( ,pollock1 ,esq2 ,rev4 ,dr4 ,rob]t ,maxwell1 ( ,fell['s ,hall1 ,irel& ,mr ,may ,mr ,?omas ,mayleigh ,?omas ,mayl91 jun4 ,esq2 ,hon4 ,*>les ,mayn>d1 ,esq2 ,?omas ,mayn>d1 ,esq2 ,dr4 ,ri*>d ,mayo ,mr ,samuel ,mayo ,samuel ,mead1 ,esq2 ,ri*>d ,mead1 ,m4 ,d4 ,rev4 ,mr ,mead[c\rt ,rev4 ,mr ,ri*>d ,mead[c\rt1 ,fell[ ( ,m]ton ,coll4 ,oxon ,mr ,me>son ,mr ,george ,m$calfe ,mr ,david ,m$ley1 #c ,books ,*>les ,m$lycott1 ,esq2 ,sir ,rob]t ,m5zies1 ( ,weem1 ,b>t4 ,mr ,?omas ,m]c]1 ,m]*ant ,john ,m]rill1 ,esq2 ,mr ,francis ,m]rit ,dr4 ,m]t9s ,mr ,john ,h5ry ,m]t9s ,libr>y ( ,m]ton ,college ,mr ,william ,messe1 ,apo!c>y ,mr ,metcalf ,mr ,?omas ,metcalf1 ( ,tr9ity ,coll4 ,cambridge ,mr ,abraham ,meure1 ( ,lea!rhead 9 ,surrey ,mr ,john ,mac ,f>lane ,dr4 ,john ,mi*el ,dr4 ,rob]t ,mi*el1 ( ,bl&=d ,mr ,rob]t ,mi*ell ,na?aniel ,mickle?wait1 ,esq2 ,mr ,jona?an ,mickle?wait1 ,m]*ant ,mr ,john ,mid=d1 ,m]*ant ,mr ,midgley ,rev4 ,mr ,mill]1 #b ,books ,rev4 ,mr ,mill+1 ( ! ,hague ,rev4 ,mr ,b5jam9 ,mills ,rev4 ,mr ,h5ry ,mills1 ,rector ( ,mea/ham1 ,head-,ma/] ( ,croyd5-,s*ool ,?omas ,miln]1 ,esq2 ,*>les ,miln]1 ,m4 ,d4 ,mr ,william ,m+ay ,john ,misaub91 ,m4 ,d4 ,mrs ,frances ,mit*el ,david ,mit*ell1 ,esq2 ,mr ,john ,mitton ,mr ,abraham de ,moivre ,john ,mon*ton1 ,esq2 ,mr ,john ,monk1 ,apo!c>y ,j4 ,monro1 ,m4 ,d4 ,sir ,william ,monson1 ,b>t4 ,edw>d ,montagu1 ,esq2 ,colonel ,john ,montagu ,rev4 ,john ,montague1 ,dean ( ,durham1 ,d4 ,d4 ,mr ,francis ,moor ,mr ,j>vis ,moore ,mr ,ri*>d ,moore1 ( ,hull1 #c ,books ,mr ,william ,moore ,sir ,*>les ,mordaunt1 ( ,walton1 9 ,w>wick%ire ,mr ,mordant1 ,g5tleman ,common] ( ,new ,college1 ,oxon ,*>les ,morgan1 ,esq2 ,francis ,morgan1 ,esq2 ,morgan ,morgan1 ,esq2 ,rev4 ,mr ,william ,morl&1 ,fell4 ( ,tr94 ,coll4 ,cambr4 #b ,books ,?omas ,morgan1 ,m4 ,d4 ,mr ,john ,morgan1 ( ,bri/ol ,mr ,b5jam9 ,morgan1 ,high-,ma/] ( ,/4 ,paul's-,s*ool ,hon4 ,coll4 ,val4 ,morris1 ( ,antigua ,mr ,gael ,morris ,mr ,john ,morse1 ( ,bri/ol ,hon4 ,ducey ,morton1 ,esq2 ,mr ,motte ,mr ,william ,m\nt ,coll4 ,moys] ,dr4 ,edw>d ,mull9s ,mr ,joseph ,murd5 ,mr ,mu/apha ,rob]t ,myddleton1 ,esq2 ,rob]t ,myhil1 ,esq2 ,n ,8 ,grace ! ,duke ( ,newca/le ,rt4 ,rev4 ,ld4 ,bi%op ( ,norwi* ,/eph5 ,napleton1 ,m4 ,d4 ,mr ,rob]t ,na%1 ,m4 ,a4 ,fell[ ( ,wadham ,college1 ,oxon ,mr ,!ophilus ,firm9 ,na% ,dr4 ,david ,natto ,mr ,an?ony ,neal ,mr ,h5ry ,neal1 ( ,bri/ol ,hampson ,n$ham1 ,esq2 ,g5tleman ,common] ( ,*ri/ ,*ur* ,oxon ,rev4 ,dr4 ,newcome1 ,s5ior-,fell[ ( ,/4 ,john's ,college1 ,cambridge1 #f ,books ,rev4 ,mr ,ri*>d ,newcome ,mr ,h5ry ,newcome ,mr ,newl& ,rev4 ,mr ,john ,newey1 ,dean ( ,*i*e/] ,mr ,b5jam9 ,new+ton1 ,m4 ,a4 ,john ,new+ton1 ,m4 ,b4 ( ,gre5wi* 9 ,k5t ,mr ,samuel ,newman ,mrs ,anne ,newnham ,mr ,na?aniel ,newnham1 s54 ,mr ,na?aniel ,newnham1 jun4 ,mr ,?omas ,newnham ,mrs ,ca!r9e ,newnham ,sir ,isaac ,newton1 #ab ,books ,sir ,mi*ael ,newton ,mr ,newton ,william ,ni*olas1 ,esq2 ,john ,ni*olas1 ,esq2 ,john ,niccol1 ,esq2 ,g5]al ,ni*olson ,mr ,samuel ,ni*olson ,john ,ni*olson1 ,m4 ,a4 ,rector ( ,donaghmore ,mr ,josias ,ni*olson1 #c ,books ,mr ,james ,nimmo1 ,m]*ant ( ,ed9burgh ,david ,nixon1 ,esq2 ,mr ,george ,noble ,/eph5 ,noquiez1 ,esq2 ,mr ,?omas ,norman1 ,booksell] at ,lewes ,mr ,an?ony ,norris ,mr ,h5ry ,norris ,rev4 ,mr ,edw>d ,norton ,ri*>d ,nutley1 ,esq2 ,mr ,john ,nutt1 ,m]*ant ,o ,"r ,hon4 ,"l ,orr]y ,rev4 ,mr ,john ,oakes ,mr ,william ,ock5d5 ,mr ,elias ,ock5d5 ,mr ,oddie ,crew ,(fley1 ,esq2 ,joseph ,(fley1 ,esq2 ,william ,ogb\rne1 ,esq2 ,sir ,william ,ogb\rne ,james ,ogle?orp1 ,esq2 ,mr ,william ,okey ,john ,oldfield1 ,m4 ,d4 ,na?aniel ,oldham1 ,esq2 ,william ,oliv]1 ,m4 ,d4 ( ,ba? ,john ,olm9s1 ,esq2 ,ar?ur ,onsl[1 ,esq2 ,paul ,or*>d1 ,esq2 ,rob]t ,ord1 ,esq2 ,john ,orleb>1 ,esq2 ,rev4 ,mr ,george ,osborne ,rev4 ,mr ,john ,h5ry ,ott ,mr ,james ,ottey ,mr ,jan4 ,oudam1 ,m]*ant at ,rott]dam ,mr ,ov]all ,john ,ov]bury1 ,esq2 ,mr ,*>les ,ov]+ ,mr ,?omas ,ow5 ,*>les ,owsley1 ,esq2 ,mr ,john ,ow5 ,mr ,?omas ,oyles ,p ,"r ,hon4 ,c\ntess ( ,pembroke1 #aj ,books ,"r ,hon4 ,"l ,paisley ,"r ,hon4 ,lady ,paisley ,! ,"r ,hon4 ,"l ,p>k] ,*ri/oph] ,pack1 ,m4 ,d4 ,mr ,samuel ,p>k]1 ,m]*ant at ,bri/ol ,mr ,?omas ,page1 ,surgeon at ,bri/ol ,sir ,gregory ,page1 ,b>4 ,william ,palgrave1 ,m4 ,d1 ,fell[ ( ,caius ,coll4 ,cambridge ,william ,palli/]1 ,esq2 ,?omas ,palm]1 ,esq2 ,samuel ,palm]1 ,esq2 ,h5ry ,palm]1 ,m]*ant ,mr ,john ,palm]1 ( ,cov5try ,mr ,samuel ,palm]1 ,surgeon ,william ,p>k]1 ,esq2 ,edmund ,p>k]1 ,g5t4 ,rev4 ,mr ,h5ry ,p>k]1 ,m4 ,a4 ,mr ,john ,p>k] ,mr ,samuel ,p>kes1 ( ,=t ,/4 ,george 9 ,ea/-,india ,mr ,daniel ,p>m9t] ,mr ,p>olet1 ,attorney ,rev4 ,?omas ,p>n1 ,fell[ ( ,tr94 ,coll4 ,cambr4 #b ,books ,rev4 ,mr ,?omas ,p>ne1 ,fell[ ( ,tr94 ,coll4 ,cambridge ,rev4 ,mr ,h5ry ,p>ratt1 ,m4 ,a4 ,rector ( ,holywell 9 ,hunt+ton%ire ,?omas ,p>ratt1 ,m4 ,d4 ,/anni] ,p>rot1 ,g5t4 ,"r ,hon4 ,b5jam9 ,p>ry1 ,esq2 ,mr ,p>ry1 ( ,jesus ,coll4 ,oxon ,b4 ,d4 ,rob]t ,paul1 ( ,gray's-,inn1 ,esq2 ,mr ,josiah ,paul1 ,surgeon ,mr ,paul9 ,rob]t ,paunce=te1 ,esq2 ,edw>d ,pawlet1 ( ,h9ton ,/4 ,george1 ,esq2 ,mr ,h5ry ,pawson1 ( ,york1 ,m]*ant ,mr ,payne ,mr ,samuel ,pea* ,mr ,m>maduke ,peacock1 ,m]*ant 9 ,rott]dam ,flavell ,peake1 ,esq2 ,capt4 ,edw>d ,pe>ce ,rev4 ,za*>y ,pe>ce1 ,d4 ,d4 ,james ,pe>se1 ,esq2 ,?omas ,pe>son1 ,esq2 ,john ,pe]s1 ,esq2 ,mr ,samuel ,pegg1 ( ,/4 ,john's ,college1 ,cambridge ,mr ,peirce1 ,surgeon at ,ba? ,mr ,adam ,peirce ,h>ry ,pelham1 ,esq2 ,james ,pelham1 ,esq2 ,j]emy ,pemb]ton1 ( ! ,inn]-,temple1 ,esq2 ,libr>y ( ,pembroke-,hall1 ,camb4 ,mr ,?omas ,p5n ,philip ,p5dock1 ,esq2 ,edw>d ,p5nant1 ,esq2 ,capt4 ,philip ,p5n+ton ,mr ,?omas ,p5ny ,mr ,h5ry ,p5ton ,mr ,francis ,p5w>ne1 at ,liskead 9 ,cornwall ,rev4 ,mr ,?omas ,p5w>ne ,mr ,john ,p]cevall ,rev4 ,mr ,edw>d ,p]cevall ,mr ,joseph ,p]cevall ,rev4 ,dr4 ,p]k9s1 ,preb5d4 ( ,ely ,mr ,f>ewell ,p]ry ,mr ,james ,petit ,mr ,john ,petit1 ( ,aldgate ,mr ,john ,petit1 ( ,ni*olas ,lane ,mr ,john ,petitt1 ( ,?ames-,/reet ,hon\rable ,coll4 ,pettit1 ( ,el?am 9 ,k5t ,mr ,h5ry ,peyton1 ( ,/4 ,john's ,college1 ,cambridge ,daniel ,phillips1 ,m4 ,d4 ,john ,phillips1 ,esq2 ,?omas ,phillips1 ,esq2 ,mr ,gravet ,phillips ,william ,phillips1 ( ,swanzey1 ,esq2 ,mr ,buckley ,phillips ,john ,phillipson1 ,esq2 ,william ,phipps1 ,l4 ,l4 ,d4 ,mr ,?omas ,phipps1 ( ,tr9ity ,college1 ,cambridge ,! ,physiological ,libr>y 9 ! ,college ( ,ed9burgh ,mr ,pi*>d ,mr ,william ,pick>d ,mr ,john ,pick]+ ,rob]t ,pigott1 ( ,*e/]ton1 ,esq2 ,mr ,ri*>d ,pike ,h5ry ,p9field1 ( ,hamp/ead1 ,esq2 ,*>les ,p9fold1 ,l4 ,l4 ,d4 ,rev4 ,mr4 ,pit1 ( ,exet] ,college1 ,oxon ,mr ,&rew ,pitt ,mr ,francis ,place ,?omas ,play]1 ,esq2 ,rev4 ,mr ,plimly ,mr ,william ,plom] ,william ,plumm]1 ,esq2 ,mr ,ri*>d ,plumpton ,john ,plumptre1 ,esq2 ,fitz-,williams ,plumptre1 ,m4 ,d4 ,h5ry ,plumptre1 ,m4 ,d4 ,john ,poll51 ,esq2 ,mr ,jo%ua ,pocock ,francis ,pole1 ( ,p>k-,hall1 ,esq2 ,mr ,isaac ,polock ,mr ,b5jam9 ,pomfret ,mr ,?omas ,pool1 ,apo!c>y ,alex&] ,pope1 ,esq2 ,mr ,ar?ur ,pond ,mr ,?omas ,port ,mr ,john ,port] ,mr ,joseph ,port] ,mr ,?omas ,pott]1 ( ,/4 ,john's ,college1 ,oxon ,mr ,john ,p[el ---- ,p[is1 ,esq2 ,mr ,daniel ,p[le ,john ,prat1 ,esq2 ,mr ,james ,pratt ,mr ,joseph ,pratt ,mr ,samuel ,pratt ,mr ,pre/on1 ,city-,remembranc] ,capt4 ,john ,price ,rev4 ,mr ,samuel ,price ,mr ,na?aniel ,primat ,dr4 ,john ,pr+le ,?omas ,prior1 ,esq2 ,mr ,h5ry ,proctor1 ,apo!c>y ,sir ,john ,pryse1 ( ,newton ,hill 9 ,montgom]y%ire ,mr ,?omas ,purcas ,mr ,rob]t ,purse ,mr ,john ,putl& ,george ,pye1 ,m4 ,d4 ,samuel ,pye1 ,m4 ,d4 ,mr ,samuel ,pye1 ,surgeon at ,bri/ol ,mr ,edmund ,pyle1 ( ,lynn ,mr ,john ,p9e1 ,engrav] ,q4 ,8 ,grace ! ,duke ( ,que5bor\gh ,rev4 ,mr4 ,"q1 ,m4 ,a4 ( ,exet] ,college1 ,oxon ,j]emiah ,qu>e1 ,m]*ant ,r4 ,8 ,grace ! ,duke ( ,ri*mond ,! ,rt4 ,rev4 ,ld4 ,bi%op ( ,raphoe ,! ,rt4 ,hon4 ,"l ,john ,russel ,rev4 ,mr ,walt] ,ra9/orp1 ( ,bri/ol ,mr ,john ,ranby1 ,surgeon ,rev4 ,mr ,r& ,mr ,ri*>d ,r&all ,rev4 ,mr ,h]b]t ,r&olph1 ,m4,a4 ,moses ,rap]1 ,esq2 ,mat!w ,rap]1 ,esq2 ,mr ,william ,ra/rick1 ( ,lynne ,mr ,ratcliffe1 ,m4 ,a4 ( ,pembroke ,college1 ,oxon ,rev4 ,mr ,john ,ratcliffe ,an?ony ,ravell1 ,esq2 ,mr ,ri*>d ,rawl9s ,mr ,rob]t ,rawl9son ,a4 ,b4 ( ,tr9ity ,college1 ,cambr4 ,mr ,walt] ,ray ,coll4 ,hugh ,raymond ,rt4 ,hon4 ,sir ,rob]t ,raymond1 ,"l ,*ief ,ju/ice ( ! ,k+'s-,b5* ,mr ,alex&] ,raymond ,samuel ,read1 ,esq2 ,rev4 ,mr ,james ,read ,mr ,john ,read1 ,m]*ant ,mr ,william ,read1 ,m]*ant ,mr ,samuel ,read ,mrs ,m>y ,reade ,mr ,?omas ,r$dall ,mr ,&rew ,reid ,felix ,r5olds1 ,esq2 ,john ,r5ton1 ( ,*ri/-,*ur*1 ,esq2 ,leon>d ,r]esby1 ,esq2 ,?omas ,reve1 ,esq2 ,mr ,gabriel ,reve ,william ,reeves1 ,m]*4 ( ,bri/ol ,mr ,ri*>d ,reynell1 ,apo!c>y ,mr ,john ,reynolds ,mr ,ri*>d ,ric>ds ,john ,ri*1 ( ,bri/ol1 ,esq2 ,francis ,ri*>ds1 ,m4 ,b4 ,rev4 ,mr ,esc\rt ,ri*>ds1 ,preb5d4 ( ,wells ,rev4 ,mr ,ri*>ds1 ,rector ( ,llanvyll91 9 ,montgom]y%ire ,william ,ri*>dson1 ( ,smally 9 ,d]by%ire1 ,esq2 ,mr ,ri*>d ,ri*>dson ,mr ,?omas ,ri*>dson1 ,apo!c>y ,edw>d ,ri*i]1 ,esq2 ,dudley ,rid]1 ,esq2 ,ri*>d ,rigby1 ,m4 ,d4 ,edw>d ,riggs1 ,esq2 ,?omas ,ripley1 ,esq4 ,comptroll] ( 8 ,maje/y's ,works ,sir ,?omas ,rob]ts1 ,b>t4 ,ri*>d ,rob]ts1 ,esq2 ,capt4 ,john ,rob]ts ,?omas ,rob9son1 ,esq2 ,mat!w ,rob9son1 ,esq2 ,tancr$ ,rob9son1 ,m4 ,d4 ,ni*olas ,rob9son1 ,m4 ,d4 ,*ri/oph] ,rob9son1 ( ,%effield1 ,a4 ,m4 ,mr ,h5ry ,rob9son ,mr ,william ,rob9son ,mrs ,elizabe? ,rob9son ,john ,ro*=t1 ,esq2 ,mr ,rodrigues ,mr ,rocke ,sir ,john ,rodes1 ,b>t4 ,mr ,francis ,rog]s ,rev4 ,mr ,sam4 ,rog]s1 ( ,bri/ol ,john ,rog]son1 ,esq2 8 ,maje/y's ,g5]al ( ,irel& ,edmund ,rolfe1 ,esq2 ,h5ry ,roll1 ,esq2 ,g5t4 ,comm4 ( ,new ,college1 ,oxon ,rev4 ,mr ,samuel ,rolle/on1 ,fell4 ( ,m]ton ,college1 ,oxon ,lancelot ,rolle/on1 ( ,wattnal1 ,esq2 ,philip ,ronayne1 ,esq2 ,rev4 ,mr de la ,roque ,mr ,b5jam9 ,rosewell1 jun4 ,joseph ,ro!ry1 ,m4 ,a4 ,ar*-,deacon ( ,d]ry ,guy ,r\ssignac1 ,m4 ,d4 ,mr ,james ,r\nd ,mr ,william ,r\ndell1 ( ,*ri/ ,*ur*1 ,oxon ,mr ,r\se1 ,m]*ant ,cu?b]t ,r\?1 ,esq2 ,john ,r[e1 ,esq2 ,mr ,john ,r[e ,dr4 ,r[el1 ( ,am/]dam ,john ,rudge1 ,esq2 ,mr ,james ,ruck ,rev4 ,dr4 ,rundle1 ,preb5d>y ( ,durham ,mr ,john ,ru/ ,john ,ru/att1 ,g5t4 ,mr ,za*ias ,ru? ,william ,rutty1 ,m4 ,d4 ,secret>y ( ! ,royal ,society ,maltis ,ryall1 ,esq2 ,s ,8 ,grace ! ,duke ( ,/4 ,albans ,rt4 ,hon4 ,e>l ( ,sund]l& ,rt4 ,hon4 ,e>l ( ,sc>bor\gh ,rt4 ,rev4 ,ld4 ,bp4 ( ,salisbury ,rt4 ,rev4 ,"l ,bi%op ( ,/4 ,asaph ,rt4 ,hon4 ,?omas ,"l ,s\?well ,rt4 ,hon4 ,"l ,sidney ,rt4 ,hon4 ,"l ,%aftsbury ,! ,rt4 ,hon4 ,"l ,%elburn ,8 ,excell5cy ,b>on ,soll5?al1 ,envoy extraord9>y f ! ,k+ ( ,d5m>k ,mrs ,m>g>ita ,sab9e ,mr ,edw>d ,sadl]1 #b ,books ,?omas ,sadl]1 ( ! ,pell-,(fice1 ,esq2 ,rev4 ,mr ,joseph ,sag]1 ,canon ( ! ,*ur* ( ,salisbury ,mr ,william ,salkeld ,mr ,rob]t ,salt] ,lady ,vanak] ,sambrooke ,j]4 ,sambrooke1 ,esq2 ,john ,sampson1 ,esq2 ,dr4 ,samuda ,mr ,john ,samwaies ,alex&] ,s&]l&1 ,m4 ,d4 ,samuel ,s&]s1 ,esq2 ,william ,s&]s1 ,esq2 ,rev4 ,mr ,daniel ,sanxey ,john ,s>g5t1 ,esq2 ,mr ,saund]son ,mr ,*>les ,savage1 jun4 ,mr ,john ,savage ,mrs ,m>y ,savage ,rev4 ,mr ,samuel ,savage ,mr ,william ,savage ,jacob ,sawbridge1 ,esq2 ,john ,sawbridge1 ,esq2 ,mr ,william ,sawrey ,humphrey ,say]1 ,esq2 ,exton ,say]1 ,l4 ,l4 ,d4 ,*ancell] ( ,durham ,rev4 ,mr ,george ,say]1 ,preb5d>y ( ,durham ,mr ,?omas ,say] ,h]m4 ,o/]dyk ,s*a*t1 ,m4 ,d4 ,m4 ,!or4 ,pratt1 9 ,acad4 ,lug4 ,bat4 ,pr(4 ,mey] ,s*amb]g1 ,m4 ,d4 ,mrs ,s*ep]s1 ( ,rott]dam ,dr4 ,s*eut*] ,mr ,?omas ,s*oles ,mr ,edw>d ,score1 ( ,exet]1 ,booksell] ,?omas ,scot1 ( ,essex1 ,esq2 ,daniel ,scott1 ,l4 ,l4 ,d4 ,rev4 ,mr ,scott1 ,fell[ ( ,w9ton ,college ,mr ,ri*>d ,scrafton1 ,surgeon ,mr ,flight ,scurry1 ,surgeon ,rev4 ,mr ,?omas ,seek] ,rev ,mr ,s$gwick ,mr ,selw9 ,mr ,pet] ,s]jeant ,mr ,john ,s]ocol1 ,m]*ant ,rev4 ,mr ,sew>d1 ( ,h]e=d ,mr ,joseph ,sewel ,mr ,?omas ,sewell ,mr ,lancelot ,%adwell ,mr ,ar?ur ,%allet ,mr ,edmund ,%allet1 ,consul at ,b>celona ,mr ,ar*deacon ,%>p ,james ,%>p1 jun4 ,surgeon ,rev4 ,mr ,?omas ,%>p1 ,ar*-,deacon ( ,nor?umb]l& ,mr ,john ,%aw1 jun4 ,mr ,joseph ,%aw ,mr ,%eafe ,mr ,edw4 ,%eldon1 ( ,w9/only ,mr ,%ell ,mr ,ri*>d ,%eph>d ,mr ,%eph]d ( ,tr9ity ,coll4 ,oxon ,mrs ,m>y ,%eph]d ,mr ,william ,%epp>d ,rev4 ,mr ,william ,%]lock1 ,m4 ,a4 ,william ,%]r>d1 ,l4 ,l4 ,d4 ,john ,%]w91 ,esq2 ,mr ,?omas ,%]wood ,mr ,?omas ,%ewell ,mr ,john ,%ipton1 ,surgeon ,mr ,john ,%ipton1 s54 ,mr ,john ,%ipton1 jun4 ,francis ,%ip)1 ,esq1 ,fell[ ,comm4 ( ,tr9ity ,coll4 ,camb4 ,john ,%i%1 ( ,gre5wi* 9 ,k5t1 ,esq2 ,mr ,abraham ,%reighly ,john ,%ore1 ,esq2 ,rev4 ,mr ,%ove ,b>?olomew ,%[]1 ,esq2 ,mr ,?omas ,sibley1 jun4 ,mr ,jacob ,silv]1 ,booksell] 9 ,s&wi* ,rob]t ,simpson1 ,esq2 ,beadle & ,fell[ ( ,caius ,coll4 ,cambr4 ,mr ,rob]t ,simpson ,pr(essor ( ! ,ma!maticks 9 ! ,univ]sity ( ,glasc[ ,h5ry ,s+leton1 ,esq2 ,prime ,s]geant ( ,irel& ,rev4 ,mr ,john ,s+leton ,rev4 ,mr ,r[l& ,s+leton ,mr ,s+leton1 ,surgeon ,mr ,jona?an ,sisson ,francis ,sitwell1 ( ,r5i%aw1 ,esq2 ,ralph ,sk]ret1 ,d4 ,d4 ,?omas ,sk9n]1 ,esq2 ,mr ,john ,sk9n] ,mr ,samuel ,sk9n]1 jun4 ,mr ,john ,skrimp%aw ,fr$]ic ,sl>e1 ,m4 ,d4 ,adam ,slat]1 ( ,*e/]field1 ,surgeon ,sir ,hans ,sloane1 ,b>4 ,william ,sloane1 ,esq2 ,william ,slop]1 ,esq2 ,william ,slop]1 ,esq1 ,fell[ ,common] ( ,tr94 ,coll4 ,cambr4 ,dr4 ,slop]1 ,*ancellor ( ! ,diocese ( ,bri/ol ,mr ,sm>t ,mr ,john ,smib>t ,rob]t ,smi?1 ,l4 ,l4 ,d4 ,pr(essor ( ,a/ronomy 9 ! ,univ]sity ( ,cambridge1 #bb ,books ,rob]t ,smi?1 ( ,bri/ol1 ,esq2 ,william ,smi?1 ( ! ,middle-,temple1 ,esq2 ,james ,smi?1 ,esq2 ,morgan ,smi?1 ,esq2 ,rev4 ,mr ,smi?1 ( ,/one 9 ! ,c\nty ( ,bucks ,john ,smi?1 ,esq2 ,mr ,john ,smi? ,mr ,john ,smi?1 ,surgeon 9 ,cov5try1 #b ,books ,mr ,john ,smi?1 ,surgeon 9 ,*i*e/] ,mr ,allyn ,smi? ,mr ,jo%ua ,smi? ,mr ,joseph ,smi? ,rev4 ,mr ,eli%a ,smi?1 ( ,tid ,/4 ,gyles's1 9 ! ,isle ( ,ely ,mr ,w>d ,smi? ,mr ,sk9n] ,smi? ,rev4 ,mr ,george ,smy? ,mr ,snabl9 ,dr4 ,snell1 ( ,norwi* ,mr ,samuel ,snell ,mr ,william ,snell ,william ,snell+1 ,esq2 ,william ,sneyd1 ,esq2 ,mr ,ralph ,sn[ ,mr ,?omas ,sn[ ,/eph5 ,soame1 ,esq2 ,fell[ ,common] ( ,sidney ,coll4 ,cambr4 ,cock9 ,sole1 ,esq2 ,joseph ,som]s1 ,esq2 ,mr ,edw9 ,somm]s1 ,m]*ant ,mr ,adam ,soresby ,?omas ,s\?by1 ,esq2 ,sontley ,s\?1 ,esq2 ,mr ,sp>r[ ,mr ,speke1 ( ,wadham ,coll4 ,ox4 ,rev4 ,mr ,joseph ,sp5ce ,mr ,abraham ,spoon] ,sir ,conrad ,joa*im ,spr+el ,mr ,william ,/amm]s ,mr ,*>les ,/anhope ,mr ,?omas ,/anhope ,sir ,john ,/anley ,george ,/anley1 ,esq2 ,rev4 ,dr4 ,/anley1 ,dean ( ,/4 ,asaph ,mr ,john ,/anly ,eaton ,/ann>d1 ,esq2 ,?omas ,/ansal1 ,esq2 ,mr ,samuel ,/anton ,temple ,/anyan1 ,esq2 ,mrs ,m>y ,/any=? ,rev4 ,mr ,?omas ,/>ges1 ,rector ( ,had/ock1 ,essex ,mr ,b5jam9 ,/eel ,mr ,john ,/ebb+1 ( ,/4 ,john's ,college1 ,cambridge ,mr ,john ,m>tis ,/ehel91 ,m]*4 ,dr4 ,/eig]?al ,mr ,/eph5s1 ( ,gl\ce/] ,mr ,joseph ,/eph5s ,sir ,james ,/eu>t ( ,gutt]s1 ,b>4 ,mr ,rob]t ,/eu>t1 ,pr(essor ( ,natural ,philosophy1 9 ! ,univ]sity ( ,ed9burgh ,rev4 ,mr ,/ev5s1 ,fell[ ( ,corp4 ,*r4 ,coll4 ,cambridge ,mr ,john ,/ev5s1 ( ,tr9ity ,college1 ,oxon ,rev4 ,mr ,b5net ,/ev5son ,hon4 ,ri*>d ,/ew>t1 ,esq2 ,major ,james ,/ew>t ,capt ,b>?olomew ,/ibbs ,mr ,d5ham ,/iles ,mr ,?omas ,/iles1 s54 ,mr ,?omas ,/iles1 jun4 ,rev4 ,mr ,/ill+fleet ,mr ,edw>d ,/ill+fleet ,mr ,john ,/ill+fleet ,mr ,william ,/i? ,mr ,/ock1 ( ,ro*dall 9 ,lanca%ire ,mr ,/octon1 ,wat*-,mak] ,mr ,rob]t ,/ogdon ,rev4 ,mr ,ri*>d ,/onehew] ,?omas ,/on]1 ,esq2 ,mr ,george ,/ory1 ( ,tr9ity ,college1 ,cambridge ,mr ,?omas ,/ory ,william ,/rahan1 ,l4 ,l4 ,d4 ,mr ,?omas ,/ratfield ,rev4 ,dr4 ,/rat=d1 ,canon ( ,*ri/ ,*ur*1 ,ox=d ,capt4 ,william ,/ratton ,rev4 ,mr ,/reat ,samuel ,/rode1 ,esq2 ,mr ,george ,/rode ,rev4 ,mr ,john ,/rong ,hon4 ,commodore ,/u>t ,alex&] ,/u>t1 ,m4 ,d4 ,*>les ,/u>t1 ,m4 ,d4 ,lewis ,/ucly ,mr ,john ,/urges1 ( ,bloomsbury ,mr ,/urgeon1 ,surgeon 9 ,bury ,hon4 ,lady ,suasso ,mr ,g]r>d ,suffield ,mr ,william ,sumn]1 ( ,w9dsor ,sir ,rob]t ,sutton1 ,kt4 ( ! ,ba? ,rev4 ,mr ,john ,sutton ,mr ,g]r>d ,sw>tz ,mr ,?omas ,swayne ,william ,sw9burn1 ,esq2 ,rev4 ,mr4 ,john ,sw9ton1 ,m4 ,a4 ,mr ,jo%ua ,symmonds1 ,surgeon ,rev4 ,mr ,edw>d ,synge ,t4 ,8 ,grace ! ,ar*bi%op ( ,tuam ,"r ,hon4 ,e>l ( ,tank]ville ,rt4 ,hon4 ,ld4 ,visc\nt ,t[n%5d1 ,"o ( ,8 ,maje/y's ,pr9cipal ,secret>ies ( ,/ate ,"r ,hon\rable ,lady ,visc\ntess ,t[n%5d ,"r ,hon ,ld ,visc\nt ,tyrconnel ,! ,hon\rable ,"l ,trevor ,*>les ,talbot1 ,esq2 ,solicitor-,g5]al4 ,francis ,talbot1 ,esq2 ,john ,ivory ,talbot1 ,esq2 ,mr ,george ,talbot1 ,m4 ,a4 ,mr ,talbot ,?omas ,tann]1 ,d4 ,d4 ,*ancellor ( ,norwi* ,mr ,?omas ,tann] ,mr ,tateham ( ,clapham ,mr ,h5ry ,ta?am ,mr ,john ,tatnall ,mr ,ar?ur ,tayldeur ,mr ,john ,tayleur ,ar?ur ,taylor1 ,esq2 ,joseph ,taylor1 ,esq2 ,simon ,taylor1 ,esq2 ,rev4 ,mr ,abraham ,taylor ,brook ,taylor1 ,l4 ,l4 ,d4 ,william ,tempe/1 ,esq2 ,william ,t5ison1 ,esq2 ,dr4 ,t5ison ,rev4 ,dr4 ,t]ry1 ,canon ( ,*ri/ ,*ur*1 ,oxon ,mr ,!$1 ,attorney ,mr ,lewis ,!obald ,james ,!obalds1 ,esq2 ,rob]t ,?i/le?wayte1 ,d4 ,d4 ,w>d5 ( ,wadham ,coll4 ,oxon ,rev4 ,mr ,?oml9son ,ri*>d ,?ompson ,coley1 ,esq2 ,rev4 ,mr ,william ,?ompson ,mr ,william ,?ompson1 ,a4 ,b4 ( ,tr9ity ,coll4 ,cambridge ,mr ,?oncas ,mr ,?ornbury1 ,vic> ( ,?ame ,sir ,james ,?ornhill1 #c ,books ,mr ,?ornhill ,william ,?ornton1 ,esq2 ,mr ,catlyn ,?or[good ,mr ,john ,?orpe ,william ,?orseby1 ,esq2 ,mr ,william ,?urlb\rn1 ,booksell] 9 ,cambridge ,m>k ,?ur/on1 ,esq2 ,ma/] 9 ,*anc]y ,rev4 ,mr ,william ,tiff91 ( ,lynn ,edmund ,tigh1 ,esq2 ,"r ,hon4 ,ri*>d ,tighe1 ,esq2 ,mr ,abraham ,tilghman ,mr ,george ,tilson ,rev ,mr ,tilson ,mr ,william ,tims ,rev4 ,mr ,john ,tiss] ,capt4 ,joseph ,tolson ,mr ,tomk9s ,mr ,william ,toml9son ,ri*>d ,topham1 ,esq2 ,dr4 ,torey ,george ,torriano1 ( ,we/-,ham1 ,esq2 ,mr ,john ,torriano ,mr ,james le ,t\* ,rev4 ,mr ,*>les ,t\gh ,mr ,john ,t[]s ,rev4 ,mr ,nehemiah ,t[good ,mr ,edw>d ,t[n ,joseph ,t[ns5d1 ,esq2 ,*>les ,t[n%5d1 ( ,l9coln's ,inn1 ,esq2 ,hon4 ,?omas ,t[n%5d1 ,esq2 ,mr ,t[nson ,john ,tracey1 ( ,/anway 9 ,gl\ce/]1 ,esq2 ,capt4 ,ri*>d ,tracey ,mr ,samuel ,trav]se1 ,m]*ant ,mr ,*>les ,trelawny1 ,/ud5t ( ,*ri/ ,*ur* ,fr$ric ,tr5*1 ,esq2 ,mr ,edmund ,tr5* ,mr ,samuel ,tr5* ,ri*>d ,trevor1 ,esq2 ,hon4 ,?omas ,trevor1 ,esq2 ,hon4 ,mr ,john ,trevor ,mr ,trimble1 ,m]*4 9 ,rott]d4 ,rev4 ,dr4 ,trimnell1 ,dean ( ,w9*e/] ,?omas ,trott]1 ,l4 ,l4 ,d4 ,john ,trub%aw1 ,esq2 ,mr ,?omas ,truman ,dr4 ,daniel ,turn] ,rev4 ,mr4 ,rob]t ,turn]1 ( ,col*e/] ,mr ,john ,turton ,mr ,william ,turton ,john ,twi/leton1 ne> ! ,city ( ,york1 ,esq2 ,col4 ,tyrrell ,mr ,william ,tyson ,mr ,samuel ,tyss5 ,capt4 ,edw>d ,tyzack ,v ,rt4 ,hon4 ,"l ,visc\nt ,vane ,rev4 ,mr ,?omas ,val5t9e ,mr ,vallack1 ( ,plym\? ,mr ,john ,v&]bank ,mr ,daniel ,v&ewall ,mr ,john ,v&ewall1 ,m]*ant ,mr ,edw>d ,vaus ,hon4 ,john ,v]ney1 ,esq2 ,william ,vesey1 ,esq2 ,rev4 ,mr ,john ,vesey ,william ,vigor1 ( ,we/bury ,college ne> ,bri/ol ,mr ,george ,virgoe ,mr ,fr$]ick ,voguel1 ,m]*ant ,mr ,?omas ,vick]s ,rob]t ,v9]1 ,esq2 ,w ,rt4 ,hon4 ! ,e>l ( ,w9*elsea ,rt4 ,rev4 ,"l ,bi%op ( ,w9*e/] ,rev4 ,mr ,wade ,sir ,*>les ,wag] ,rev4 ,mr ,wag/affe ,rev4 ,dr4 ,edw>d ,wake ,mr ,jasp] ,wakefield ,mr ,samuel ,walbank ,mr ,walbridge ,mr ,waldron ,edmund ,waldrond4 ,m4 ,a4 ,mr ,wal=d1 ( ,wadham ,coll4 ,oxon ,rev4 ,mr ,edw>d ,walk] ,mr ,samuel ,walk]1 ( ,tr9ity ,college1 ,cambridge ,mr ,?omas ,walk] ,h5ry ,wall]1 ,esq2 ,william ,wall]1 ,esq2 ,mrs ,wall] ,mr ,john ,wall]1 ( ,l9coln's-,inn ,mr ,george ,wallis ,rev4 ,mr ,william ,wallis ,mr ,edw>d ,walmsley1 #b ,books ,edw>d ,walpole1 ,esq2 ,mr ,pet] ,walt] ,john ,walton1 ,esq2 ,pet] ,w>burton ( ,=d 9 ,*e%ire1 ,esq2 ,ri*>d ,w>burton1 ,esq2 ,john ,w>d1 jun4 ,esq2 ,mi*ael ,w>d1 ,esq2 ,edw>d ,w>d1 ,esq2 ,knox ,w>d1 ,esq2 ,mr ,john ,w>d1 ,pr(essor ( ,rhetoric 9 ,gre%am ,college ,william ,w>d1 ,l4 ,l4 ,d4 ,mr ,ri*>d ,w>r+ ,mr ,jacob ,w>neck ,mr ,ri*>d ,w>n] ,mr ,rob]t ,w>n] ,william ,wasey1 ,m4 ,d4 ,rev4 ,mr ,wa%+ton1 ,fell[ ( ,pet]h\se1 ,cambridge ,mr ,edw>d ,wa/field ,mr ,watk9s ,rev4 ,mr ,?omas ,watkis1 ( ,knuts=d ,rob]t ,watley1 ,esq2 ,mr ,joel ,watson ,mr ,john ,watson ,mr ,?omas ,watson ,ri*>d ,watts1 ,m4 ,d4 #b ,books ,mr ,?omas ,watts ,rev4 ,mr ,isaac ,watts ,mr ,william ,weam5 ,mr ,?omas ,we> ,mr ,william ,wea!rs ,edw>d ,weav]1 ,esq2 ,an?ony ,weav]1 ,m4 ,d4 ,mr ,webb ,mr ,willam ,webb1 ,a4 ,b4 ( ,tr9ity ,college1 ,cambridge ,mr ,humphrey ,webb1 ,m4 ,a4 ,rt4 ,hon4 ,edw>d ,web/]1 ,esq2 ,william ,w5man1 ( ,edw9/[e1 ,esq2 ,mr ,samuel ,wesley1 jun4 ,gilb]t ,we/1 ,esq2 ,rt4 ,hon ,ri*>d ,we/1 ,esq2 late ,"l high ,*ancellor ( ,irel& ,?omas ,we/1 ,esq2 ,dr4 ,?omas ,we/ ,mrs ,anne ,we/ ,daniel ,we/comb1 ,esq2 ,h]b]t ,we/fal+1 ,esq2 ,messieurs ,w]/e9 & ,smi?1 ,booksell]s 9 ,am/]dam ,mr ,we/]n1 9 ,dov]-,/reet ,mr ,mat!w ,we/ly ,mr ,?o4 ,we/on1 ( ,gre5wi* ,mat!w ,weymondefold1 ,esq2 ,mr ,edw>d ,:>ton ,mr ,/eph5 ,:atley ,mr ,james ,:atman ,granville ,:el]1 ,esq2 ,rev4 ,mr ,william ,:i/on ,dr4 ,william ,:itak] ,taylor ,:ite1 ,esq2 ,mr ,*>les ,:ite ,mr ,edw>d ,:ite1 ,s*ol> ( ,caius ,college1 ,cambridge ,mr ,john ,:ite ,mr ,joseph ,:ite ,mr ,ni*olas ,:ite ,mr ,william ,:itehead ,rev4 ,mr ,:itehead1 ,fell[ ( ,emanuel ,college1 ,cambridge #f ,books ,john ,:itfield1 ,d4 ,d4 ,rector ( ,dickleburgh ,rev4 ,mr ,:itfield ,mr ,na?aniel ,:itlock ,mr ,john ,:itt]+ ,rob]t ,wild1 ,esq2 ,mr ,william ,wildman ,rev4 ,mr ,wilkes1 ,preb5d>y ( ,we/m9/] ,dr4 ,wilk9 ,mr ,wilk9s1 ,booksell] ,mr ,abel ,wilk9son ,mr ,william ,wilks ,john ,willes1 ,esq2 ,john ,willet1 ,esq2 ( ! ,isl& ( ,/4 ,*ri/oph]s ,john ,williams1 ,esq2 ,william ,pe] ,williams1 jun4 ,esq2 ,rev4 ,mr ,philip ,williams1 ,b4 ,d4 ,mr ,williams1 ,b4 ,a4 ( ,jesus ,college1 ,oxon ,mr ,francis ,williams ,hon4 ,coll4 ,adam ,williamson ,mr ,rob]t ,willimott ,john ,willis1 ,esq2 ,edw>d ,wilmot1 ,m4 ,d4 ,mr ,rob]t ,willmott ,mr ,joseph ,will\ghby ,william ,willys1 ,esq2 ,mr ,john ,wilm]1 ,m]*ant ,mr ,john ,wilm]1 ,apo!c>y ,mr ,wilmott1 ,booksell] 9 ,ox=d ,ri*>d ,wilson1 ( ,le$s1 ,esq2 ,rev4 ,mr ,daniel ,wilson1 ,preb5d>y ( ! ,*ur* ( ,h]e=d ,william ,w9de1 ,esq2 ,mr ,samuel ,w9d]1 jun4 ,sir ,william ,w9dham ,b>4 ,mr ,john ,w9dsor ,libr>y ( ,w9dsor ,college ,mr ,w9n+ton ,mr ,w9nock ,mr ,abraham ,w9t]bottom ,w4 ,)]s1 ( ,gray's-,inn1 ,esq2 ,mr ,conway ,)orne1 ( ! ,inn]-,temple ,rev4 ,mr ,john ,witt] ,jacobus ,witti*ius1 ,phil4 ,d4 9 ,acad4 ,lugd4 ,bat4 ,pr(4 ,mr ,john ,witt+ham ,rev4 ,mr ,john ,witton1 ,rector ( ,h[ton ,witton1 ,cambridge ,mr ,?omas ,wood ,?omas ,woodcock1 ,esq2 ,?omas ,wood=d1 ,esq2 ,william ,wood=d1 ,m4 ,d4 ,john ,woodh\se1 ,m4 ,d4 ,mr ,j4 ,woods1 ( ,bram%ot1 ,m]*4 ,rev4 ,mr ,b5jam9 ,woodro(1 ,preb5d>y ( ,worce/] ,mr ,joseph ,woodw>d ,josiah ,woola/on1 ,esq2 ,mr ,woolball1 ,m]*ant ,francis ,woolla/on1 ,esq2 ,*>lton ,woolla/on1 ,esq2 ,mr ,william ,woolla/on ,wight ,woolly1 ,esq2 ,libr>y ( ! ,ca!d4 ( ,worce/] ,josias ,wordswor?1 jun4 ,esq2 ,mr ,john ,wor/]1 ,m]*ant ,rev4 ,dr4 ,william ,wotton ,mr ,john ,w[5 ,edw>d ,wright1 ( ! ,middle-,temple1 ,esq2 ,h5ry ,wright1 ( ,molb]ly1 9 ,*e%ire1 ,esq2 ,samual ,wright1 ,esq2 ,william ,wright1 ( ,(f]ton1 9 ,*e%ire1 ,esq2 ,mr ,wright ,mr ,william ,wright1 ( ,baldock1 ,h]t=d%ire ,rev4 ,mr ,wrigley1 ,fell[ ( ,/4 ,john's ,college1 ,cambridge ,rt4 ,hon4 ,?omas ,wyndham1 ,ld4 ,*ief ,ju/ice ( ! ,common ,pleas1 ( ,irel& ,mr ,joseph ,wye? ,?omas ,wyndham1 ,esq2 ,rev4 ,mr ,john ,wynne ,y ,mr ,john ,y>dley1 ,surg4 9 ,cov54 ,mr ,?omas ,yates ,mrs ,yeo1 ( ,exet]1 ,booksell] ,sir ,william ,yonge ,lady ,york ,ni*olas ,"y1 ( ! ,inn]-,temple1 ,esq2 ,hit* ,"y1 ,esq2 ,rev4 ,edw>d ,"y1 ,l4 ,l4 ,d4 ,illu/ration ,,introduction4 ,,! mann]1 9 :i* ,sir ,,isaac ,,newton has publi%$ 8 philosophical discov]ies1 occasions !m to lie v mu* conceal$ f all1 :o h n made ! ma!matics p>ticul>ly _! /udy4 ,he once1 inde$1 int5d$ to deliv]1 9 a m famili> way1 t "p ( 8 inv5tions1 :i* relates to ! sy/em ( ! _w2 b ^u f>!r consid]ation he alt]$ 8 design4 ,= z ! nature ( ^? discov]ies made x impossible to prove !m ^u any o!r ?an geometrical pr9ciples2 he appreh5d$1 t ^?1 :o %\ld n fully p]ceive ! =ce ( 8 argum5ts1 w\ld h>dly be prevail$ on to ex*ange _! =m] s5tim5ts = new op9ions1 s v diff]5t f :at 7 commonly receiv$#a4 ,he !re=e *ose r to expla9 himself only to ma!matical read]s2 & decl9$ ! attempt+ to in/ruct su* 9 any ( 8 pr9ciples1 :o1 by n compreh5d+ 8 me?od ( reason+1 c\ld n1 at ! fir/ appe>ance ( 8 discov]ies1 h be5 p]suad$ ( _! tru?4 ,b n[1 s9ce ,sir ,,isaac ,,newton's doctr9e has be5 fully e/abli%$ by ! unanim\s approbation ( all1 :o are qualifi$ to und]/& ! same2 x is )\t d\bt to be wi%$1 t ! :ole ( 8 improvem5ts 9 philosophy might be univ]sally kn[n4 ,= ?is purpose !re=e ,i drew up ! foll[+ pap]s1 to give a g5]al notion ( our great philosoph]'s inv5tions to su*1 z are n prep>$ to read 8 own works1 & yet might desire to be in=m$ ( ! progress1 he has made 9 natural k2 n d\bt+ b !re 7 _m1 besides ^?1 ^: turn ( m9d _h l$ !m into a c\rse ( ma!matical /udies1 t w\ld take great pleasure 9 ta/+ ( ?is delightful f\nta9 ( sci5ce4 #b4 ,,x is a j rem>k1 :i* has be5 made ^u ! human m9d1 t no?+ is m suitable to x1 ?an ! contemplation ( tru?2 & t all m5 are mov$ ) a /rong desire aft] k2 e/eem+ x hon\rable to excel !re92 & hold+ x1 on ! contr>y1 disgraceful to mi/ake1 err1 or be 9 any way deceiv$4 ,& ?is s5tim5t is by no?+ m fully illu/rat$1 ?an by ! incl9ation ( m5 to ga9 an acqua9tance ) ! op]ations ( nature2 :i* disposition to enquire aft] ! causes ( ?+s is s g5]al1 t all m5 ( lett]s1 ,i believe1 f9d !mselves influ5c$ by x4 ,nor is x difficult to assign a reason = ?is1 if we consid] only1 t our desire aft] k is an effect ( t ta/e = ! sublime & ! beautiful 9 ?+s1 :i* *iefly con/itutes ! diff]5ce betwe5 ! human life1 & ! life ( brutes4 ,^! inf]ior animals p>take ) u ( ! pleasures1 t imm$iately fl[ f ! bodily s5ses & appetites2 b our m9ds are furni%$ ) a sup]ior s5se1 by :i* we are capable ( receiv+ v>i\s degrees ( delight1 :]e ! creatures bel[ u p]ceive no diff]5ce4 ,h5ce arises t pursuit ( grace & elegance 9 our ?\ghts & actions1 & 9 all ?+s belong+ to u1 :i* pr9cipally creates imploym5t = ! active m9d ( man4 ,! ?\ghts ( ! human m9d are too ext5sive to be conf9$ only to ! provid+ & enjoy+ ( :at is necess>y = ! support ( our be+4 ,x is ?is ta/e1 :i* has giv5 rise to poetry1 oratory1 & e bran* ( lit]ature & sci5ce4 ,f h5ce we feel great pleasure 9 conceiv+ /rongly1 & 9 appreh5d+ cle>ly1 ev5 :]e ! passions are n conc]n$4 ,p]spicu\s reason+ appe>s n only beautiful2 b1 :5 set =? 9 its full /r5g? & dignity1 x p>takes ( ! sublime1 & n only pleases1 b w>ms & elevates ! s\l4 ,?is is ! s\rce ( our /rong desire ( k2 & ! same ta/e = ! sublime & ! beautiful directs u to *use p>ticul>ly ! productions ( nature = ! subject ( our contemplation3 our creator hav+ s adapt$ our m9ds to ! condition1 :]e9 he has plac$ u1 t all 8 visible works1 be=e we inquire into _! make1 /rike u ) ! mo/ lively ideas ( beauty & magnific5ce4 #c4 ,,b if !re be s /rong a passion 9 contemplative m9ds = natural philosophy2 all su* mu/ c]ta9ly receive a p>ticul> pleasure 9 be+ in=m$ ( ,sir ,,isaac ,,newton's discov]ies1 :o alone has be5 able to make any great advancem5ts 9 ! true c\rse lead+ to natural k3 :]eas ?is important subject _h be=e be5 usually attempt$ ) t neglig5ce1 z _c be reflect$ on )\t surprize4 ,except+ a v few1 :o1 by pursu+ a m rational me?od1 _h ga9$ a little true k 9 "s p>ticul> p>ts ( nature2 ! writ]s 9 ?is sci5ce _h g5]ally treat$ ( x aft] su* a mann]1 z if !y ?\ght1 t no degree ( c]ta9ty 0 ev] to be hop$ =4 ,! cu/om 0 to frame conjectures2 & if ^u comp>+ !m ) ?+s1 !re appe>$ "s k9d ( agreem5t1 ?\gh v imp]fect1 x 0 held suffici5t4 ,yet at ! same "t no?+ less 0 und]tak5 ?an intire sy/ems1 & fa?om+ at once ! greate/ dep?s ( nature2 z if ! secret causes ( natural effects1 contriv$ & fram$ by inf9ite wisdom1 c\ld be se>*$ out by ! slighte/ endeav\rs ( our weak und]/&+s4 ,:]eas ! only me?od1 t c af=d u any prospect ( success 9 ?is difficult "w1 is to make our enquiries ) ! utmo/ caution1 & by v sl[ degrees4 ,& aft] our mo/ dilig5t lab\r1 ! greate/ "p ( nature w1 no d\bt1 = ev] rema9 beyond our rea*4 #d4 ,,?is neglect ( ! prop] means to enl>ge our k1 jo9$ ) ! presumption to attempt1 :at 0 q out ( ! p[] ( our limit$ faculties1 ! ,"l ,,bacon judici\sly obs]ves to be ! great ob/ruction to ! progress ( sci5ce#b4 ,inde$ t excell5t p]son 0 ! fir/1 :o expresly writ aga9/ ?is way ( philosophiz+2 & he has laid op5 at l>ge ! absurdity ( x 9 8 admirable treatise1 intitl$ ,,novum ,,organon ,,sci5ti>um2 & has !re likewise describ$ ! true me?od1 :i* ought to be foll[$4 #e4 ,,!re are1 sai? he1 b two me?ods1 t c be tak5 9 ! pursuit ( natural k4 ,"o is to make a ha/y transition f our fir/ & slight obs]vations on ?+s to g5]al axioms1 & !n to proce$ ^u ^? axioms1 z c]ta9 & unconte/able pr9ciples1 )\t f>!r exam9ation4 ,! o!r me?od2 7:i* he obs]ves to be ! only true "o1 b to 8 "t unattempt$27 is to proce$ cauti\sly1 to advance /ep by /ep1 res]v+ ! mo/ g5]al pr9ciples = ! la/ result ( our inquiries#c4 ,conc]n+ ! fir/ ( ^! two me?ods2 :]e objections1 :i* happ5 to appe> aga9/ any su* axioms tak5 up 9 ha/e1 are evad$ by "s frivol\s di/9ction1 :5 ! axiom x self ought r to be correct$#d2 he affirms1 t ! unit$ endeav\rs ( all ages _c make x successful2 because ?is orig9al error 9 ! fir/ dige/ion ( ! m9d 7z he expresses himself7 _c aft]w>ds be rem$i$#e3 :]eby he w\ld signify to u1 t if we set out 9 a wrong way2 no dilig5ce or art1 we c use1 :ile we foll[ s errone\s a c\rse1 w ev] br+ u to our design$ end4 ,& d\btless x _c prove o!rwise2 = 9 ?is spaci\s field ( nature1 if once we =sake ! true pa?1 we %all imm$iately lose our selves1 & mu/ = ev] w&] ) unc]ta9ty4 #f4 ,,! impossibility ( succe$+ 9 s faulty a me?od ( philosophiz+ 8 ,lord%ip endeav\rs to prove f ! _m false notions & prejudices1 to :i* ! m9d ( man is expos$#f4 ,& s9ce ?is judici\s writ] appreh5ds1 t m5 are s exce$+ liable to fall into ^! wrong tracts ( ?9k+1 z to incur great dang] ( be+ misl$ by !m1 ev5 :ile !y ent] on ! true c\rse 9 pursuit ( nature#g2 ,i tru/1 ,i %all be excus$1 if1 by insi/+ a little p>ticul>ly ^u ?is argum5t1 ,i endeav\r to remove :atev] prejudice ( ?is k9d1 might possibly entangle ! m9d ( any ( my read]s4 #g4 ,,8 ,lord%ip has r$uc$ ^! prejudices & false modes ( conception "u f\r di/9ct heads#h4 #h4 ,,! fir/ head conta9s su*1 z we are subject to f ! v condition ( humanity1 ?r\gh ! weakness bo? ( our s5ses1 & ( ! faculties ( ! m9d#i2 see+1 z ?is au?or well obs]ves1 ! subtilty ( nature f> exce$s ! greate/ subtilty ( our s5ses or acute/ reason+s#aj4 ,"o ( ! false modes ( conception1 :i* he m5tions "u ?is head1 is ! =m+ to our selves a fanciful simplicity & regul>ity 9 natural ?+s4 ,?is he illu/rates by ! foll[+ in/ances2 ! conceiv+ ! planets to move 9 p]fect circles2 ! add+ an orb ( fire to ! o!r ?ree elem5ts1 & ! suppos+ ea* ( ^! to exce$ ! o!r 9 r>ity1 j 9 a decuple proportion#aa4 ,& ( ! same nature is ! ass]tion ( ,,des ,,c>tes1 )\t any pro(1 t all ?+s are made up ( ?ree k9ds ( matt] only#ab4 ,z also ?is op9ion ( ano!r philosoph]2 t light1 9 pass+ ?r\gh diff]5t m$iums1 0 refract$1 s z to proce$ by t way1 ?r\gh :i* x w\ld move m spe$ily1 ?an ?r\gh any o!r#ac4 ,! second errone\s turn ( m9d1 tak5 notice ( by 8 ,lord%ip "u ?is head1 is1 t all m5 are 9 "s degree prone to a fondness = any notions1 :i* !y h once imbib$2 :]eby !y (t5 wre/ ?+s to reconcile !m to ^? notions1 & neglect ! consid]ation ( :atev] w n be br\ght to an agreem5t ) !m2 j z ^? d1 :o are addict$ to judicial a/rology1 to ! obs]vation ( dreams1 & to su*-l sup]/itions2 :o c>efully pres]ve ! memory ( e incid5t1 :i* s]ves to confirm _! prejudices1 & let slip out ( _! m9ds all in/ances1 t make aga9/ !m#ad4 ,!re is also a f>!r imp$im5t to true k1 m5tion$ "u ! same head by ?is noble writ]1 :i* is2 t :]eas1 ?r\gh ! weakness & imp]fection ( our s5ses1 _m ?+s are conceal$4 f u1 :i* h ! greate/ effect 9 produc+ natural appe>ances2 our m9ds are ord9>ily mo/ affect$ by t1 :i* makes ! /ronge/ impression on our organs ( s5se2 :]eby we are apt to judge ( ! real importance ( ?+s 9 nature by a wrong measure#ae4 ,s1 because ! figuration & ! motion ( bodies /rike our s5ses m imm$iately ?an mo/ ( _! o!r prop]ties1 ,,des ,,c>tes & 8 foll[]s w n all[ any o!r explication ( natural appe>ances1 ?an f ! figure & motion ( ! p>ts ( matt]4 ,by :i* example we see h[ ju/ly 8 ,lord%ip obs]ves ?is cause ( error to be ! greate/ ( any#af2 s9ce x has giv5 rise to a fundam5tal pr9ciple 9 a sy/em ( philosophy1 t n long ago obta9$ almo/ an univ]sal reputation4 #i4 ,,^! are ! *ief bran*es ( ^? ob/ructions to k1 :i* ?is au?or has r$uc$ "u 8 fir/ head ( false conceptions4 ,! second head conta9s ! errors1 to :i* p>ticul> p]sons are m especially obnoxi\s#ag4 ,"o ( ^! is ! consequ5ce ( a prec$+ obs]vation3 t z we are expos$ to be captivat$ by any op9ions1 :i* h once tak5 possession ( our m9ds2 s 9 p>ticul>1 natural k has be5 mu* corrupt$ by ! /rong atta*m5t ( m5 to "s "o "p ( sci5ce1 ( :i* !y reput$ !mselves ! inv5t]s1 or ab\t :i* !y h sp5t mu* ( _! "t2 & h5ce h be5 apt to conceive x to be ( great] use 9 ! /udy ( natural philosophy ?an x 03 l ,,ari/otle1 :o r$uc$ 8 physics to logical disputations2 & ! *ymi/s1 :o ?\ght1 t nature c\ld be laid op5 only by ! =ce ( _! fires#ah4 ,"s aga9 are :olly c>ri$ away by an excessive v5]ation = antiquity2 o!rs1 by too great fondness = ! mod]ns2 few hav+ _! m9ds s well balanc$1 z nei!r to depreciate ! m]it ( ! anci5ts1 nor yet to despise ! real improvem5ts ( lat] times#ai4 ,to ?is is add$ by 8 ,lord%ip a diff]5ce 9 ! g5ius ( m51 t "s are mo/ fitt$ to obs]ve ! similitude1 !re is 9 ?+s1 :ile o!rs are m qualifi$ to disc]n ! p>ticul>s1 :]e9 !y disagree2 bo? :i* dispositions ( m9d are useful3 b to ! prejudice ( philosophy m5 are apt to run into excess 9 ea*2 :ile "o sort ( g5ius dwells too mu* ^u ! gross & sum ( ?+s1 & ! o!r ^u trifl+ m9ut5esses & %ad[y di/9ctions#bj4 #aj4 ,,"u ! ?ird head ( prejudices & false notions ?is writ] consid]s su*1 z foll[ f ! lax & indef9ite use ( words 9 ord9>y disc\rse2 :i* occasions great ambiguities & unc]ta9ties 9 philosophical debates 7z ano!r em95t philosoph] has s9ce %ewn m at l>ge#ba27 insomu* t ?is our au?or ?9ks a /rict def9+ ( t]ms to be sc>ce an infallible rem$y aga9/ ?is inconv5i5ce#bb4 ,& p]haps he has no small reason on 8 side3 = ! common inaccurate s5se ( words1 not)/&+ ! limitations giv5 !m by def9itions1 w (f] x self s con/antly to ! m9d1 z to require great caution & circumspection = u n to be deceiv$ !reby4 ,( ?is we h a v em95t in/ance 9 ! great disputes1 t h be5 rais$ ab\t ! use ( ! ^w attraction 9 philosophy2 ( :i* we %all be oblig$ h]eaft] to make p>ticul> m5tion#bc4 ,words ?us to be gu>d$ aga9/ are ( two k9ds4 ,"s are names ( ?+s1 t are only imag9>y#bd2 su* words are :olly to be reject$4 ,b !re are o!r t]ms1 t allude to :at is real1 ?\gh _! signification is confus$#be4 ,& ^! latt] mu/ ( necessity be cont9u$ 9 use2 b _! s5se cle>$ up1 & fre$1 z mu* z possible1 f obscurity4 #aa4 ,,! la/ g5]al head ( ^! errors compreh5ds su*1 z foll[ f ! v>i\s sects ( false philosophies2 :i* ?is au?or divides into ?ree sorts1 ! sophi/ical1 empirical1 & sup]/iti\s#bf4 ,by ! fir/ ( ^! he means a philosophy built ^u speculations only )\t exp]im5ts#bg2 by ! second1 :]e exp]im5ts are bl9dly adh]$ to1 )\t prop] reason+ ^u !m#bh2 & by ! ?ird1 wrong op9ions ( nature fix$ 9 m5s m9ds ei!r ?r\gh false religions1 or f misund]/&+ ! decl>ations ( ! true#bi4 #ab4 ,,^! are ! f\r pr9cipal canals1 by :i* ?is judici\s au?or ?9ks1 t philosophical errors h fl[$ 9 ^u u4 ,& he rightly obs]ves1 t ! faulty me?od ( proce$+ 9 philosophy1 aga9/ :i* he writes#cj1 is s f> f assi/+ u t[>ds ov]com+ ^! prejudices2 t he appreh5ds x r suit$ to rivet !m m firmly to ! m9d#ca4 ,h[ great reason !n has 8 ,lord%ip to call ?is way ( philosophiz+ ! p>5t ( error1 & ! bane ( all k#cb8 ,=1 inde$1 :at else b mi/akes c s bold & presumptu\s a treatm5t ( nature produce8 h we ! wisdom necess>y to frame a _w1 t we %\ld ?9k s easily1 & ) s slight a se>* to ent] into ! mo/ secret spr+s ( nature1 & discov] ! orig9al causes ( ?+s8 :at *im]as1 :at mon/]s has n ?is prepo/]\s me?od br\ght =?8 :at s*emes1 or :at hypo!sis's ( ! subtile/ wits has n a /rict] enquiry into nature n only ov]?r[n1 b manife/$ to be ridicul\s & absurd8 ,e new improvem5t1 :i* we make 9 ?is sci5ce1 lets u see m & m ! weakness ( our guesses4 ,dr4 ,,h>vey1 by t "o discov]y ( ! circulation ( ! blood1 has dissipat$ all ! speculations & reason+s ( _m ages ^u ! animal oeconomy4 ,,asellius1 by detect+ ! lacteal ve9s1 %ew$ h[ little gr\nd all physicians & philosoph]s _h 9 conjectur+1 t ! nutritive "p ( ! alim5t 0 absorb$ by ! m\?s ( ! ve9s spread ^u ! b[els3 & !n ,,pecquet1 by f9d+ out ! ?oracic duct1 z evid5tly prov$ ! vanity ( ! op9ion1 :i* 0 p]si/$ 9 aft] ! lacteal vessels 7 kn[n1 t ! alim5tal juice 0 convey$ imm$iately to ! liv]1 & !re conv]t$ into blood4 #ac4 ,,z ^! ?+s set =? ! great absurdity ( proce$+ 9 philosophy on conjectures1 by in=m+ u h[ f> ! op]ations ( nature are above our l[ conceptions2 s on ! o!r h&1 su* in/ances ( success f a m judici\s me?od %ew u1 t our b\ntiful mak] has n left u :olly )\t means ( delight+ our selves 9 ! contemplation ( 8 wisdom4 ,t by a j way ( inquiry into nature1 we c\ld n fail ( arriv+ at discov]ies v remote f our appreh5sions2 ! ,"l ,,bacon himself argues f ! exp]i5ce ( mank9d4 ,if1 says he1 ! =ce ( guns %\ld be describ$ to any "o ignorant ( !m1 by _! effects only1 he might reasonably suppose1 t ^? eng9es ( de/ruction 7 only a m artificial composition1 ?an he knew1 ( :eels & o!r me*anical p[]s3 b x c\ld nev] ent] 8 ?\ghts1 t _! imm5se =ce %\ld be ow+ to a peculi> sub/ance1 :i* w\ld enk9dle into s viol5t an explosion1 z we exp]i5ce 9 gunp[d]3 s9ce he w\ld no :]e see ! lea/ example ( any su* op]ation2 except p]haps 9 e>?quakes & ?und]1 :i* he w\ld d\btless look ^u z exalt$ p[]s ( nature1 greatly surpass+ any art ( man to imitate4 ,9 ! same mann]1 if a /rang] to ! orig9al ( silk 7 %ewn a g>m5t made ( x1 he w\ld be v f> f imag9+ s /rong a sub/ance to be spun out ( ! b[els ( a small worm2 b mu/ c]ta9ly believe x ei!r a vegetable sub/ance1 l flax or cotton2 or ! natural cov]+ ( "s animal1 z wool is ( %eep4 ,or _h we be5 told1 be=e ! inv5tion ( ! magnetic ne$le among u1 t ano!r p 0 9 possession ( a c]ta9 contrivance1 by :i* !y 7 inabl$ to discov] ! position ( ! heav5s1 ) va/ly m ease1 ?an we c\ld d2 :at c\ld h be5 imag9$ m1 ?an t !y 7 provid$ ) "s fitt] a/ronomical in/rum5t = ?is purpose ?an we8 ,t any /one %\ld h s amaz+ a prop]ty1 z we f9d 9 ! magnet1 mu/ h be5 ! remote/ f our ?\ghts#cc4 #ad4 ,,b :at surpriz+ advancem5ts 9 ! k ( nature may be made by pursu+ ! true c\rse 9 philosophical inquiries2 :5 ^? se>*es are conduct$ by a g5ius equal to s div9e a "w1 w be be/ und]/ood by consid]+ ,sir ,,isaac ,,newton discov]ies4 ,t my's read] may appreh5d z j a notion ( ^!1 z c be convey$ to him1 by ! brief acc\nt1 :i* ,i int5d to lay be=e him2 ,i h set ap>t ?is introduction = expla9+1 9 ! fulle/ mann] ,i am able1 ! pr9ciples1 :]eon ,sir ,,isaac ,,newton proce$s4 ,= )\t a cle> conception ( ^!1 x is impossible to =m any true idea ( ! s+ul> excell5ce ( ! inv5tions ( ?is great philosoph]4 #ae4 ,,! pr9ciples !n ( ?is philosophy are2 ^u no consid]ation to indulge conjectures conc]n+ ! p[]s & laws ( nature1 b to make x our endeav\r ) all dilig5ce to se>* out ! real & true laws1 by :i* ! con/itution ( ?+s is regulat$4 ,! philosoph]'s fir/ c>e mu/ be to di/+ui%1 :at he sees to be )9 8 p[]1 f :at is beyond 8 rea*2 to assume no great] degree ( k1 ?an :at he f9ds himself possess$ (2 b to advance by sl[ & cauti\s /eps2 to se>* gradually into natural causes2 to secure to himself ! k ( ! mo/ imm$iate cause ( ea* appe>ance1 be=e he ext5ds 8 views f>!r to causes m remote4 ,?is is ! me?od1 9 :i* philosophy ought to be cultivat$2 :i* does n pret5d to s great ?+s1 z ! m airy speculations2 b w p]=m abundantly m3 we %all n p]haps seem to ! unskilful to "k s mu*1 b our real k w be great]4 ,& c]ta9ly x is no objection aga9/ ?is me?od1 t "s o!rs promise1 :at is ne>] to ! ext5t ( our wi%es3 s9ce ?is1 if x w n tea* u all we c\ld desire to be in=m$ (1 w h[ev] give u "s true light into nature2 :i* no o!r c d4 ,nor has ! philosoph] any reason to ?9k 8 lab\r lo/1 :5 he f9ds himself /opt at ! cause fir/ discov]$ by him1 or at any o!r m remote cause1 %ort ( ! orig9al3 = if he has b suffici5tly prov$ any "o cause1 he has ent]$ s f> into ! real con/itution ( ?+s1 has laid a safe f\ndation = o!rs to "w ^u1 & has facilitat$ _! endeav\rs 9 ! se>* aft] yet m di/ant causes2 & besides1 9 ! mean "t he may apply ! k ( ^! int]m$iate causes to _m useful purposes4 ,inde$ ! be+ able to make practical d$uctions f natural causes1 con/itutes ! great di/9ction betwe5 ! true philosophy & ! false4 ,causes assum$ ^u conjecture1 mu/ be s loose & undef9$1 t no?+ p>ticul> c be collect$ f !m4 ,b ^? causes1 :i* are br\ght to light by a /rict exam9ation ( ?+s1 w be m di/9ct4 ,h5ce x appe>s to h be5 no unuseful discov]y1 t ! asc5t ( wat] 9 pumps is ow+ to ! pressure ( ! air by its weight or spr+2 ?\gh ! causes1 :i* make ! air gravitate1 & r5d] x ela/ic1 be unkn[n3 = not)/&+ we are ignorant ( ! orig9al1 :5ce ^! p[]s ( ! air are d]iv$2 yet we may receive mu* advantage f ! b>e k ( ^! p[]s4 ,if we are b c]ta9 ( ! degree ( =ce1 :]e) !y act1 we %all "k ! ext5t ( :at is to be expect$ f !m2 we %all "k ! greate/ height1 to :i* x is possible by pumps to raise wat]2 & %all !reby be prev5t$ f mak+ any useless ef=ts t[>ds improv+ ^! in/rum5ts beyond ! limits prescrib$ to !m by nature2 :]eas )\t s mu* k z ?is1 we might probably h wa/$ 9 attempts ( ?is k9d mu* "t & lab\r4 ,h[ long did philosoph]s busy !mselves to no purpose 9 endeav\r+ to p]fect telescopes1 by =m+ ! glasses into "s new figure2 till ,sir ,,isaac ,,newton demon/rat$1 t ! effects ( telescopes 7 limit$ f ano!r cause1 ?an 0 suppos$2 :i* no alt]ation 9 ! figure ( ! glasses c\ld rem$y8 ,:at me?od ,sir ,,isaac ,,newton himself has f\nd = ! improvem5t ( telescopes %all be expla9$ h]eaft]#cd4 ,b at pres5t ,i %all proce$ to illu/rate1 by "s f>!r in/ances1 ?is di/+ui%+ "* ( ! true philosophy1 :i* we h n[ "u consid]ation4 ,x 0 no trifl+ discov]y1 t ! contraction ( ! muscles ( animals puts _! limbs 9 motion1 ?\gh ! orig9al cause ( t contraction rema9s a secret1 & p]haps may always d s2 = ! k ( ?us mu* only has giv5 rise to _m speculations ^u ! =ce & artificial disposition ( ! muscles1 & has op5$ no n>r[ prospect into ! animal fabrick4 ,! f9d+ out1 t ! n]ves are great ag5ts 9 ?is action1 leads u yet ne>] to ! orig9al cause1 & yields u a wid] view ( ! subject4 ,& ea* ( ^! /eps af=ds u assi/ance t[>ds re/or+ ?is animal motion1 :5 impair$ 9 our selves1 by po9t+ out ! seats ( ! injuries1 to :i* x is obnoxi\s4 ,to neglect all ?is1 because we c hi!rto advance no f>!r1 is pla9ly ridicul\s4 ,x is confess$ by all1 t ,,galileo greatly improv$ philosophy1 by %ew+1 z we %all relate h]eaft]1 t ! p[] 9 bodies1 :i* we call gravity1 occasions !m to move d[nw>ds ) a velocity equably accel]at$#ce2 & t :5 any body is ?r[n =w>ds1 ! same p[] obliges x to describe 9 its motion t l9e1 :i* is call$ by geomet]s a p>abola#cf3 yet we are ignorant ( ! cause1 :i* makes bodies gravitate4 ,b al?\gh we are unacqua9t$ ) ! spr+1 :5ce ?is p[] 9 nature is d]iv$1 nev]!less we c e/imate its effects4 ,:5 a body falls p]p5dicul>ly1 x is kn[n1 h[ long "t x takes 9 desc5d+ f any height :atev]3 & if x be ?r[n =w>ds1 we "k ! real pa?1 :i* x describes2 we c det]m9e 9 :at direction1 & ) :at degree ( swiftness x mu/ be project$1 9 ord] to its /rik+ aga9/ any object desir$2 & we c also asc]ta9 ! v =ce1 :]e) x w /rike4 ,sir ,,isaac ,,newton has f>!r taught1 t ?is p[] ( gravitation ext5ds up to ! moon1 & causes t planet to gravitate z mu* t[>ds ! e>?1 z any ( ! bodies1 :i* are famili> to u1 w\ld1 if plac$ at ! same di/ance#cg3 he has prov$ likewise1 t all ! planets gravitate t[>ds ! sun1 & t[>ds "o ano!r2 & t _! respective motions foll[ f ?is gravitation4 ,all ?is he has demon/rat$ ^u indisputable geometrical pr9ciples1 :i* _c be r5d]$ prec>i\s = want ( kn[+ :at x is1 :i* causes ^! bodies ?us mutually to gravitate3 any m ?an we c d\bt ( ! prop5sity 9 all ! bodies ab\t u1 to desc5d t[>ds ! e>?2 or c call 9 "q ! =em5tion$ propositions ( ,,galileo1 :i* are built ^u t pr9ciple4 ,& z ,,galileo has %ewn m fully1 ?an 0 kn[n be=e1 :at effects 7 produc$ 9 ! motion ( bodies by _! gravitation t[>ds ! e>?2 s ,sir ,,isaac ,,newton1 by ?is 8 inv5tion1 has mu* advanc$ our k 9 ! cele/ial motions4 ,by discov]+ t ! moon gravitates t[>ds ! sun1 z well z t[>ds ! e>?2 he has laid op5 ^? intricacies 9 ! moon's motion1 :i* no a/ronom]1 f obs]vations only1 c\ld ev] f9d out#ch3 & "o k9d ( heav5ly bodies1 ! comets1 h _! motion n[ cle>ly asc]ta9$2 :]e( we _h be=e no true k at all#ci4 #af4 ,,d\btless x might be expect$1 t su* surpriz+ success %\ld h sil5c$1 at once1 e cavil4 ,b we h se5 ! contr>y4 ,= because ?is philosophy pr(esses mode/ly to keep )9 ! ext5t ( our faculties1 & is ready to confess its imp]fections1 r ?an to make any fruitless attempts to conceal !m1 by seek+ to cov] ! defects 9 our k ) ! va9 o/5tation ( ra% & gr\ndless conjectures2 h5ce has be5 tak5 an occasion to ins9uate t we are l$ to miracul\s causes1 & ! occult qualities ( ! s*ools4 #ag4 ,,b ! fir/ ( ^! accusations is v extraord9>y4 ,if by call+ ^! causes miracul\s no?+ m is meant ?an only1 t !y (t5 appe> to u wond]ful & surpriz+1 x is n easy to see :at difficulty c be rais$ f !nce2 = ! works ( nature discov] e :]e su* pro(s ( ! unb\nd$ p[]1 & ! consummate wisdom ( _! au?or1 t ! m !y are kn[n1 ! m !y w excite our admiration3 & x is too manife/ to be insi/$ on1 t ! common s5se ( ! ^w miracul\s c h no place "h1 :5 x implies :at is above ! ord9>y c\rse ( ?+s4 ,! o!r imputation1 t ^! causes are occult ^u ! acc\nt ( our n p]ceiv+ :at produces !m1 conta9s 9 x great ambiguity4 ,t some?+ relat+ to !m lies hid1 ! foll[]s ( ?is philosophy are ready to ackn[l$ge1 nay desire x %\ld be c>efully rem>k$1 z po9t+ out prop] subjects = future inquiry4 ,b ?is is v diff]5t f ! proce$+ ( ! s*oolm5 9 ! causes call$ by !m occult4 ,= z _! occult qualities 7 und]/ood to op]ate 9 a mann] occult1 & n appreh5d$ by u2 s !y 7 obtrud$ ^u u = su* orig9al & ess5tial prop]ties 9 bodies1 z made x va9 to seek any f>!r cause2 & a great] p[] 0 attribut$ to !m1 ?an any natural appe>ances au?oriz$4 ,= in/ance1 ! rise ( wat] 9 pumps 0 ascrib$ to a c]ta9 abhorr5ce ( a vacuum1 :i* !y ?\ght fit to assign to nature4 ,& ?is 0 s f> a true obs]vation1 t ! wat] does move1 contr>y to its usual c\rse1 into ! space1 :i* o!rwise w\ld be left void ( any s5sible matt]2 &1 t ! procur+ su* a vacuity 0 ! app>5t cause ( ! wat]'s asc5t4 ,b :ile we 7 n 9 ! lea/ in=m$ h[ ?is p[]1 call$ an abhorr5ce ( a vacuum1 produc$ ! visible effects2 in/ead ( mak+ any advancem5t 9 ! k ( nature1 we only gave an artificial "n to "o ( h] op]ations3 & :5 ! speculation 0 pu%$ s beyond :at any appe>ances requir$1 z to h x conclud$1 t ?is abhorr5ce ( a vacuum 0 a p[] inh]5t 9 all matt]1 & s unlimit$ z to r5d] x impossible = a vacuum to exi/ at all2 x !n became a mu* great] absurdity1 9 be+ made ! f\ndation ( a mo/ ridicul\s mann] ( reason+2 z at l5g? evid5tly appe>$1 :5 x came to be discov]$1 t ?is rise ( ! wat] foll[$ only f ! pressure ( ! air1 & ext5d$ x self no f>!r1 ?an ! p[] ( t cause4 ,! s*ola/ic /ile 9 disc\rs+ ( ^! occult qualities1 z if !y 7 ess5tial diff]5ces 9 ! v sub/ances1 ( :i* bodies consi/$1 0 c]ta9ly v absurd2 by reason x t5d$ to disc\rage all f>!r inquiry4 ,b no su* ill consequ5ces c foll[ f ! consid]+ ( any natural causes1 :i* confess$ly are n trac$ up to _! fir/ orig9al4 ,h[ %all we ev] come to ! k ( ! sev]al orig9al causes ( ?+s1 o!rwise ?an by /or+ up all int]m$iate causes :i* we c discov]8 ,are all ! orig9al & ess5tial prop]ties ( matt] s v obvi\s1 t none ( !m c escape our fir/ view8 ,?is is n probable4 ,x is mu* m likely1 t1 if "s ( ! ess5tial prop]ties are discov]$ by our fir/ obs]vations1 a /rict] exam9ation %\ld br+ m to light4 #ah4 ,,b 9 ord] to cle> up ?is po9t conc]n+ ! ess5tial prop]ties ( matt]1 let u consid] ! subject a little di/9ctly4 ,we are to conceive1 t ! matt]1 out ( :i* ! univ]se ( ?+s is =m$1 is furni%$ ) c]ta9 qualities & p[]s1 :]eby x is r5d]$ fit to answ] ! purposes1 = :i* x 0 creat$4 ,b e prop]ty1 ( :i* any p>ticle ( ?is matt] is 9 x self possess$1 & :i* is n b>ely ! consequ5ce ( ! union ( ?is p>ticle ) o!r portions ( matt]1 we may call an ess5tial prop]ty3 :]eas all o!r qualities or attributes belong+ to bodies1 :i* dep5d on _! p>ticul> frame & composition1 are n ess5tial to ! matt]1 :]e( su* bodies are made2 because ! matt] ( ^! bodies w be depriv$ ( ^? qualities1 only by ! dissolution ( ! body1 )\t work+ any *ange 9 ! orig9al con/itution ( "o s+le p>ticle ( ?is mass ( matt]4 ,ext5sion we appreh5d to be "o ( ^! ess5tial prop]ties1 & imp5etrability ano!r4 ,^! two belong univ]sally to all matt]2 & are ! pr9cipal +r$i5ts 9 ! idea1 :i* ?is ^w matt] usually excites 9 ! m9d4 ,yet z ! idea1 m>k$ by ?is "n1 is n purely ! creature ( our own und]/&+s1 b is tak5 = ! repres5tation ( a c]ta9 sub/ance )\t u2 if we %\ld discov]1 t e "p ( ! sub/ance1 9 :i* we f9d ^! two prop]ties1 %\ld likewise be end[$ univ]sally ) any o!r ess5tial qualities2 all ^!1 f ! "t !y come to our notice1 mu/ be unit$ "u our g5]al idea ( matt]4 ,h[ _m su* prop]ties !re are actually 9 all matt] we "k n2 ^?1 ( :i* we are at pres5t appriz$1 h be5 f\nd out only by our obs]vations on ?+s2 h[ _m m a f>!r se>* may br+ to light1 no "o c say2 nor are we c]ta91 t we are provid$ ) suffici5t me?ods ( p]ception to disc]n !m all4 ,!re=e1 s9ce we h no o!r way ( mak+ discov]ies 9 nature1 b by gradual inquiries into ! prop]ties ( bodies2 our fir/ /ep mu/ be to admit )\t di/9ction all ! prop]ties1 :i* we obs]ve2 & aft]w>ds we mu/ endeav\r1 z f> z we are able1 to di/+ui% betwe5 ! qualities1 :]e) ! v sub/ances !mselves are indu$1 & ^? appe>ances1 :i* result f ! /ructure only ( comp\nd bodies4 ,"s ( ! prop]ties1 :i* we obs]ve 9 ?+s1 are ! attributes ( p>ticul> bodies only2 o!rs univ]sally belong to all1 t fall "u our notice4 ,:e!r "s ( ! qualities & p[]s ( p>ticul> bodies1 be d]iv$ f diff]5t k9ds ( matt] entr+ _! composition1 _c1 9 ! pres5t imp]fect /ate ( our k1 absolutely be decid$2 ?\gh we h n yet any reason to conclude1 b t all ! bodies1 ) :i* we conv]se1 are fram$ out ( ! v same k9d ( matt]1 & t _! di/9ct qualities are occasion$ only by _! /ructure2 ?r\gh ! v>iety :]e( ! g5]al p[]s ( matt] are caus$ to produce diff]5t effects4 ,on ! o!r h&1 we %\ld n ha/ily conclude1 t :atev] is f\nd to app]ta9 to all matt]1 :i* falls "u our exam9ation1 mu/ = t reason only be an ess5tial prop]ty !re(1 & n be d]iv$ f "s unse5 disposition 9 ! frame ( nature4 ,sir ,,isaac ,,newton has f\nd reason to conclude1 t gravity is a prop]ty univ]sally belong+ to all ! p]ceptible bodies 9 ! univ]se1 & to e p>ticle ( matt]1 :]e( !y are compos$4 ,b yet he no :]e ass]ts ?is prop]ty to be ess5tial to matt]4 ,& he 0 s f> f hav+ any design ( e/abli%+ x z su*1 t1 on ! contr>y1 he has giv5 "s h9ts wor?y ( himself at a cause = x#dj2 & expresly says1 t he propos$ ^? h9ts to %ew1 t he _h no su* int5tion#da4 #ai4 ,,x appe>s f h5ce1 t x is n easy to det]m9e1 :at prop]ties ( bodies are ess5tially inh]5t 9 ! matt]1 out ( :i* !y are made1 & :at dep5d ^u _! frame & composition4 ,b c]ta9ly :atev] prop]ties are f\nd to belong ei!r to any p>ticul> sy/ems ( matt]1 or univ]sally to all1 mu/ be consid]$ 9 philosophy2 because philosophy w be o!rwise imp]fect4 ,:e!r ^? prop]ties c be d$uc$ f "s o!r app]ta9+ to matt]1 ei!r among ^?1 :i* are already kn[n1 or among su* z c be discov]$ by u1 is aft]w>ds to be s\ght = ! f>!r improvem5t ( our k4 ,b ?is inquiry _c prop]ly h place 9 ! delib]ation ab\t admitt+ any prop]ty ( matt] or bodies into philosophy2 = t purpose x is only to be consid]$1 :e!r ! exi/5ce ( su* a prop]ty has be5 ju/ly prov$ or n4 ,!re=e to decide :at causes ( ?+s are rightly receiv$ into natural philosophy1 requires only a di/9ct & cle> conception ( :at k9d ( reason+ is to be all[$ ( z conv9c+1 :5 we argue ^u ! works ( nature4 #bj4 ,,! pro(s 9 natural philosophy _c be s absolutely conclusive1 z 9 ! ma!matics4 ,= ! subjects ( t sci5ce are purely ! ideas ( our own m9ds4 ,!y may be repres5t$ to our s5ses by mat]ial objects1 b !y are !mselves ! arbitr>y productions ( our own ?\ghts2 s t z ! m9d c h a full & adequate k ( its own ideas1 ! reason+ 9 geometry c be r5d]$ p]fect4 ,b 9 natural k ! subject ( our contemplation is )\t u1 & n s compleatly to be kn[n3 !re=e our me?od ( argu+ mu/ fall a little %ort ( absolute p]fection4 ,x is only "h requir$ to /e] a j c\rse betwe5 ! conjectural me?od ( proce$+1 aga9/ :i* ,i h s l>gely spoke2 & dem&+ s rigor\s a pro(1 z w r$uce all philosophy to m]e scepticism1 & exclude all prospect ( mak+ any progress 9 ! k ( nature4 #ba4 ,,! concessions1 :i* are to be all[$ 9 ?is sci5ce1 are by ,sir ,,isaac ,,newton includ$ "u a v few simple precepts4 #bb4 ,,! fir/ is1 t m causes are n to be receiv$ into philosophy1 ?an are suffici5t to expla9 ! appe>ances ( nature4 ,t ?is rule is approv$ ( unanim\sly1 is evid5t f ^? expressions s frequ5t among all philosoph]s1 t nature does no?+ 9 va92 & t a v>iety ( means1 :]e few] w\ld suffice1 is ne$less4 ,& c]ta9ly !re is ! highe/ reason = comply+ ) ?is rule4 ,= %\ld we indulge ! lib]ty ( multiply+1 )\t necessity1 ! causes ( ?+s1 x w\ld r$uce all philosophy to m]e unc]ta9ty2 s9ce ! only pro(1 :i* we c h1 ( ! exi/5ce ( a cause1 is ! necessity ( x = produc+ kn[n effects4 ,!re=e :]e "o cause is suffici5t1 if !re really %\ld 9 nature be two1 :i* is 9 ! la/ degree improbable1 we c h no possible means ( kn[+ x1 & consequ5tly ought n to take ! lib]ty ( imag9+1 t !re are m ?an "o4 #bc4 ,,! second precept is ! direct consequ5ce ( ! fir/1 t to l effects are to be ascrib$ ! same causes4 ,= in/ance1 t respiration 9 m5 & 9 brutes is br\ght ab\t by ! same means2 t bodies desc5d to ! e>? "h 9 ,,europe1 & 9 ,,am]ica f ! same pr9ciple2 t ! light ( a cul9>y fire1 & ( ! sun h ! same mann] ( production2 t ! reflection ( light is effect$ 9 ! e>?1 & 9 ! planets by ! same p[]2 & ! l4 #bd4 ,,! ?ird ( ^! precepts has equally evid5t reason = x4 ,x is only1 t ^? qualities1 :i* 9 ! same body c nei!r be less5$ nor increas$1 & :i* belong to all bodies t are 9 our p[] to make trial ^u1 ought to be acc\nt$ ! univ]sal prop]ties ( all bodies :atev]4 #be4 ,,9 ?is precept is f\nd$ t me?od ( argu+ by induction1 )\t :i* no progress c\ld be made 9 natural philosophy4 ,= z ! qualities ( bodies become kn[n to u by exp]im5ts only2 we h no o!r way ( f9d+ ! prop]ties ( su* bodies1 z are out ( our rea* to exp]im5t ^u1 b by draw+ conclusions f ^? :i* fall "u our exam9ation4 ,! only caution "h requir$ is1 t ! obs]vations & exp]im5ts1 we argue ^u1 be num]\s en\gh1 & t due reg>d be paid to all objections1 t occur1 z ! ,"l ,,bacon v judici\sly directs#db4 ,& ?is admonition is suffici5tly compli$ )1 :5 by virtue ( ?is rule we ascribe imp5etrability & ext5sion to all bodies1 ?\gh we h no s5sible exp]im5t1 t af=ds a direct pro( ( any ( ! cele/ial bodies be+ imp5etrable2 nor t ! fix$ />s are s mu* z ext5d$4 ,= ! m p]fect our in/rum5ts are1 :]eby we attempt to f9d _! visible magnitude1 ! less !y appe>2 insomu* t all ! s5sible magnitude1 :i* we obs]ve 9 !m1 seems only to be an optical deception by ! scatt]+ ( _! light4 ,h[ev]1 ,i suppose no "o w imag9e !y are )\t any magnitude1 ?\gh _! imm5se di/ance makes x undisc]nable by u4 ,aft] ! same mann]1 if x c be prov$1 t all bodies "h gravitate t[>ds ! e>?1 9 proportion to ! quantity ( solid matt] 9 ea*2 & t ! moon gravitates to ! e>? likewise1 9 proportion to ! quantity ( matt] 9 x2 & t ! sea gravitates t[>ds ! moon1 & all ! planets t[>ds ea* o!r2 & t ! v comets h ! same gravitat+ faculty2 we %all h z great reason to conclude by ?is rule1 t all bodies gravitate t[>ds ea* o!r4 ,= inde$ ?is rule w m /rongly hold 9 ?is case1 ?an 9 t ( ! imp5etrability ( bodies2 because !re w m in/ances be _h ( bodies gravitat+1 ?an ( _! be+ imp5etrable4 #be4 ,,?is is t me?od ( induction1 :]eon all philosophy is f\nd$2 :i* our au?or f>!r in=ces by ?is additional precept1 t :atev] is collect$ f ?is induction1 ought to be receiv$1 not)/&+ any conjectural hypo!sis to ! contr>y1 till su* times z x %all be contradict$ or limit$ by f>!r obs]vations on nature4 ,illu/ration ,illu/ration ,,book ,i4 ,,conc]n+ ,,! ,,motion ( ,,bodies ,,9 ,,g5]al4 ,,*ap4 ,i4 ,( ! ,,laws ( ,,motion4 ,,hav+ ?us expla9$ ,sir ,,isaac ,,newton's me?od ( reason+ 9 philosophy1 ,i %all n[ proce$ to my int5d$ acc\nt ( 8 discov]ies4 ,^! are conta9$ 9 two treatises4 ,9 "o ( !m1 ! ,,ma!matical ,,pr9ciples ,,( ,,natural ,,philosophy1 8 *ief design is to %ew by :at laws ! heav5ly motions are regulat$2 9 ! o!r1 8 ,,optics1 he disc\rses ( ! nature ( light & col\rs1 & ( ! action betwe5 light & bodies4 ,?is second treatise is :olly conf9$ to ! subject ( light3 except "s conjectures propos$ at ! end conc]n+ o!r p>ts ( nature1 :i* lie hi!rto m conceal$4 ,9 ! o!r treatise our au?or 0 oblig$ to smoo? ! way to 8 pr9cipal int5tion1 by expla9+ _m ?+s ( a m g5]al nature3 = ev5 "s ( ! mo/ simple prop]ties ( matt] 7 sc>ce well e/abli%$ at t "t4 ,we may !re=e r$uce ,sir ,,isaac ,,newton's doctr9e "u ?ree g5]al heads2 & ,i %all accord+ly divide my acc\nt into ?ree books4 ,9 ! fir/ ,i %all speak ( :at he has deliv]$ conc]n+ ! motion ( bodies1 )\t reg>d to any p>ticul> sy/em ( matt]2 9 ! second ,i %all treat ( ! heav5ly motions2 & ! ?ird %all be employ$ ^u light4 #b4 ,,9 ! fir/ "p ( my design1 we mu/ beg9 ) an acc\nt ( ! g5]al laws ( motion4 #c4 ,,^! laws are "s univ]sal affections & prop]ties ( matt] drawn f exp]i5ce1 :i* are made use ( z axioms & evid5t pr9ciples 9 all our argu+s ^u ! motion ( bodies4 ,= z x is ! cu/om ( geomet]s to assume 9 _! demon/rations "s propositions1 )\t exhibit+ ! pro( ( !m2 s 9 philosophy1 all our reason+ mu/ be built ^u "s prop]ties ( matt]1 fir/ admitt$ z pr9ciples :]eon to argue4 ,9 geometry ^! axioms are ?us assum$1 on acc\nt ( _! be+ s evid5t z to make any pro( 9 =m ne$less4 ,b 9 philosophy no prop]ties ( bodies c be 9 ?is mann] receiv$ = self-evid5t2 s9ce x has be5 obs]v$ above1 t we c conclude no?+ conc]n+ matt] by any reason+s ^u its nature & ess5ce1 b t we owe all ! k1 we h !re(1 to exp]i5ce4 ,yet :5 our obs]vations on matt] h in=m'd u ( "s ( its prop]ties1 we may securely reason ^u !m 9 our f>!r inquiries into nature4 ,& ^! laws ( motion1 ( :i* ,i am "h to speak1 are f\nd s univ]sally to belong to bodies1 t !re is no motion kn[n1 :i* is n regulat$ by !m4 ,^! are by ,sir ,,isaac ,,newton r$uc$ to ?ree#dc4 #d4 ,,! fir/ law is1 t all bodies h su* an indiff]5ce to re/1 or motion1 t if once at re/ !y rema9 s1 till di/urb$ by "s p[] act+ ^u !m3 b if once put 9 motion1 !y p]si/ 9 x2 cont9u+ to move "r =w>ds p]petually1 aft] ! p[]1 :i* gave ! motion1 is remov$2 & also pres]v+ ! same degree ( velocity or quickness1 z 0 fir/ communicat$1 n /opp+ or remitt+ _! c\rse1 till int]rupt$ or o!rwise di/urb$ by "s new p[] impress$4 #e4 ,,! second law ( motion is1 t ! alt]ation ( ! /ate ( any body1 :e!r f re/ to motion1 or f motion to re/1 or f "o degree ( motion to ano!r1 is always proportional to ! =ce impress$4 ,a body at re/1 :5 act$ ^u by any p[]1 yields to t p[]1 mov+ 9 ! same l9e1 9 :i* ! p[] appli$ is direct$2 & moves ) a less or great] degree ( velocity1 accord+ to ! degree ( ! p[]2 s t twice ! p[] %all communicate a d\ble velocity1 & ?ree times ! p[] a ?reefold velocity4 ,if ! body be mov+1 & ! p[] impress$ act ^u ! body 9 ! direction ( its motion1 ! body %all receive an addition to its motion1 z great z ! motion1 into :i* t p[] w\ld h put x f a /ate ( re/2 b if ! p[] impress$ ^u a mov+ body act directly opposite to its =m] motion1 t p[] %all !n take away f ! body's motion1 z mu* z 9 ! o!r case x w\ld h add$ to x4 ,la/ly1 if ! p[] be impress$ obliquely1 !re w arise an oblique motion diff]+ m or less f ! =m] direction1 accord+ z ! new impression is great] or less4 ,= example1 if ! body ,a 79 fig4 #a47 be mov+ 9 ! direction ,a ,b1 & :5 x is at ! po9t ,a1 a p[] be impress$ ^u x 9 ! direction ,a ,c1 ! body %all f h5ce=? nei!r move 9 its fir/ direction ,a ,b1 nor 9 ! direction ( ! adv5titi\s p[]1 b %all take a c\rse z ,a ,d betwe5 !m3 & if ! p[] la/ impress$ be j equal to t1 :i* fir/ gave to ! body its motion2 ! l9e ,a ,d %all pass 9 ! middle betwe5 ,a ,b & ,a ,c1 divid+ ! angle "u ,b ,a ,c into two equal p>ts2 b if ! p[] la/ impress$ be great] ?an ! fir/1 ! l9e ,a ,d %all incl9e mo/ to ,a ,c2 :]eas if ! la/ impression be less ?an ! fir/1 ! l9e ,a ,d %all incl9e mo/ to ,a ,b4 ,to be m p>ticul>1 ! situation ( ! l9e ,a ,d is always to be det]m9$ aft] ?is mann]4 ,let ,a ,e be ! space1 :i* ! body w\ld h mov$ ?r\gh 9 ! l9e ,a ,b dur+ any c]ta9 portion ( "t2 provid$ t body1 :5 at ,a1 _h receiv$ no second impulse4 ,suppose likewise1 t ,a ,f is ! "p ( ! l9e ,a ,c1 ?r\gh :i* ! body w\ld h mov$ dur+ an equal portion ( "t1 if x _h be5 at re/ 9 ,a1 :5 x receiv$ ! impulse 9 ! direction ,a ,c3 !n if f ,e be drawn a l9e p>allel to1 or equidi/ant f ,a ,c1 & f ,f ano!r l9e p>allel to ,a ,b1 ^? two l9es w meet 9 ! l9e ,a ,d4 #f4 ,,! ?ird & la/ ( ^! laws ( motion is1 t :5 any body acts ^u ano!r1 ! action ( t body ^u ! o!r is equall$ by ! contr>y reaction ( t o!r body ^u ! fir/4 #g4 ,,^! laws ( motion are abundantly confirm$ by ?is1 t all ! d$uctions made f !m1 9 relation to ! motion ( bodies1 h[ complicat$ soev]1 are f\nd to agree p]fectly ) obs]vation4 ,?is %all be %ewn m at l>ge 9 ! next *apt]4 ,b be=e we proce$ to s diffusive a pro(2 ,i *use "h to po9t out ^? appe>ances ( bodies1 :]eby ! laws ( motion are fir/ sugge/$ to u4 #h4 ,,daily obs]vation makes x appe> to u1 t any body1 :i* we once see at re/1 nev] puts x self into fre% motion2 b cont9ues always 9 ! same place1 till remov$ by "s p[] appli$ to x4 #i4 ,,aga91 :5ev] a body is once 9 motion1 x cont9ues 9 t motion "s "t aft] ! mov+ p[] has quitt$ x1 & x is left to x self4 ,n[ if ! body cont9ue to move b a s+le mom5t1 aft] ! mov+ p[] has left x1 !re c no reason be assign$1 :y x %\ld ev] /op )\t "s ext]nal =ce4 ,= x is pla91 t ?is cont9uance ( ! motion is caus$ only by ! body's hav+ already mov$1 ! sole op]ation ( ! p[] ^u ! body be+ ! putt+ x 9 motion2 !re=e t motion cont9u$ w equally be ! cause ( its f>!r motion1 & s on )\t end4 ,! only d\bt t c rema91 is1 :e!r ?is motion communicat$ cont9ues intire1 aft] ! p[]1 t caus$ x1 ceases to act2 or :e!r x does n gradually langui% & decrease4 ,& ?is suspicion _c be remov$ by a transi5t & slight obs]vation on bodies1 b w be fully cle>$ up by ^? m accurate pro(s ( ! laws ( motion1 :i* are to be consid]$ 9 ! next *apt]4 #aj4 ,,la/ly1 bodies 9 motion appe> to affect a /raight c\rse )\t any deviation1 unless :5 di/urb$ by "s adv5titi\s p[] act+ ^u !m4 ,if a body be ?r[n p]p5dicul>ly upw>ds or d[nw>ds1 x appe>s to cont9ue 9 ! same /raight l9e dur+ ! :ole "t ( its motion4 ,if a body be ?r[n 9 any o!r direction1 x is f\nd to deviate f ! l9e1 9 :i* x began to move1 m & m cont9ually t[>ds ! e>?1 :i!r x is direct$ by its weight3 b s9ce1 :5 ! weight ( a body does n alt] ! direction ( its motion1 x always moves 9 a /raight l9e1 )\t d\bt 9 ?is o!r case ! body's1 decl9+ f its fir/ c\rse is no m1 ?an :at is caus$ by its weight alone4 ,z ?is appe>s at fir/ sight to be unque/ionable1 s we %all h a v di/9ct pro( !re( 9 ! next *apt]1 :]e ! oblique motion ( bodies w be p>ticul>ly consid]$4 #aa4 ,,?us we see h[ ! fir/ ( ! laws ( motion agrees ) :at appe>s to u 9 mov+ bodies4 ,b "h occurs ?is f>!r consid]ation1 t ! real & absolute motion ( any body is n visible to u3 = we are our selves also 9 con/ant motion along ) ! e>? :]eon we dwell2 insomu* t we p]ceive bodies to move s f> only1 z _! motion is diff]5t f our own4 ,:5 a body appe>s to u to lie at re/1 9 reality x only cont9ues ! motion1 x has receiv$1 )\t putt+ =? any p[] to *ange t motion4 ,if we ?r[ a body 9 ! c\rse or direction1 :]e9 we are c>ri$ our selves2 s mu* motion z we seem to h giv5 to ! body1 s mu* we h truly add$ to ! motion1 x _h1 :ile x appe>$ to u to be at re/4 ,b if we impel a body ! contr>y way1 al?\gh ! body appe>s to u to h receiv$ by su* an impulse z mu* motion1 z :5 impell$ ! o!r way2 yet 9 ?is case we h tak5 f ! body s mu* real motion1 z we seem to h giv5 x4 ,?us ! motion1 :i* we see 9 bodies1 is n _! real motion1 b only relative ) respect to u2 & ! =em5tion$ obs]vations only %ew u1 t ?is fir/ law ( motion has place 9 ?is relative or app>5t motion4 ,h[ev]1 ?\gh we _c make any obs]vation imm$iately on ! absolute motion ( bodies1 yet by reason+ ^u :at we obs]ve 9 visible motion1 we c discov] ! prop]ties & effects ( real motion4 #ab4 ,,) reg>d to ?is fir/ law ( motion1 :i* is n[ "u consid]ation1 we may f ! =ego+ obs]vations mo/ truly collect1 t bodies are dispos$ to cont9ue 9 ! absolute motion1 :i* !y h once receiv$1 )\t increas+ or dim9i%+ _! velocity4 ,:5 a body appe>s to u to lie at re/1 x really pres]ves )\t *ange ! motion1 :i* x has 9 common ) our selves3 & :5 we put x into visible motion1 & we see x cont9ue t motion2 ?is proves1 t ! body reta9s t degree ( its absolute motion1 into :i* x is put by our act+ ^u x3 if we give x su* an app>5t motion1 :i* adds to its real motion1 x pres]ves t addition2 & if our act+ on ! body takes (f f its real motion1 x cont9ues aft]w>ds to move ) no m real motion1 ?an we h left x4 #ac4 ,,aga91 we d n obs]ve 9 bodies any disposition or p[] )9 !mselves to *ange ! direction ( _! motion2 & if !y _h any su* p[]1 x w\ld easily be discov]$4 ,= suppose a body by ! /ructure or disposition ( its p>ts1 or by any o!r circum/ance 9 its make1 0 indu$ ) a p[] ( mov+ x self2 ?is self-mov+ pr9ciple1 :i* %\ld be ?us inh]5t 9 ! body1 & n dep5d on any ?+ ext]nal1 mu/ *ange ! direction :]e9 x w\ld act1 z (t5 z ! position ( ! body 0 *ang$3 s t = in/ance1 if a body 0 ly+ be=e me 9 su* a position1 t ! direction1 :]e9 ?is pr9ciple disposes ! body to move1 0 po9t$ directly f me2 if ,i !n gradually turn$ ! body ab\t1 ! direction ( ?is self-mov+ pr9ciple w\ld no long] be po9t$ directly f me1 b w\ld turn ab\t along ) ! body4 ,n[ if any body1 :i* appe>s to u at re/1 7 furni%$ ) any su* self-mov+ pr9ciple2 f ! body's appe>+ )\t motion we mu/ conclude1 t ?is self-mov+ pr9ciple lies direct$ ! same way z ! e>? is c>ry+ ! body2 & su* a body might imm$iately be put into visible motion only by turn+ x ab\t 9 any degree1 t ?is self-mov+ pr9ciple might receive a diff]5t direction4 #ad4 ,,f ^! consid]ations x v pla9ly foll[s1 t if a body 7 once absolutely at re/2 n be+ furni%$ ) any pr9ciple1 :]eby x c\ld put x self into motion1 x mu/ = ev] cont9ue 9 ! same place1 till act$ ^u by some?+ ext]nal3 & also t :5 a body is put into motion1 x has no p[] )9 x self to make any *ange 9 ! direction ( t motion2 & consequ5tly t ! body mu/ move on /raight =w>d )\t decl9+ any way :atev]4 ,b x has be=e be5 %ewn1 t bodies d n appe> to h 9 !mselves any p[] to *ange ! velocity ( _! motion3 !re=e ?is fir/ law ( motion has be5 illu/rat$ & confirm$1 z mu* z c be f ! transi5t obs]vations1 :i* h "h be5 disc\rs$ ^u2 & 9 ! next *apt] all ?is w be f>!r e/abli%$ by m correct obs]vations4 #ae4 ,,b ,i %all n[ pass to ! second law ( motion2 :]e91 :5 x is ass]t$1 t ! velocity1 ) :i* any body is mov$ by ! action ( a p[] ^u x1 is proportional to t p[]2 ! degree ( p[] is suppos$ to be measur$ by ! greatness ( ! body1 :i* x c move ) a giv5 cel]ity4 ,s t ! s5se ( ?is law is1 t if any body 7 put into motion ) t degree ( swiftness1 z to pass 9 "o h\r ! l5g? ( a ?\s& y>ds2 ! p[]1 :i* w\ld give ! same degree ( velocity to a body twice z great1 w\ld give ?is less] body twice ! velocity1 caus+ x to describe 9 ! same space ( an h\r two ?\s& y>ds4 ,b by a body twice z great z ano!r1 ,i d n "h mean simply ( twice ! bulk1 b "o t conta9s a d\ble quantity ( solid matt]4 #af4 ,,:y ! p[]1 :i* c move a body twice z great z ano!r ) ! same degree ( velocity1 %\ld be call$ twice z great z ! p[]1 :i* c give ! less] body ! same velocity1 is evid5t4 ,= if we %\ld suppose ! great] body to be divid$ into two equal p>ts1 ea* equal to ! less] body1 ea* ( ^! halves w require ! same degree ( p[] to move !m ) ! velocity ( ! less] body1 z ! less] body x self requires2 & !re=e bo? ^? halves1 or ! :ole great] body1 w require ! mov+ p[] to be d\bl$4 #ag4 ,,t ! mov+ p[] be+ 9 ?is s5se d\bl$1 %\ld j d\ble likewise ! velocity ( ! same body1 seems ne> z evid5t1 if we consid]1 t ! effect ( ! p[] appli$ mu/ ne$s be ! same1 :e!r t p[] be appli$ to ! body at once1 or 9 p>ts4 ,suppose !n ! d\ble p[] n appli$ to ! body at once1 b half ( x fir/1 & aft]w>ds ! o!r half2 x is n conceivable = :at reason ! half la/ appli$ %\ld come to h a diff]5t effect ^u ! body1 f t :i* is appli$ fir/2 z x mu/ h1 if ! velocity ( ! body 0 n j d\bl$ by ! application ( x4 ,s f> z exp]i5ce c det]m9e1 we see no?+ to fav\r su* a supposition4 ,we _c inde$ 7by reason ( ! con/ant motion ( ! e>?7 make trial ^u any body p]fectly at re/1 :]eby to see :e!r a p[] appli$ 9 t case w\ld h a diff]5t effect1 f :at x has1 :5 ! body is already mov+2 b we f9d no alt]ation 9 ! effect ( ! same p[] on acc\nt ( any diff]5ce !re may be 9 ! motion ( ! body1 :5 ! p[] is appli$4 ,! e>? does n always c>ry bodies ) ! same degree ( velocity2 yet we f9d ! visible effects ( any p[] appli$ to ! same body to be1 at all times ! v same3 & a bale ( goods1 or o!r moveable body ly+ 9 a %ip is z easily remov$ f place to place1 :ile ! %ip is "u sail1 if its motion be /eady1 z :5 x is fix$ at an*or4 #ah4 ,,n[ ?is exp]i5ce is alone suffici5t to %ew to u ! :ole ( ?is law ( motion4 #ai4 ,,s9ce we f9d1 t ! same p[] w always produce ! same *ange 9 ! motion ( any body1 :e!r t body 7 be=e mov+ ) a swift] or sl[] motion2 ! *ange wr\ght 9 ! motion ( a body dep5ds only on ! p[] appli$ to x1 )\t any reg>d to ! body's =m] motion3 & !re=e ! degree ( motion1 :i* ! body already possesses1 hav+ no influ5ce on ! p[] appli$ to di/urb its op]ation1 ! effects ( ! same p[] w n only be ! same 9 all degrees ( motion ( ! body2 b we h likewise no reason to d\bt1 b t a body p]fectly at re/ w\ld receive f any p[] z mu* motion1 z w\ld be equival5t to ! effect ( ! same p[] appli$ to t body already 9 motion4 #bj4 ,,aga91 suppose a body be+ at re/1 any numb] ( equal p[]s %\ld be successively appli$ to x2 pu%+ x =w>d f "t to "t 9 ! same c\rse or direction4 ,^u ! application ( ! fir/ p[] ! body w\ld beg9 to move2 :5 ! second p[] 0 appli$1 x appe>s f :at has be5 said1 t ! motion ( ! body w\ld become d\ble2 ! ?ird p[] w\ld treble ! motion ( ! body2 & s on1 till aft] ! op]ation ( ! la/ p[] ! motion ( ! body w\ld be z _m times ! motion1 :i* ! fir/ p[] gave x1 z !re are p[]s 9 numb]4 & ! effect ( ?is numb] ( p[]s w be always ! same1 )\t any reg>d to ! space ( "t tak5 up 9 apply+ !m3 s t great] or less] int]vals betwe5 ! application ( ea* ( ^! p[]s w produce no diff]5ce at all 9 _! effects4 ,s9ce !re=e ! di/ance ( "t betwe5 ! action ( ea* p[] is ( no consequ5ce2 )\t d\bt ! effect w /ill be ! same1 ?\gh ! p[]s %\ld all be appli$ at ! v same in/ant2 or al?\gh a s+le p[] %\ld be appli$ equal 9 /r5g? to ! collective =ce ( all ^! p[]s4 ,h5ce x pla9ly foll[s1 t ! degree ( motion1 into :i* any body w be put out ( a /ate ( re/ by any p[]1 w be proportional to t p[]4 ,a d\ble p[] w give twice ! velocity1 a treble p[] ?ree times ! velocity1 & s on4 ,! =ego+ reason+ w equally take place1 ?\gh ! body 7 n suppos$ to be at re/1 :5 ! p[]s began to be appli$ to x2 provid$ ! direction1 9 :i* ! p[]s 7 appli$1 ei!r conspir$ ) ! action ( ! body1 or 0 directly opposite to x4 ,!re=e if any p[] be appli$ to a mov+ body1 & act ^u ! body ei!r 9 ! direction :]e) ! body moves1 s z to accel]ate ! body2 or if x act directly opposite to ! motion ( ! body1 s z to ret>d x3 9 bo? ^! cases ! *ange ( motion w be proportional to ! p[] appli$2 nay1 ! augm5tation ( ! motion 9 "o case1 & ! dim9ution !re( 9 ! o!r1 w be equal to t degree ( motion1 into :i* ! same p[] w\ld put ! body1 _h x be5 at re/1 :5 ! p[] 0 appli$4 #ba4 ,,f>!r1 a p[] may be s appli$ to a mov+ body1 z to act obliquely to ! motion ( ! body4 ,& ! effects ( su* an oblique motion may be d$uc$ f ?is obs]vation2 t z all bodies are cont9ually mov+ along ) ! e>?1 we see t ! visible effects ( ! same p[] are always ! same1 9 :atev] direction ! p[] acts3 & !re=e ! visible effects ( any p[] ^u a body1 :i* seems only to be at re/1 is always to appe>ance ! same z ! real effect w\ld be ^u a body truly at re/4 ,n[ suppose a body 7 mov+ along ! l9e ,a ,b 79 fig4 #b47 & ! eye accompani$ x ) an equal motion 9 ! l9e ,c ,d equidi/ant f ,a ,b2 s t :5 ! body is at ,a1 ! eye %all be at ,c1 & :5 ! body is advanc$ to ,e 9 ! l9e ,a ,b1 ! eye %all be advanc$ to ,f 9 ! l9e ,c ,d1 ! di/ances ,a ,e & ,c ,f be+ equal4 ,x is evid5t1 t "h ! body w appe> to ! eye to be at re/2 & ! l9e ,f ,e ,g drawn f ! eye ?r\gh ! body %all seem to ! eye to be immoveable2 ?\gh z ! body & eye move =w>d toge!r1 ?is l9e %all really also move2 s t :5 ! body %all be advanc$ to ,h & ! eye to ,k1 ! l9e ,f ,e ,g %all be transf]r$ into ! situation ,k ,h ,l1 ?is l9e ,k ,h ,l be+ equidi/ant f ,f ,e ,g4 ,n[ if ! body :5 at ,e 7 to receive an impulse 9 ! direction ( ! l9e ,f ,e ,g2 :ile ! eye is mov+ on f ,f to ,k & c>ry+ along ) x ! l9e ,f ,e ,g1 ! body w appe> to ! eye to move along ?is l9e ,f ,e ,g3 = ?is is :at has j n[ be5 said2 t :ile bodies are mov+ along ) ! e>?1 & ! spectator's eye p>takes ( ! same motion1 ! effect ( any p[] ^u ! body w appe> to be :at x w\ld really h be51 _h ! body be5 truly at re/1 :5 ! p[] 0 appli$4 ,f h5ce x foll[s1 t :5 ! eye is advanc$ to ,k1 ! body w appe> some:]e 9 ! l9e ,k ,h ,l4 ,suppose x appe> 9 ,m2 !n x is manife/1 f :at has be5 premis$ at ! beg9n+ ( ?is p>agraph1 t ! di/ance ,h ,m is equal to :at ! body w\ld h run ^u ! l9e ,e ,g1 dur+ ! "t1 :]e9 ! eye has pass$ f ,f to ,k1 provid$ t ! body _h be5 at re/1 :5 act$ ^u 9 ,e4 ,if x be f>!r ask$1 aft] :at mann] ! body has mov$ f ,e to ,m8 ,i answ]1 ?r\gh a /raight l9e2 = x has be5 %ewn above 9 ! explication ( ! fir/ law ( motion1 t a mov+ body1 f ! "t x is left to x self1 w proce$ on 9 "o cont9u$ /raight l9e4 #bb4 ,,if ,e ,n be tak5 equal to ,h ,m & ,n ,m be drawn2 s9ce ,h ,m is equidi/ant f ,e ,n1 ,n ,m w be equidi/ant f ,e ,h4 ,!re=e ! effect ( any p[] ^u a mov+ body1 :5 t p[] acts obliquely to ! motion ( ! body1 is to be det]m9$ 9 ?is mann]4 ,suppose ! body is mov+ along ! /raight l9e ,a ,e ,b1 if :5 ! body is come to ,e1 a p[] gives x an impulse 9 ! direction ( ! l9e ,e ,g1 to f9d :at c\rse ! body w aft]w>ds take we mu/ proce$ ?us4 ,take 9 ,e ,b any l5g? ,e ,h1 & 9 ,e ,g take su* a l5g? ,e ,n1 t if ! body _h be5 at re/ 9 ,e1 ! p[] appli$ to x w\ld h caus$ x to move ov] ,e ,n 9 ! same space ( "t1 z x w\ld h employ$ 9 pass+ ov] ,e ,h1 if ! p[] _h n act$ at all ^u x4 ,!n draw ,h ,l equidi/ant f ,e ,g1 & ,n ,m equidi/ant f ,e ,b4 ,aft] ?is1 if a l9e be drawn f ,e to ! po9t ,m1 :]e ^! two l9es meet1 ! l9e ,e ,m w be ! c\rse into :i* ! body w be put by ! action ( ! p[] ^u x at ,e4 #bc4 ,a ,,ma!matical read] w\ld "h expect 9 "s p>ticul>s m regul> demon/rations2 b z ,i d n at pres5t address my self to su*1 s ,i hope1 :at ,i h n[ writt5 w r5d] my mean+ evid5t en\gh to ^?1 :o are unacqua9t$ ) t k9d ( reason+4 #bd4 ,,n[ z we h be5 %ew+1 t "s actual =ce is necess>y ei!r to put bodies out ( a /ate ( re/ into motion1 or to *ange ! motion1 :i* !y h once receiv$2 x is prop] "h to obs]ve1 t ?is quality 9 bodies1 :]eby !y pres]ve _! pres5t /ate1 ) reg>d to motion or re/1 till "s active =ce di/urb !m1 is call$ ! ,,vis ,,in]tiae ( matt]3 & by ?is prop]ty1 matt]1 sluggi% & unactive ( x self1 reta9s all ! p[] impress$ ^u x1 & _c be made to cease f action1 b by ! opposition ( z great a p[]1 z t :i* fir/ mov$ x4 ,by ! degree ( ?is ,,vis ,,in]tiae1 or p[] ( inactivity1 z we %all h5ce=? call x1 we prim>ily judge ( ! quantity ( solid matt] 9 ea* body2 = z ?is quality is inh]5t 9 all ! bodies1 ^u :i* we c make any trial1 we conclude x to be a prop]ty ess5tial to all matt]2 & z we yet "k no reason to suppose1 t bodies are compos$ ( diff]5t k9ds ( matt]1 we r presume1 t ! matt] ( all bodies is ! same2 & t ! degree ( ?is p[] ( inactivity is 9 e body proportional to ! quantity ( ! solid matt] 9 x4 ,b al?\gh we h no absolute pro(1 t all ! matt] 9 ! univ]se is uni=m1 & possesses ?is p[] ( inactivity 9 ! same degree2 yet we c ) c]ta9ty comp>e toge!r ! diff]5t degrees ( ?is p[] ( inactivity 9 diff]5t bodies4 ,p>ticul>ly ?is p[] is proportional to ! weight ( bodies1 z ,sir ,,isaac ,,newton has demon/rat$#dd4 ,h[ev]1 not)/&+ t ?is p[] ( inactivity 9 any body c be m c]ta9ly kn[n1 ?an ! quantity ( solid matt] 9 x2 yet s9ce !re is no reason to suspect t "o is n proportional to ! o!r1 we %all h]eaft] speak )\t hesitation ( ! quantity ( matt] 9 bodies1 z ! measure ( ! degree ( _! p[] ( inactivity4 #be4 ,,?is be+ e/abli%$1 we may n[ comp>e ! effects ( ! same p[] ^u diff]5t bodies1 z hi!rto we h %ewn ! effects ( diff]5t p[]s ^u ! same body4 ,& "h if we limit ! ^w motion to ! peculi> s5se giv5 to x 9 philosophy1 we may compreh5d all t is to be said ^u ?is head "u "o %ort precept2 t ! same p[]1 to :atev] body x is appli$1 w always produce ! same degree ( motion4 ,b "h motion does n signify ! degree ( cel]ity or velocity ) :i* a body moves1 9 :i* s5se only we h hi!rto us$ x2 b x is made use ( p>ticul>ly 9 philosophy to signify ! =ce ) :i* a body moves3 z if two bodies ,a & ,b be+ 9 motion1 twice ! =ce w\ld be requir$ to /op ,a z to /op ,b1 ! motion ( ,a w\ld be e/eem$ d\ble ! motion ( ,b4 ,9 mov+ bodies1 ^! two ?+s are c>efully to be di/+ui%$2 _! velocity or cel]ity1 :i* is measur$ by ! space !y pass ?r\gh dur+ any det]m9ate portion ( "t2 & ! quantity ( _! motion1 or ! =ce1 ) :i* !y w press aga9/ any resi/ance4 ,:i* =ce1 :5 diff]5t bodies move ) ! same velocity1 is proportional to ! quantity ( solid matt] 9 ! bodies2 b if ! bodies are equal1 ?is =ce is proportional to _! respective velocities1 & 9 o!r cases x is proportional bo? to ! quantity ( solid matt] 9 ! body1 & also to its velocity4 ,to in/ance 9 two bodies ,a & ,b3 if ,a be twice z great z ,b1 & !y h bo? ! same velocity1 ! motion ( ,a %all be d\ble ! motion ( ,b2 & if ! bodies be equal1 & ! velocity ( ,a be twice t ( ,b1 ! motion ( ,a %all likewise be d\ble t ( ,b2 b if ,a be twice z l>ge z ,b1 & move twice z swift1 ! motion ( ,a w be f\r times ! motion ( ,b2 & la/ly1 if ,a be twice z l>ge z ,b1 & move b half z fa/1 ! degree ( _! motion %all be ! same4 #bf4 ,,?is is ! p>ticul> s5se giv5 to ! ^w motion by philosoph]s1 & 9 ?is s5se ( ! ^w ! same p[] always produces ! same quantity or degree ( motion4 ,if ! same p[] act ^u two bodies ,a & ,b1 ! velocities1 x %all give to ea* ( !m1 %all be s adju/$ to ! respective bodies1 t ! same degree ( motion %all be produc$ 9 ea*4 ,if ,a be twice z great z ,b1 its velocity %all be half t ( ,b2 if ,a has ?ree times z mu* solid matt] z ,b1 ! velocity ( ,a %all be "o ?ird ( ! velocity ( ,b2 & g5]ally ! velocity giv5 to ,a %all be> ! same proportion to ! velocity giv5 to ,b1 z ! quantity ( solid matt] conta9$ 9 ! body ,b be>s to ! quantity ( solid matt] conta9$ 9 ,a4 #bg4 ,,! reason ( all ?is is evid5t f :at has gone be=e4 ,if a p[] 7 appli$ to ,b1 :i* %\ld be> ! same proportion to ! p[] appli$ to ,a1 z ! body ,b be>s to ,a1 ! bodies ,b & ,a w\ld bo? receive ! same velocity2 & ! velocity1 :i* ,b w receive f ?is p[]1 w be> ! same proportion to ! velocity1 :i* x w\ld receive f ! action ( ! p[] appli$ to ,a1 z ! =m] ( ^! p[]s be>s to ! latt]3 t is1 ! velocity1 :i* ,a receives f ! p[] appli$ to x1 w be> to ! velocity1 :i* ,b w\ld receive f ! same p[]1 ! same proportion z ! body ,b be>s to ,a4 #bh4 ,,f h5ce we may n[ pass to ! ?ird law ( motion1 :]e ?is di/9ction betwe5 ! velocity ( a body & its :ole motion is f>!r necess>y to be reg>d$1 z %all imm$iately be %ewn2 aft] hav+ fir/ illu/rat$ ! mean+ ( ?is law by a famili> in/ance4 ,if a /one or o!r load be drawn by a horse2 ! load re-acts ^u ! horse1 z mu* z ! horse acts ^u ! load2 = ! h>ness1 :i* is /ra9$ betwe5 !m1 presses aga9/ ! horse z mu* z aga9/ ! load2 & ! progressive motion ( ! horse =w>d is h9dr$ z mu* by ! load1 z ! motion ( ! load is promot$ by ! endeav\r ( ! horse3 t is1 if ! horse put =? ! same /r5g?1 :5 loos5$ f ! load1 he w\ld move himself =w>ds ) great] swiftness 9 proportion to ! diff]5ce betwe5 ! weight ( 8 own body & ! weight ( himself & load toge!r4 #bi4 ,,?is in/ance w af=d "s g5]al notion ( ! mean+ ( ?is law4 ,b to proce$ to a m philosophical explication3 if a body 9 motion /rike aga9/ ano!r at re/1 let ! body /rik+ be ev] s small1 yet %all x communicate "s degree ( motion to ! body x /rikes aga9/1 ?\gh ! less t body be 9 comp>ison ( t x imp+es ^u1 & ! less ! velocity is1 ) :i* x moves1 ! small] w be ! motion communicat$4 ,b :atev] degree ( motion x gives to ! re/+ body1 ! same x %all lose x self4 ,?is is ! necess>y consequ5ce ( ! =em5tion$ p[] ( inactivity 9 matt]4 ,= suppose ! two bodies equal1 x is evid5t f ! "t !y meet1 bo? ! bodies are to be mov$ by ! s+le motion ( ! fir/2 !re=e ! body 9 motion by means ( its p[] ( inactivity reta9+ ! motion fir/ giv5 x1 /rikes ^u ! o!r ) ! same =ce1 :]e) x 0 act$ ^u x self3 b n[ bo? ! bodies be+ to be mov$ by t =ce1 :i* be=e mov$ "o only1 ! ensu+ velocity w be ! same1 z if ! p[]1 :i* 0 appli$ to "o ( ! bodies1 & put x into motion1 _h be5 appli$ to bo?2 :5ce x appe>s1 t !y w proce$ =w>ds1 ) half ! velocity1 :i* ! body fir/ 9 motion _h3 t is1 ! body fir/ mov$ w h lo/ half its motion1 & ! o!r w h ga9$ exactly z mu*4 ,?is rule is j1 provid$ ! bodies keep contigu\s aft] meet+2 z !y w\ld always d1 if x 7 n = a c]ta9 cause t (t5 int]v5es1 & :i* mu/ n[ be expla9$4 ,bodies ^u /rik+ aga9/ ea* o!r1 suff] an alt]ation 9 _! figure1 hav+ _! p>ts press$ inw>ds by ! /roke1 :i* = ! mo/ "p recoil aga9 aft]w>ds1 ! bodies endeav\r+ to recov] _! =m] %ape4 ,?is p[]1 :]eby bodies are inabl$ to rega9 _! fir/ figure1 is usually call$ _! ela/icity1 & :5 x acts1 x =ces ! bodies f ea* o!r1 & causes !m to sep>ate4 ,n[ ! effect ( ?is ela/icity 9 ! pres5t case is su*1 t if ! bodies are p]fectly ela/ic1 s z to recoil ) z great a =ce z !y are b5t )1 t !y recov] _! figure 9 ! same space ( "t1 z has be5 tak5 up 9 ! alt]ation made 9 x by _! compression toge!r2 !n ?is p[] w sep>ate ! bodies z swiftly1 z !y be=e approa*$1 & act+ ^u bo? equally1 ^u ! body fir/ 9 motion contr>y to ! direction 9 :i* x moves1 & ^u ! o!r z mu* 9 ! direction ( its motion1 x w take f ! fir/1 & add to ! o!r equal degrees ( velocity3 s t ! p[] be+ /rong en\gh to sep>ate !m ) z great a velocity1 z !y approa*$ )1 ! fir/ w be q /opt1 & t :i* 0 at re/1 w receive all ! motion ( ! o!r4 ,if ! bodies are ela/ic 9 a less degree1 ! fir/ w n lose all its motion1 nor w ! o!r acquire ! motion ( ! fir/1 b fall z mu* %ort ( x1 z ! o!r reta9s4 ,= ?is rule is nev] deviat$ f1 t ?\gh ! degree ( ela/icity det]m9es h[ mu* m ?an half its velocity ! body fir/ 9 motion %all lose2 yet 9 e case ! loss 9 ! motion ( ?is body %all be transf]r$ to ! o!r1 t o!r body always receiv+ by ! /roke z mu* motion1 z is tak5 f ! fir/4 #cj4 ,?is is ! case ( a body /rik+ directly aga9/ an equal body at re/1 & ! reason+ "h us$ is fully confirm$ by exp]i5ce4 ,!re are _m o!r cases ( bodies imp++ aga9/ "o ano!r3 b ! m5tion ( ^! %all be res]v$ to ! next *apt]1 :]e we int5d to be m p>ticul> & diffusive 9 ! pro( ( ^! laws ( motion1 ?an we h be5 "h4 ,,*ap4 ,,ii4 ,f>!r pro(s ( ! ,,laws ,,( ,,motion4 ,,hav+ 9 ! prec$+ *apt] d$uc$ ! ?ree laws ( motion1 deliv]$ by our great philosoph]1 f ! mo/ obvi\s obs]vations1 t sugge/ !m to u2 ,i n[ int5d to give m p>ticul> pro(s ( !m1 by rec\nt+ "s ( ! discov]ies :i* h be5 made 9 philosophy be=e ,sir ,isaac ,newton4 ,= z !y 7 all collect$ by reason+ ^u ^? laws2 s ! con=mity ( ^! discov]ies to exp]i5ce makes !m s _m pro(s ( ! tru? ( ! pr9ciples1 f :i* !y 7 d]iv$4 #b4 ,,let u beg9 ) ! subject1 :i* conclud$ ! la/ *apt]4 ,al?\gh ! body 9 motion be n equal to ! body at re/1 on :i* x /rikes2 yet ! motion aft] ! /roke is to be e/imat$ 9 ! same mann] z above4 ,let ,a 79 fig4 #c47 be a body 9 motion t[>ds ano!r body ,b ly+ at re/4 ,:5 ,a is arriv$ at ,b1 x _c proce$ f>!r )\t putt+ ,b into motion2 & :at motion x gives to ,b1 x mu/ lose x self1 t ! :ole degree ( motion ( ,a & ,b toge!r1 if nei!r ( ! bodies be ela/ic1 %all be equal1 aft] ! meet+ ( ! bodies1 to ! s+le motion ( ,a be=e ! /roke4 ,!re=e1 f :at has be5 said above1 x is manife/1 t z soon z ! two bodies are met1 !y w move on toge!r ) a velocity1 :i* w be> ! same proportion to ! orig9al velocity ( ,a1 z ! body ,a be>s to ! sum ( bo? ! bodies4 #c4 ,,if ! bodies are ela/ic1 s t !y %all sep>ate aft] ! /roke1 ,a mu/ lose a great] "p ( its motion1 & ! subsequ5t motion ( ,b w be augm5t$ by ?is ela/icity1 z mu* z ! motion ( ,a is dim9i%$ by x4 ,! ela/icity act+ equally betwe5 bo? ! bodies1 x w communicate to ea* ! same degree ( motion2 t is1 x w sep>ate ! bodies by tak+ f ! body ,a & add+ to ! body ,b diff]5t degrees ( velocity1 s proportion$ to _! respective quantities ( matt]1 t ! degree ( motion1 :]e) ,a sep>ates f ,b1 %all be equal to ! degree ( motion1 :]e) ,b sep>ates f ,a4 ,x foll[s !re=e1 t ! velocity tak5 f ,a by ! ela/icity be>s to ! velocity1 :i* ! same ela/icity adds to ,b1 ! same proportion1 z ,b be>s to ,a3 consequ5tly ! velocity1 :i* ! ela/icity takes f ,a1 w be> ! same proportion to ! :ole velocity1 :]e) ?is ela/icity causes ! two bodies to sep>ate f ea* o!r1 z ! body ,b be>s to ! sum ( ! two bodies ,a & ,b2 & ! velocity1 :i* is add$ to ,b by ! ela/icity1 be>s to ! velocity1 :]e) ! bodies sep>ate1 ! same proportion1 z ! body ,a be>s to ! sum ( ! two bodies ,a & ,b4 ,?us is f\nd1 h[ mu* ! ela/icity takes f ! velocity ( ,a1 & adds to ! velocity ( ,b2 provid$ ! degree ( ela/icity be kn[n1 :]eby to det]m9e ! :ole velocity :]e) ! bodies sep>ate f ea* o!r aft] ! /roke#de4 #d4 ,,aft] ?is mann] is det]m9$ 9 e case ! result ( a body 9 motion /rik+ aga9/ ano!r at re/4 ,! same pr9ciples w also det]m9e ! effects1 :5 bo? bodies are 9 motion4 #e4 ,,let two equal bodies move aga9/ ea* o!r ) equal swiftness4 ,!n ! =ce1 ) :i* ea* ( !m presses =w>ds1 be+ equal :5 !y /rike2 ea* press+ 9 its own direction ) ! same en]gy1 nei!r %all surm\nt ! o!r1 b bo? be /opt1 if !y be n ela/ic3 = if !y be ela/ic1 !y %all f !nce recov] new motion1 & rec$e f ea* o!r1 z swiftly z !y met1 if !y be p]fectly ela/ic2 b m sl[ly1 if less s4 ,9 ! same mann]1 if two bodies ( unequal bigness /rike aga9/ ea* o!r1 & _! velocities be s relat$1 t ! velocity ( ! less] body %all exce$ ! velocity ( ! great] 9 ! same proportion1 z ! great] body exce$s ! less] 7= in/ance1 if "o body conta9s twice ! solid matt] z ! o!r1 & moves b half z fa/7 two su* bodies w entirely suppress ea* o!r's motion1 & rema9 f ! "t ( _! meet+ fix$2 if1 z be=e1 !y are n ela/ic3 b1 if !y are s 9 ! highe/ degree1 !y %all rec$e aga91 ea* ) ! same velocity1 :]e) !y met4 ,= ?is ela/ic p[]1 z 9 ! prec$+ case1 %all r5ew _! motion1 & press+ equally ^u bo?1 %all give ! same motion to bo?2 t is1 %all cause ! velocity1 :i* ! less] body receives1 to be> ! same proportion to ! velocity1 :i* ! great] receives1 z ! great] body be>s to ! less]3 s t ! velocities %all be> ! same proportion to ea* o!r aft] ! /roke1 z be=e4 ,!re=e if ! bodies1 by be+ p]fectly ela/ic1 h ! sum ( _! velocities aft] ! /roke equal to ! sum ( _! velocities be=e ! /roke1 ea* body aft] ! /roke w receive its fir/ velocity4 ,& ! same proportion w hold likewise betwe5 ! velocities1 :]e) !y g (f1 ?\gh !y are ela/ic b 9 a less degree2 only !n ! velocity ( ea* w be less 9 proportion to ! defect ( ela/icity4 #f4 ,,if ! velocities1 :]e) ! bodies meet1 are n 9 ! proportion "h suppos$2 b if "o ( ! bodies1 z ,a1 has a swift] velocity 9 comp>ison to ! velocity ( ! o!r2 !n ! effect ( ?is excess ( velocity 9 ! body ,a mu/ be jo9$ to ! effect n[ m5tion$1 aft] ! mann] ( ?is foll[+ example4 ,let ,a be twice z great z ,b1 & move ) ! same swiftness z ,b4 ,"h ,a moves ) twice t degree ( swiftness1 :i* w\ld answ] to ! =em5tion$ proportion4 ,= ,a be+ d\ble to ,b1 if x mov$ b ) half ! swiftness1 :]e) ,b advances1 x has be5 j n[ %ewn1 t ! two bodies ^u meet+ w\ld /op1 if !y 7 n ela/ic2 & if !y 7 ela/ic1 t !y w\ld ea* recoil1 s z to cause ,a to return ) half ! velocity1 :]e) ,b w\ld return4 ,b x is evid5t f h5ce1 t ,b by enc\ntr+ ,a w annul half its velocity1 if ! bodies be n ela/ic2 & ! future motion ( ! bodies w be ! same1 z if ,a _h advanc$ aga9/ ,b at re/ ) half ! velocity "h assign$ to x4 ,if ! bodies be ela/ic1 ! velocity ( ,a & ,b aft] ! /roke may be ?us discov]$4 ,z ! two bodies advance aga9/ ea* o!r1 ! velocity1 ) :i* !y meet1 is made up ( ! velocities ( bo? bodies add$ toge!r4 ,aft] ! /roke _! ela/icity w sep>ate !m aga94 ,! degree ( ela/icity w det]m9e :at proportion ! velocity1 :]e) !y sep>ate1 mu/ be> to t1 :]e) !y meet4 ,divide ?is velocity1 ) :i* ! bodies sep>ate into two p>ts1 t "o ( ! p>ts be> to ! o!r ! same proportion1 z ! body ,a be>s to ,b2 & ascribe ! less] "p to ! great] body ,a1 & ! great] "p ( ! velocity to ! less] body ,b4 ,!n take ! "p ascrib$ to ,a f ! common velocity1 :i* ,a & ,b w\ld h _h aft] ! /roke1 if !y _h n be5 ela/ic2 & add ! "p ascrib$ to ,b to ! same common velocity4 ,by ?is means ! true velocities ( ,a & ,b aft] ! /roke w be made kn[n4 #g4 ,,if ! bodies are p]fectly ela/ic1 ! great ,,huyg5s has laid d[n ?is rule = f9d+ _! motion aft] conc\rse#df4 ,any /raight l9e ,c ,d 79 fig4 #d1 #e47 be+ drawn1 let x be divid$ 9 ,e1 t ,c ,e be> ! same proportion to ,e ,d1 z ! swiftness ( ,a bore to ! swiftness ( ,b be=e ! /roke4 ,let ! same l9e ,c ,d be also divid$ 9 ,f1 t ,c ,f be> ! same proportion to ,f ,d1 z ! body ,b be>s to ! body ,a4 ,!n ,f ,g be+ tak5 equal to ,f ,e1 if ! po9t ,g falls )9 ! l9e ,c ,d1 bo? ! bodies %all recoil aft] ! /roke1 & ! velocity1 :]e) ! body ,a %all return1 w be> ! same proportion to ! velocity1 :]e) ,b %all return1 z ,g ,c be>s to ,g ,d2 b if ! po9t ,g falls )\t ! l9e ,c ,d1 !n ! bodies aft] _! conc\rse %all bo? proce$ to move ! same way1 & ! velocity ( ,a %all be> to ! velocity ( ,b ! same proportion1 t ,g ,c be>s to ,g ,d1 z be=e4 #h4 ,,if ! body ,b _h /ood /ill1 & receiv$ ! impulse ( ! o!r body ,a ^u x2 ! effect has be5 already expla9$ 9 ! case1 :5 ! bodies are n ela/ic4 ,& :5 !y are ela/ic1 ! result ( _! collision is f\nd by comb9+ ! effect ( ! ela/icity ) ! o!r effect1 9 ! same mann] z 9 ! la/ case4 #i4 ,,:5 ! bodies are p]fectly ela/ic1 ! rule ( ,,huyg5s#dg "h is to divide ! l9e ,c ,d 7fig4 #f47 9 ,e z be=e1 & to take ,e ,g equal to ,e ,d4 ,& by ^! po9ts ?us f\nd1 ! motion ( ea* body aft] ! /roke is det]m9$1 z be=e4 #aj4 ,,9 ! next place1 suppose ! bodies ,a & ,b 7 bo? mov+ ! same way1 b ,a ) a swift] motion1 s z to ov]take ,b1 & /rike aga9/ x4 ,! effect ( ! p]cussion or /roke1 :5 ! bodies are n ela/ic1 is discov]$ by f9d+ ! common motion1 :i* ! two bodies w\ld h aft] ! /roke1 if ,b 7 at re/1 & ,a 7 to advance aga9/ x ) a velocity equal to ! excess ( ! pres5t velocity ( ,a above ! velocity ( ,b2 & by add+ to ?is common velocity ?us f\nd ! velocity ( ,b4 #aa4 ,,if ! bodies are ela/ic1 ! effect ( ! ela/icity is to be unit$ ) ?is o!r1 z 9 ! =m] cases4 #ab4 ,,:5 ! bodies are p]fectly ela/ic1 ! rule ( ,,huyg5s#dh 9 ?is case is to prolong ,c ,d 7fig4 #g47 & to take 9 x ?us prolong$ ,c ,e 9 ! same proportion to ,e ,d1 z ! great] velocity ( ,a be>s to ! less] velocity ( ,b2 aft] :i* ,f ,g be+ tak5 equal to ,f ,e1 ! velocities ( ! two bodies aft] ! /roke w be det]m9$1 z 9 ! two prec$+ cases4 #ac4 ,,?us ,i h giv5 ! sum ( :at has be5 writt5 conc]n+ ! effects ( p]cussion1 :5 two bodies freely 9 motion /rike directly aga9/ ea* o!r2 & ! results "h set d[n1 z ! consequ5ce ( our reason+ f ! laws ( motion1 answ] mo/ exactly to exp]i5ce4 ,a p>ticul> set ( exp]im5ts has be5 inv5t$ to make trial ( ^! effects ( p]cussion ) ! greate/ exactness4 ,b ,i mu/ def] ^! exp]im5ts1 till ,i h expla9$ ! nature ( p5dulums#di4 ,i %all !re=e n[ proce$ to describe "s ( ! appe>ances1 :i* are caus$ 9 bodies f ! influ5ce ( ! p[] ( gravity unit$ ) ! g5]al laws ( motion2 among :i* ! motion ( ! p5dulum w be includ$4 #ad4 ,,! mo/ simple ( ^! appe>ances is1 :5 bodies fall d[n m]ely by _! weight4 ,9 ?is case ! body increases cont9ually its velocity1 dur+ ! :ole "t ( its fall1 & t 9 ! v same proportion z ! "t increases4 ,= ! p[] ( gravity acts con/antly on ! body ) ! same degree ( /r5g?3 & x has be5 obs]v$ above 9 ! fir/ law ( motion1 t a body be+ once 9 motion w p]petually pres]ve t motion )\t ! cont9uance ( any ext]nal influ5ce ^u x3 !re=e1 aft] a body has be5 once put 9 motion by ! =ce ( gravity1 ! body w\ld cont9ue t motion1 ?\gh ! p[] ( gravity %\ld cease to act any f>!r ^u x2 b1 if ! p[] ( gravity cont9ues /ill to draw ! body d[n1 fre% degrees ( motion mu/ cont9ually be add$ to ! body2 & ! p[] ( gravity act+ at all times ) ! same /r5g?1 equal degrees ( motion w con/antly be add$ 9 equal portions ( "t4 #ae4 ,,?is conclusion is n inde$ absolutely true3 = we %all f9d h]eaft]#ej1 t ! p[] ( gravity is n ( ! same /r5g? at all di/ances f ! c5t] ( ! e>?4 ,b no?+ ( ?is is 9 ! lea/ s5sible 9 any di/ance1 to :i* we c convey bodies4 ,! weight ( bodies is ! v same to s5se ^u ! highe/ t[]s or m\nta9s1 z ^u ! level gr\nd2 s t 9 all ! obs]vations we c make1 ! =em5tion$ proportion betwe5 ! velocity ( a fall+ body & ! "t1 9 :i* x has be5 desc5d+1 obta9s )\t any ! lea/ p]ceptible diff]5ce4 #af4 ,,f h5ce x foll[s1 t ! space1 ?r\gh :i* a body falls1 is n proportional to ! "t ( ! fall2 = s9ce ! body increases its velocity1 a great] space w be pass$ ov] 9 ! same portion ( "t at ! latt] "p ( ! fall1 ?an at ! beg9n+4 ,suppose a body let fall f ! po9t ,a 79 fig4 #h47 7 to desc5d f ,a to ,b 9 any portion ( "t2 !n if 9 an equal portion ( "t x 7 to proce$ f ,b to ,c2 ,i say1 ! space ,b ,c is great] ?an ,a ,b2 s t ! "t ( ! fall f ,a to ,c be+ d\ble ! "t ( ! fall f ,a to ,b1 ,a ,c %all be m ?an d\ble ( ,a ,b4 #ag4 ,,! geomet]s h prov$1 t ! spaces1 ?r\gh :i* bodies fall ?us by _! weight1 are j 9 a duplicate or two-fold proportion ( ! times1 9 :i* ! body has be5 fall+4 ,t is1 if we 7 to take ! l9e ,d ,e 9 ! same proportion to ,a ,b1 z ! "t1 :i* ! body has imploy$ 9 fall+ f ,a to ,c1 be>s to ! "t ( ! fall f ,a to ,b2 !n ,a ,c w be to ,d ,e 9 ! same proportion4 ,9 p>ticul>1 if ! "t ( ! fall ?r\gh ,a ,c be twice ! "t ( ! fall ?r\gh ,a ,b2 !n ,d ,e w be twice ,a ,b1 & ,a ,c twice ,d ,e2 or ,a ,c f\r times ,a ,b4 ,b if ! "t ( ! fall ?r\gh ,a ,c _h be5 ?rice ! "t ( ! fall ?r\gh ,a ,b2 ,d ,e w\ld h be5 treble ( ,a ,b1 & ,a ,c treble ( ,d ,e2 t is1 ,a ,c w\ld h be5 equal to n9e times ,a ,b4 #ah4 ,,if a body fall obliquely1 x w approa* ! gr\nd by sl[] degrees1 ?an :5 x falls p]p5dicul>ly4 ,suppose two l9es ,a ,b1 ,a ,c 79 fig4 #i47 7 drawn1 "o p]p5dicul>1 & ! o!r oblique to ! gr\nd ,d ,e3 !n if a body 7 to desc5d 9 ! slant+ l9e ,a ,c2 because ! p[] ( gravity draws ! body directly d[nw>ds1 if ! l9e ,a ,c supports ! body f fall+ 9 t mann]1 x mu/ take (f "p ( ! effect ( ! p[] ( gravity2 s t 9 ! "t1 :i* w\ld h be5 suffici5t = ! body to h fall5 ?r\gh ! :ole p]p5dicul> l9e ,a ,b1 ! body %all n h pass$ 9 ! l9e ,a ,c a l5g? equal to ,a ,b2 consequ5tly ! l9e ,a ,c be+ long] ?an ,a ,b1 ! body %all mo/ c]ta9ly take up m "t 9 pass+ ?r\gh ,a ,c1 ?an x w\ld h done 9 fall+ p]p5dicul>ly d[n ?r\gh ,a ,b4 #ai4 ,,! geomet]s demon/rate1 t ! "t1 9 :i* ! body w desc5d ?r\gh ! oblique /raight l9e ,a ,c1 be>s ! same proportion to ! "t ( its desc5t ?r\gh ! p]p5dicul> ,a ,b1 z ! l9e x self ,a ,c be>s to ,a ,b4 ,& 9 respect to ! velocity1 :i* ! body w h acquir$ 9 ! po9t ,c1 !y likewise prove1 t ! l5g? ( ! "t imploy$ 9 ! desc5t ?r\gh ,a ,c s comp5sates ! dim9ution ( ! influ5ce ( gravity f ! obliquity ( ?is l9e1 t ?\gh ! =ce ( ! p[] ( gravity on ! body is oppos$ by ! obliquity ( ! l9e ,a ,c1 yet ! "t ( ! body's desc5t %all be s mu* prolong$1 t ! body %all acquire ! v same velocity 9 ! po9t ,c1 z x w\ld h got at ! po9t ,b by fall+ p]p5dicul>ly d[n4 #bj4 ,,if a body 7 to desc5d 9 a crook$ l9e1 ! "t ( its desc5t _c be det]m9$ 9 s simple a mann]2 b ! same prop]ty1 9 relation to ! velocity1 is demon/rat$ to take place 9 all cases3 t is1 9 :atev] l9e ! body desc5ds1 ! velocity w always be answ]able to ! p]p5dicul> height1 f :i* ! body has fell4 ,= in/ance1 suppose ! body ,a 79 fig4 #aj47 7 hung by a /r+ to ! p9 ,b4 ,if ?is body 7 let fall1 till x came to ! po9t ,c p]p5dicul>ly "u ,b1 x w h mov$ f ,a to ,c 9 ! ar* ( a circle4 ,!n ! horizontal l9e ,a ,d be+ drawn1 ! velocity ( ! body 9 ,c w be ! same1 z if x _h fall5 f ! po9t ,d directly d[n to ,c4 #ba4 ,,if a body be ?r[n p]p5dicul>ly upw>d ) any =ce1 ! velocity1 :]e) ! body asc5ds1 %all cont9ually dim9i%1 till at l5g? x be :olly tak5 away2 & f t "t ! body w beg9 to fall d[n aga91 & pass ov] a second "t 9 its desc5t ! l9e1 :]e9 x asc5d$2 fall+ ?r\gh ?is l9e ) an increas+ velocity 9 su* a mann]1 t 9 e po9t !re(1 ?r\gh :i* x falls1 x %all h ! v same velocity1 z x _h 9 ! same place1 :5 x asc5d$2 & consequ5tly %all come d[n into ! place1 :5ce x fir/ asc5d$1 ) ! velocity :i* 0 at fir/ giv5 to x4 ,?us if a body 7 ?r[n p]p5dicul>ly up 9 ! l9e ,a ,b 79 fig4 ,,ii47 ) su* a =ce1 z t x %\ld /op at ! po9t ,b1 & !re beg9 to fall aga92 :5 x %all h arriv$ 9 its desc5t to any po9t z ,c 9 ?is l9e1 x %all !re h ! same velocity1 z t :]e) x pass$ by ?is po9t ,c 9 its asc5t2 & at ! po9t ,a x %all h ga9$ z great a velocity1 z t :]e) x 0 fir/ ?r[n upw>ds4 ,z ?is is demon/rat$ by ! geometrical writ]s2 s1 ,i ?9k1 x w appe> evid5t1 by consid]+ only1 t :ile ! body desc5ds1 ! p[] ( gravity mu/ act ov] aga91 9 an inv]t$ ord]1 all ! influ5ce x _h on ! body 9 its asc5t2 s z to give aga9 to ! body ! same degrees ( velocity1 :i* x _h tak5 away be=e4 #bb4 ,,aft] ! same mann]1 if ! body 7 ?r[n upw>ds 9 ! oblique /raight l9e ,c ,a 79 fig4 #i47 f ! po9t ,c1 ) su* a degree ( velocity z j to rea* ! po9t ,a2 x %all by its own weight return aga9 ?r\gh ! l9e ,a ,c by ! same degrees1 z x asc5d$4 #bc4 ,,& la/ly1 if a body 7 ?r[n ) any velocity 9 a l9e cont9ually incurvat$ upw>ds1 ! l effect w be produc$ ^u its return to ! po9t1 :5ce x 0 ?r[n4 ,suppose = in/ance1 ! body ,a 79 fig4 #ab47 7 hung by a /r+ ,a ,b4 ,!n if ?is body be impell$ any way1 x mu/ move 9 ! ar* ( a circle4 ,let x receive su* an impulse1 z %all cause x to move 9 ! ar* ,a ,c2 & let ?is impulse be ( su* /r5g?1 t ! body may be c>ri$ f ,a z f> z ,d1 be=e its motion is ov]come by its weight3 ,i say "h1 t ! body =?) return+ f ,d1 %all come aga9 into ! po9t ,a ) ! same velocity1 z t :]e) x began to move4 #bd4 ,,x w be prop] 9 ?is place to obs]ve conc]n+ ! p[] ( gravity1 t its =ce ^u any body does n at all dep5d ^u ! %ape ( ! body2 b t x cont9ues con/antly ! same )\t any v>iation 9 ! same body1 :atev] *ange be made 9 ! figure ( ! body3 & if ! body be divid$ into any numb] ( pieces1 all ^? pieces %all weigh j ! same1 z !y did1 :5 unit$ toge!r 9 "o body3 & if ! body be ( a uni=m contexture1 ! weight ( ea* piece w be proportional to its bulk4 ,?is has giv5 reason to conclude1 t ! p[] ( gravity acts ^u bodies 9 proportion to ! quantity ( matt] 9 !m4 ,:5ce x %\ld foll[1 t all bodies mu/ fall f equal heights 9 ! same space ( "t4 ,& z we evid5tly see ! contr>y 9 fea!rs & su* l sub/ances1 :i* fall v sl[ly 9 comp>ison ( m solid bodies2 x is reasonable to suppose1 t "s o!r cause concurs to make s manife/ a diff]5ce4 ,?is cause has be5 f\nd by p>ticul> exp]im5ts to be ! air4 ,! exp]im5ts = ?is purpose are made ?us4 ,!y set up a v tall holl[ glass2 )9 :i* ne> ! top !y lodge a fea!r & "s v pond]\s body1 usually a piece ( gold1 ?is metal be+ ! mo/ weighty ( any body kn[n to u4 ,?is glass !y empty ( ! air conta9$ )9 x1 & by mov+ a wire1 :i* passes ?r\gh ! top ( ! glass1 !y let ! fea!r & ! heavy body fall toge!r2 & x is always f\nd1 t z ! two bodies beg9 to desc5d at ! same "t1 s !y accompany ea* o!r 9 ! fall1 & come to ! bottom at ! v same in/ant1 z ne> z ! eye c judge4 ,?us1 z f> z ?is exp]im5t c be dep5d$ on1 x is c]ta91 t ! effect ( ! p[] ( gravity ^u ea* body is proportional to ! quantity ( solid matt]1 or to ! p[] ( inactivity 9 ea* body4 ,= 9 ! limit$ s5se1 :i* we h giv5 above to ! ^w motion1 x has be5 %[n1 t ! same =ce gives to all bodies ! same degree ( motion1 & diff]5t =ces communicate diff]5t degrees ( motion proportional to ! respective p[]s#ea4 ,9 ?is case1 if ! p[] ( gravity 7 to act equally ^u ! fea!r1 & ^u ! m solid body1 ! solid body w\ld desc5d s mu* sl[] ?an ! fea!r1 z to h no great] degree ( motion ?an ! fea!r3 b z bo? bodies desc5d ) equal swiftness1 ! degree ( motion 9 ! solid body is great] ?an 9 ! fea!r1 be>+ ! same proportion to x1 z ! quantity ( matt] 9 ! solid body to ! quantity ( matt] 9 ! fea!r4 ,!re=e ! effect ( gravity on ! solid body is great] ?an on ! fea!r1 9 proportion to ! great] degree ( motion communicat$2 t is1 ! effect ( ! p[] ( gravity on ! solid body be>s ! same proportion to its effect on ! fea!r1 z ! quantity ( matt] 9 ! solid body be>s to ! quantity ( matt] 9 ! fea!r4 ,?us x is ! prop] d$uction f ?is exp]im5t1 t ! p[] ( gravity acts n on ! surface ( bodies only1 b p5etrates ! bodies !mselves mo/ intimately1 & op]ates alike on e p>ticle ( matt] 9 !m4 ,b z ! great quickness1 ) :i* ! bodies fall1 leaves x some?+ unc]ta91 :e!r !y d desc5d absolutely 9 ! same "t1 or only s ne>ly toge!r1 t ! diff]5ce 9 _! swift motion is n disc]nable to ! eye2 ?is prop]ty ( ! p[] ( gravity1 :i* has "h be5 d$uc$ f ?is exp]im5t1 is f>!r confirm$ by p5dulums1 ^: motion is su*1 t a v m9ute diff]5ce w\ld become suffici5tly s5sible4 ,?is w be f>!r disc\rs$ on 9 ano!r place#eb2 b "h ,i %all make use ( ! pr9ciple n[ laid d[n to expla9 ! nature ( :at is call$ ! c5t] ( gravity 9 bodies4 #be4 ,,! c5t] ( gravity is t po9t1 by :i* if a body be susp5d$1 x %all hang at re/ 9 any situation4 ,9 a globe ( a uni=m texture ! c5t] ( gravity is ! same ) ! c5t] ( ! globe2 = z ! p>ts ( ! globe on e side ( its c5t] are simil>ly dispos$1 & ! p[] ( gravity acts alike on e "p2 x is evid5t1 t ! p>ts ( ! globe on ea* side ( ! c5t] are drawn ) equal =ce1 & !re=e nei!r side c yield to ! o!r2 b ! globe1 if support$ at its c5t]1 mu/ ( necessity hang at re/4 ,9 l mann]1 if two equal bodies ,a & ,b 79 fig4 #ac47 be hung at ! extremities ( an inflexible rod ,c ,d1 :i* %\ld h no weight2 ^! bodies1 if ! rod be support$ at its middle ,e1 %all equipond]ate2 & ! rod rema9 )\t motion4 ,= ! bodies be+ equal & at ! same di/ance f ! po9t ( support ,e1 ! p[] ( gravity w act ^u ea* ) equal /r5g?1 & 9 all respects "u ! same circum/ances2 !re=e ! weight ( "o _c ov]come ! weight ( ! o!r4 ,! weight ( ,a c no m surm\nt ! weight ( ,b1 ?an ! weight ( ,b c surm\nt ! weight ( ,a4 ,aga91 suppose a body z ,a ,b 79 fig4 #ad47 ( a uni=m texture 9 ! =m ( a roll]1 or z x is m usually call$ a cyl9d]1 ly+ horizontally4 ,if a /raight l9e be drawn betwe5 ,c & ,d1 ! c5t]s ( ! extreme circles ( ?is cyl9d]2 & if ?is /raight l9e1 commonly call$ ! axis ( ! cyl9d]1 be divid$ into two equal p>ts 9 ,e3 ?is po9t ,e w be ! c5t] ( gravity ( ! cyl9d]4 ,! cyl9d] be+ a uni=m figure1 ! p>ts on ea* side ( ! po9t ,e are equal1 & situat$ 9 a p]fectly simil> mann]2 !re=e ?is cyl9d]1 if support$ at ! po9t ,e1 mu/ hang at re/1 = ! same reason z ! inflexible rod above-m5tion$ w rema9 )\t motion1 :5 susp5d$ at its middle po9t4 ,& x is evid5t1 t ! =ce appli$ to ! po9t ,e1 :i* w\ld uphold ! cyl9d]1 mu/ be equal to ! cyl9d]'s weight4 ,n[ suppose two cyl9d]s ( equal ?ickness ,a ,b & ,c ,d to be jo9$ toge!r at ,c ,b1 s t ! two axis's ,e ,f1 & ,f ,g lie 9 "o /raight l9e4 ,let ! axis ,e ,f be divid$ into two equal p>ts at ,h1 & ! axis ,f ,g into two equal p>ts at ,i4 ,!n because ! cyl9d] ,a ,b w\ld be upheld at re/ by a p[] appli$ 9 ,h equal to ! weight ( ?is cyl9d]1 & ! cyl9d] ,c ,d w\ld likewise be upheld by a p[] appli$ 9 ,i equal to ! weight ( ?is cyl9d]2 ! :ole cyl9d] ,a ,d w be support$ by ^! two p[]s3 b ! :ole cyl9d] may likewise be support$ by a p[] appli$ to ,k1 ! middle po9t ( ! :ole axis ,e ,g1 provid$ t p[] be equal to ! weight ( ! :ole cyl9d]4 ,x is evid5t !re=e1 t ?is p[] appli$ 9 ,k w produce ! same effect1 z ! two o!r p[]s appli$ 9 ,h & ,i4 ,x is f>!r to be obs]v$1 t ,h ,k is equal to half ,f ,g1 & ,k ,i equal to half ,e ,f2 = ,e ,k be+ equal to half ,e ,g1 & ,e ,h equal to half ,e ,f1 ! rema9d] ,h ,k mu/ be equal to half ! rema9d] ,f ,g2 s likewise ,g ,k be+ equal to half ,g ,e1 & ,g ,i equal to half ,g ,f1 ! rema9d] ,i ,k mu/ be equal to half ! rema9d] ,e ,f4 ,x foll[s !re=e1 t ,h ,k be>s ! same proportion to ,k ,i1 z ,f ,g be>s to ,e ,f4 ,besides1 ,i believe1 my read]s w p]ceive1 & x is demon/rat$ 9 =m by ! geomet]s1 t ! :ole body ( ! cyl9d] ,c ,d be>s ! same proportion to ! :ole body ( ! cyl9d] ,a ,b1 z ! axis ,f ,g be>s to ! axis ,e ,f#ec4 ,b h5ce x foll[s1 t 9 ! two p[]s appli$ at ,h & ,i1 ! p[] appli$ at ,h be>s ! same proportion to ! p[] appli$ at ,i1 z ,k ,i be>s to ,k ,h4 ,n[ suppose two /r+s ,h ,l & ,i ,m ext5d$ upw>ds1 "o f ! po9t ,h & ! o!r f ,i1 & to be laid hold on by two p[]s1 "o /rong en\gh to hold up ! cyl9d] ,a ,b1 & ! o!r ( /r5g? suffici5t to support ! cyl9d] ,c ,d4 ,"h z ^! two p[]s uphold ! :ole cyl9d]1 & !re=e produce an effect1 equal to :at w\ld h be5 produc$ by a p[] appli$ to ! po9t ,k ( suffici5t =ce to su/a9 ! :ole cyl9d]3 x is manife/1 t if ! cyl9d] be tak5 away1 ! axis only be+ left1 & f ! po9t ,k a /r+1 z ,k ,n1 be ext5d$1 :i* %all be drawn d[n by a p[] equival5t to ! weight ( ! cyl9d]1 ?is p[] %all act aga9/ ! o!r two p[]s1 z mu* z ! cyl9d] act$ aga9/ !m2 & consequ5tly ^! ?ree p[]s %all be ^u a balance1 & hold ! axis ,h ,i fix$ betwe5 !m4 ,b if ^! ?ree p[]s pres]ve a mutual balance1 ! two p[]s appli$ to ! /r+s ,h ,l & ,i ,m are a balance to ea* o!r2 ! p[] appli$ to ! /r+ ,h ,l be>+ ! same proportion to ! p[] appli$ to ! /r+ ,i ,m1 z ! di/ance ,i ,k be>s to ! di/ance ,k ,h4 ,h5ce x f>!r appe>s1 t if an inflexible rod ,a ,b 79 fig4 #ae47 be susp5d$ by any po9t ,c n 9 ! middle !re(2 & if at ,a ! end ( ! %ort] arm be hung a weight1 & at ,b ! end ( ! long] arm be also hung a weight less ?an ! o!r1 & t ! great] ( ^! weights be>s to ! less] ! same proportion1 z ! long] arm ( ! rod be>s to ! %ort]2 !n ^! two weights w equipond]ate3 = a p[] appli$ at ,c equal to bo? ^! weights w support )\t motion ! rod ?us *>g$2 s9ce "h no?+ is *ang$ f ! prec$+ case b ! situation ( ! p[]s1 :i* are n[ plac$ on ! contr>y sides ( ! l9e1 to :i* !y are fix$4 ,also = ! same reason1 if two weights ,a & ,b 79 fig4 #af47 7 connect$ toge!r by an inflexible rod ,c ,d1 drawn f ,c ! c5t] ( gravity ( ,a to ,d ! c5t] ( gravity ( ,b2 & if ! rod ,c ,d 7 to be s divid$ 9 ,e1 t ! "p ,d ,e be> ! same proportion to ! o!r "p ,c ,e1 z ! weight ,a be>s to ! weight ,b3 !n ?is rod be+ support$ at ,e w uphold ! weights1 & keep !m at re/ )\t motion4 ,?is po9t ,e1 by :i* ! two bodies ,a & ,b w be support$1 is call$ _! common c5t] ( gravity4 ,& if a great] numb] ( bodies 7 jo9$ toge!r1 ! po9t1 by :i* !y c\ld all be support$1 is call$ ! common c5t] ( gravity ( !m all4 ,suppose 79 fig4 #ag47 !re 7 ?ree bodies ,a1 ,b1 ,c1 ^: respective c5t]s ( gravity 7 jo9$ by ! ?ree l9es ,d ,e1 ,d ,f1 ,e ,f3 ! l9e ,d ,e be+ s divid$ 9 ,g1 t ,d ,g be> ! same proportion to ,g ,e1 z ,b be>s to ,a2 ,g is ! c5t] ( gravity common to ! two bodies ,a & ,b2 t is1 a p[] equal to ! weight ( bo? ! bodies appli$ to ,g w\ld support !m1 & ! po9t ,g is press$ z mu* by ! two weights ,a & ,b1 z x w\ld be1 if !y 7 bo? hung toge!r at t po9t4 ,!re=e1 if a l9e be drawn f ,g to ,f1 & divid$ 9 ,h1 s t ,g ,h be> ! same proportion to ,h ,f1 z ! weight ,c be>s to bo? ! weights ,a & ,b1 ! po9t ,h w be ! common c5t] ( gravity ( all ! ?ree weights2 = ,h w\ld be _! common c5t] ( gravity1 if bo? ! weights ,a & ,b 7 hung toge!r at ,g1 & ! po9t ,g is press$ z mu* by !m 9 _! pres5t situation1 z x w\ld be 9 t case4 ,9 ! same mann] f ! common c5t] ( ^! ?ree weights1 y might proce$ to f9d ! common c5t]1 if a f\r? weight 7 add$1 & by a gradual progress might f9d ! common c5t] ( gravity belong+ to any numb] ( weights :atev]4 #bf4 ,,z all ?is is ! obvi\s consequ5ce ( ! proposition laid d[n = assign+ ! common c5t] ( gravity ( any two weights1 by ! same proposition ! c5t] ( gravity ( all figures is f\nd4 ,9 a triangle1 z ,a ,b ,c 79 fig4 #ah47 ! c5t] ( gravity lies 9 ! l9e drawn f ! middle po9t ( any "o ( ! sides to ! opposite angle1 z ! l9e ,b ,d is drawn f ,d ! middle ( ! l9e ,a ,c to ! opposite angle ,b#ed2 s t if f ! middle ( ei!r ( ! o!r sides1 z f ! po9t ,e 9 ! side ,a ,b1 a l9e be drawn1 z ,e ,c1 to ! opposite angle2 ! po9t ,f1 :]e ?is l9e crosses ! o!r l9e ,b ,d1 w be ! c5t] ( gravity ( ! triangle#ee4 ,likewise ,d ,f is equal to half ,f ,b1 & ,e ,f equal to half ,f ,c#ef4 ,9 a hemisph]e1 z ,a ,b ,c 7fig4 #ai47 if f ,d ! c5t] ( ! base ! l9e ,d ,b be erect$ p]p5dicul> to t base1 & ?is l9e be s divid$ 9 ,e1 t ,d ,e be equal to ?ree fif?s ( ,b ,e1 ! po9t ,e is ! c5t] ( gravity ( ! hemisph]e#eg4 #bg4 ,,x w be ( use to obs]ve conc]n+ ! c5t] ( gravity ( bodies2 t s9ce a p[] appli$ to ?is c5t] alone c support a body aga9/ ! p[] ( gravity1 & hold x fix$ at re/2 ! effect ( ! p[] ( gravity on a body is ! same1 z if t :ole p[] 7 to ex]t itself on ! c5t] ( gravity only4 ,:5ce x foll[s1 t1 :5 ! p[] ( gravity acts on a body susp5d$ by any po9t1 if ! body is s susp5d$1 t ! c5t] ( gravity ( ! body c desc5d2 ! p[] ( gravity w give motion to t body1 o!rwise n3 or if a numb] ( bodies are s connect$ toge!r1 t1 :5 any "o is put into motion1 ! re/ %all1 by ! mann] ( _! be+ jo9$1 receive su* motion1 z %all keep _! common c5t] ( gravity at re/2 !n ! p[] ( gravity %all n be able to produce any motion 9 ^! bodies1 b 9 all o!r cases x w4 ,?us1 if ! body ,a ,b 79 fig4 #bj1 #ba47 ^: c5t] ( gravity is ,c1 be hung on ! po9t ,a1 & ! c5t] ,c be p]p5dicul>ly "u ,a 7z 9 fig4 #bj47 ! weight ( ! body w hold x /ill )\t motion1 because ! c5t] ,c _c desc5d any l[]4 ,b if ! body be remov$ into any o!r situation1 :]e ! c5t] ,c is n p]p5dicul>ly "u ,a 7z 9 fig4 #ba47 ! body by its weight w be put into motion t[>ds ! p]p5dicul> situation ( its c5t] ( gravity4 ,also if two bodies ,a1 ,b 79 fig4 #bb47 be jo9$ toge!r by ! rod ,c ,d ly+ 9 an horizontal situation1 & be support$ at ! po9t ,e2 if ?is po9t be ! c5t] ( gravity common to ! two bodies1 _! weight w n put !m into motion2 b if ?is po9t ,e is n _! common c5t] ( gravity1 ! bodies w move2 t "p ( ! rod ,c ,d desc5d+1 9 :i* ! common c5t] ( gravity is f\nd4 ,s 9 l mann]1 if ^! two bodies 7 connect$ toge!r by any m complex contrivance2 yet if "o ( ! bodies _c move )\t s mov+ ! o!r1 t _! common c5t] ( gravity %all re/1 ! weight ( ! bodies w n put !m 9 motion1 o!rwise x w4 #bh4 ,i ,,%all proce$ 9 ! next place to speak ( ! me*anical p[]s4 ,^! are c]ta9 in/rum5ts or ma*9es1 contriv$ = ! mov+ great weights ) small =ce2 & _! effects are all d$ucible f ! obs]vation we h j be5 mak+4 ,!y are usually reckon$ 9 numb] five2 ! lev]1 ! :eel & axis1 ! pulley1 ! w$ge1 & ! screw2 to :i* "s add ! incl9$ plane4 ,z ^! in/rum5ts h be5 ( v anci5t use1 s ! celebrat$ ,,ar*im$es seems to h be5 ! fir/1 :o discov]$ ! true reason ( _! effects4 ,?is1 ,i ?9k1 may be collect$ f :at is relat$ ( him1 t "s expressions1 :i* he us$ to d5ote ! unlimit$ =ce ( ^! in/rum5ts1 7 receiv$ z v extraord9>y p>adoxes3 :]eas to ^?1 :o _h und]/ood ! cause ( _! great =ce1 no expressions ( t k9d c\ld h appe>$ surpriz+4 #bi4 ,,all ! effects ( ^! p[]s may be judg$ ( by ?is "o rule1 t1 :5 two weights are appli$ to any ( ^! in/rum5ts1 ! weights w equipond]ate1 if1 :5 put into motion1 _! velocities w be reciprocally proportional to _! respective weights4 ,& :at is said ( weights1 mu/ ( necessity be equally und]/ood ( any o!r =ces equival5t to weights1 su* z ! =ce ( a man's arm1 a /ream ( wat]1 or ! l4 #cj4 ,,b to compreh5d ! mean+ ( ?is rule1 ! read] mu/ "k1 :at is to be und]/ood by reciprocal proportion2 :i* ,i %all n[ endeav\r to expla91 z di/9ctly z ,i c2 = ,i %all be oblig$ v frequ5tly to make use ( ?is t]m4 ,:5 any two ?+s are s relat$1 t "o increases 9 ! same proportion z ! o!r1 !y are directly proportional4 ,s if any numb] ( m5 c p]=m 9 a det]m9$ space ( "t a c]ta9 quantity ( any "w1 suppose dra9 a fi%-pond1 or ! l2 & twice ! numb] ( m5 c p]=m twice ! quantity ( ! same "w1 9 ! same "t2 & ?ree times ! numb] ( m5 c p]=m z soon ?rice ! "w2 "h ! numb] ( m5 & ! quantity ( ! "w are directly proportional4 ,on ! o!r h&1 :5 two ?+s are s relat$1 t "o decreases 9 ! same proportion1 z ! o!r increases1 !y are said to be reciprocally proportional4 ,?us if twice ! numb] ( m5 c p]=m ! same "w 9 half ! "t1 & ?ree times ! numb] ( m5 c f9i% ! same 9 a ?ird "p ( ! "t2 !n ! numb] ( m5 & ! "t are reciprocally proportional4 ,we %ew$ above#eh h[ to f9d ! common c5t] ( gravity ( two bodies1 !re ! di/ances ( t common c5t] f ! c5t]s ( gravity ( ! two bodies are reciprocally proportional to ! respective bodies4 ,= ,c ,e 9 fig4 #af4 be+ 9 ! same proportion to ,e ,d1 z ,b be>s to ,a2 ,c ,e is s mu* great] 9 proportion ?an ,e ,d1 z ,a is less 9 proportion ?an ,b4 #ca4 ,,n[ ?is be+ und]/ood1 ! reason ( ! rule "h /at$ w easily appe>4 ,= if ^! two bodies 7 put 9 motion1 :ile ! po9t ,e re/$1 ! velocity1 :]e) ,a w\ld move1 w\ld be> ! same proportion to ! velocity1 :]e) ,b w\ld move1 z ,e ,c be>s to ,e ,d4 ,! velocity !re=e ( ea* body1 :5 ! common c5t] ( gravity re/s1 is reciprocally proportional to ! body4 ,b we h %ewn above#ei1 t if two bodies are s connect$ toge!r1 t ! putt+ !m 9 motion w n move _! common c5t] ( gravity2 ! weight ( ^? bodies w n produce 9 !m any motion4 ,!re=e 9 any ( ^! me*anical eng9es1 if1 :5 ! bodies are put into motion1 _! velocities are reciprocally proportional to _! respective weights1 :]eby ! common c5t] ( gravity w\ld rema9 at re/2 ! bodies w n receive any motion f _! weight1 t is1 !y w equipond]ate4 ,b ?is p]haps w be yet m cle>ly conceiv$ by ! p>ticul> description ( ea* me*anical p[]4 #cb4 ,,! lev] 0 fir/ nam$ above4 ,?is is a b> made use ( to su/a9 & move great weights4 ,! b> is appli$ 9 "o "p to "s /rong support2 z ! b> ,a ,b 79 fig4 #bc1 #bd47 is appli$ at ! po9t ,c to ! support ,d4 ,9 "s o!r "p ( ! b>1 z ,e1 is appli$ ! weight to be su/a9$ or mov$2 & 9 a ?ird place1 z ,f1 is appli$ ano!r weight or equival5t =ce1 :i* is to su/a9 or move ! weight at ,e4 ,n[ "h1 if1 :5 ! level %\ld be put 9 motion1 & turn$ ^u ! po9t ,c1 ! velocity1 :]e) ! po9t ,f w\ld move1 be>s ! same proportion to ! velocity1 :]e) ! po9t ,e w\ld move1 z ! weight at ,e be>s to ! weight or =ce at ,f2 !n ! lev] ?us *>g$ w h no prop5sity to move ei!r way4 ,if ! weight or o!r =ce at ,f be n s great z to be> ?is proportion1 ! weight at ,e w n be su/a9$2 b if ! =ce at ,f be great] ?an ?is1 ! weight at ,e w be surm\nt$4 ,?is is evid5t f :at has be5 said above#fj1 :5 ! =ces at ,e & ,f are plac$ 7z 9 fig4 #bc47 on diff]5t sides ( ! support ,d4 ,x w appe> also equally manife/ 9 ! o!r case1 by cont9u+ ! b> ,b ,c 9 fig4 #bd4 on ! o!r side ( ! support ,d1 till ,c ,g be equal to ,c ,f1 & by hang+ at ,g a weight equival5t to ! p[] at ,f2 = !n1 if ! p[] at ,f 7 remov$1 ! two weights at ,g & ,e w\ld c\nt]poize ea* o!r1 z 9 ! =m] case3 & x is evid5t1 t ! po9t ,f w be lift$ up by ! weight at ,g ) ! same degree ( =ce1 z by ! o!r p[] appli$ to ,f2 s9ce1 if ! weight at ,e 7 remov$1 a weight hung at ,f equal to t at ,g w\ld balance ! lev]1 ! di/ances ,c ,g & ,c ,f be+ equal4 #cc4 ,,if ! two weights1 or o!r p[]s1 appli$ to ! lev] d n c\nt]balance ea* o!r2 a ?ird p[] may be appli$ 9 any place propos$ ( ! lev]1 :i* %all hold ! :ole 9 a j c\nt]poize4 ,suppose 79 fig4 #be47 ! two p[]s at ,e & ,f did n equipond]ate1 & x 7 requir$ to apply a ?ird p[] to ! po9t ,g1 t might be suffici5t to balance ! lev]4 ,f9d :at p[] 9 ,f w\ld j c\nt]balance ! p[] 9 ,e2 !n if ! diff]5ce betwe5 ?is p[] & t1 :i* is actually appli$ at ,f1 be> ! same proportion to ! ?ird p[] to be appli$ at ,g1 z ! di/ance ,c ,g be>s to ,c ,f2 ! lev] w be c\nt]poiz$ by ! help ( ?is ?ird p[]1 if x be s appli$ z to act ! same way ) ! p[] 9 ,f1 :5 t p[] is too small to c\nt]balance ! p[] 9 ,e2 b o!rwise ! p[] 9 ,g mu/ be s appli$1 z to act aga9/ ! p[] 9 ,f4 ,9 l mann]1 if a lev] 7 *>g$ ) ?ree1 or any great] numb] ( weights or o!r p[]s1 :i* did n c\nt]poize ea* o!r1 ano!r p[] might be appli$ 9 any place propos$1 :i* %\ld br+ ! :ole to a j balance4 ,& :at is "h said conc]n+ a plurality ( p[]s1 may be equally appli$ to all ! foll[+ cases4 #cd4 ,,if ! lev] %\ld consi/ ( two arms mak+ an angle at ! po9t ,c 7z 9 fig4 #bf47 yet if ! =ces are appli$ p]p5dicul>ly to ea* arm1 ! same proportion w hold betwe5 ! =ces appli$1 & ! di/ances ( ! c5t]1 :]eon ! lev] re/s1 f ! po9ts to :i* !y are appli$4 ,t is1 ! weight at ,e w be to ! =ce 9 ,f 9 ! same proportion1 z ,c ,f be>s to ,c ,e4 #ce4 ,,b :5ev] ! =ces appli$ to ! lev] act obliquely to ! arm1 to :i* !y are appli$ 7z 9 fig4 #bg47 !n ! /r5g? ( ! =ces is to be e/imat$ by l9es let fall f ! c5t] ( ! lev] to ! directions1 :]e9 ! =ces act4 ,to balance ! lev]s 9 fig4 #bg1 ! weight or o!r =ce at ,f w be> ! same proportion to ! weight at ,e1 z ! di/ance ,c ,e be>s to ,c ,g ! p]p5dicul> let fall f ! po9t ,c ^u ! l9e1 :i* d5otes ! direction :]e9 ! =ce appli$ to ,f acts3 = "h1 if ! lev] be put into motion1 ! p[] appli$ to ,f w beg9 to move 9 ! direction ( ! l9e ,f ,g2 & !re=e its fir/ motion w be ! same1 z ! motion ( ! po9t ,g4 #cf4 ,,:5 two weights hang ^u a lev]1 & ! po9t1 by :i* ! lev] is support$1 is plac$ 9 ! middle betwe5 ! two weights1 t ! arms ( ! lev] are bo? ( equal l5g?2 !n ?is lev] is p>ticul>ly call$ a balance2 & equal weights equipond]ate z 9 common scales4 ,:5 ! po9t ( support is n equally di/ant f bo? weights1 x con/itutes t in/rum5t = weigh+1 :i* is call$ a /eely>d4 ,?\gh bo? 9 common scales1 & ! /eely>d1 ! po9t1 on :i* ! beam is hung1 is n usually plac$ j 9 ! same /raight l9e ) ! po9ts1 t hold ! weights1 b r a little above 7z 9 fig4 #bh47 :]e ! l9es drawn f ! po9t ,c1 :]eon ! beam is susp5d$1 to ! po9ts ,e & ,f1 on :i* ! weights are hung1 d n make absolutely "o cont9u$ l9e4 ,if ! ?ree po9ts ,e1 ,c1 & ,f 7 9 "o /raight l9e1 ^? weights1 :i* equipond]at$1 :5 ! beam hung horizontally1 w\ld also equipond]ate 9 any o!r situation4 ,illu/ration ,b we see 9 ^! in/rum5ts1 :5 !y are *>g$ ) weights1 :i* equipond]ate ) ! beam hang+ horizontally2 t1 if ! beam be incl9$ ei!r way1 ! weight mo/ elevat$ surm\nts ! o!r1 & desc5ds1 caus+ ! beam to sw+1 till by degrees x recov]s its horizontal position4 ,?is effect arises f ! =em5tion$ /ructure3 = by ?is /ructure ^! in/rum5ts are lev]s compos$ ( two arms1 :i* make an angle at ! po9t ( support 7z 9 fig4 #bi1 #cj47 ! fir/ ( :i* repres5ts ! case ( ! common balance1 ! second ! case ( ! /eely>d4 ,9 ! fir/1 :]e ,c ,e & ,c ,f are equal1 equal weights hung at ,e & ,f w equipond]ate1 :5 ! po9ts ,e & ,f are 9 an horizontal situation4 ,suppose ! l9es ,e ,g & ,f ,h to be p]p5dicul> to ! horizon1 !n !y w d5ote ! directions1 :]e9 ! =ces appli$ to ,e & ,f act4 ,!re=e ! proportion betwe5 ! weights at ,e & ,f1 :i* %all equipond]ate1 are to be judg$ ( by p]p5dicul>s1 z ,c ,i1 ,c ,k1 let fall f ,c ^u ,e ,g & ,f ,h3 s t ! weights be+ equal1 ! l9es ,c ,i1 ,c ,k1 mu/ be equal also1 :5 ! weights equipond]ate4 ,b ,i believe my read]s w easily see1 t s9ce ,c ,e & ,c ,f are equal1 ! l9es ,c ,i & ,c ,k w be equal1 :5 ! po9ts ,e & ,f are horizontally situat$4 #cg4 ,,if ?is lev] be set into any o!r position 7z 9 fig4 #ca47 !n ! weight1 :i* is rais$ highe/1 w outweigh ! o!r4 ,"h1 if ! po9t ,f be rais$ high] ?an ,e1 ! p]p5dicul> ,c ,k w be long] ?an ,c ,i3 & !re=e ! weights w\ld equipond]ate1 if ! weight at ,f 7 less ?an ! weight at ,e4 ,b ! weight at ,f is equal to t at ,e2 !re=e is great]1 ?an is necess>y to c\nt]balance ! weight at ,e1 & consequ5tly w outweigh x1 & draw ! beam ( ! lev] d[n4 #ch4 ,,9 l mann] 9 ! case ( ! /eely>d 7fig4 #cb47 if ! weights at ,e & ,f are s proportion$1 z to equipond]ate1 :5 ! po9ts ,e & ,f are horizontally situat$2 !n 9 any o!r situation ( ?is lev] ! weight1 :i* is rais$ highe/1 w prepond]ate4 ,t is1 if 9 ! horizontal situation ( ! po9ts ,e & ,f ! weight at ,f be>s ! same proportion to ! weight at ,e1 z ,c ,i be>s to ,c ,k2 !n1 if ! po9t ,f be rais$ high] ?an ,e 7z 9 fig4 #cb47 ! weight at ,f %all be> a great] proportion to ! weight at ,e1 ?an ,c ,i be>s to ,c ,k4 #ci4 ,,f>!r a lev] may be hung ^u an axis1 & !n ! two arms ( ! lev] ne$ n be cont9u\s1 b fix$ to diff]5t p>ts ( ?is axis2 z 9 fig4 #cc1 :]e ! axis ,a ,b is support$ by its two extremities ,a & ,b4 ,to ?is axis "o arm ( ! lev] is fix$ at ! po9t ,c1 ! o!r at ! po9t ,d4 ,n[ "h1 if a weight be hung at ,e1 ! extremity ( t arm1 :i* is fix$ to ! axis at ! po9t ,c2 & ano!r weight be hung at ,f1 ! extremity ( ! arm1 :i* is fix$ on ! axis at ,d2 !n ^! weights w equipond]ate1 :5 ! weight at ,e be>s ! same proportion to ! weight at ,f1 z ! arm ,d ,f be>s to ,c ,e4 #dj4 ,,?is is ! case1 if bo? ! arms are p]p5dicul> to ! axis1 & lie 7z ! geomet]s express !mselves7 9 ! same plane2 or1 9 o!r words1 if ! arms are s fix$ p]p5dicul>ly ^u ! axis1 t1 :5 "o ( !m lies horizontally1 ! o!r %all also be horizontal4 ,if ei!r arm /& n p]p5dicul> to ! axis2 !n1 9 det]m9+ ! proportion betwe5 ! weights1 in/ead ( ! l5g? ( t arm1 y mu/ use ! p]p5dicul> let fall ^u ! axis f ! extremity ( t arm4 ,if ! arms are n s fix$ z to become horizontal1 at ! same "t2 ! me?od ( assign+ ! proportion betwe5 ! weights is analog\s to t made use ( above 9 lev]s1 :i* make an angle at ! po9t1 :]eon !y are support$4 #da4 ,,f ?is case ( ! lev] hung on an axis1 x is easy to make a transition to ano!r me*anical p[]1 ! :eel & axis4 #db4 ,,?is in/rum5t is a :eel fix$ on a roll]1 ! roll] be+ support$ at ea* extremity s z to turn r\nd freely ) ! :eel1 9 ! mann] repres5t$ 9 fig4 #cd1 :]e ,a ,b is ! :eel1 ,c ,d ! roll]1 & ,e ,f its two supports4 ,n[ suppose a weight ,g hung by a cord w\nd r\nd ! roll]1 & ano!r weight ,h hung by a cord w\nd ab\t ! :eel ! contr>y way3 t ^! weights may support ea* o!r1 ! weight ,h mu/ be> ! same proportion to ! weight ,g1 z ! ?ickness ( ! roll] be>s to ! diamet] ( ! :eel4 #dc4 ,,suppose ! l9e k l to be drawn ?r\gh ! middle ( ! roll]2 & f ! place ( ! roll]1 :]e ! cord1 on :i* ! weight ,g hangs1 beg9s to leave ! roll]1 z at m1 let ! l9e m n be drawn p]p5dicul>ly to k l2 & f ! po9t1 :]e ! cord hold+ ! weight ,h beg9s to leave ! :eel1 z at o1 let ! l9e o p be drawn p]p5dicul> to k l4 ,?is be+ done1 ! two l9es o p & m n repres5t two arms ( a lev] fix$ on ! axis k l2 consequ5tly ! weight ,h w be> to ! weight ,g ! same proportion1 z m n be>s to o p4 ,b m n be>s ! same proportion to o p1 z ! ?ickness ( ! roll] be>s to ! diamet] ( ! :eel2 = m n is half ! ?ickness ( ! roll]1 & o p half ! diamet] ( ! :eel4 #dd4 ,,if ! :eel be put into motion1 & turn$ once r\nd1 t ! cord1 on :i* ! weight ,g hangs1 be w\nd once m r\nd ! axis2 !n at ! same "t ! cord1 :]eon ! weight ,h hangs1 w be w\nd (f f ! :eel "o circuit4 ,!re=e ! velocity ( ! weight ,g w be> ! same proportion to ! velocity ( ! weight ,h1 z ! circumf]5ce ( ! roll] to ! circumf]5ce ( ! :eel4 ,b ! circumf]5ce ( ! roll] be>s ! same proportion to ! circumf]5ce ( ! :eel1 z ! ?ickness ( ! roll] be>s to ! diamet] ( ! :eel1 consequ5tly ! velocity ( ! weight ,g be>s to ! velocity ( ! weight ,h ! same proportion1 z ! ?ickness ( ! roll] be>s to ! diamet] ( ! :eel1 :i* is ! proportion t ! weight ,h be>s to ! weight ,g4 ,!re=e z be=e 9 ! lev]1 s "h also ! g5]al rule laid d[n above is v]ifi$1 t ! weights equipond]ate1 :5 _! velocities w\ld be reciprocally proportional to _! respective weights4 #de4 ,,9 l mann]1 if on ! same axis two :eels ( diff]5t sizes are fix$ 7z 9 fig4 #ce47 & a weight hung on ea*2 ! weights w equipond]ate1 if ! weight hung on ! great] :eel be> ! same proportion to ! weight hung on ! less]1 z ! diamet] ( ! less] :eel be>s to ! diamet] ( ! great]4 #df4 ,,x is usual to jo9 _m :eels toge!r 9 ! same frame1 :i* by ! means ( c]ta9 tee?1 =m$ 9 ! circumf]5ce ( ea* :eel1 %all communicate motion to ea* o!r4 ,a ma*9e ( ?is nature is repres5t$ 9 fig4 #cf4 ,"h ,a ,b ,c is a w9*1 ^u :i* is fix$ a small :eel ,d ind5t$ ) tee?1 :i* move 9 ! l tee? ( a l>g] :eel ,e ,f fix$ on ! axis ,g ,h4 ,let ?is axis c>ry ano!r :eel ,i1 :i* %all move 9 l mann] a great] :eel ,k ,l fix$ on ! axis ,m ,n4 ,let ?is axis c>ry ano!r small :eel ,o1 :i* aft] ! same mann] %all turn ab\t a l>g] :eel ,p ,q fix$ on ! roll] ,r ,s1 on :i* a cord %all be w\nd1 t holds a weight1 z ,t4 ,n[ ! proportion requir$ betwe5 ! weight ,t & a p[] appli$ to ! w9* at ,a suffici5t to support ! weight1 w mo/ easily be e/imat$1 by comput+ ! proportion1 :i* ! velocity ( ! po9t ,a w\ld be> to ! velocity ( ! weight4 ,if ! w9* be turn$ r\nd1 ! po9t ,a w describe a circle z ,a ,v4 ,suppose ! :eel ,e ,f to h t5 times ! numb] ( tee?1 z ! :eel ,d2 !n ! w9* mu/ turn r\nd t5 times to c>ry ! :eel ,e ,f once r\nd4 ,if :eel ,k ,l has also t5 times ! numb] ( tee?1 z ,i1 ! :eel ,i mu/ turn r\nd t5 times to c>ry ! :eel ,k ,l once r\nd2 & consequ5tly ! w9* ,a ,b ,c mu/ turn r\nd an hundr$ times to turn ! :eel ,k ,l once r\nd4 ,la/ly1 if ! :eel ,p ,q has t5 times ! numb] ( tee?1 z ! :eel ,o1 ! w9* mu/ turn ab\t "o ?\s& times 9 ord] to turn ! :eel ,p ,q1 or ! roll] ,r ,s once r\nd4 ,!re=e "h ! po9t ,a mu/ h gone ov] ! circle ,a ,v a ?\s& times1 9 ord] to lift ! weight ,t ?r\gh a space equal to ! circumf]5ce ( ! roll] ,r ,s3 :5ce x foll[s1 t ! p[] appli$ at ,a w balance ! weight ,t1 if x be> ! same proportion to x1 z ! circumf]5ce ( ! roll] to "o ?\s& times ! circle ,a ,v2 or ! same proportion z half ! ?ickness ( ! roll] be>s to "o ?\s& times ,a ,b4 #dg4 ,i ,,%all n[ expla9 ! effect ( ! pulley4 ,let a weight hang by a pulley1 z 9 fig4 #cg4 ,"h x is evid5t1 t ! p[] ,a1 by :i* ! weight ,b is support$1 mu/ be equal to ! weight2 = ! cord ,c ,d is equally /ra9$ betwe5 !m2 & if ! weight ,b move1 ! p[] ,a mu/ move ) equal velocity4 ,! pulley ,e has no o!r effect1 ?an to p]mit ! p[] ,a to act 9 ano!r direction1 ?an x mu/ h done1 if x _h be5 directly appli$ to support ! weight )\t ! int]v5tion ( any su* in/rum5t4 #dh4 ,,aga91 let a weight be support$1 z 9 fig4 #ch2 :]e ! weight ,a is fix$ to ! pulley ,b1 & ! cord1 by :i* ! weight is upheld1 is annex$ by "o extremity to a hook ,c1 & at ! o!r end is held by ! p[] ,d4 ,"h ! weight is support$ by a cord d\bl$2 insomu* t al?\gh ! cord 7 n /rong en\gh to hold ! weight s+le1 yet be+ ?us d\bl$ x might support x4 ,if ! end ( ! cord held by ! p[] ,d 7 hung on ! hook ,c1 z well z ! o!r end2 !n1 :5 bo? ends ( ! cord 7 ti$ to ! hook1 x is evid5t1 t ! hook w\ld be> ! :ole weight2 & ea* end ( ! /r+ w\ld be> aga9/ ! hook ) ! =ce ( half ! weight only1 see+ bo? ends toge!r be> ) ! =ce ( ! :ole4 ,h5ce x is evid5t1 t1 :5 ! p[] ,d holds "o end ( ! weight1 ! =ce1 :i* x mu/ ex]t to support ! weight1 mu/ be equal to j half ! weight4 ,& ! same proportion betwe5 ! weight & p[] might be collect$ f comp>+ ! respective velocities1 ) :i* !y w\ld move2 = x is evid5t1 t ! p[] mu/ move ?r\gh a space equal to twice ! di/ance ( ! pulley f ! hook1 9 ord] to lift ! pulley up to ! hook4 #di4 ,,x is equally easy to e/imate ! effect1 :5 _m pulleys are comb9$ toge!r1 z 9 fig4 #ci1 #dj2 9 ! fir/ ( :i* ! "u set ( pulleys1 & consequ5tly ! weight is held by six /r+s2 & 9 ! latt] figure by five3 !re=e 9 ! fir/ ( ^! figures ! p[] to support ! weight1 mu/ be "o six? "p only ( ! weight1 & 9 ! latt] figure ! p[] mu/ be "o fif? "p4 #ej4 ,,!re are two o!r ways ( support+ a weight by pulleys1 :i* ,i %all p>ticul>ly consid]4 #ea4 ,,"o ( ^! ways is repres5t$ 9 fig4 #da4 ,"h ! weight be+ connect$ to ! pulley ,b1 a p[] equal to half ! weight ,a w\ld support ! pulley ,c1 if appli$ imm$iately to x4 ,!re=e ! pulley ,c is drawn d[n ) a =ce equal to half ! weight ,a4 ,b if ! pulley ,d 7 to be imm$iately support$ by half ! =ce1 ) :i* ! pulley ,c is drawn d[n1 ?is pulley ,d w uphold ! pulley ,c2 s t if ! pulley ,d be upheld ) a =ce equal to "o f\r? "p ( ! weight ,a1 t =ce w support ! weight4 ,b1 = ! same reason z be=e1 if ! p[] 9 ,e be equal to half ! =ce necess>y to uphold ! pulley ,d2 ?is pulley1 & consequ5tly ! weight ,a1 w be upheld3 !re=e1 if ! p[] 9 ,e be "o eigh? "p ( ! weight ,a1 x w support ! weight4 #eb4 ,,ano!r way ( apply+ pulleys to a weight is repres5t$ 9 fig4 #db4 ,to expla9 ! effect ( pulleys ?us appli$1 x w be prop] to consid] diff]5t weights hang+1 z 9 fig4 #dc4 ,"h1 if ! p[] & weights balance ea* o!r1 ! p[] ,a is equal to ! weight ,b2 ! weight ,c is equal to twice ! p[] ,a1 or ! weight ,b2 & = ! same reason ! weight ,d is equal to twice ! weight ,c1 or equal to f\r times ! p[] ,a4 ,x is evid5t !re=e1 t all ! ?ree weights ,b1 ,c1 ,d toge!r are equal to sev5 times ! p[] ,a4 ,b if ^! ?ree weights 7 jo9$ 9 "o1 !y w\ld produce ! case ( fig4 #dj3 s t 9 t figure ! weight ,a1 :]e !re are ?ree pulleys1 is sev5 times ! p[] ,b4 ,if !re _h be5 b two pulleys1 ! weight w\ld h be5 ?ree times ! p[]2 & if !re _h be5 f\r pulleys1 ! weight w\ld h be5 fifte5 times ! p[]4 #ec4 ,,! w$ge is next to be consid]$4 ,! =m ( ?is in/rum5t is suffici5tly kn[n4 ,:5 x is put "u any weight 7z 9 fig4 #dd47 ! =ce1 ) :i* ! w$ge w lift ! weight1 :5 drove "u x by a bl[ ^u ! end ,a ,b1 w be> ! same proportion to ! =ce1 :]e) ! bl[ w\ld act on ! weight1 if directly appli$ to x2 z ! velocity1 :i* ! w$ge receives f ! bl[1 be>s to ! velocity1 :]e) ! weight is lift$ by ! w$ge4 #ed4 ,,! screw is ! fif? me*anical p[]4 ,!re are two ways ( apply+ ?is in/rum5t4 ,sometimes x is screw$ into a hole1 z 9 fig4 #de1 :]e ! screw ,a ,b is screw$ ?r\gh ! plank ,c ,d4 ,sometimes ! screw is appli$ to ! tee? ( a :eel1 z 9 fig4 #df1 :]e ! ?read ( ! screw ,a ,b turns 9 ! tee? ( a :eel ,c ,d4 ,9 bo? ^! cases1 if a b>1 z ,a ,e1 be fix$ to ! end ,a ( ! screw2 ! =ce1 :]e) ! end ,b ( ! screw 9 fig4 #de is =c$ d[n1 & ! =ce1 :]e) ! tee? ( ! :eel ,c ,d 9 fig4 #dd are held1 be>s ! same proportion to ! p[] appli$ to ! end ,e ( ! b>2 z ! velocity1 :]e) ! end ,e w move1 :5 ! screw is turn$1 be>s to ! velocity1 :]e) ! end ,b ( ! screw 9 fig4 #dc1 or ! tee? ( ! :eel ,c ,d 9 fig4 #df1 w be mov$4 #ee4 ,,! incl9$ plane af=ds also a means ( rais+ a weight ) less =ce1 ?an :at is equal to ! weight x self4 ,suppose x 7 requir$ to raise ! globe ,a 79 fig4 #dg47 f ! gr\nd ,b ,c up to ! po9t1 ^: p]p5dicul> height f ! gr\nd is ,e ,d4 ,if ?is globe be drawn along ! slant ,d ,f1 less =ce w be requir$ to raise x1 ?an if x 7 lift$ directly up4 ,"h if ! =ce appli$ to ! globe be> ! same proportion only to its weight1 z ,e ,d be>s to ,f ,d1 x w be suffici5t to hold up ! globe2 & !re=e any addition to t =ce w put x 9 motion1 & draw x up2 unless ! globe1 by press+ aga9/ ! plane1 :]eon x lies1 adh]e 9 "s degree to ! plane4 ,?is inde$ x mu/ always d m or less1 s9ce no plane c be made s absolutely smoo? z to h no inequalities at all2 nor yet s inf9itely h>d1 z n to yield 9 ! lea/ to ! pressure ( ! weight4 ,!re=e ! globe _c be laid on su* a plane1 :]eon x w slide ) p]fect fre$om1 b !y mu/ 9 "s measure rub aga9/ ea* o!r2 & ?is friction w make x necess>y to imploy a c]ta9 degree ( =ce m1 ?an :at is necess>y to support ! globe1 9 ord] to give x any motion4 ,b z all ! me*anical p[]s are subject 9 "s degree or o!r to ! l imp$im5t f friction2 ,i %all "h only %ew :at =ce w\ld be necess>y to su/a9 ! globe1 if x c\ld lie ^u ! plane )\t caus+ any friction at all4 ,& ,i say1 t if ! globe 7 drawn by ! cord ,g ,h1 ly+ p>allel to ! plane ,d ,f2 & ! =ce1 :]e) ! cord is pull$1 be> ! same proportion to ! weight ( ! globe1 z ,e ,d be>s to ,d ,f2 ?is =ce w su/a9 ! globe4 ,9 ord] to ! mak+ pro( ( ?is1 let ! cord ,g ,h be cont9u$ on1 & turn$ ov] ! pulley ,i1 & let ! weight ,k be hung to x4 ,n[ ,i say1 if ?is weight be>s ! same proportion to ! globe ,a1 z ,d ,e be>s to ,d ,f1 ! weight w support ! globe4 ,i ?9k x is v manife/1 t ! c5t] ( ! globe ,a w lie 9 "o cont9u$ l9e ) ! cord ,h ,g4 ,let ,l be ! c5t] ( ! globe1 & ,m ! c5t] ( gravity ( ! weight ,k4 ,9 ! fir/ place let ! weight hang s1 t a l9e drawn f ,l to ,m %all lie horizontally2 & ,i say1 if ! globe be mov$ ei!r up or d[n ! plane ,d ,f1 ! weight w s move along ) x1 t ! c5t] ( gravity common to bo? ! weights %all cont9ue 9 ?is l9e ,l ,m1 & !re=e %all 9 no case desc5d4 ,to prove ?is m fully1 ,i %all dep>t a little f ! me?od ( ?is treatise1 & make use ( a ma!matical proportion or two3 b !y are su*1 z any p]son1 :o has read ,,euclid',s ,,elem5ts1 w fully compreh5d2 & are 9 !mselves s evid5t1 t1 ,i believe1 my read]s1 :o are :olly /rang]s to geometrical writ+s1 w make no difficulty ( admitt+ !m4 ,?is be+ premis$1 let ! globe be mov$ up1 till its c5t] be at ,g1 !n w ,m ! c5t] ( gravity ( ! weight ,k be sunk to ,n2 s t ,m ,n %all be equal to ,g ,l4 ,draw ,n ,g cross+ ! l9e ,m ,l 9 ,o2 !n ,i say1 t ,o is ! common c5t] ( gravity ( ! two weights 9 ?is _! new situation4 ,let ,g ,p be drawn p]p5dicul> to ,m ,l2 !n ,g ,l w be> ! same proportion to ,g ,p1 z ,d ,f be>s to ,d ,e2 & ,m ,n be+ equal to ,g ,l1 ,m ,n w be> ! same proportion to ,g ,p1 z ,d ,f be>s to ,d ,e4 ,b ,n ,o be>s ! same proportion to ,o ,g1 z ,m ,n be>s to ,g ,p2 consequ5tly ,n ,o w be> ! same proportion to ,o ,g1 z ,d ,f be>s to ,d ,e4 ,9 ! la/ place1 ! weight ( ! globe ,a be>s ! same proportion to ! o!r weight ,k1 z ,d ,f be>s to ,d ,e2 !re=e ,n ,o be>s ! same proportion to ,o ,g1 z ! weight ( ! globe ,a be>s to ! weight ,k4 ,:5ce x foll[s1 t1 :5 ! c5t] ( ! globe ,a is 9 ,g1 & ! c5t] ( gravity ( ! weight ,k is 9 ,n1 ,o w be ! c5t] ( gravity common to bo? ! weights4 ,aft] ! same mann]1 if ! globe _h be5 caus$ to desc5d1 ! common c5t] ( gravity w\ld h be5 f\nd 9 ?is l9e ,m ,l4 ,s9ce !re=e no motion ( ! globe ei!r way w make ! common c5t] ( gravity desc5d1 x is manife/1 f :at has be5 said above1 t ! weights ,a & ,k c\nt]poize ea* o!r4 #ef4 ,i ,,%all n[ consid] ! case ( p5dulums4 ,a p5dulum is made by hang+ a weight to a l9e1 s t x may sw+ backw>ds & =w>ds4 ,?is motion ! geomet]s h v c>efully consid]$1 because x is ! mo/ commodi\s in/rum5t ( any = ! exact measurem5t ( "t4 #eg4 ,i ,,h obs]v$ already#fa1 t if a body hang+ p]p5dicul>ly by a /r+1 z ! body ,a 79 fig4 #dh47 hangs by ! /r+ ,a ,b1 be put s into motion1 z to be made to asc5d up ! circul> ar* ,a ,c2 !n z soon z x has arriv$ at ! highe/ po9t1 to :i* ! motion1 t ! body has receiv$1 w c>ry x2 x w imm$iately beg9 to desc5d1 & at ,a w receive aga9 z great a degree ( motion1 z x _h at fir/4 ,?is motion !re=e w c>ry ! body up ! ar* ,a ,d1 z high z x asc5d$ be=e 9 ! ar* ,a ,c4 ,consequ5tly 9 its return ?r\gh ! ar* ,d ,a x w acquire aga9 at ,a its orig9al velocity1 & advance a second "t up ! ar* ,a ,c z high z at fir/2 by ?is means cont9u+ )\t end its reciprocal motion4 ,x is true inde$1 t 9 fact e p5dulum1 :i* we c put 9 motion1 w gradually less5 its sw+1 & at l5g? /op1 unless !re be "s p[] con/antly appli$ to x1 :]eby its motion %all be r5ew$2 b ?is arises f ! resi/ance1 :i* ! body meets ) bo? f ! air1 & ! /r+ by :i* x is hung3 = z ! air w give "s ob/ruction to ! progress ( ! body mov+ ?r\gh x2 s also ! /r+1 :]eon ! body hangs1 w be a f>!r imp$im5t2 = ?is /r+ mu/ ei!r slide on ! p91 :]eon x hangs1 or x mu/ b5d to ! motion ( ! weight2 9 ! fir/ !re mu/ be "s degree ( friction1 & 9 ! latt] ! /r+ w make "s resi/ance to its inflection4 ,h[ev]1 if all resi/ance c\ld be remov$1 ! motion ( a p5dulum w\ld be p]petual4 #eh4 ,,b to proce$1 ! fir/ prop]ty1 ,i %all take notice ( 9 ?is motion1 is1 t ! great] ar* ! p5dul\s body moves ?r\gh1 ! great] "t x takes up3 ?\gh ! l5g? ( "t does n increase 9 s great a proportion z ! ar*4 ,?us if ,c ,d be a great] ar*1 & ,e ,f a less]1 :]e ,c ,a is equal to ,a ,d1 & ,e ,a equal to ,a ,f2 ! body1 :5 x sw+s ?r\gh ! great] ar* ,c ,d1 %all take up 9 its sw+ f ,c to ,d a long] "t ?an 9 sw++ f ,e to ,f1 :5 x moves only 9 t less] ar*2 or ! "t 9 :i* ! body let fall f ,c w desc5d ?r\gh ! ar* ,c ,a is great] ?an ! "t1 9 :i* x w desc5d ?r\gh ! ar* ,e ,a1 :5 let fall f ,e4 ,b ! fir/ ( ^! times w n hold ! same proportion to ! latt]1 z ! fir/ ar* ,c ,a be>s to ! o!r ar* ,e ,a2 :i* w appe> ?us4 ,let ,c ,g & ,e ,h be two horizontal l9es4 ,x has be5 rem>k$ above#fb1 t ! body 9 fall+ ?r\gh ! ar* ,c ,a w acquire z great a velocity at ! po9t ,a1 z x w\ld h ga9$ by fall+ directly d[n ?r\gh ,g ,a2 & 9 fall+ ?r\gh ! ar* ,e ,a x w acquire 9 ! po9t ,a only t velocity1 :i* x w\ld h got 9 fall+ ?r\gh ,h ,a4 ,!re=e1 :5 ! body desc5ds ?r\gh ! great] ar* ,c ,a1 x %all ga9 a great] velocity1 ?an :5 x passes only ?r\gh ! less]2 s t ?is great] velocity w 9 "s degree comp5sate ! great] l5g? ( ! ar*4 #ei4 ,,! increase ( velocity1 :i* ! body acquires 9 fall+ f a great] height1 has su* an effect1 t1 if /raight l9es be drawn f ,a to ,c & ,e1 ! body w\ld fall ?r\gh ! long] /raight l9e ,c ,a j 9 ! same "t1 z ?r\gh ! %ort] /raight l9e ,e ,a4 ,?is is demon/rat$ by ! geomet]s1 :o prove1 t if any circle1 z ,a ,b ,c ,d 7fig4 #di47 be plac$ 9 a p]p5dicul> situation2 a body %all fall obliquely ?r\gh e l9e1 z ,a ,b drawn f ! l[e/ po9t ,a 9 ! circle to any o!r po9t 9 ! circumf]5ce j 9 ! same "t1 z w\ld be imploy$ by ! body 9 fall+ p]p5dicul>ly d[n ?r\gh ! diamet] ,c ,a4 ,b ! "t 9 :i* ! body w desc5d ?r\gh ! ar*1 is diff]5t f ! "t1 :i* x w\ld take up 9 fall+ ?r\gh ! l9e ,a ,b4 #fj4 ,,x has be5 ?\ght by "s1 t because 9 v small ar*es ?is correspond5t /raight l9e diff]s b little f ! ar* itself2 !re=e ! desc5t ?r\gh ?is /raight l9e w\ld be p]=m$ 9 su* small ar*es ne>ly 9 ! same "t z ?r\gh ! ar*es !mselves3 s t if a p5dulum 7 to sw+ 9 small ar*es1 half ! "t ( a s+le sw+ w\ld be ne>ly equal to ! "t1 9 :i* a body w\ld fall p]p5dicul>ly ?r\gh twice ! l5g? ( ! p5dulum4 ,t is1 ! :ole "t ( ! sw+1 accord+ to ?is op9ion1 w be f\r fold ! "t requir$ = ! body to fall ?r\gh half ! l5g? ( ! p5dulum2 because ! "t ( ! body's fall+ d[n twice ! l5g? ( ! p5dulum is half ! "t requir$ = ! fall ?r\gh "o qu>t] ( ?is space1 t is ?r\gh half ! p5dulum's l5g?4 ,h[ev] !re is "h a mi/ake2 = ! :ole "t ( ! sw+1 :5 ! p5dulum moves ?r\gh small ar*es1 be>s to ! "t requir$ = a body to fall d[n ?r\gh half ! l5g? ( ! p5dulum v ne>ly ! same proportion1 z ! circumf]5ce ( a circle be>s to its diamet]2 t is v ne>ly ! proportion ( #cee to #aac1 or little m ?an ! proportion ( #c to #a4 ,if ! p5dulum takes s great a sw+1 z to pass ov] an ar* equal to "o six? "p ( ! :ole circumf]5ce ( ! circle1 x w sw+ #aae times1 :ile x ought accord+ to ?is proportion to h swung #aag times2 s t1 :5 x sw+s 9 s l>ge an ar*1 x loses some?+ less ?an two sw+s 9 an hundr$4 ,if x sw+ ?r\gh #a_/aj only ( ! circle1 x %all n lose above "o vibration 9 #afj4 ,if x sw+ 9 #a_/bj ( ! circle1 x %all lose ab\t "o vibration 9 #fij4 ,if its sw+ be conf9$ to #a_/dj ( ! :ole circle1 x %all lose v little m ?an "o sw+ 9 #bfjj4 ,& if x take no great] a sw+ ?an ?r\gh #a_/fj ( ! :ole circle1 x %all n lose "o sw+ 9 #ehjj4 #fa4 ,,n[ x foll[s f h5ce1 t1 :5 p5dulums sw+ 9 small ar*es1 !re is v ne>ly a con/ant proportion obs]v$ betwe5 ! "t ( _! sw+1 & ! "t1 9 :i* a body w\ld fall p]p5dicul>ly d[n ?r\gh half _! l5g?4 ,& we h decl>$ above1 t ! spaces1 ?r\gh :i* bodies fall1 are 9 a two fold proportion ( ! times1 :i* !y take up 9 fall+#fc4 ,!re=e 9 p5dulums ( diff]5t l5g?s1 sw++ ?r\gh small ar*es1 ! l5g?s ( ! p5dulums are 9 a two fold or duplicate proportion ( ! times1 !y take 9 sw++2 s t a p5dulum ( f\r times ! l5g? ( ano!r %all take up twice ! "t 9 ea* sw+1 "o ( n9e times ! l5g? w make "o sw+ only = ?ree sw+s ( ! %ort]1 & s on4 #fb4 ,,?is proportion 9 ! sw+s ( diff]5t p5dulums n only holds 9 small ar*es2 b 9 l>ge ones also1 provid$ !y be su*1 z ! geomet]s call simil>2 t is1 if ! ar*es be> ! same proportion to ! :ole circumf]5ces ( _! respective circles4 ,suppose 79 fig4 #dh47 ,a ,b1 ,c ,d to be two p5dulums4 ,let ! ar* ,e ,f be describ$ by ! motion ( ! p5dulum ,a ,b1 & ! ar* ,g ,h be describ$ by ! p5dulum ,c ,d2 & let ! ar* ,e ,f be> ! same proportion to ! :ole circumf]5ce1 :i* w\ld be =m$ by turn+ ! p5dulum ,a ,b q r\nd ab\t ! po9t ,a1 z ! ar* ,g ,h be>s to ! :ole circumf]5ce1 t w\ld be =m$ by turn+ ! p5dulum ,c ,d q r\nd ! po9t ,c4 ,!n ,i say1 ! proportion1 :i* ! l5g? ( ! p5dulum ,a ,b be>s to ! l5g? ( ! p5dulum ,c ,d1 w be two fold ( ! proportion1 :i* ! "t tak5 up 9 ! description ( ! ar* ,e ,f be>s to ! "t employ$ 9 ! description ( ! ar* ,g ,h4 #fc4 ,,?us p5dulums1 :i* sw+ 9 v small ar*es1 are ne>ly an equal measure ( "t4 ,b z !y are n su* an equal measure to geometrical exactness2 ! ma!maticians h f\nd out a me?od ( caus+ a p5dulum s to sw+1 t1 if its motion 7 n ob/ruct$ by any resi/ance1 x w\ld always p]=m ea* sw+ 9 ! same "t1 :e!r x mov$ ?r\gh a great]1 or a less] space4 ,?is 0 fir/ discov]$ by ! great ,,huyg5s1 & is z foll[s4 ,^u ! /raight l9e ,a ,b 79 fig4 #di47 let ! circle ,c ,d ,e be s plac$1 z to t\* ! /raight l9e 9 ! po9t ,c4 ,!n let ?is circle roll along ^u ! /raight l9e ,a ,b1 z a coa*-:eel rolls along ^u ! gr\nd4 ,x is evid5t1 t1 z soon z ev] ! circle beg9s to move1 ! po9t ,c 9 ! circle w be lift$ (f f ! /raight l9e ,a ,b2 & 9 ! motion ( ! circle w describe a crook$ c\rse1 :i* is repres5t$ by ! l9e ,c ,f ,g ,h4 ,"h ! "p ,c ,h ( ! /raight l9e includ$ betwe5 ! two extremities ,c & ,h ( ! l9e ,c ,f ,g ,h w be equal to ! :ole circumf]5ce ( ! circle ,c ,d ,e2 & if ,c ,h be divid$ into two equal p>ts at ! po9t ,i1 & ! /raight l9e ,i ,k be drawn p]p5dicul> to ,c ,h1 ?is l9e ,i ,k w be equal to ! diamet] ( ! circle ,c ,d ,e4 ,n[ 9 ?is l9e if a body 7 to be let fall f ! po9t ,h1 & 7 to be c>ri$ by its weight d[n ! l9e ,h ,g ,k1 z f> z ! po9t ,k1 :i* is ! l[e/ po9t ( ! l9e ,c ,f ,g ,h2 & if f any o!r po9t ,g a body 7 to be let fall 9 ! same mann]2 ?is body1 :i* falls f ,g1 w take j ! same "t 9 com+ to ,k1 z ! body takes up1 :i* falls f ,h4 ,!re=e if a p5dulum c be s hung1 t ! ball %all move 9 ! l9e ,a ,g ,f ,e1 all its sw+s1 :e!r long or %ort1 w be p]=m$ 9 ! same "t2 = ! "t1 9 :i* ! ball w desc5d to ! po9t ,k1 is always half ! "t ( ! :ole sw+4 ,b ! ball ( a p5dulum w be made to sw+ 9 ?is l9e by ! foll[+ means4 ,let ,k ,i 79 fig4 #eb47 be prolong$ upw>ds to ,l1 till ,i ,l is equal to ,i ,k4 ,!n let ! l9e ,l ,m ,h equal & l to ,k ,h be appli$1 z 9 ! figure betwe5 ! po9ts ,l & ,h1 s t ! po9t :i* 9 ?is l9e ,l ,m ,h answ]s to ! po9t ,h 9 ! l9e ,k ,h %all be appli$ to ! po9t ,l1 & ! po9t answ]+ to ! po9t ,k %all be appli$ to ! po9t ,h4 ,also let su* ano!r l9e ,l ,n ,c be appli$ betwe5 ,l & ,c 9 ! same mann]4 ,?is prep>ation be+ made2 if a p5dulum be hung at ! po9t ,l ( su* a l5g?1 t ! ball !re( %all rea* to ,k2 & if ! /r+ %all cont9ually b5d aga9/ ! l9es ,h ,m ,l & ,l ,n ,c1 z ! p5dulum sw+s to & fro2 by ?is means ! ball %all con/antly keep 9 ! l9e ,c ,k ,h4 #fd4 ,,n[ 9 ?is p5dulum1 z all ! sw+s1 :e!r long or %ort1 w be p]=m$ 9 ! same "t2 s ! "t ( ea* w exactly be> ! same proportion to ! "t requir$ = a body to fall p]p5dicul>ly d[n1 ?r\gh half ! l5g? ( ! p5dulum1 t is f ,i to ,k1 z ! circumf]5ce ( a circle be>s to its diamet]4 #fe4 ,,x may f h5ce be und]/ood 9 "s measure1 :y1 :5 p5dulums sw+ 9 circul> ar*es1 ! times ( _! sw+s are ne>ly equal1 if ! ar*es are small1 ?\gh ^? ar*es be ( v unequal l5g?s2 = if ) ! semidiamet] ,l ,k ! circul> ar* ,o ,k ,p be describ$1 ?is ar* 9 ! l[] "p ( x w diff] v little f ! l9e ,c ,k ,h4 #ff4 ,,x may n be amiss "h to rem>k1 t a body w fall 9 ?is l9e ,c ,k ,h 7fig4 #ec47 f ,c to any o!r po9t1 z ,q or ,r 9 a %ort] space ( "t1 ?an if x mov$ ?r\gh ! /raight l9e drawn f ,c to ! o!r po9t2 or ?r\gh any o!r l9e :atev]1 t c be drawn betwe5 ^! two po9ts4 #fg4 ,,b z ,i h obs]v$1 t ! "t1 :i* a p5dulum takes 9 sw++1 dep5ds ^u its l5g?2 ,i %all n[ say some?+ conc]n+ ! way1 9 :i* ?is l5g? ( ! p5dulum is to be e/imat$4 ,if ! :ole ball ( ! p5dulum c\ld be cr\d$ into "o po9t1 ?is l5g?1 by :i* ! motion ( ! p5dulum is to be comput$1 w\ld be ! l5g? ( ! /r+ or rod4 ,b ! ball ( ! p5dulum mu/ h a s5sible magnitude1 & ! sev]al p>ts ( ?is ball w n move ) ! same degree ( swiftness2 = ^? p>ts1 :i* are f>!/ f ! po9t1 :]eon ! p5dulum is susp5d$1 mu/ move ) ! greate/ velocity4 ,!re=e to "k ! "t 9 :i* ! p5dulum sw+s1 x is necess>y to f9d t po9t ( ! ball1 :i* moves ) ! same degree ( velocity1 z if ! :ole ball 7 to be contract$ into t po9t4 #fh4 ,,?is po9t is n ! c5t] ( gravity1 z ,i %all n[ endeav\r to %ew4 ,suppose ! p5dulum ,a ,b 79 fig4 #ed47 compos$ ( an inflexible rod ,a ,c & ball ,c ,b1 to be fix$ on ! po9t ,a1 & lift$ up into an horizontal situation4 ,"h if ! rod 7 n fix$ to ! po9t ,a1 ! body ,c ,b w\ld desc5d directly ) ! :ole =ce ( its weight2 & ea* "p ( ! body w\ld move d[n ) ! same degree ( swiftness4 ,b :5 ! rod is fix$ at ! po9t ,a1 ! body mu/ fall aft] ano!r mann]2 = ! p>ts ( ! body mu/ move ) diff]5t degrees ( velocity1 ! p>ts m remote f ,a desc5d+ ) a swift] motion1 ?an ! p>ts ne>] to ,a2 s t ! body w receive a k9d ( roll+ motion :ile x desc5ds4 ,b x has be5 obs]v$ above1 t ! effect ( gravity ^u any body is ! same1 z if ! :ole =ce 7 ex]t$ on ! body's c5t] ( gravity#fd4 ,illu/ration ,s9ce !re=e ! p[] ( gravity 9 draw+ d[n ! body mu/ also communicate to x ! roll+ motion j describ$2 x seems evid5t1 t ! c5t] ( gravity ( ! body _c be drawn d[n z swiftly1 z :5 ! p[] ( gravity has no o!r effect to produce on ! body1 ?an m]ely to draw x d[nw>d4 ,if !re=e ! :ole matt] ( ! body ,c ,b c\ld be cr\d$ into its c5t] ( gravity1 s t be+ unit$ into "o po9t1 ?is roll+ motion "h m5tion$ might give no h9drance to its desc5t2 ?is c5t] w\ld desc5d fa/]1 ?an x c n[ d4 ,& ! po9t1 :i* n[ desc5ds z fa/1 z if ! :ole matt] or ! body ,c ,b 7 cr\d$ into x1 w be f>!r remov$ f ! po9t ,a1 ?an ! c5t] ( gravity ( ! body ,c ,b4 #fi4 ,,aga91 suppose ! p5dulum ,a ,b 79 fig4 #ee47 to hang obliquely4 ,"h ! p[] ( gravity w op]ate less ^u ! ball ( ! p5dulum1 ?an be=e3 b ! l9e ,d ,e be+ drawn s1 z to /& p]p5dicul> to ! rod ,a ,c ( ! p5dulum2 ! =ce ( gravity ^u ! body ,c ,b1 n[ x is 9 ?is situation1 w produce ! same effect1 z if ! body 7 to glide d[n an incl9$ plane 9 ! position ( ,d ,e4 ,b "h ! motion ( ! body1 :5 ! rod is fix$ to ! po9t ,a1 w n be equal to ! un9t]rupt$ desc5t ( ! body d[n ?is plane2 = ! body w "h also receive ! same k9d ( rotation 9 its motion1 z be=e2 s t ! motion ( ! c5t] ( gravity w 9 l mann] be ret>d$2 & ! po9t1 :i* "h desc5ds ) t degree ( swiftness1 :i* ! body w\ld h1 if n h9d]$ by be+ fix$ to ! po9t ,a2 t is1 ! po9t1 :i* desc5ds z fa/1 z if ! :ole body 7 cr\d$ into x1 w be z f> remov$ f ! po9t ,a1 z be=e4 #gj4 ,,?is po9t1 by :i* ! l5g? ( ! p5dulum is to be e/imat$1 is call$ ! c5t] ( oscillation4 ,& ! ma!maticians h laid d[n g5]al directions1 :]eby to f9d ?is c5t] 9 all bodies4 ,if ! globe ,a ,b 79 fig4 #ef47 be hung by ! /r+ ,c ,d1 ^: weight ne$ n be reg>d$1 ! c5t] ( oscillation is f\nd ?us4 ,let ! /raight l9e drawn f ,c to ,d be cont9u$ ?r\gh ! globe to ,f4 ,t x w pass ?r\gh ! c5t] ( ! globe is evid5t4 ,suppose ,e to be ?is c5t] ( ! globe2 & take ! l9e ,g ( su* a l5g?1 t x %all be> ! same proportion to ,e ,d1 z ,e ,d be>s to ,e ,c4 ,!n ,e ,h be+ made equal to ( ,g1 ! po9t ,h %all be ! c5t] ( oscillation#fe4 ,if ! weight ( ! rod ,c ,d is too consid]able to be neglect$1 divide ,c ,d 7fig4 #eg7 9 ,i1 t ,d ,i be equal to 1 "p ( ,c ,d2 & take ,k 9 ! same proportion to ,c ,i1 z ! weight ( ! globe ,a ,b to ! weight ( ! rod ,c ,d4 ,!n hav+ f\nd ,h1 ! c5t] ( oscillation ( ! globe1 z be=e1 divide ,i ,k 9 ,i1 s t ,i ,l %all be> ! same proportion to ,l ,h1 z ! l9e ,c ,h be>s to ,k2 & ,l %all be ! c5t] ( oscillation ( ! :ole p5dulum4 #ga4 ,,?is computation is made ^u supposition1 t ! c5t] ( oscillation ( ! rod ,c ,d1 if t 7 to sw+ alone )\t any o!r weight annex$1 w\ld be ! po9t ,i4 ,& ?is po9t w\ld be ! true c5t] ( oscillation1 s f> z ! ?ickness ( ! rod is n to be reg>d$4 ,if any "o *uses to take into consid]ation ! ?ickness ( ! rod1 he mu/ place ! c5t] ( oscillation !re( s mu* bel[ ! po9t ,i1 t eight times ! di/ance ( ! c5t] f ! po9t ,i %all be> ! same proportion to ! ?ickness ( ! rod1 z ! ?ickness ( ! rod be>s to its l5g? ,c ,d#ff4 #gb4 ,,x has be5 obs]v$ above1 t :5 a p5dulum sw+s 9 an ar* ( a circle1 z "h 9 fig4 #eh1 ! p5dulum ,a ,b sw+s 9 ! circul> ar* ,c ,d2 if y draw an horizontal l9e1 z ,e ,f1 f ! place :5ce ! p5dulum is let fall1 to ! l9e ,a ,g1 :i* is p]p5dicul> to ! horizon3 !n ! velocity1 :i* ! p5dulum w acquire 9 com+ to ! po9t ,g1 w be ! same1 z any body w\ld acquire 9 fall+ directly d[n f ,f to ,g4 ,n[ ?is is to be und]/ood ( ! circul> ar*1 :i* is describ$ by ! c5t] ( oscillation ( ! p5dulum4 ,i %all "h f>!r obs]ve1 t if ! /raight l9e ,e ,g be drawn f ! po9t1 :5ce ! p5dulum falls1 to ! l[e/ po9t ( ! ar*2 9 ! same or 9 equal p5dulums ! velocity1 :i* ! p5dulum acquires 9 ,g1 is proportional to ?is l9e3 t is1 if ! p5dulum1 aft] x has desc5d$ f ,e to ,g1 be tak5 back to ,h1 & let fall f !nce1 & ! l9e ,h ,g be drawn2 ! velocity1 :i* ! p5dulum %all acquire 9 ,g by its desc5t f ,h1 %all be> ! same proportion to ! velocity1 :i* x acquires 9 fall+ f ,e to ,g1 z ! /raight l9e ,h ,g be>s to ! /raight l9e ,e ,g4 #gc4 ,,we may n[ proce$ to ^? exp]im5ts ^u ! p]cussion ( bodies1 :i* ,i obs]v$ above might be made ) p5dulums4 ,?is exp$i5t = exam9+ ! effects ( p]cussion 0 fir/ propos$ by our late great ar*itect ,sir ,,*ri/oph] ,,wr54 ,& x is z foll[s4 ,two balls1 z ,a & ,b 79 fig4 #ei47 ei!r equal or unequal1 are hung by two /r+s f two po9ts ,c & ,d1 s t1 :5 ! balls hang d[n )\t motion1 !y %all j t\* ea* o!r1 & ! /r+s be p>allel4 ,"h if "o ( ^! balls be remov$ to any di/ance f its p]p5dicul> situation1 & !n let fall to desc5d & /rike aga9/ ! o!r2 by ! la/ prec$+ p>agraph x w be kn[n1 ) :at velocity ?is ball %all return into its fir/ p]p5dicul> situation1 & consequ5tly ) :at =ce x %all /rike aga9/ ! o!r ball2 & by ! height to :i* ?is o!r ball asc5ds aft] ! /roke1 ! velocity communicat$ to ?is ball w be discov]$4 ,= in/ance1 let ! ball ,a be tak5 up to ,e1 & f !nce be let fall to /rike aga9/ ,b1 pass+ ov] 9 its desc5t ! circul> ar* ,e ,f4 ,by ?is impulse let ,b fly up to ,g1 mov+ ?r\gh ! circul> ar* ,h ,g4 ,!n ,e ,i & ,g ,k be+ drawn horizontally1 ! ball ,a w /rike aga9/ ,b ) ! velocity1 :i* x w\ld acquire 9 fall+ directly d[n f ,i2 & ! ball ,b has receiv$ a velocity1 :]e)1 if x _h be5 ?r[n directly upw>d1 x w\ld h asc5d$ up to ,k4 ,likewise if /raight l9es be drawn f ,e to ,f & f ,h to ,g1 ! velocity ( ,a1 :]e) x /rikes1 w be> ! same proportion to ! velocity1 :i* ,b has receiv$ by ! bl[1 z ! /raight l9e ,e ,f be>s to ! /raight l9e ,h ,g4 ,9 ! same mann] by not+ ! place to :i* ,a asc5ds aft] ! /roke1 its rema9+ velocity may be comp>$ ) t1 :]e) x /ruck aga9/ ,b4 ,?us may be exp]im5t$ ! effects ( ! body ,a /rik+ aga9/ ,b at re/4 ,if bo? ! bodies are lift$ up1 & s let fall z to meet & imp+e aga9/ ea* o!r j ^u ! com+ ( bo? into _! p]p5dicul> situation2 by obs]v+ ! places into :i* !y move aft] ! /roke1 ! effects ( _! p]cussion 9 all ^! cases may be f\nd 9 ! same mann] z be=e4 #gd4 ,,sir ,,isaac ,,newton has describ$ ^! exp]im5ts2 & has %ewn h[ to improve !m to a great] exactness by mak+ all[ance = ! resi/ance1 :i* ! air gives to ! motion ( ! balls#fg4 ,b z ?is resi/ance is exce$+ small1 & ! mann] ( all[+ = x is deliv]$ by himself 9 v pla9 t]ms1 ,i ne$ n enl>ge ^u x "h4 ,i %all r speak to a discov]y1 :i* he made by ^! exp]im5ts ^u ! ela/icity ( bodies4 ,x has be5 expla9$ above#fh1 t :5 two bodies /rike1 if !y be n ela/ic1 !y rema9 contigu\s aft] ! /roke2 b t if !y are ela/ic1 !y sep>ate1 & t ! degree ( _! ela/icity det]m9es ! proportion betwe5 ! cel]ity :]e) !y sep>ate1 & ! cel]ity :]e) !y meet4 ,n[ our au?or f\nd1 t ! degree ( ela/icity appe>$ 9 ! same bodies always ! same1 ) :atev] degree ( =ce !y /ruck2 t is1 ! cel]ity :]e) !y sep>at$1 always bore ! same proportion to ! cel]ity :]e) !y met3 s t ! ela/ic p[] 9 all ! bodies1 he made trial ^u1 ex]t$ x self 9 "o con/ant proportion to ! compress+ =ce4 ,our au?or made trial ) balls ( wool b\nd up v compact1 & f\nd ! cel]ity ) :i* !y rec$$1 to be> ab\t ! proportion ( #e to #i to ! cel]ity :]e) !y met2 & 9 /eel he f\nd ne>ly ! same proportion2 9 cork ! ela/icity 0 some?+ less2 b 9 glass mu* great]2 = ! cel]ity1 :]e) balls ( t mat]ial sep>at$ aft] p]cussion1 he f\nd to be> ! proportion ( #ae to #af to ! cel]ity :]e) !y met#fi4 #ge4 ,i ,,%all f9i% my disc\rse on p5dulums1 ) ?is f>!r obs]vation only1 t ! c5t] ( oscillation is also ! c5t] ( ano!r =ce4 ,if a body be fix$ to any po9t1 & be+ put 9 motion turns r\nd x2 ! body1 if un9t]rupt$ by ! p[] ( gravity or any o!r means1 w cont9ue p]petually to move ab\t ) ! same equable motion4 ,n[ ! =ce1 ) :i* su* a body moves1 is all unit$ 9 ! po9t1 :i* 9 relation to ! p[] ( gravity is call$ ! c5t] ( oscillation4 ,let ! cyl9d] ,a ,b ,c ,d 79 fig4 #fj47 ^: axis is ,e ,f1 be fix$ to ! po9t ,e4 ,& suppos+ ! po9t ,e to be t on :i* ! cyl9d] is susp5d$1 let ! c5t] ( oscillation be f\nd 9 ! axis ,e ,f1 z has be5 expla9$ above#gj4 ,let ,g be t c5t]3 !n ,i say1 t ! =ce1 :]e) ?is cyl9d] turns r\nd ! po9t ,e1 is s unit$ 9 ! po9t ,g1 t a suffici5t =ce appli$ 9 t po9t %all /op ! motion ( ! cyl9d]1 9 su* a mann]1 t ! cyl9d] %\ld imm$iately rema9 )\t motion1 ?\gh x 7 to be loos5$ f ! po9t ,e at ! same in/ant1 t ! imp$im5t 0 appli$ to ,g3 :]eas1 if ?is imp$im5t _h be5 appli$ to any o!r po9t ( ! axis1 ! cyl9d] w\ld turn ^u ! po9t1 :]e ! imp$im5t 0 appli$4 ,if ! imp$im5t _h be5 appli$ betwe5 ,e & ,g1 ! cyl9d] w\ld s turn on ! po9t1 :]e ! imp$im5t 0 appli$1 t ! end ,b ,c w\ld cont9ue to move on ! same way x mov$ be=e along ) ! :ole cyl9d]2 b if ! imp$im5t 7 appli$ to ! axis f>!r (f f ,e ?an ,g1 ! end ,a ,d ( ! cyl9d] w\ld />t out ( its pres5t place t way 9 :i* ! cyl9d] mov$4 ,f ?is prop]ty ( ! c5t] ( oscillation1 x is also call$ ! c5t] ( p]cussion4 ,t excell5t ma!matician1 ,dr4 ,,brook ,,taylor1 has f>!r improv$ ?is doctr9e conc]n+ ! c5t] ( p]cussion1 by %ew+1 t if ?r\gh ?is po9t ,g a l9e1 z ,g ,h ,i1 be drawn p]p5dicul> to ,e ,f1 & ly+ 9 ! c\rse ( ! body's motion2 a suffici5t p[] appli$ to any po9t ( ?is l9e w h ! same effect1 z ! l p[] appli$ to ,g#ga3 s t z we be=e %ew$ ! c5t] ( p]cussion )9 ! body on its axis2 by ?is means we may f9d ?is c5t] on ! surface ( ! body also1 = x w be :]e ?is l9e ,h ,i crosses t surface4 #gf4 ,i ,,%all n[ proce$ to ! la/ k9d ( motion1 to be treat$ on 9 ?is place1 & %ew :at l9e ! p[] ( gravity w cause a body to describe1 :5 x is ?r[n =w>ds by any =ce4 ,?is 0 fir/ discov]$ by ! great ,,galileo1 & is ! pr9ciple1 ^u :i* eng9e]s %\ld direct ! %ot ( great guns4 ,b z 9 ?is case bodies describe 9 _! motion "o ( ^? l9es1 :i* 9 geometry are call$ conic sections2 x is necess>y "h to premise a description ( ^? l9es4 ,9 :i* ,i %all be ! m p>ticul>1 because ! k ( !m is n only necess>y = ! pres5t purpose1 b w be also requir$ h]eaft] 9 "s ( ! pr9cipal p>ts ( ?is treatise4 #gg4 ,,! fir/ l9es consid]$ by ! anci5t geomet]s 7 ! /raight l9e & ! circle4 ,( ^! !y compos$ v>i\s figures1 ( :i* !y demon/rat$ _m prop]ties1 & resolv$ div]s problems conc]n+ !m4 ,^! problems !y attempt$ always to resolve by ! describ+ /raight l9es & circles4 ,= in/ance1 let a squ>e ,a ,b ,c ,d 7fig4 #fa47 be propos$1 & let x be requir$ to make ano!r squ>e 9 any assign$ proportion to ?is4 ,prolong "o side1 z ,d ,a1 ( ?is squ>e to ,e1 till ,a ,e be> ! same proportion to ,a ,d1 z ! new squ>e is to be> to ! squ>e ,a ,c4 ,if ! opposite side ,b ,c ( ! squ>e ,a ,c be also prolong$ to ,f1 till ,b ,f be equal to ,a ,e1 & ,e ,f be aft]w>ds drawn1 ,i suppose my read]s w easily conceive1 t ! figure ,a ,b ,f ,e w be> to ! squ>e ,a ,b ,c ,d ! same proportion1 z ! l9e ,a ,e be>s to ! l9e ,a ,d4 ,!re=e ! figure ,a ,b ,f ,e w be equal to ! new squ>e1 :i* is to be f\nd1 b is n x self a squ>e1 because ! side ,a ,e is n ( ! same l5g? ) ! side ,e ,f4 ,b to f9d a squ>e equal to ! figure ,a ,b ,f ,e y mu/ proce$ ?us4 ,divide ! l9e ,d ,e into two equal p>ts 9 ! po9t ,g1 & to ! c5t] ,g ) ! int]val ,g ,d describe ! circle ,d ,h ,e ,i2 !n prolong ! l9e ,a ,b1 till x meets ! circle 9 ,k2 & make ! squ>e ,a ,k ,l ,m1 :i* squ>e w be equal to ! figure ,a ,b ,f ,e1 & be> to ! squ>e ,a ,b ,c ,d ! same proportion1 z ! l9e ,a ,e be>s to ,a ,d4 #gh4 ,i ,,%all n proce$ to ! pro( ( ?is1 hav+ only "h set x d[n z a specim5 ( ! me?od ( resolv+ geometrical problems by ! description ( /raight l9es & circles4 ,b !re are "s problems1 :i* _c be resolv$ by draw+ /raight l9es or circles ^u a plane4 ,= ! managem5t !re=e ( ^! !y took into consid]ation solid figures1 & ( ! solid figures !y f\nd t1 :i* is call$ a cone1 to be ! mo/ useful4 #gi4 ,a ,,cone is ?us def9$ by ,,euclide 9 8 elem5ts ( geometry#gb4 ,if to ! /raight l9e ,a ,b 79 fig4 #fb47 ano!r /raight l9e1 z ,a ,c1 be drawn p]p5dicul>1 & ! two extremities ,b & ,c be jo9$ by a ?ird /raight l9e compos+ ! triangle ,a ,c ,b 7= s e figure is call$1 :i* is includ$ "u ?ree /raight l9es7 !n ! two po9ts ,a & ,b be+ held fix$1 z two c5t]s1 & ! triangle ,a ,c ,b be+ turn$ r\nd ^u ! l9e ,a ,b1 z on an axis2 ! l9e ,a ,c w describe a circle1 & ! figure ,a ,c ,b w describe a cone1 ( ! =m repres5t$ by ! figure ,b ,c ,d ,e ,f 7fig4 #fc47 9 :i* ! circle ,c ,d ,e ,f is usually call$ ! base ( ! cone1 & ,b ! v]tex4 #hj4 ,,n[ by ?is figure may sev]al problems be resolv$1 :i* _c by ! simple description ( /raight l9es & circles ^u a plane4 ,suppose = in/ance1 x 7 requir$ to make a cube1 :i* %\ld be> any assign$ proportion to "s o!r cube nam$4 ,i ne$ n "h in=m my read]s1 t a cube is ! figure ( a dye4 ,?is problem 0 mu* celebrat$ among ! anci5ts1 & 0 once in=c$ by ! comm& ( an oracle4 ,?is problem may be p]=m$ by a cone ?us4 ,fir/ make a cone f a triangle1 ^: side ,a ,c %all be half ! l5g? ( ! side ,b ,c ,!n on ! plane ,a ,b ,c ,d 7fig4 #fd47 let ! l9e ,e ,f be exhibit$ equal 9 l5g? to ! side ( ! cube propos$2 & let ! l9e ,f ,g be drawn p]p5dicul> to ,e ,f1 & ( su* a l5g?1 t x be> ! same proportion to ,e ,f1 z ! cube to be s\ght is requir$ to be> to ! cube propos$4 ,?r\gh ! po9ts ,e1 ,f1 & ,g let ! circle ,f ,h ,i be describ$4 ,!n let ! l9e ,e ,f be prolong$ beyond ,f to ,k1 t ,f ,k be equal to ,f ,e1 & let ! triangle ,f ,k ,l1 hav+ all its sides ,f ,k1 ,k ,l1 ,l ,f equal to ea* o!r1 be hung d[n p]p5dicul>ly f ! plane ,a ,b ,c ,d4 ,aft] ?is1 let ano!r plane ,m ,n ,o ,p be ext5d$ ?r\gh ! po9t ,l1 s z to be equidi/ant f ! =m] plane ,a ,b ,c ,d1 & 9 ?is plane let ! l9e ,q ,l ,r be drawn s1 z to be equidi/ant f ! l9e ,e ,f ,k4 ,all ?is be+ ?us prep>$1 let su* a cone1 z 0 above direct$ to be made1 be s appli$ to ! plane ,m ,n ,o ,p1 t x t\* ?is plane ^u ! l9e ,q ,r1 & t ! v]tex ( ! cone be appli$ to ! po9t ,l4 ,?is cone1 by cutt+ ?r\gh ! fir/ plane ,a ,b ,c ,d1 w cross ! circle ,f ,h ,i be=e describ$4 ,& if f ! po9t ,s1 :]e ! surface ( ?is cone int]sects ! circle1 ! l9e ,s ,t be drawn s1 z to be equidi/ant f ! l9e ,e ,f2 ! l9e ,f ,t w be equal to ! side ( ! cube s\ght3 t is1 if !re be two cubes or dyes =m$1 ! side ( "o be+ equal to ,e ,f1 & ! side ( ! o!r equal to ,f ,t2 ! =m] ( ^! cubes %all be> ! same proportion to ! latt]1 z ! l9e ,e ,f be>s to ,f ,g4 #ha4 ,,inde$ ?is plac+ a cone to cut ?r\gh a plane is n a practicable me?od ( resolv+ problems4 ,b :5 ! geomet]s _h discov]$ ?is use ( ! cone1 !y appli$ !mselves to consid] ! nature ( ! l9es1 :i* w be produc$ by ! int]section ( ! surface ( a cone & a plane2 :]eby !y might be enabl$ bo? to r$uce ^! k9ds ( solutions to practice1 & also to r5d] _! demon/rations concise & elegant4 #hb4 ,,:5ev] ! plane1 :i* cuts ! cone1 is equidi/ant f ano!r plane1 t t\*es ! cone on ! side2 7:i* is ! case ( ! pres5t figure27 ! l9e1 :]e9 ! plane cuts ! surface ( ! cone1 is call$ a p>abola4 ,b if ! plane1 :i* cuts ! cone1 be s incl9$ to ?is o!r1 t x w pass q ?r\gh ! cone 7z 9 fig4 #fe47 su* a plane by cutt+ ! cone produces ! figure call$ an ellipsis1 9 :i* we %all h]eaft] %ew ! e>? & o!r planets to move r\nd ! sun4 ,if ! plane1 :i* cuts ! cone1 recl9e ! o!r way 7z 9 fig4 #ff47 s z n to be p>allel to any plane1 :]eon ! cone c lie1 nor yet to cut q ?r\gh ! cone2 su* a plane %all produce 9 ! cone a ?ird k9d ( l9e1 :i* is call$ an hyp]bola4 ,b x is ! fir/ ( ^! l9es nam$ ! p>abola1 :]e9 bodies1 t are ?r[n obliquely1 w be c>ri$ by ! =ce ( gravity2 z ,i %all "h proce$ to %ew1 aft] hav+ fir/ direct$ my read]s h[ to describe ?is sort ( l9e ^u a plane1 by :i* ! =m ( x may be se54 #hc4 ,,to any /raight l9e ,a ,b 7fig4 #fg47 let a /raight rul] ,c ,d be s appli$1 z to /& aga9/ x p]p5dicul>ly4 ,^u ! edge ( ?is rul] let ano!r rul] ,e ,f be s plac$1 z to move along ^u ! edge ( ! fir/ rul] ,c ,d1 & keep always p]p5dicul> to x4 ,?is be+ s dispos$1 let any po9t1 z ,g1 be tak5 9 ! l9e ,a ,b1 & let a /r+ equal 9 l5g? to ! rul] ,e ,f be fa/5$ by "o end to ! po9t ,g1 & by ! o!r to ! extremity ,f ( ! rul] ,e ,f4 ,!n if ! /r+ be held d[n to ! rul] ,e ,f by a p9 ,h1 z is repres5t$ 9 ! figure2 ! po9t ( ?is p91 :ile ! rul] ,e ,f moves on ! rul] ,c ,d1 %all describe ! l9e ,i ,k ,l1 :i* w be "o "p ( ! curve l9e1 ^: description we 7 "h to tea*3 & by apply+ ! rul]s 9 ! l mann] on ! o!r side ( ! l9e ,a ,b1 we may describe ! o!r "p ,i ,m ( ?is l9e4 ,if ! di/ance ,c ,g be equal to half ! l9e ,e ,f 9 fig4 #fd1 ! l9e ,m ,i ,l w be t v l9e1 :]e9 ! plane ,a ,b ,c ,d 9 t figure cuts ! cone4 #hd4 ,,! l9e ,a ,i is call$ ! axis ( ! p>abola ,m ,i ,l1 & ! po9t ,g is call$ ! focus4 #he4 ,,n[ by comp>+ ! effects ( gravity ^u fall+ bodies1 ) :at is demon/rat$ ( ?is figure by ! geomet]s1 x is prov$1 t e body ?r[n obliquely is c>ri$ =w>d 9 "o ( ^! l9es1 ! axis :]e( is p]p5dicul> to ! horizon4 #hf4 ,,! geomet]s demon/rate1 t if a l9e be drawn to t\* a p>abola 9 any po9t1 z ! l9e ,a ,b 79 fig4 #fh47 t\*es ! p>abola ,c ,d1 ^: axis is ,y ,z1 9 ! po9t ,e2 & sev]al l9es ,f ,g1 ,h ,i1 ,k ,l be drawn p>allel to ! axis ( ! p>abola3 !n ! l9e ,f ,g w be to ,h ,i 9 ! duplicate proportion ( ,e ,f to ,e ,h1 & ,f ,g to ,k ,l 9 ! duplicate proportion ( ,e ,f to ,e ,k2 likewise ,h ,i to ,k ,l 9 ! duplicate proportion ( ,e ,h to ,e ,k4 ,:at is to be und]/ood by duplicate or two-fold proportion1 has be5 already expla9$#gc4 ,accord+ly ,i mean "h1 t if ! l9e ,m be tak5 to be> ! same proportion to ,e ,h1 z ,e ,h be>s to ,e ,f1 ,h ,i w be> ! same proportion to ,f ,g1 z ,m be>s to ,e ,f2 & if ! l9e ,n be>s ! same proportion to ,e ,k1 z ,e ,k be>s to ,e ,f1 ,k ,l w be> ! same proportion to ,f ,g1 z ,n be>s to ,e ,f2 or if ! l9e ,o be> ! same proportion to ,e ,k1 z ,e ,k be>s to ,e ,h1 ,k ,l w be> ! same proportion to ,h ,i1 z ,o be>s to ,e ,h4 #hg4 ,,?is prop]ty is ess5tial to ! p>abola1 be+ s connect$ ) ! nature ( ! figure1 t e l9e possess+ ?is prop]ty is to be call$ by ?is "n4 #hh4 ,,n[ suppose a body to be ?r[n f ! po9t ,a 79 fig4 #fi47 t[>ds ,b 9 ! direction ( ! l9e ,a ,b4 ,?is body1 if left to x self1 w\ld move on ) a uni=m motion ?r\gh ?is l9e ,a ,b4 ,suppose ! eye ( a spectator to be plac$ at ! po9t ,c j "u ! po9t ,a2 & let u imag9e ! e>? to be s put into motion along ) ! body1 z to c>ry ! spectator's eye along ! l9e ,c ,d p>allel to ,a ,b2 & t ! eye w\ld move on ) ! same velocity1 :]e) ! body w\ld proce$ 9 ! l9e ,a ,b1 if x 7 to be left to move )\t any di/urbance f its gravitation t[>ds ! e>?4 ,9 ?is case if ! body mov$ on )\t be+ drawn t[>ds ! e>?1 x w\ld appe> to ! spectator to be at re/4 ,b if ! p[] ( gravity ex]t$ x self on ! body1 x w\ld appe> to ! spectator to fall directly d[n4 ,suppose at ! di/ance ( "t1 :]e9 ! body by its own progressive motion w\ld h mov$ f ,a to ,e1 x %\ld appe> to ! spectator to h fall5 ?r\gh a l5g? equal to ,e ,f3 !n ! body at ! end ( ?is "t w actually h arriv$ at ! po9t ,f4 ,if 9 ! space ( "t1 :]e9 ! body w\ld h mov$ by its progressive motion f ,a to ,g1 x w\ld h appe>$ to ! spectator to h fall5 d[n ! space ,g ,h3 !n ! body at ! end ( ?is great] int]val ( "t w be arriv$ at ! po9t ,h4 ,n[ if ! l9e ,a ,f ,h ,i be t1 ?r\gh :i* ! body actually passes2 f :at has "h be5 said1 x w foll[1 t ?is l9e is "o ( ^?1 :i* ,i h be5 describ+ "u ! "n ( ! p>abola4 ,= ! di/ances ,e ,f1 ,g ,h1 ?r\gh :i* ! body is se5 to fall1 w increase 9 ! duplicate proportion ( ! times#gd2 b ! l9es ,a ,e1 ,a ,g w be proportional to ! times :]e9 !y w\ld h be5 describ$ by ! s+le progressive motion ( ! body3 !re=e ! l9es ,e ,f1 ,g ,h w be 9 ! duplicate proportion ( ! l9es ,a ,f1 ,a ,g2 & ! l9e ,a ,f ,h ,i possesses ! prop]ty ( ! p>abola4 #hi4 ,,if ! e>? be n suppos$ to move along ) ! body1 ! case w be a little diff]5t4 ,= ! body be+ con/antly drawn directly t[>ds ! c5t] ( ! e>?1 ! body 9 its motion w be drawn 9 a direction a little oblique to t1 :]e9 x w\ld be drawn by ! e>? 9 motion1 z be=e suppos$4 ,b ! di/ance to ! c5t] ( ! e>? be>s s va/ a proportion to ! greate/ l5g?1 to :i* we c ?r[ bodies1 t ?is obliquity does n m]it any reg>d4 ,f ! sequel ( ?is disc\rse x may inde$ be collect$1 :at l9e ! body be+ ?r[n ?us w\ld be f\nd to describe1 all[ance be+ made = ?is obliquity ( ! e>?'s action#ge4 ,?is is ! discov]y ( ,sir ,,is4 ,,newton2 b has no use 9 ?is place4 ,"h x is abundantly suffici5t to consid] ! body z mov+ 9 a p>abola4 #ij4 ,,! l9e1 :i* a project$ body describes1 be+ ?us kn[n1 practical me?ods h be5 d$uc$ f h5ce = direct+ ! %ot ( great guns to /rike any object desir$4 ,?is "w 0 fir/ attempt$ by ,,galileo1 & soon aft] f>!r improv$ by 8 s*ol> ,,torricelli2 b has lately be5 r5dr$ m complete by ! great ,mr4 ,,cotes1 ^: immature dea? is an unspeakable loss to ma!matical le>n+4 ,if x be requir$ to ?r[ a body f ! po9t ,a 79 fig4 #gj47 s z to /rike ! po9t ,b2 ?r\gh ! po9ts ,a1 ,b draw ! /raight l9e ,c ,d1 & erect ! l9e ,a ,e p]p5dicul> to ! horizon1 & ( f\r times ! height1 f :i* a body mu/ fall to acquire ! velocity1 :]e) ! body is int5d$ to be ?r[n4 ,?r\gh ! po9ts ,a & ,e describe a circle1 t %all t\* ! l9e ,c ,d 9 ! po9t ,a4 ,!n f ! po9t ,b draw ! l9e ,b ,f p]p5dicul> to ! horizon1 int]sect+ ! circle 9 ! po9ts ,g & ,h4 ,?is be+ done1 if ! body be project$ directly t[>ds ei!r ( ^! po9ts ,g or ,h1 x %all fall ^u ! po9t ,b2 b ) ?is diff]5ce1 t1 if x be ?r[n 9 ! direction ,a ,g1 x %all soon] arrive at ,b1 ?an if x 7 project$ 9 ! direction ,a ,h4 ,:5 ! body is project$ 9 ! direction ,a ,g2 ! "t1 x w take up 9 arriv+ at ,b1 w be> ! same proportion to ! "t1 :]e9 x w\ld fall d[n ?r\gh "o f\r? "p ( ,a ,e1 z ,a ,g be>s to half ,a ,e4 ,b :5 ! body is ?r[n 9 ! direction ( ,a ,h1 ! "t ( its pass+ to ,b w be> ! same proportion to ! "t1 :]e9 x w\ld fall ?r\gh "o f\r? "p ( ,a ,e1 z ,a ,h be>s to half ,a ,e4 #ia4 ,,if ! l9e ,a ,i be drawn s z to divide ! angle "u ,e ,a ,d 9 ! middle1 & ! l9e ,i ,k be drawn p]p5dicul> to ! horizon2 ?is l9e w t\* ! circle 9 ! po9t ,i1 & if ! body be ?r[n 9 ! direction ,a ,i1 x w fall ^u ! po9t ,k3 & ?is po9t ,k is ! f>!/ po9t 9 ! l9e ,a ,d1 :i* ! body c be made to /rike1 )\t increas+ its velocity4 #ib4 ,,! velocity1 :]e) ! body e :]e moves1 may be f\nd ?us4 ,suppose ! body to move 9 ! p>abola ,a ,b 7fig4 #ga47 ,erect ,a ,c p]p5dicul> to ! horizon1 & equal to ! height1 f :i* a body mu/ fall to acquire ! velocity1 :]e) ! body sets out f ,a4 ,if y take any po9ts z ,d & ,e 9 ! p>abola1 & draw ,d ,f & ,e ,g p>allel to ! horizon2 ! velocity ( ! body 9 ,d w be equal to :at a body w acquire 9 fall+ d[n by its own weight ?r\gh ,c ,f1 & 9 ,e ! velocity w be ! same1 z w\ld be acquir$ 9 fall+ ?r\gh ,c ,g4 ,?us ! body moves sl[e/ at ! highe/ po9t ,h ( ! p>abola2 & at equal di/ances f ?is po9t w move ) equal swiftness1 & desc5d f t highe/ po9t ?r\gh ! l9e ,h ,b altoge!r l to ! l9e ,a ,h 9 :i* x asc5d$2 abat+ only ! resi/ance ( ! air1 :i* is n "h consid]$4 ,if ! l9e ,h ,i be drawn f ! highe/ po9t ,h p>allel to ! horizon1 ,a ,i w be equal to ( ,b ,g 9 fig4 #gj1 :5 ! body is project$ 9 ! direction ,a ,g1 & equal to ( ,b ,h1 :5 ! body is ?r[n 9 ! direction ,a ,h provid$ ,a ,d be drawn horizontally4 #ic4 ,,?us ,i h rec\nt$ ! pr9cipal discov]ies1 :i* _h be5 made conc]n+ ! motion ( bodies by ,sir ,,isaac ,,newton',s pr$ecessors2 all ^! discov]ies1 by be+ f\nd to agree ) exp]i5ce1 contribut+ to e/abli% ! laws ( motion1 f :5ce !y 7 d$uc$4 ,i %all !re=e "h f9i% :at ,i _h to say ^u ^? laws2 & conclude ?is *apt] ) a few words conc]n+ ! di/9ction :i* ought to be made betwe5 absolute & relative motion4 ,= "s h ?\ght fit to conf\nd !m toge!r2 because !y obs]ve ! laws ( motion to take place "h on ! e>?1 :i* is 9 motion1 aft] ! same mann] z if x 7 at re/4 ,b ,sir ,,isaac ,,newton has be5 c>eful to di/+ui% betwe5 ! relative & absolute consid]ation bo? ( motion & "t#gf4 ,! a/ronom]s anci5tly f\nd x necess>y to make ?is di/9ction 9 "t4 ,"t consid]$ 9 x self passes on equably )\t relation to any ?+ ext]nal1 be+ ! prop] measure ( ! cont9uance & duration ( all ?+s4 ,b x is mo/ frequ5tly conceiv$ ( by u "u a relative view to "s succession 9 s5sible ?+s1 ( :i* we take cognizance4 ,! succession ( ! ?\ghts 9 our own m9ds is t1 f :5ce we receive our fir/ idea ( "t1 b is a v unc]ta9 measure !re(2 = ! ?\ghts ( "s m5 fl[ on mu* m swiftly1 ?an ! ?\ghts ( o!rs2 nor does ! same p]son ?9k equally quick at all times4 ,! motions ( ! heav5ly bodies are m regul>2 & ! em95t division ( "t into night & day1 made by ! sun1 leads u to measure our "t by ! motion ( t lum9>y3 nor d we 9 ! affairs ( life conc]n our selves ) any inequality1 :i* !re may be 9 t motion2 b ! space ( "t :i* compreh5ds a day & night is r suppos$ to be always ! same4 ,h[ev] a/ronom]s anci5tly f\nd ^! spaces ( "t n to be always ( ! same l5g?1 & h taught h[ to compute _! diff]5ces4 ,n[ ! "t1 :5 s equat$ z to be r5d]$ p]fectly equal1 is ! true measure ( duration1 ! o!r n4 ,& !re=e ?is latt]1 :i* is absolutely true "t1 diff]s f ! o!r1 :i* is only app>5t4 ,& z we ord9>ily make no di/9ction betwe5 app>5t "t1 z measur$ by ! sun1 & ! true2 s we (t5 d n di/+ui% 9 our usual disc\rse betwe5 ! real1 & ! app>5t or relative motion ( bodies2 b use ! same words = "o1 z we %\ld = ! o!r4 ,?\gh all ?+s ab\t u are really 9 motion ) ! e>?2 z ?is motion is n visible1 we speak ( ! motion ( e ?+ we see1 z if our selves & ! e>? /ood /ill4 ,& ev5 9 o!r cases1 :]e we disc]n ! motion ( bodies1 we (t5 speak ( !m n 9 relation to ! :ole motion we see1 b ) reg>d to o!r bodies1 to :i* !y are contigu\s4 ,if any body 7 ly+ on a table2 :5 t table %all be c>ri$ along1 we say ! body re/s ^u ! table1 or p]haps absolutely1 t ! body is at re/4 ,h[ev] philosoph]s mu/ n reject all di/9ction betwe5 true & app>5t motions1 any m ?an a/ronom]s d ! di/9ction betwe5 true & vulg> "t2 = !re is z real a diff]5ce betwe5 !m1 z w appe> by ! foll[+ consid]ation4 ,suppose all ! bodies ( ! univ]se to h _! c\rses /opp$1 & r$uc$ to p]fect re/4 ,!n suppose _! pres5t motions to be aga9 re/or$2 ?is _c be done )\t an actual impression made ^u "s ( !m at lea/4 ,if any ( !m be left unt\*$1 !y w reta9 _! =m] /ate1 t is1 /ill rema9 at re/2 b ! o!r bodies1 :i* are wr\ght ^u1 w h *ang$ _! =m] /ate ( re/1 = ! contr>y /ate ( motion4 ,let u n[ suppose ! bodies left at re/ to be annihilat$1 ?is w make no alt]ation 9 ! /ate ( ! mov+ bodies2 b ! effect ( ! impression1 :i* 0 made ^u !m1 w /ill subsi/4 ,?is %ews ! motion !y receiv$ to be an absolute ?+1 & to h no necess>y dep5d5ce ^u ! relation :i* ! body said to be 9 motion has to any o!r body#gg4 #id4 ,,besides absolute & relative motion are di/+ui%able by _! ,effects4 ,"o effect ( motion is1 t bodies1 :5 mov$ r\nd any c5t] or axis1 acquire a c]ta9 p[]1 by :i* !y =cibly press !mselves f t c5t] or axis ( motion4 ,z :5 a body is :irl$ ab\t 9 a sl+1 ! body presses aga9/ ! sl+1 & is ready to fly out z soon z lib]ty is giv5 x4 ,& ?is p[] is proportional to ! true1 n relative motion ( ! body r\nd su* a c5t] or axis4 ,( ?is ,sir ,,isaac ,,newton gives ! foll[+ in/ance#gh4 ,if a pail or su* l vessel ne> full ( wat] be susp5d$ by a /r+ ( suffici5t l5g?1 & be turn$ ab\t till ! /r+ be h>d twi/$4 ,if !n z soon z ! vessel & wat] 9 x are become /ill & at re/1 ! vessel be nimbly turn$ ab\t ! contr>y way ! /r+ 0 twi/$1 ! vessel by ! /r+s untwi/+ x self %all cont9ue its motion a long "t4 ,& :5 ! vessel fir/ beg9s to turn1 ! wat] 9 x %all receive little or no?+ ( ! motion ( ! vessel1 b by degrees %all receive a communication ( motion1 till at la/ x %all move r\nd z swiftly z ! vessel x self4 ,n[ ! def9ition ( motion1 :i* ,,des ,,c>tes has giv5 u ^u ?is pr9ciple ( mak+ all motion me]ly relative1 is ?is3 t motion1 is a removal ( any body f its vic9ity to o!r bodies1 :i* 7 9 imm$iate contact ) x1 & are consid]$ z at re/#gi4 ,& if ?is be comp>$ ) :at he soon aft] says1 t !re is no?+ real or positive 9 ! body mov$1 = ! sake ( :i* we ascribe motion to x1 :i* is n to be f\nd z well 9 ! contigu\s bodies1 :i* are consid]$ z at re/#hj2 x w foll[ f !nce1 t we may consid] ! vessel z at re/ & ! wat] z mov+ 9 x3 & ! wat] 9 respect ( ! vessel has ! greate/ motion1 :5 ! vessel fir/ beg9s to turn1 & loses ?is relative motion m & m1 till at l5g? x q ceases4 ,b n[1 :5 ! vessel fir/ beg9s to turn1 ! surface ( ! wat] rema9s smoo? & flat1 z be=e ! vessel began to move2 b z ! motion ( ! vessel communicates by degrees motion to ! wat]1 ! surface ( ! wat] w be obs]v$ to *ange1 ! wat] subsid+ 9 ! middle & ris+ at ! edges3 :i* elevation ( ! wat] is caus$ by ! p>ts ( x press+ f ! axis1 !y move ab\t2 & !re=e ?is =ce ( rec$+ f ! axis ( motion dep5ds n ^u ! relative motion ( ! wat] )9 ! vessel1 b on its absolute motion2 = x is lea/1 :5 t relative motion is greate/1 & greate/1 :5 t relative motion is lea/1 or none at all4 #ie4 ,,?us ! true cause ( :at appe>s 9 ! surface ( ?is wat] _c be assign$1 )\t consid]+ ! wat]'s motion )9 ! vessel4 ,s also 9 ! sy/em ( ! _w1 9 ord] to f9d out ! cause ( ! planet>y motions1 we mu/ "k m ( ! real motions1 :i* belong to ea* planet1 ?an is absolutely necess>y = ! uses ( a/ronomy4 ,if ! a/ronom] %\ld suppose ! e>? to /& /ill1 he c\ld ascribe su* motions to ! cele/ial bodies1 z %\ld answ] all ! appe>ances2 ?\gh he w\ld n acc\nt = !m 9 s simple a mann]1 z by attribut+ motion to ! e>?4 ,b ! motion ( ! e>? mu/ ( necessity be consid]$1 be=e ! real causes1 :i* actuate ! planet>y sy/em1 c be discov]$4 ,,*ap4 ,,iii4 ,( ,,c5tripetal ,,=ces4 ,,we h j be5 describ+ 9 ! prec$+ *apt] ! effects produc$ on a body 9 motion1 f its be+ cont9ually act$ ^u by a p[] always equal 9 /r5g?1 & op]at+ 9 p>allel directions#ha4 ,b bodies may be act$ ^u by p[]s1 :i* 9 diff]5t places %all h diff]5t degrees ( =ce1 & ^: sev]al directions %all be v>i\sly incl9$ to ea* o!r4 ,! mo/ simple ( ^! 9 respect to direction is1 :5 ! p[] is po9t$ con/antly to "o c5t]4 ,?is is truly ! case ( t p[]1 ^: effects we describ$ 9 ! =ego+ *apt]2 ?\gh ! c5t] ( t p[] is s f> remov$1 t ! subject !n be=e u is mo/ conv5i5tly to be consid]$ 9 ! light1 :]e9 we h plac$ x3 ,b ,sir ,,isaac ,,newton has consid]$ v p>ticul>ly ?is o!r case ( p[]s1 :i* are con/antly direct$ to ! same c5t]4 ,x is ^u ?is f\ndation1 t all 8 discov]ies 9 ! sy/em ( ! _w are rais$4 ,& !re=e1 z ?is subject be>s s v great a %>e 9 ! philosophy1 ( :i* ,i am disc\rs+1 ,i ?9k x prop] 9 ?is place to take a %ort view ( "s ( ! g5]al effects ( ^! p[]s1 be=e we come to apply !m p>ticul>ly to ! sy/em ( ! _w4 #b4 ,,^! p[]s or =ces are by ,sir ,,isaac ,,newton call$ c5tripetal2 & _! fir/ effect is to cause ! body1 on :i* !y act1 to quit ! /raight c\rse1 :]e9 x w\ld proce$ if undi/urb$1 & to describe an incurvat$ l9e1 :i* %all always be b5t t[>ds ! c5t] ( ! =ce4 ,x is n necess>y1 t su* a p[] %\ld cause ! body to approa* t c5t]4 ,! body may cont9ue to rec$e f ! c5t] ( ! p[]1 not)/&+ its be+ drawn by ! p[]2 b ?is prop]ty mu/ always belong to its motion1 t ! l9e1 9 :i* x moves1 w cont9ually be concave t[>ds ! c5t]1 to :i* ! p[] is direct$4 ,suppose ,a 79 fig4 #gb47 to be ! c5t] ( a =ce4 ,let a body 9 ,b be mov+ 9 ! direction ( ! /raight l9e ,b ,c1 9 :i* l9e x w\ld cont9ue to move1 if undi/urb$2 b be+ attract$ by ! c5tripetal =ce t[>ds ,a1 ! body mu/ necess>ily dep>t f ?is l9e ,b ,c1 & be+ drawn into ! curve l9e ,b ,d1 mu/ pass betwe5 ! l9es ,a ,b & ,b ,c4 ,x is evid5t !re=e1 t ! body 9 ,b be+ gradually turn$ (f f ! /raight l9e ,b ,c1 x w at fir/ be convex t[>d ! l9e ,b ,c1 & consequ5tly concave t[>ds ! po9t ,a3 = ^! c5tripetal p[]s are suppos$ to be 9 /r5g? proportional to ! p[] ( gravity1 &1 l t1 n to be able aft] ! mann] ( an impulse to turn ! body s5sibly out ( its c\rse into a diff]5t "o 9 an in/ant1 b to take up "s space ( "t 9 produc+ a visible effect4 ,t ! curve w always cont9ue to h its concavity t[>ds ,a may ?us appe>4 ,9 ! l9e ,b ,c ne> to ,b take any po9t z ,e1 f :i* ! l9e ,e ,f ,g may be s drawn1 z to t\* ! curve l9e ,b ,d 9 "s po9t z ,f4 ,n[ :5 ! body is come to ,f1 if ! c5tripetal p[] 7 imm$iately to be susp5d$1 ! body w\ld no long] cont9ue to move 9 a curve l9e1 b be+ left to x self w\ld =?) reassume a /raight c\rse2 & t /raight c\rse w\ld be 9 ! l9e ,f ,g3 = t l9e is 9 ! direction ( ! body's motion at ! po9t ,f4 ,b ! c5tripetal =ce cont9u+ its en]gy1 ! body w be gradually drawn f ?is l9e ,f ,g s z to keep 9 ! l9e ,f ,d1 & make t l9e ne> ! po9t ,f to be convex t[>d ,f ,g1 & concave t[>d ,a4 ,aft] ! same mann] ! body may be foll[$ on 9 its c\rse ?r\gh ! l9e ,b ,d1 & e "p ( t l9e be %ewn to be concave t[>d ! po9t ,a4 #c4 ,,?is !n is ! con/ant "* belong+ to ^? motions1 :i* are c>ri$ on by c5tripetal =ces2 t ! l9e1 :]e9 ! body moves1 is ?r\gh\t concave t[>ds ! c5t] ( ! =ce4 ,9 respect to ! successive di/ances ( ! body f ! c5t] !re is no g5]al rule to be laid d[n2 = ! di/ance ( ! body f ! c5t] may ei!r increase1 or decrease1 or ev5 keep always ! same4 ,! po9t ,a 79 fig4 #gc47 be+ ! c5t] ( a c5tripetal =ce1 let a body at ,b set out 9 ! direction ( ! /raight l9e ,b ,c p]p5dicul> to ! l9e ,a ,b drawn f ,a to ,b4 ,x w be easily conceiv$1 t !re is no o!r po9t 9 ! l9e ,b ,c s ne> to ,a1 z ! po9t ,b2 t ,a ,b is ! %orte/ ( all ! l9es1 :i* c be drawn f ,a to any "p ( ! l9e ,b ,c2 all o!r l9es1 z ,a ,d1 or ,a ,e1 drawn f ,a to ! l9e ,b ,c be+ long] ?an ,a ,b4 ,h5ce x foll[s1 t ! body sett+ out f ,b1 if x mov$ 9 ! l9e ,b ,c1 x w\ld rec$e m & m f ! po9t ,a4 ,n[ z ! op]ation ( a c5tripetal =ce is to draw a body t[>ds ! c5t] ( ! =ce3 if su* a =ce act ^u a re/+ body1 x mu/ necess>ily put t body s into motion1 z to cause x to move t[>ds ! c5t] ( ! =ce3 if ! body 7 ( x self mov+ t[>ds t c5t]1 ! c5tripetal =ce w\ld accel]ate t motion1 & cause x to move fa/] d[n3 b if ! body 7 9 su* a motion1 z be+ left to itself x w\ld rec$e f ?is c5t]1 x is n necess>y1 t ! action ( a c5tripetal p[] ^u x %\ld imm$iately compel ! body to approa* ! c5t]1 f :i* x w\ld o!rwise h rec$$2 ! c5tripetal p[] is n )\t effect1 if x cause ! body to rec$e m sl[ly f t c5t]1 ?an o!rwise x w\ld h done4 ,?us 9 ! case be=e u1 ! smalle/ c5tripetal p[]1 if x act on ! body1 w =ce x out ( ! l9e ,b ,c1 & cause x to pass 9 a b5t l9e betwe5 ,b ,c & ! po9t ,a1 z has be5 be=e expla9$4 ,:5 ! body1 = in/ance1 has advanc$ to ! l9e ,a ,d1 ! effect ( ! c5tripetal =ce discov]s x self by hav+ remov$ ! body out ( ! l9e ,b ,c1 & br\ght x to cross ! l9e ,a ,d some:]e betwe5 ,a & ,d3 suppose at ,f4 ,n[ ,a ,d be+ long] ?an ,a ,b1 ,a ,f may also be long] ?an ,a ,b4 ,! c5tripetal p[] may inde$ be s /rong1 t ,a ,f %all be %ort] ?an ,a ,b2 or x may be s ev5ly balanc$ ) ! progressive motion ( ! body1 t ,a ,f & ,a ,b %all be j equal3 & 9 ?is la/ case1 :5 ! c5tripetal =ce is ( t /r5g?1 z con/antly to draw ! body z mu* t[>d ! c5t]1 z ! progressive motion w\ld c>ry x (f1 ! body w describe a circle ab\t ! c5t] ,a1 ?is c5t] ( ! =ce be+ also ! c5t] ( ! circle4 #d4 ,,if ! body1 in/ead ( sett+ out 9 ! l9e ,b ,c p]p5dicul> to ,a ,b1 _h set out 9 ano!r l9e ,b ,g m incl9$ t[>ds ! l9e ,a ,b1 mov+ 9 ! curve l9e ,b ,h2 !n z ! body1 if x 7 to cont9ue its motion 9 ! l9e ,b ,g1 w\ld = "s "t approa* ! c5t] ,a2 ! c5tripetal =ce w\ld cause x to make great] advances t[>d t c5t]4 ,b if ! body 7 to set out 9 ! l9e ,b ,i recl9$ ! o!r way f ! p]p5dicul> ,b ,c1 & 7 to be drawn by ! c5tripetal =ce into ! curve l9e ,b ,k2 ! body1 not)/&+ any c5tripetal =ce1 w\ld = "s "t rec$e f ! c5t]2 s9ce "s "p at lea/ ( ! curve l9e ,b ,k lies betwe5 ! l9e ,b ,i & ! p]p5dicul> ,b ,c4 #e4 ,,?us f> we h expla9$ su* effects1 z att5d e c5tripetal =ce4 ,b z ^! =ces may be v diff]5t 9 reg>d to ! diff]5t degrees ( /r5g?1 :]e) !y act ^u bodies 9 diff]5t places2 ,i %all n[ proce$ to make m5tion 9 g5]al ( "s ( ! diff]5ces att5d+ ^! c5tripetal motions4 #f4 ,,to reassume ! consid]ation ( ! la/ m5tion$ case4 ,suppose a c5tripetal p[] direct$ t[>d ! po9t ,a 79 fig4 #gd47 to act on a body 9 ,b1 :i* is mov+ 9 ! direction ( ! /raight l9e ,b ,c1 ! l9e ,b ,c recl9+ (f f ,a ,b4 ,if f ,a ! /raight l9es ,a ,d1 ,a ,e1 ,a ,f are drawn at pleasure to ! l9e ,c ,b2 ! l9e ,c ,b be+ prolong$ beyond ,b to ,g1 x appe>s t ,a ,d is incl9$ to ! l9e ,g ,c m obliquely1 ?an ,a ,b is incl9$ to x1 ,a ,e is incl9$ m obliquely ?an ,a ,d1 & ,a ,f m ?an ,a ,e4 ,to speak m correctly1 ! angle "u ,a ,d ,g is less ?an t "u ,a ,b ,g1 ! angle "u ,a ,e ,g less ?an t "u ,a ,d ,g1 & ! angle "u ,a ,f ,g less ?an t "u ,a ,e ,g4 ,n[ suppose ! body to move 9 ! curve l9e ,b ,h ,i ,k4 ,!n x is "h likewise evid5t1 t ! l9e ,b ,h ,i ,k be+ concave t[>ds ,a1 & convex t[>ds ! l9e ,b ,c1 x is m & m turn$ (f f ! l9e ,b ,c2 s t 9 ! po9t ,h ! l9e ,a ,h w be less obliquely incl9$ to ! curve l9e ,b ,h ,i ,k1 ?an ! same l9e ,a ,h ,d is incl9$ to ,b ,c at ! po9t ,d2 at ! po9t ,i ! incl9ation ( ! l9e ,a ,i to ! curve l9e w be m diff]5t f ! incl9ation ( ! same l9e ,a ,i ,e to ! l9e ,b ,c1 at ! po9t ,e2 & 9 ! po9ts ,k & ,f ! diff]5ce ( incl9ation w be /ill great]2 & 9 bo? ! incl9ation at ! curve w be less oblique1 ?an at ! /raight l9e ,b ,c4 ,b ! /raight l9e ,a ,b is less obliquely incl9$ to ,b ,g1 ?an ,a ,d is incl9$ t[>ds ,d ,g3 !re=e al?\gh ! l9e ,a ,h be less obliquely incl9$ t[>ds ! curve ,h ,b1 ?an ! same l9e ,a ,h ,d is incl9$ t[>ds ,d ,g2 yet x is possible1 t ! incl9ation at ,h may be m oblique1 ?an ! incl9ation at ,b4 ,! incl9ation at ,h may inde$ be less oblique ?an ! o!r1 or !y may be bo? ! same4 ,?is dep5ds ^u ! degree ( /r5g?1 :]e) ! c5tripetal =ce ex]ts x self1 dur+ ! passage ( ! body f ,b to ,h4 ,aft] ! same mann] ! incl9ations at ,i & ,k dep5d entirely on ! degree ( /r5g?1 :]e) ! c5tripetal =ce acts on ! body 9 its passage f ,h to ,k3 if ! c5tripetal =ce be weak en\gh1 ! l9es ,a ,h & ,a ,i drawn f ! c5t] ,a to ! body at ,h & at ,i %all be m obliquely incl9$ to ! curve1 ?an ! l9e ,a ,b is incl9$ t[>ds ,b ,g4 ,! c5tripetal =ce may be ( t /r5g? z to r5d] all ^! incl9ations equal1 or if /rong]1 ! incl9ations at ,i & ,k w be less oblique ?an at ,b4 ,sir ,,isaac ,,newton has p>ticul>ly %ewn1 t if ! c5tripetal p[] decreases aft] a c]ta9 mann] ) ! increase ( di/ance1 a body may describe su* a curve l9e1 t all ! l9es drawn f ! c5t] to ! body %all be equally incl9$ to t curve l9e4#hb ,b ,i d n "h ent] into any p>ticul>s1 my pres5t int5tion be+ only to %ew1 t x is possible = a body to be act$ ^u by a =ce cont9ually draw+ x d[n t[>ds a c5t]1 & yet t ! body %all cont9ue to rec$e f t c5t]2 = "h z long z ! l9es ,a ,h1 ,a ,i1 c drawn f ! c5t] ,a to ! body d n become less oblique to ! curve1 9 :i* ! body moves2 s long %all ^? l9es p]petually increase1 & consequ5tly ! body %all m & m rec$e f ! c5t]4 #g4 ,,b we may obs]ve f>!r1 t if ! c5tripetal p[]1 :ile ! body increases its di/ance f ! c5t]1 reta9 suffici5t /r5g? to make ! l9es drawn f ! c5t] to ! body to become at l5g? less oblique to ! curve2 !n if ?is dim9ution ( ! obliquity cont9ue1 till at la/ ! l9e drawn f ! c5t] to ! body %all cease to be obliquely incl9$ to ! curve1 & %all become p]p5dicul> !reto2 f ?is in/ant ! body %all no long] rec$e f ! c5t]1 b 9 its foll[+ motion x %all aga9 desc5d1 & %all describe a curve l9e 9 all respects l to t1 :i* x has describ$ already2 provid$ ! c5tripetal p[]1 e :]e at ! same di/ance f ! c5t]1 acts ) ! same /r5g?4 ,s we obs]v$ 9 ! prec$+ *apt]1 t1 :5 ! motion ( a projectile became p>allel to ! horizon1 ! projectile no long] asc5d$1 b =?) direct$ its c\rse d[nw>ds1 desc5d+ 9 a l9e altoge!r l t1 :]e9 x _h be=e asc5d$#hc4 #h4 ,,?is return ( ! body may be prov$ by ! foll[+ proposition3 t if ! body 9 any place1 suppose at ,i1 7 to be /opt1 & be ?r[n directly backw>d ) ! velocity1 :]e) x 0 mov+ =w>d 9 t po9t ,i2 !n ! body1 by ! action ( ! c5tripetal =ce ^u x1 w\ld move back aga9 ov] ! pa? ,i ,h ,b1 9 :i* x _h be=e advanc$ =w>d1 & w\ld arrive aga9 at ! po9t ,b 9 ! same space ( "t1 z 0 tak5 up 9 its passage f ,b to ,i2 ! velocity ( ! body at its return to ! po9t ,b be+ ! same1 z t :]e) x fir/ set out f t po9t4 ,to give a full demon/ration ( ?is proposition1 w\ld require t use ( ma!matics1 :i* ,i "h purpose to avoid2 b1 ,i believe1 x w appe> 9 great measure evid5t f ! foll[+ consid]ations4 #i4 ,,suppose 79 fig4 #ge47 t a body 7 c>ri$ aft] ! foll[+ mann] ?r\gh ! b5t figure ,a ,b ,c ,d ,e ,f1 compos$ ( ! /raight l9es ,a ,b1 ,b ,c1 ,c ,d1 ,d ,e1 ,e ,f4 ,fir/ let x be mov+ 9 ! l9e ,a ,b1 f ,a t[>ds ,b1 ) any uni=m velocity4 ,at ,b let ! body receive an impulse direct$ t[>d "s po9t1 z ,g1 tak5 )9 ! concavity ( ! figure4 ,n[ :]eas ?is body1 :5 once mov+ 9 ! /raight l9e ,a ,b1 w cont9ue to move on 9 ?is l9e1 s long z x %all be left to x self2 b be+ di/urb$ at ! po9t ,b 9 its motion by ! impulse1 :i* !re acts ^u x1 x w be turn$ out ( ?is l9e ,a ,b into "s o!r /raight l9e1 :]e9 x w aft]w>ds cont9ue to move1 z long z x %all be left to itself4 ,!re=e let ?is impulse h /r5g? suffici5t to turn ! body into ! l9e ,b ,c4 ,!n let ! body move on undi/urb$ f ,b to ,c1 b at ,c let x receive ano!r impulse po9t$ t[>d ! same po9t ,g1 & ( suffici5t /r5g? to turn ! body into ! l9e ,c ,d4 ,at ,d let a ?ird impulse1 direct$ l ! re/ to ! po9t ,g1 turn ! body into ! l9e ,d ,e4 ,& at ,e let ano!r impulse1 direct$ likewise to ! po9t ,g1 turn ! body into ! l9e ,e ,f4 ,n[1 ,i say1 if ! body :ile mov+ 9 ! l9e ,e ,f be /opt1 & turn$ back aga9 9 ?is l9e ) ! same velocity1 z t :]e) x 0 mov+ =w>d 9 ?is l9e2 !n by ! repetition ( ! =m] impulse at ,e ! body w be turn$ into ! l9e ,e ,d1 & move 9 x f ,e to ,d ) ! same velocity z be=e x mov$ ) f ,d to ,e2 by ! repetition ( ! impulse at ,d1 :5 ! body %all h return$ to t po9t1 x w be turn$ into ! l9e ,d ,c2 & by ! repetition ( ! o!r impulses at ,c & ,b ! body w be br\ght back aga9 into ! l9e ,b ,a1 ) ! velocity1 :]e) x fir/ mov$ 9 t l9e4 #aj4 ,,?is ,i prove z foll[s4 ,let ,d ,e & ,f ,e be cont9u$ beyond ,e4 ,9 ,d ,e ?us cont9u$ take at pleasure ! l5g? ,e ,h1 & let ,h ,i be s drawn1 z to be equidi/ant f ! l9e ,g ,e4 ,!n1 by :at has be5 writt5 ^u ! second law ( motion#hd1 x foll[s1 t aft] ! impulse on ! body 9 ,e x w move ?r\gh ,e ,i 9 ! same "t1 z x w\ld h imploy$ 9 mov+ f ,e to ,h1 ) ! velocity :i* x _h 9 ! l9e ,d ,e4 ,9 ,f ,e prolong$ take ,e ,k equal to ,e ,i1 & draw ,k ,l equidi/ant f ,g ,e4 ,!n1 because ! body is ?r[n back 9 ! l9e ,f ,e ) ! same velocity z t :]e) x w5t =w>d 9 t l9e2 if1 :5 ! body 0 return$ to ,e1 x 7 p]mitt$ to g /raight on1 x w\ld pass ?r\gh ,e ,k 9 ! same "t1 z x took up 9 pass+ ?r\gh ,e ,i1 :5 x w5t =w>d 9 ! l9e ,e ,f4 ,b1 if at ! body's return to ! po9t ,e1 su* an impulse direct$ t[>d ! po9t ,d 7 to be giv5 x1 :]eby x %\ld be turn$ into ! l9e ,d ,e2 ,i say1 t ! impulse necess>y to produce ?is effect mu/ be equal to t1 :i* turn$ ! body out ( ! l9e ,d ,e into ,e ,f2 & t ! velocity1 ) :i* ! body w return into ! l9e ,e ,d1 is ! same1 z t :]e) x be=e mov$ ?r\gh ?is l9e f ,d to ,e4 ,because ,e ,k is equal to ,e ,i1 & ,k ,l & ,h ,i1 be+ ea* equidi/ant f ,g ,e1 are by consequ5ce equidi/ant f ea* o!r2 x foll[s1 t ! two triangul> figures ,i ,e ,h & ,k ,e ,l are altoge!r l & equal to ea* o!r4 ,if ,i 7 writ+ to ma!maticians1 ,i might ref] !m to "s proportions 9 ! elem5ts ( ,,euclid = ! pro( ( ?is#he b z ,i d n "h address my self to su*1 s ,i ?9k ?is ass]tion w be evid5t en\gh )\t a pro( 9 =m2 at lea/ ,i mu/ desire my read]s to receive x z a proposition true 9 geometry4 ,b ^! two triangul> figures be+ altoge!r l ea* o!r & equal2 z ,e ,k is equal to ,e ,i1 s ,e ,l is equal to ,e ,h1 & ,k ,l equal to ,h ,i4 ,n[ ! body aft] its return to ,e be+ turn$ out ( ! l9e ,f ,e into ,e ,d by an impulse act+ ^u x 9 ,e1 aft] ! mann] above express$2 ! body w receive su* a velocity by ?is impulse1 z w c>ry x ?r\gh ,e ,l 9 ! same "t1 z x w\ld h imploy$ 9 pass+ ?r\gh ,e ,k1 if x _h gone on 9 t l9e undi/urb$4 ,& x has already be5 obs]v$1 t ! "t1 9 :i* ! body w\ld pass ov] ,e ,k ) ! velocity :]e) x returns1 is equal to ! "t x took up 9 go+ =w>d f ,e to ,i2 t is1 equal to ! "t1 9 :i* x w\ld h gone ?r\gh ,e ,h ) ! velocity1 :]e) x mov$ f ,d to ,e4 ,!re=e ! "t1 9 :i* ! body w pass ?r\gh ,e ,l aft] its return into ! l9e ,e ,d1 is ! same1 z w\ld h be5 tak5 up by ! body 9 pass+ ?r\gh ,e ,h ) ! velocity1 :]e) ! body fir/ mov$ 9 ! l9e ,d ,e4 ,s9ce !re=e ,e ,l & ,e ,h are equal1 ! body returns into ! l9e ,d ,e ) ! velocity1 :i* x _h be=e 9 t l9e4 ,aga9 ,i say1 ! second impulse 9 ,e is equal to ! fir/4 ,by :at has be5 said on ! second law ( motion conc]n+ ! effect ( oblique impulses#hf1 x w be und]/ood1 t ! impulse 9 ,e1 :]eby ! body 0 turn$ out ( ! l9e ,d ,e into ! l9e ,e ,f1 is ( su* /r5g?1 t if ! body _h be5 at re/1 :5 ?is impulse _h act$ ^u x1 ?is impulse w\ld h communicat$ s mu* motion to ! body1 z w\ld h c>ri$ x ?r\gh a l5g? equal to ,h ,i1 9 ! "t :]e9 ! body w\ld h pass$ f ,e to ,h1 or 9 ! "t :]e9 x pass$ f ,e to ,i4 ,9 ! same mann]1 on ! return ( ! body1 ! impulse 9 ,e1 :]eby ! body is turn$ out ( ! l9e ,f ,e into ,e ,d1 is ( su* /r5g?1 t if x _h act$ on ! body at re/1 x w\ld h caus$ ! body to move ?r\gh a l5g? equal to ,k ,l1 9 ! same "t1 z ! body w\ld imploy 9 pass+ ?r\gh ,e ,k ) ! velocity1 :]e) x returns 9 ! l9e ,f ,e4 ,!re=e ! second impulse1 _h x act$ on ! body at re/1 w\ld h caus$ x to move ?r\gh a l5g? equal to ,k ,l 9 ! same space ( "t1 z w\ld be tak5 up by ! body 9 pass+ ?r\gh a l5g? equal to ,h ,i1 7 ! fir/ impulse to act on ! body :5 at re/4 ,t is1 ! effects ( ! fir/ & second impulse on ! body :5 at re/ w\ld be ! same2 = ,k ,l & ,h ,i are equal3 consequ5tly ! second impulse is equal to ! fir/4 #aa4 ,,?us if ! body be return$ ?r\gh ,f ,e ) ! velocity1 :]e) x mov$ =w>d2 we h %ewn h[ by ! repetition ( ! impulse1 :i* act$ on x at ,e1 ! body w return aga9 into ! l9e ,d ,e ) ! velocity1 :i* x _h be=e 9 t l9e4 ,by ! same process ( reason+ x may be prov$1 t1 :5 ! body is return$ back to ,d1 ! impulse1 :i* be=e act$ on ! body at t po9t1 w ?r[ ! body into ! l9e ,d ,c ) ! velocity1 :i* x fir/ _h 9 t l9e2 & ! o!r impulses be+ successively repeat$1 ! body w at l5g? be br\ght back aga9 into ! l9e ,b ,a ) ! velocity1 :]e) x set out 9 t l9e4 #ab4 ,,?us ^! impulses1 by act+ ov] aga9 9 an inv]t$ ord] all _! op]ation on ! body1 br+ x back aga9 ?r\gh ! pa?1 9 :i* x _h proce$$ =w>d4 ,& ?is obta9s equally1 :atev] be ! numb] ( ! /raight l9es1 :]e( ?is curve figure is compos$4 ,n[ by a me?od ( reason+1 :i* ,sir ,,isaac ,,newton makes great use (1 & :i* he introduc$ into geometry1 !reby greatly inri*+ t sci5ce#hg2 we might make a transition f ?is figure compos$ ( a numb] ( /raight l9es to a figure ( "o cont9u$ curvature1 & f a numb] ( sep>ate impulses repeat$ at di/9ct int]vals to a cont9ual c5tripetal =ce1 & %ew1 t1 because :at has be5 "h advanc$ holds univ]sally true1 :atev] be ! numb] ( /raight l9es1 :]e( ! curve figure ,a ,c ,f is compos$1 & h[soev] frequ5tly ! impulses at ! angles ( ?is figure are repeat$2 !re=e ! same w /ill rema9 true1 al?\gh ?is figure %\ld be conv]t$ into "o ( a cont9u$ curvature1 & ^! di/9ct impulses %\ld be *ang$ into a cont9ual c5tripetal =ce4 ,b z ! expla9+ ?is me?od ( reason+ is =eign to my pres5t design2 s ,i hope my read]s1 aft] :at has be5 said1 w f9d no difficulty 9 receiv+ ! proposition laid d[n above3 t1 if ! body1 :i* has mov$ ?r\gh ! curve l9e ,b ,h ,i 79 fig4 #gd47 f ,b to ,i1 :5 x is come to ,i1 be ?r[n directly back ) ! same velocity z t1 :]e) x proce$$ =w>d1 ! c5tripetal =ce1 by act+ ov] aga9 all its op]ation on ! body1 %all br+ ! body back aga9 9 ! l9e ,i ,h ,b3 & z ! motion ( ! body 9 its c\rse f ,b to ,i 0 e :]e 9 su* a mann] oblique to ! l9e drawn f ! c5t] to ! body1 t ! c5tripetal p[] act$ 9 "s degree aga9/ ! body's motion1 & gradually dim9i%$ x2 s 9 ! return ( ! body1 ! c5tripetal p[] w e :]e draw ! body =w>d1 & accel]ate its motion by ! same degrees1 z be=e x ret>d$ x4 #ac4 ,,?is be+ agre$1 suppose ! body 9 ,k to h ! l9e ,a ,k no long] obliquely incl9$ to its motion4 ,9 ?is case1 if ! body be turn$ back1 9 ! mann] we h be5 consid]+1 x mu/ be direct$ back p]p5dicul>ly to ,a ,k4 ,b if x _h proce$$ =w>d1 x w\ld likewise h mov$ 9 a direction p]p5dicul> to ,a ,k2 consequ5tly1 :e!r x move f ?is po9t ,k backw>d or =w>d1 x mu/ describe ! same k9d ( c\rse4 ,!re=e s9ce by be+ turn$ back x w g ov] aga9 ! l9e ,k ,i ,h ,b2 if x be p]mitt$ to g =w>d1 ! l9e ,k ,l1 :i* x %all describe1 w be altoge!r simil> to ! l9e ,k ,h ,b4 #ad4 ,,9 l mann] we may det]m9e ! nature ( ! motion1 if ! l9e1 :]e9 ! body sets out1 be incl9$ 7z 9 fig4 #gf47 d[n t[>d ! l9e ,b ,a drawn betwe5 ! body & ! c5t]4 ,if ! c5tripetal p[] s mu* increases 9 /r5g?1 z ! body approa*es1 t x c b5d ! pa?1 9 :i* ! body moves1 to t degree1 z to cause all ! l9es z ,a ,h1 ,a ,i1 ,a ,k to rema9 no less oblique to ! motion ( ! body1 ?an ,a ,b is oblique to ,b ,c2 ! body %all cont9ually m & m approa* ! c5t]4 ,b if ! c5tripetal p[] increases 9 s mu* less a degree1 z to p]mit ! l9e drawn f ! c5t] to ! body1 z x accompanies ! body 9 its motion1 at l5g? to become m & m erect to ! curve :]e9 ! body moves1 & 9 ! end1 suppose at ,k1 to become p]p5dicul> !reto2 f t "t ! body %all rise aga94 ,?is is evid5t f :at has be5 said above2 because = ! v same reason "h also ! body %all proce$ f ! po9t ,k to describe a l9e altoge!r simil> to ! l9e1 9 :i* x has mov$ f ,b to ,k4 ,?us1 z x 0 obs]v$ ( ! p5dulum 9 ! prec$+ *apt]#hh1 t all ! "t x approa*es t[>ds be+ p]p5dicul> to ! horizon1 x m & m desc5ds2 b1 z soon z x is come into t p]p5dicul> situation1 x imm$iately rises aga9 by ! same degrees1 z x desc5d$ by be=e3 s "h ! body m & m approa*es ! c5t] all ! "t x is mov+ f ,b to ,k2 b !nce =w>d x rises f ! c5t] aga9 by ! same degrees1 z x approa*$ by be=e4 #ae4 ,,if 79 fig4 #gg47 ! l9e ,b ,c be p]p5dicul> to ,a ,b2 !n x has be5 obs]v$ above#hi1 t ! c5tripetal p[] may be s balanc$ ) ! progressive motion ( ! body1 t ! body may keep mov+ r\nd ! c5t] ,a con/antly at ! same di/ance2 z a body does1 :5 :irl$ ab\t any po9t1 to :i* x is ty$ by a /r+4 ,if ! c5tripetal p[] be too weak to produce ?is effect1 ! motion ( ! body w pres5tly become oblique to ! l9e drawn f itself to ! c5t]1 aft] ! mann] ( ! fir/ ( ! two cases1 :i* we h be5 consid]+4 ,if ! c5tripetal p[] be /rong]1 ?an :at is requir$ to c>ry ! body 9 a circle1 ! motion ( ! body w pres5tly fall 9 ) ! second ( ! cases1 we h be5 consid]+4 #af4 ,,if ! c5tripetal p[] s *ange ) ! *ange ( di/ance1 t ! body1 aft] its motion has become oblique to ! l9e drawn f itself to ! c5t]1 %all aga9 become p]p5dicul> !reto2 :i* we h %ewn to be possible 9 bo? ! cases treat$ ( above2 !n ! body %all 9 its subsequ5t motion return aga9 to ! di/ance ( ,a ,b1 & f t di/ance take a c\rse simil> to ! =m]3 & ?us1 if ! body move 9 a space free f all resi/ance1 :i* has be5 "h all along suppos$2 x %all cont9ue 9 a p]petual motion ab\t ! c5t]1 desc5d+ & asc5d+ alt]nately !refrom4 ,if ! body sett+ out f ,b 79 fig4 #gh47 9 ! l9e ,b ,c p]p5dicul> to ,a ,b1 describe ! l9e ,b ,d ,e1 :i* 9 ,d %all be oblique to ! l9e ,a ,d1 b 9 ,e %all aga9 become erect to ,a ,e drawn f ! body 9 ,e to ! c5t] ,a2 !n f ?is po9t ,e ! body %all describe ! l9e ,e ,f ,g altoge!r l to ! l9e ,b ,d ,e1 & at ,g %all be at ! same di/ance f ,a1 z x 0 at ,b4 ,b likewise ! l9e ,a ,g %all be erect to ! body's motion4 ,!re=e ! body %all proce$ to describe f ,g ! l9e ,g ,h ,i altoge!r simil> to ! l9e ,g ,f ,e1 & at ,i h ! same di/ance f ! c5t]1 z x _h at ,e2 & also h ! l9e ,a ,i erect to its motion3 s t its foll[+ motion mu/ be 9 ! l9e ,i ,k ,l simil> to ,i ,h ,g1 & ! di/ance ,a ,l equal to ,a ,g4 ,?us ! body w g on 9 a p]petual r\nd )\t ceas+1 alt]nately inl>g+ & contract+ its di/ance f ! c5t]4 ,illu/ration #ag4 ,,if x s happ51 t ! po9t ,e fall ^u ! l9e ,b ,a cont9u$ beyond ,a2 !n ! po9t ,g w fall on ,b1 ,i on ,e1 & ,l also on ,b2 s t ! body w describe 9 ?is case a simple curve l9e r\nd ! c5t] ,a1 l ! l9e ,b ,d ,e ,f 9 fig4 #gi1 9 :i* x w cont9ually revolve f ,b to ,e & f ,e to ,b )\t end4 #ah4 ,,if ,a ,e 9 fig4 #gh %\ld happ5 to be p]p5dicul> to ,a ,b1 9 ?is case also a simple l9e w be describ$2 = ! po9t ,g w fall on ! l9e ,b ,a prolong$ beyond ,a1 ! po9t ,i on ! l9e ,a ,e prolong$ beyond ,a1 & ! po9t ,l on ,b3 s t ! body w describe a l9e l ! curve l9e ,b ,e ,g ,i 9 fig4 #hj1 9 :i* ! opposite po9ts ,b & ,g are equally di/ant f ,a1 & ! opposite po9ts ,e & ,i are also equally di/ant f ! same po9t ,a4 #ai4 ,,9 o!r cases ! l9e describ$ w h a m complex figure4 #bj4 ,,?us we h endeav\r$ to %ew h[ a body1 :ile x is con/antly attract$ t[>ds a c5t]1 may not)/&+ by its progressive motion keep x self f fall+ d[n to t c5t]2 b describe ab\t x an endless circuit1 sometimes approa*+ t[>d t c5t]1 & at o!r times z mu* rec$+ f ! same4 #ba4 ,,b "h we h suppos$1 t ! c5tripetal p[] is ( equal /r5g? e :]e at ! same di/ance f ! c5t]4 ,& ?is is ! case ( t c5tripetal p[]1 :i* w h]eaft] be %ewn to be ! cause1 t keeps ! planets 9 _! c\rses4 ,b a body may be kept on 9 a p]petual circuit r\nd a c5t]1 al?\gh ! c5tripetal p[] h n ?is prop]ty4 ,inde$ a body may by a c5tripetal =ce be kept mov+ 9 any curve l9e :atev]1 t %all h its concavity turn$ e :]e t[>ds ! c5t] ( ! =ce4 #bb4 ,,to make ?is evid5t ,i %all fir/ propose ! case ( a body mov+ ?r\gh ! incurvat$ figure ,a ,b ,c ,d ,e 79 fig4 #ha47 :i* is compos$ ( ! /raight l9es ,a ,b1 ,b ,c1 ,c ,d1 ,d ,e1 & ,e ,a2 ! motion be+ c>ri$ on 9 ! foll[+ mann]4 ,let ! body fir/ move 9 ! l9e ,a ,b ) any uni=m velocity4 ,:5 x is arriv$ at ! po9t ,b1 let x receive an impulse direct$ t[>d any po9t ,f tak5 )9 ! figure2 & let ! impulse be ( t /r5g? z to turn ! body out ( ! l9e ,a ,b into ! l9e ,b ,c4 ,! body aft] ?is impulse1 :ile left to itself1 w cont9ue mov+ 9 ! l9e ,b ,c4 ,at ,c let ! body receive ano!r impulse direct$ t[>ds ! same po9t ,f1 ( su* /r5g?1 z to turn ! body f ! l9e ,b ,c into ! l9e ,c ,d4 ,at ,d let ! body by ano!r impulse1 direct$ likewise to ! po9t ,f1 be turn$ out ( ! l9e ,c ,d into ,d ,e4 ,& at ,e let ano!r impulse1 direct$ t[>d ! po9t ,f1 turn ! body f ! l9e ,d ,e into ,e ,a4 ,?us we see h[ a body may be c>ri$ ?r\gh ! figure ,a ,b ,c ,d ,e by c]ta9 impulses direct$ always t[>d ! same c5t]1 only by _! act+ on ! body at prop] int]vals1 & ) due degrees ( /r5g?4 #bc4 ,,b f>!r1 :5 ! body is come to ! po9t ,a1 if x !re receive ano!r impulse direct$ l ! re/ t[>d ! po9t ,f1 & ( su* a degree ( /r5g? z to turn ! body into ! l9e ,a ,b1 :]e9 x fir/ mov$2 ,i say t ! body %all return into ?is l9e ) ! same velocity1 z x _h at fir/4 #bd4 ,,let ,a ,b be prolong$ beyond ,b at pleasure1 suppose to ,g2 & f ,g let ,g ,h be drawn1 :i* if produc$ %\ld always cont9ue equidi/ant f ,b ,f1 or1 accord+ to ! m usual phrase1 let ,g ,h be drawn p>allel to ,b ,f4 ,!n x appe>s1 f :at has be5 said ^u ! second law ( motion#ij1 t 9 ! "t1 :]e9 ! body w\ld h mov$ f ,b to ,g1 _h x n receiv$ a new impulse 9 ,b1 by ! means ( t impulse x w h acquir$ a velocity1 :i* w c>ry x f ,b to ,h4 ,aft] ! same mann]1 if ,c ,i be tak5 equal to ,b ,h1 & ,i ,k be drawn equidi/ant f or p>allel to ,c ,f2 ! body w h mov$ f ,c to ,k ) ! velocity1 :i* x has 9 ! l9e ,c ,d1 9 ! same "t1 z x w\ld h employ$ 9 mov+ f ,c to ,i ) ! velocity1 x _h 9 ! l9e ,b ,c4 ,!re=e s9ce ,c ,i & ,b ,h are equal1 ! body w move ?r\gh ,c ,k 9 ! same "t1 z x w\ld h tak5 up 9 mov+ f ,b to ,g ) ! orig9al velocity1 :]e) x mov$ ?r\gh ! l9e ,a ,b4 ,aga91 ,d ,l be+ tak5 equal to ,c ,k & ,l ,m drawn p>allel to ,d ,f2 = ! same reason z be=e ! body w move ?r\gh ,d ,m ) ! velocity1 :i* x has 9 ! l9e ,d ,e1 9 ! same "t1 z x w\ld imploy 9 mov+ ?r\gh ,b ,g ) its orig9al velocity4 ,9 ! la/ place1 if ,e ,n be tak5 equal to ,d ,m1 & ,n ,o be drawn p>allel to ,e ,f2 likewise if ,a ,p be tak5 equal to ,e ,o1 & ,p ,q be drawn p>allel to ,a ,f3 !n ! body ) ! velocity1 :]e) x returns into ! l9e ,a ,b1 w pass ?r\gh ,a ,q 9 ! same "t1 z x w\ld h imploy$ 9 pass+ ?r\gh ,b ,g ) its orig9al velocity4 ,n[ z all ?is foll[s directly f :at has above be5 deliv]$1 conc]n+ ! effect ( oblique impulses impress$ ^u bodies 9 motion2 s we mu/ "h obs]ve f>!r1 t x c be prov$ by geometry1 t ,a ,q w always be equal to ,e ,g4 ,! pro( ( ?is ,i am oblig$1 f ! nature ( my pres5t design1 to omit2 b ?is geometrical proportion be+ grant$1 x foll[s1 t ! body has return$ into ! l9e ,a ,b ) ! velocity1 :i* x _h1 :5 x fir/ mov$ 9 t l9e2 = ! velocity1 ) :i* x returns into ! l9e ,a ,b1 w c>ry x ov] ! l9e ,a ,q 9 ! same "t1 z w\ld h be5 tak5 up 9 its pass+ ov] an equal l9e ,b ,g ) ! orig9al velocity4 #be4 ,,?us we h f\nd1 h[ a body may be c>ri$ r\nd ! figure ,a ,b ,c ,d ,e by ! action ( c]ta9 impulses ^u x :i* %\ld all be po9t$ t[>d "o c5t]4 ,& we likewise see1 t :5 ! body is br\ght back aga9 to ! po9t1 :5ce x fir/ set out2 if x !re meet ) an impulse suffici5t to turn x aga9 into ! l9e1 :]e9 x mov$ at fir/1 its orig9al velocity w be aga9 re/or$2 & by ! repetition ( ! same impulses1 ! body w be c>ri$ aga9 9 ! same r\nd4 ,!re=e if ^! impulses1 :i* act on ! body at ! po9ts ,b1 ,c1 ,d1 ,e1 & ,a1 cont9ue always ! same1 ! body w make r\nd ?is figure innum]able revolutions4 #bf4 ,,! pro(1 :i* we h "h made use (1 holds ! same 9 any numb] ( /raight l9es1 :]e( ! figure ,a ,b ,d %\ld be compos$2 & !re=e by ! me?od ( reason+ ref]r$ to above#ia we are to conclude1 t :at has "h be5 said ^u ?is rectil9e> figure1 w rema9 true1 if ?is figure 7 *ang$ into "o ( a cont9u$ curvature1 & in/ead ( di/9ct impulses act+ by int]vals at ! angles ( ?is figure1 we _h a cont9ual c5tripetal =ce4 ,we h !re=e %ewn1 t a body may be c>ri$ r\nd 9 any curve figure ,a ,b ,c 7 fig4 #hb47 :i* %all e :]e be concave t[>ds any "o po9t z ,d1 by ! cont9ual action ( a c5tripetal p[] direct$ to t po9t1 & :5 x is return$ to ! po9t1 f :5ce x set out1 x %all recov] aga9 ! velocity1 ) :i* x dep>t$ f t po9t4 ,x is n inde$ always necess>y1 t x %\ld return aga9 into its fir/ c\rse2 = ! curve l9e may h "s su* figure z ! l9e ,a ,b ,c ,d ,b ,e 9 fig4 #hc4 ,9 ?is curve l9e1 if ! body set out f ,b 9 ! direction ,b ,f1 & mov$ ?r\gh ! l9e ,b ,c ,d1 till x return$ to ,b2 "h ! body w\ld n ent] aga9 into ! l9e ,b ,c ,d1 because ! two p>ts ,b ,d & ,b ,c ( ! curve l9e make an angle at ! po9t ,b3 s t ! c5tripetal p[]1 :i* at ! po9t ,b c\ld turn ! body f ! l9e ,b ,f into ! curve1 w n be able to turn ! body into ! l9e ,b ,c f ! direction1 9 :i* x returns to ! po9t ,b2 a =ceable impulse mu/ be giv5 ! body 9 ! po9t ,b to produce t effect4 #bg4 ,,if at ! po9t ,b1 :5ce ! body sets out1 ! curve l9e return into x self 7z 9 fig4 #hb27 !n ! body1 ^u its arrival aga9 at ,b1 may return into its =m] c\rse1 & ?us make an endless circuit ab\t ! c5t] ( ! c5tripetal p[]4 #bh4 ,,:at has "h be5 said1 ,i hope1 w 9 "s measure enable my read]s to =m a j idea ( ! nature ( ^! c5tripetal motions4 #bi4 ,i ,,h n attempt$ to %ew1 h[ to f9d p>ticul>ly1 :at k9d ( c5tripetal =ce is necess>y to c>ry a body 9 any curve l9e propos$4 ,?is is to be d$uc$ f ! degree ( curvature1 :i* ! figure has 9 ea* po9t ( x1 & requires a long & complex ma!matical reason+4 ,h[ev] ,i %all speak a little to ! fir/ proportion1 :i* ,sir ,,isaac ,,newton lays d[n = ?is purpose4 ,by ?is proposition1 :5 a body is f\nd mov+ 9 a curve l9e1 x may be kn[n1 :e!r ! body be kept 9 its c\rse by a p[] always po9t$ t[>d ! same c5t]2 & if x be s1 :]e t c5t] is plac$4 ,! proposition is ?is3 t if a l9e be drawn f "s fix$ po9t to ! body1 & rema9+ by "o extream unit$ to t po9t1 x be c>ri$ r\nd along ) ! body2 !n1 if ! p[]1 :]eby ! body is kept 9 its c\rse1 be always po9t$ to ?is fix$ po9t z a c5t]1 ?is l9e w move ov] equal spaces 9 equal portions ( "t4 ,suppose a body 7 mov+ ?r\gh ! curve l9e ,a ,b ,c ,d 79 fig4 #hd47 & pass$ ov] ! ar*es ,a ,b1 ,b ,c1 ,c ,d 9 equal portions ( "t2 !n if a po9t1 z ,e1 c be f\nd1 f :5ce ! l9e ,e ,a be+ drawn to ! body 9 ,a1 & accompany+ ! body 9 its motion1 x %all make ! spaces ,e ,a ,b1 ,e ,b ,c1 & ,e ,c ,d equal1 ov] :i* x passes1 :ile ! body describes ! ar*es ,a ,b1 ,b ,c1 & ,c ,d3 & if ?is hold ! same 9 all o!r ar*es1 bo? great & small1 ( ! curve l9e ,a ,b ,c ,d1 t ^! spaces are always equal1 :]e ! times are equal2 !n is ! body kept 9 ?is l9e by a p[] always po9t$ to ,e z a c5t]4 #cj4 ,,! pr9ciple1 ^u :i* ,sir ,,isaac ,,newton has demon/rat$ ?is1 requires b small skill 9 geometry to compreh5d4 ,i %all !re=e take ! lib]ty to close ! pres5t *apt] ) an explication ( x2 because su* an example w give ! cle>e/ notion ( our au?or's me?od ( apply+ ma!matical reason+ to ^! philosophical subjects4 #ca4 ,,he reasons ?us4 ,suppose a body set out f ! po9t ,a 79 fig4 #he47 to move 9 ! /raight l9e ,a ,b2 & aft] x _h mov$ = "s "t 9 t l9e1 x 7 to receive an impulse direct$ to "s po9t z ,c4 ,let x receive t impulse at ,d2 & !reby be turn$ into ! l9e ,d ,e2 & let ! body aft] ?is impulse take ! same l5g? ( "t 9 pass+ f ,d to ,e1 z x imploy$ 9 ! pass+ f ,a to ,d4 ,!n ! /raight l9es ,c ,a1 ,c ,d1 & ,c ,e be+ drawn1 ,sir ,,isaac ,,newton proves1 t ! & triangul> spaces ,c ,a ,d & ,c ,d ,e are equal4 ,?is he does 9 ! foll[+ mann]4 #cb4 ,,let ,e ,f be drawn p>allel to ,c ,d4 ,!n1 f :at has be5 said ^u ! second law ( motion#ib1 x is evid5t1 t s9ce ! body 0 mov+ 9 ! l9e ,a ,b1 :5 x receiv$ ! impulse 9 ! direction ,d ,c2 x w h mov$ aft] t impulse ?r\gh ! l9e ,d ,e 9 ! same "t1 z x w\ld h tak5 up 9 mov+ ?r\gh ,d ,f1 provid$ x _h receiv$ no di/urbance 9 ,d4 ,b ! "t ( ! body's mov+ f ,d to ,e is suppos$ to be equal to ! "t ( its mov+ ?r\gh ,a ,d2 !re=e ! "t1 :i* ! body w\ld h imploy$ 9 mov+ ?r\gh ,d ,f1 _h x n be5 di/urb$ 9 ,d1 is equal to ! "t1 :]e9 x mov$ ?r\gh ,a ,d3 consequ5tly ,d ,f is equal 9 l5g? to ,a ,d2 = if ! body _h gone on to move ?r\gh ! l9e ,a ,b )\t int]ruption1 x w\ld h mov$ ?r\gh all p>ts !re( ) ! same velocity1 & h pass$ ov] equal p>ts ( t l9e 9 equal portions ( "t4 ,n[ ,c ,f be+ drawn1 s9ce ,a ,d & ,d ,f are equal1 ! triangul> space ,c ,d ,f is equal to ! triangul> space ,c ,a ,d4 ,f>!r1 ! l9e ,e ,f be+ p>allel to ,c ,d1 x is prov$ by ,,euclid1 t ! triangle ,c ,e ,d is equal to ! triangle ,c ,f ,d#ic3 !re=e ! triangle ,c ,e ,d is equal to ! triangle ,c ,a ,d4 #cc4 ,,aft] ! same mann]1 if ! body receive at ,e ano!r impulse direct$ t[>d ! po9t ,c1 & be turn$ by t impulse into ! l9e ,e ,g2 if x move aft]w>ds f ,e to ,g 9 ! same space ( "t1 z 0 tak5 up by its motion f ,d to ,e1 or f ,a to ,d2 !n ,c ,g be+ drawn1 ! triangle ,c ,e ,g is equal to ,c ,d ,e4 ,a ?ird impulse at ,g direct$ z ! two =m] to ,c1 :]eby ! body %all be turn$ into ! l9e ,g ,h1 w h also ! l effect ) ! re/4 ,if ! body move ov] ,g ,h 9 ! same "t1 z x took up 9 mov+ ov] ,e ,g1 ! triangle ,c ,g ,h w be equal to ! triangle ,c ,e ,g4 ,la/ly1 if ! body at ,h be turn$ by a fre% impulse direct$ t[>d ,c into ! l9e ,h ,i1 & at ,i by ano!r impulse direct$ also to ,c be turn$ into ! l9e ,i ,k2 & if ! body move ov] ea* ( ! l9es ,h ,i1 & ,i ,k 9 ! same "t1 z x imploy$ 9 mov+ ov] ea* ( ! prec$+ l9es ,a ,d1 ,d ,e1 ,e ,g1 & ,g ,h3 !n ea* ( ! triangles ,c ,h ,i1 & ,c ,i ,k w be equal to ea* ( ! prec$+4 ,likewise z ! "t1 9 :i* ! body moves ov] ,a ,d ,e1 is equal to ! "t ( its mov+ ov] ,e ,g ,h1 & to ! "t ( its mov+ ov] ,h ,i ,k2 ! space ,c ,a ,d ,e w be equal to ! space ,c ,e ,g ,h1 & to ! space ,c ,h ,i ,k4 ,9 ! same mann] z ! "t1 9 :i* ! body mov$ ov] ,a ,d ,e ,g is equal to ! "t ( its mov+ ov] ,g ,h ,i ,k1 s ! space ,c ,a ,d ,e ,g w be equal to ! space ,c ,g ,h ,i ,k4 #cd4 ,,f ?is pr9ciple ,sir ,,isaac ,,newton demon/rates ! proposition m5tion$ above1 by t me?od ( argu+ introduc$ by him into geometry1 :]e( we h be=e tak5 notice#id1 by mak+ accord+ to ! pr9ciples ( t me?od a transition f ?is incurvat$ figure compos$ ( /raight l9es1 to a figure ( cont9u$ curvature2 & by %ew+1 t s9ce equal spaces are describ$ 9 equal times 9 ?is pres5t figure compos$ ( /raight l9es1 ! same relation betwe5 ! spaces describ$ & ! times ( _! description w also h place 9 a figure ( "o cont9u$ curvature4 ,he also d$uces f ?is proposition ! rev]se ( x2 & proves1 t :5ev] equal spaces are cont9ually describ$2 ! body is act$ ^u by a c5tripetal =ce direct$ to ! c5t]1 at :i* ! spaces t]m9ate4 ,,*ap4 ,,iv4 ,( ! ,,resi/ance ( ,,fluids4 ,,be=e ! cause c be discov]$1 :i* keeps ! planets 9 motion1 x is necess>y fir/ to "k1 :e!r ! space1 :]e9 !y move1 is empty & void1 or fill$ ) any quantity ( matt]4 ,x has be5 a prevail+ op9ion1 t all space conta9s 9 x matt] ( "s k9d or o!r2 s t :]e no s5sible matt] is f\nd1 !re 0 yet a subtle fluid sub/ance by :i* ! space 0 fill$ up2 ev5 s z to make an absolute pl5itude4 ,9 ord] to exam9e ?is op9ion1 ,sir ,,isaac ,,newton has l>gely consid]$ ! effects ( fluids ^u bodies mov+ 9 !m4 #b4 ,,^! effects he has r$uc$ "u ^! ?ree heads4 ,9 ! fir/ place he %ews h[ to det]m9e 9 :at mann] ! resi/ance1 :i* bodies suff]1 :5 mov+ 9 a fluid1 gradually increases 9 proportion to ! space1 !y describe 9 any fluid2 to ! velocity1 ) :i* !y describe x2 & to ! "t !y h be5 9 motion4 ,"u ! second head he consid]s :at degree ( resi/ance diff]5t bodies mov+ 9 ! same fluid und]go1 accord+ to ! diff]5t proportion betwe5 ! d5sity ( ! fluid & ! d5sity ( ! body4 ,! d5sities ( bodies1 :e!r fluid or solid1 are measur$ by ! quantity ( matt]1 :i* is compreh5d$ "u ! same magnitude2 t body be+ ! mo/ d5se or compact1 :i* "u ! same bulk conta9s ! greate/ quantity ( solid matt]1 or :i* weighs mo/1 ! weight ( e body be+ obs]v$ above to be proportional to ! quantity ( matt] 9 x#ie4 ,?us wat] is m d5se ?an cork or wood1 iron m d5se ?an wat]1 & gold ?an iron4 ,! ?ird p>ticul> ,sir ,,is4 ,,newton consid]s conc]n+ ! resi/ance ( fluids is ! influ5ce1 :i* ! div]sity ( figure 9 ! resi/$ body has ^u its resi/ance4 #c4 ,,= ! m p]fect illu/ration ( ! fir/ ( ^! heads1 he di/9ctly %ews ! relation betwe5 all ! p>ticul>s specifi$ ^u ?ree diff]5t suppositions4 ,! fir/ is1 t ! same body be resi/$ m or less 9 ! simple proportion to its velocity2 s t if its velocity be d\bl$1 its resi/ance %all become ?reefold4 ,! second is ( ! resi/ance increas+ 9 ! duplicate proportion ( ! velocity2 s t1 if ! velocity ( a body be d\bl$1 its resi/ance %all be r5d]$ f\r times2 & if ! velocity be trebl$1 n9e times z great z at fir/4 ,b :at is to be und]/ood by duplicate proportion has be5 already expla9$#if4 ,! ?ird supposition is1 t ! resi/ance increases p>tly 9 ! s+le proportion ( ! velocity1 & p>tly 9 ! duplicate proportion !re(4 #d4 ,,9 all ^! suppositions1 bodies are consid]$ "u two respects1 ei!r z mov+1 & oppos+ !mselves aga9/ ! fluid by t p[] alone1 :i* is ess5tial to !m1 ( resi/+ to ! *ange ( _! /ate f re/ to motion1 or f motion to re/1 :i* we h above call$ _! p[] ( inactivity2 or else1 z desc5d+ or asc5d+1 & s hav+ ! p[] ( gravity comb9$ ) t o!r p[]4 ,?us our au?or has %ewn 9 all ^? ?ree suppositions1 9 :at mann] bodies are resi/$ 9 an uni=m fluid1 :5 !y move ) ! a=esaid progressive motion#ig2 & :at ! resi/ance is1 :5 !y asc5d or desc5d p]p5dicul>ly#ih4 ,& if a body asc5d or desc5d obliquely1 & ! resi/ance be s+ly proportional to ! velocity1 x is %ewn h[ ! body is resi/$ 9 a fluid ( an uni=m d5sity1 & :at l9e x w describe#ii1 :i* is det]m9$ by ! measurem5t ( ! hyp]bola1 & appe>s to be no o!r ?an t l9e1 fir/ consid]$ 9 p>ticul> by ,dr4 ,,b>r[#ajj1 :i* is n[ commonly kn[n by ! "n ( ! log>i?mical curve4 ,9 ! supposition t ! resi/ance increases 9 ! duplicate proportion ( ! velocity1 our au?or has n giv5 u ! l9e :i* w\ld be describ$ 9 an uni=m fluid2 b has in/ead !re( discuss$ a problem1 :i* is 9 "s sort ! rev]se2 to f9d ! d5sity ( ! fluid at all altitudes1 by :i* any giv5 curve l9e may be describ$2 :i* problem is s treat$ by him1 z to be applicable to any k9d ( resi/ance :atev]#aja4 ,b "h n unm9dful ( practice1 he %ews t a body 9 a fluid ( uni=m d5sity1 l ! air1 w describe a l9e1 :i* approa*es t[>ds an hyp]bola2 t is1 its motion w be ne>] to t curve l9e ?an to ! p>abola4 ,& consequ5t ^u ?is rem>k1 he %ews h[ to det]m9e ?is hyp]bola by exp]im5t1 & briefly resolves ! *ief ( ^? problems relat+ to projectiles1 :i* are 9 use 9 ! art ( gunn]y1 9 ?is curve#ajb2 z ,,torricelli & o!rs h done 9 ! p>abola#ajc1 ^: inv5tions h be5 expla9$ at l>ge above#ajd4 #e4 ,,our au?or has also h&l$ di/9ctly t p>ticul> sort ( motion1 :i* is describ$ by p5dulums#aje2 & has likewise consid]$ "s few cases ( bodies mov+ 9 resi/+ fluids r\nd a c5t]1 to :i* !y are impell$ by a c5tripetal =ce1 9 ord] to give an idea ( ^? k9ds ( motions#ajf4 #f4 ,,! treat+ ( ! resi/ance ( p5dulums has giv5 him an opportunity ( ins]t+ into ano!r "p ( 8 "w "s speculations ^u ! motions ( !m )\t resi/ance1 :i* h a v peculi> elegance2 :]e 9 he treats ( !m z mov$ by a gravitation act+ 9 ! law1 :i* he %ews to belong to ! e>? bel[ its surface#ajg2 p]=m+ 9 ?is k9d ( gravitation1 :]e ! =ce is proportional to ! di/ance f ! c5t]1 all t ,,huyg5s _h be=e done 9 ! common supposition ( its be+ uni=m1 & act+ 9 p>allel l9es#ajh4 #g4 ,,huyg5s at ! end ( 8 treatise ( ! cause ( gravity#aji in=ms u1 t he likewise _h c>ri$ 8 speculations on ! fir/ ( ^! suppositions1 ( ! resi/ance 9 fluids be+ proportional to ! velocity ( ! body1 z f> z our au?or4 ,b f9d+ by exp]im5t t ! second 0 m con=mable to nature1 he aft]w>ds made "s progress 9 t1 till he 0 /opt1 by n be+ able to execute to 8 wi% :at relat$ to ! p]p5dicul> desc5t ( bodies2 n obs]v+ t ! measurem5t ( ! curve l9e1 he made use ( to expla9 x by1 dep5d$ on ! hyp]bola4 ,:i* ov]sight may well be p>don$ 9 t great man1 consid]+ t our au?or _h n be5 pleas$ at t "t to communicate to ! publick 8 admirable disc\rse ( ! ,,quadrature or ,,measurem5t ,,( ,,curve ,,l9es1 ) :i* he has s9ce oblig$ ! _w3 = )\t ! use ( t treatise1 x is ,i ?9k no injury ev5 to our au?or's unp>allel$ abilities to believe1 x w\ld n h be5 easy = himself to h succe$$ s happily 9 ?is & _m o!r p>ts ( 8 writ+s4 #h4 ,,:at ,,huyg5s f\nd by exp]im5t1 t bodies 7 9 reality resi/$ 9 ! duplicate proportion ( _! velocity1 agrees ) ! reason+ ( our au?or#aaj1 :o di/+ui%es ! resi/ance1 :i* fluids give to bodies by ! t5acity ( _! p>ts1 & ! friction betwe5 !m & ! body1 f t1 :i* arises f ! p[] ( inactivity1 ) :i* ! con/itu5t p>ticles ( fluids are endu$ l all o!r portions ( matt]1 by :i* p[] ! p>ticles ( fluids l o!r bodies make resi/ance aga9/ be+ put into motion4 #i4 ,,! resi/ance1 :i* arises f ! friction ( ! body aga9/ ! p>ts ( ! fluid1 mu/ be v inconsid]able2 & ! resi/ance1 :i* foll[s f ! t5acity ( ! p>ts ( fluids1 is n usually v great1 & does n dep5d mu* ^u ! velocity ( ! body 9 ! fluid2 = z ! p>ts ( ! fluid adh]e toge!r ) a c]ta9 degree ( =ce1 ! resi/ance1 :i* ! body receives f !nce1 _c mu* dep5d ^u ! velocity1 ) :i* ! body moves2 b l ! p[] ( gravity1 its effect mu/ be proportional to ! "t ( its act+4 ,?is ! read] may f9d f>!r expla9$ by ,sir ,,isaac ,,newton himself 9 ! po/script to a disc\rse publi%$ by me 9 ,,! ,,philosophical ,,transactions1 ,no #cga4 ,! pr9cipal resi/ance1 :i* mo/ fluids give to bodies1 arises f ! p[] ( inactivity 9 ! p>ts ( ! fluids1 & ?is dep5ds ^u ! velocity1 ) :i* ! body moves1 on a d\ble acc\nt4 ,9 ! fir/ place1 ! quantity ( ! fluid mov$ out ( place by ! mov+ body 9 any det]m9ate space ( "t is proportional to ! velocity1 :]e) ! body moves2 & 9 ! next place1 ! velocity ) :i* ea* p>ticle ( ! fluid is mov$1 w also be proportional to ! velocity ( ! body3 !re=e s9ce ! resi/ance1 :i* any body makes aga9/ be+ put into motion1 is proportional bo? to ! quantity ( matt] mov$ & ! velocity x is mov$ )2 ! resi/ance1 :i* a fluid gives on ?is acc\nt1 w be d\bly increas$ ) ! increase ( ! velocity 9 ! mov+ body2 t is1 ! resi/ance w be 9 a two-fold or duplicate proportion ( ! velocity1 :]e) ! body moves ?r\gh ! fluid4 #aj4 ,,f>!r x is mo/ manife/1 t ?is latt] k9d ( resi/ance increas+ ) ! increase ( velocity1 ev5 9 a great] degree ?an ! velocity x self increases1 ! swift] ! body moves1 ! less proportion ! o!r species ( resi/ance w be> to ?is3 nay t ?is "p ( ! resi/ance may be s mu* augm5t$ by a due increase ( velocity1 till ! =m] resi/ances %all be> a less proportion to ?is1 ?an any t might be assign$4 ,& inde$ exp]i5ce %ews1 t no o!r resi/ance1 ?an :at arises f ! p[] ( inactivity 9 ! p>ts ( ! fluid1 is ( mom5t1 :5 ! body moves ) any consid]able swiftness4 #aa4 ,,!re is besides ^! yet ano!r species ( resi/ance1 f\nd only 9 su* fluids1 z1 l our air1 are ela/ic4 ,ela/icity belongs to no fluid kn[n to u beside ! air4 ,by ?is prop]ty any quantity ( air may be contract$ into a less space by a =cible pressure1 & z soon z ! compress+ p[] is remov$1 x w spr+ out aga9 to its =m] dim5sions4 ,! air we brea? is held to its pres5t d5sity by ! weight ( ! air above u4 ,& z ?is incumb5t weight1 by ! motion ( ! w9ds1 or o!r causes1 is frequ5tly v>i$ 7:i* appe>s by ! b>omet]27 s :5 ?is weight is greate/1 we brea? a m d5se air ?an at o!r times4 ,to :at degree ! air w\ld exp& x self by its spr+1 if all pressure 7 remov$1 is n kn[n1 nor yet into h[ n>r[ a compass x is capable ( be+ compress$4 ,mr4 ,,boyle f\nd x by exp]im5t capable bo? ( expansion & compression to su* a degree1 t he c\ld cause a quantity ( air to exp& x self ov] a space "s hundr$ ?\s& times great]1 ?an ! space to :i* he c\ld conf9e ! same quantity#aaa4 ,b ,i %all treat m fully ( ?is spr+ 9 ! air h]eaft]#aab4 ,i am n[ only to consid] :at resi/ance to ! motion ( bodies arises f x4 #ab4 ,,b be=e our au?or %ews 9 :at mann] ?is cause ( resi/ance op]ates1 he proposes a me?od1 by :i* fluids may be r5d]$ ela/ic1 demon/rat+ t if _! p>ticles be provid$ ) a p[] ( repell+ ea* o!r1 :i* %all ex]t x self ) degrees ( /r5g? reciprocally proportional to ! di/ances betwe5 ! c5t]s ( ! p>ticles2 t !n su* fluids w obs]ve ! same rule 9 be+ compress$1 z our air does1 :i* is ?is1 t ! space1 into :i* x yields ^u compression1 is reciprocally proportional to ! compress+ weight#aac4 ,! t]m reciprocally proportional has be5 expla9$ above#aad4 ,& if ! c5trifugal =ce ( ! p>ticles act$ by o!r laws1 su* fluids w\ld yield 9 a diff]5t mann] to compression#aae4 #ac4 ,,:e!r ! p>ticles ( ! air be endu$ ) su* a p[]1 by :i* !y c act ^u ea* o!r out ( contact1 our au?or does n det]m9e1 b leaves t to future exam9ation1 & to be discuss$ by philosoph]s4 ,only he takes occasion f h5ce to consid] ! resi/ance 9 ela/ic fluids1 "u ?is notion2 mak+ rem>ks1 z he passes along1 ^u ! diff]5ces1 :i* w arise1 if _! ela/icity be d]iv$ f any o!r f\nta9#aaf4 ,& ?is1 ,i ?9k1 mu/ be confess$ to be done by him ) great judgm5t2 = ?is is f> ! mo/ reasonable acc\nt1 :i* has be5 giv5 ( ?is surpriz+ p[]1 z mu/ )\t d\bt be freely ackn[l$g$ by any "o1 :o 9 ! lea/ consid]s ! insuffici5cy ( all ! o!r conjectures1 :i* h be5 fram$2 & also h[ little reason !re is to d5y to bodies o!r p[]s1 by :i* !y may act ^u ea* o!r at a di/ance1 z well z t ( gravity2 :i* we %all h]eaft] %ew to be a prop]ty univ]sally belong+ to all ! bodies ( ! univ]se1 & to all _! p>ts#aag4 ,nay we actually f9d 9 ! load/one a v app>5t repell+1 z well z an attractive p[]4 ,b ( ?is m 9 ! conclusion ( ?is disc\rse4 #ad4 ,,by ^! /eps our au?or leads ! way to expla9 ! resi/ance1 :i* ! air & su* l fluids w give to bodies by _! ela/icity2 :i* resi/ance he expla9s ?us4 ,if ! ela/ic p[] ( ! fluid 7 to be v>i$ s1 z to be always 9 ! duplicate proportion ( ! velocity ( ! resi/$ body1 x is %ewn t !n ! resi/ance d]iv$ f ! ela/icity1 w\ld increase 9 ! duplicate proportion ( ! velocity2 9 s mu* t ! :ole resi/ance w\ld be 9 t proportion1 except+ only t small "p1 :i* arises f ! friction betwe5 ! body & ! p>ts ( ! fluid4 ,f :5ce x foll[s1 t because ! ela/ic p[] ( ! same fluid does 9 tru? cont9ue ! same1 if ! velocity ( ! mov+ body be dim9i%$1 ! resi/ance f ! ela/icity1 & !re=e ! :ole resi/ance1 w decrease 9 a less proportion1 ?an ! duplicate ( ! velocity2 & if ! velocity be increas$1 ! resi/ance f ! ela/icity w increase 9 a less proportion1 ?an ! duplicate ( ! velocity1 t is 9 a less proportion1 ?an ! resi/ance made by ! p[] ( inactivity ( ! p>ts ( ! fluid4 ,& f ?is f\ndation is rais$ ! pro( ( a prop]ty ( ?is resi/ance1 giv5 by ! ela/icity 9 common ) ! o!rs f ! t5acity & friction ( ! p>ts ( ! fluid2 t ! velocity may be increas$1 till ?is resi/ance f ! fluid's ela/icity %all be> no consid]able proportion to t1 :i* is produc$ by ! p[] ( inactivity !re(#aah4 ,f :5ce our au?or draws ?is conclusion2 t ! resi/ance ( a body1 :i* moves v swiftly 9 an ela/ic fluid1 is ne> ! same1 z if ! fluid 7 n ela/ic2 provid$ ! ela/icity arises f ! c5trifugal p[] ( ! p>ts ( ! m$ium1 z be=e expla9$1 especially if ! velocity be s great1 t ?is c5trifugal p[] %all want "t to ex]t x self#aai4 ,b x is to be obs]v$1 t 9 ! pro( ( all ?is our au?or proce$s ^u ! supposition ( ?is c5trifugal p[] 9 ! p>ts ( ! fluid2 b if ! ela/icity be caus$ by ! expansion ( ! p>ts 9 ! mann] ( wool compress$1 & su* l bodies1 by :i* ! p>ts ( ! fluid w be 9 "s measure entangl$ toge!r1 & _! motion be ob/ruct$1 ! fluid w be 9 a mann] t5aci\s1 & give a resi/ance ^u t acc\nt ov] & above :at dep5ds ^u its ela/icity only#abj2 & ! resi/ance d]iv$ f t cause is to be judg$ ( 9 ! mann] be=e set d[n4 #ae4 ,,x is n[ "t to pass to ! second "p ( ?is !ory2 :i* is to assign ! measure ( resi/ance1 accord+ to ! proportion betwe5 ! d5sity ( ! body & ! d5sity ( ! fluid4 ,:at is "h to be und]/ood by ! ^w d5sity has be5 expla9$ above#aba4 ,= ?is purpose z our au?or be=e consid]$ two di/9ct cases ( bodies mov+ 9 m$iums2 "o :5 !y oppos$ !mselves to ! fluid by _! p[] ( inactivity only1 & ano!r :5 by asc5d+ or desc5d+ _! weight 0 comb9$ ) t o!r p[]3 s likewise1 ! fluids !mselves are to be reg>d$ "u a d\ble capacity2 ei!r z hav+ _! p>ts at re/1 & dispos$ freely )\t re/ra9t1 or z be+ compress$ toge!r by _! own weight1 or any o!r cause4 #af4 ,,9 ! fir/ case1 if ! p>ts ( ! fluid be :olly dis+ag$ f "o ano!r1 s t ea* p>ticle is at lib]ty to move all ways )\t any imp$im5t1 x is %ewn1 t if a globe move 9 su* a fluid1 & ! globe & p>ticles ( ! fluid are endu$ ) p]fect ela/icity2 s t z ! globe imp+es ^u ! p>ticles ( x1 !y %all b\nd (f & sep>ate !mselves f ! globe1 ) ! same velocity1 ) :i* ! globe /rikes ^u !m2 !n ! resi/ance1 :i* ! globe mov+ ) any kn[n velocity suff]s1 is to be ?us det]m9$4 ,f ! velocity ( ! globe1 ! "t1 :]e9 x w\ld move ov] two ?ird p>ts ( its own diamet] ) t velocity1 w be kn[n4 ,& su* proportion z ! d5sity ( ! fluid be>s to ! d5sity ( ! globe1 ! same ! resi/ance giv5 to ! globe w be> to ! =ce1 :i* act+1 l ! p[] ( gravity1 on ! globe )\t int]mission dur+ ! space ( "t n[ m5tion$1 w\ld g5]ate 9 ! globe ! same degree ( motion1 z t :]e) x moves 9 ! fluid#abb4 ,b if nei!r ! globe nor ! p>ticles ( ! fluid be ela/ic1 s t ! p>ticles1 :5 ! globe /rikes aga9/ !m1 d n reb\nd f x1 !n ! resi/ance w be b half s mu*#abc4 ,aga91 if ! p>ticles ( ! fluid & ! globe are imp]fectly ela/ic1 s t ! p>ticles w spr+ f ! globe ) "p only ( t velocity :]e) ! globe imp+es ^u !m2 !n ! resi/ance w be a mean betwe5 ! two prec$+ cases1 approa*+ ne>] to ! fir/ or second1 accord+ z ! ela/icity is m or less#abd4 #ag4 ,,! ela/icity1 :i* is "h ascrib$ to ! p>ticles ( ! fluid1 is n t p[] ( repell+ "o ano!r1 :5 out ( contact1 by :i*1 z has be=e be5 m5tion$1 ! :ole fluid may be r5dr$ ela/ic2 b su* an ela/icity only1 z _m solid bodies h ( recov]+ _! figure1 :5ev] any =cible *ange is made 9 x1 by ! impulse ( ano!r body or o!rwise4 ,:i* ela/icity has be5 expla9$ above at l>ge#abe4 #ah4 ,,?is is ! case ( discont9u$ fluids1 :]e ! body1 by press+ aga9/ _! p>ticles1 drives !m be=e itself1 :ile ! space beh9d ! body is left empty4 ,b 9 fluids :i* are compress$1 s t ! p>ts ( !m remov$ out ( place by ! body resi/$ imm$iately retire beh9d ! body1 & fill t space1 :i* 9 ! o!r case is left vacant1 ! resi/ance is /ill less2 = a globe 9 su* a fluid :i* %all be free f all ela/icity1 w be resi/$ b half z mu* z ! lea/ resi/ance 9 ! =m] case#abf4 ,b by ela/icity ,i n[ mean t p[]1 :i* r5d]s ! :ole fluid s2 ( :i* if ! compress$ fluid be possess$1 9 ! mann] ( ! air1 !n ! resi/ance w be great] ?an by ! =ego+ rule2 = ! fluid be+ capable 9 "s degree ( cond5sation1 x w resemble s f> ! case ( uncompress$ fluids#abg4 ,b1 z has be5 be=e relat$1 ?is diff]5ce is mo/ consid]able 9 sl[ motions4 #ai4 ,,9 ! next place our au?or is p>ticul> 9 det]m9+ ! degrees ( resi/ance accompany+ bodies ( diff]5t figures2 :i* is ! la/ ( ! ?ree heads1 we divid$ ! :ole disc\rse ( resi/ance into4 ,& 9 ?is disquisition he f9ds a v surpriz+ & un?\ght ( diff]5ce1 betwe5 free & compress$ fluids4 ,he proves1 t 9 ! =m] k9d1 a globe suff]s b half ! resi/ance1 :i* ! cyl9d]1 t circumscribes ! globe1 w d1 if x move 9 ! direction ( its axis#abh4 ,b 9 ! latt] he proves1 t ! globe & cyl9d] are resi/$ alike#abi4 ,& 9 g5]al1 t let ! %ape ( bodies be ev] s diff]5t1 yet if ! greate/ sections ( ! bodies p]p5dicul> to ! axis ( _! motion be equal1 ! bodies w be resi/$ equally#acj4 #bj4 ,,pursuant to ! diff]5ce f\nd betwe5 ! resi/ance ( ! globe & cyl9d] 9 r>e & uncompress$ fluids1 our au?or gives u ! result ( "s o!r inquiries ( ! same nature4 ,?us ( all ! fru/ums ( a cone1 t c be describ$ ^u ! same base & ) ! same altitude1 he %ews h[ to f9d t1 :i* ( all o!rs w be ! lea/ resi/$1 :5 mov+ 9 ! direction ( its axis#aca4 ,& f h5ce he draws an easy me?od ( alt]+ ! figure ( any sph]oidical solid1 s t its capacity may be enl>g$1 & yet ! resi/ance ( x dim9i%$#acb3 a note :i* he ?9ks may n be useless to %ip-wrights4 ,he concludes ) det]m9+ ! solid1 :i* w be resi/$ ! lea/ t is possible1 9 ^! discont9u$ fluids#acc4 #ba4 ,,t ,i may "h be und]/ood by read]s unacqua9t$ ) ma!matical t]ms1 ,i %all expla9 :at ,i mean by a fru/um ( a cone1 & a sph]oidical solid4 ,a cone has be5 def9$ above4 ,a fru/um is :at rema9s1 :5 "p ( ! cone next ! v]tex is cut away by a section p>allel to ! base ( ! cone1 z 9 fig4 #hf4 ,a sph]oid is produc$ f an ellipsis1 z a sph]e or globe is made f a circle4 ,if a circle turn r\nd on its diamet]1 x describes by its motion a sph]e2 s if an ellipsis 7:i* figure has be5 def9$ above1 & w be m fully expla9$ h]eaft]#acd7 be turn$ r\nd ei!r ^u ! longe/ or %orte/ l9e1 t c be drawn ?r\gh ! middle ( x1 !re w be describ$ a k9d ( oblong or flat sph]e1 z 9 fig4 #hg4 ,bo? ^! figures are call$ sph]oids1 & any solid resembl+ ^! ,i "h call sph]oidical4 #bb4 ,,if x %\ld be ask$1 h[ ! me?od ( alt]+ sph]oidical bodies1 "h m5tion$1 c contribute to ! facilitat+ a %ip's motion1 :5 ,i j above affirm$1 t ! figure ( bodies1 :i* move 9 a compress$ fluid n ela/ic1 has no relation to ! augm5tation or dim9ution ( ! resi/ance2 ! reply is1 t :at 0 !re spok5 relates to bodies deep imm]g$ into su* fluids1 b n ( ^?1 :i* swim ^u ! surface ( !m2 = 9 ?is latt] case ! fluid1 by ! appulse ( ! ant]ior p>ts ( ! body1 is rais$ above ! level ( ! surface1 & beh9d ! body is sunk some:at bel[2 s t by ?is inequality 9 ! sup]ficies ( ! fluid1 t "p ( x1 :i* at ! head ( ! body is high] ?an ! fluid beh9d1 w resi/ 9 "s measure aft] ! mann] ( discont9u$ fluids#ace1 analog\s to :at 0 be=e obs]v$ to happ5 9 ! air ?r\gh its ela/icity1 ?\gh ! body be surr\nd$ on e side by x#acf4 ,& z f> z ! p[] ( ^! causes ext5ds1 ! figure ( ! mov+ body affects its resi/ance2 = x is evid5t1 t ! figure1 :i* presses lea/ directly aga9/ ! p>ts ( ! fluid1 & s raises lea/ ! surface ( a fluid n ela/ic1 & lea/ compresses "o t is ela/ic1 w be lea/ resi/$4 #bc4 ,,! way ( collect+ ! diff]5ce ( ! resi/ance 9 r>e fluids1 :i* arises f ! div]sity ( figure1 is by consid]+ ! diff]5t effect ( ! p>ticles ( ! fluid ^u ! body mov+ aga9/ !m1 accord+ to ! diff]5t obliquity ( ! sev]al p>ts ( ! body ^u :i* !y respectively /rike2 z x is kn[n1 t any body imp++ aga9/ a plane obliquely1 /rikes ) a less =ce1 ?an if x fell ^u x p]p5dicul>ly2 & ! great] ! obliquity is1 ! weak] is ! =ce4 ,& x is ! same ?+1 if ! body be at re/1 & ! plane move aga9/ x#acg4 #bd4 ,,t !re is no connexion betwe5 ! figure ( a body & its resi/ance 9 compress$ fluids1 is prov$ ?us4 ,suppose ,a ,b ,c ,d 79 fig4 #hh47 to be a canal1 hav+ su* a fluid1 wat] = in/ance1 runn+ ?r\gh x ) an equable velocity2 & let any body ,e1 by be+ plac$ 9 ! axis ( ! canal1 h9d] ! passage ( ! wat]4 ,x is evid5t1 t ! figure ( ! =e "p ( ?is body w h little influ5ce 9 ob/ruct+ ! wat]'s motion1 b ! :ole imp$im5t w arise f ! space tak5 up by ! body1 by :i* x dim9i%es ! bore ( ! canal1 & /raight5s ! passage ( ! wat]#ach4 ,b proportional to ! ob/ruction ( ! wat]'s motion1 w be ! =ce ( ! wat] ^u ! body ,e#aci4 ,n[ suppose bo? orifices ( ! canal to be clos$1 & ! wat] 9 x to rema9 at re/2 ! body ,e to move1 s t ! p>ts ( ! wat] may pass by x ) ! same degree ( velocity1 z !y did be=e2 x is beyond contradiction1 t ! pressure ( ! wat] ^u ! body1 t is1 ! resi/ance x gives to its motion1 w rema9 ! same2 & !re=e w h little connexion ) ! figure ( ! body#adj4 #be4 ,,by a me?od ( reason+ drawn f ! same f\nta9 is det]m9$ ! measure ( resi/ance ^! compress$ fluids give to bodies1 9 ref]5ce to ! proportion betwe5 ! d5sity ( ! body & t ( ! fluid4 ,?is %all be expla9$ p>ticul>ly 9 my comm5t on ,sir ,,is4 ,,newton's ma!matical pr9ciples ( natural philosophy2 b is n a prop] subject to be insi/$ on f>!r 9 ?is place4 #bf4 ,,we h n[ gone ?r\gh all ! p>ts ( ?is !ory4 ,!re rema9s no?+ m1 b 9 few words to m5tion ! exp]im5ts1 :i* our au?or has made1 bo? ) bodies fall+ p]p5dicul>ly ?r\gh wat]1 & ! air#ada1 & ) p5dulums#adb3 all :i* agree ) ! !ory4 ,9 ! case ( fall+ bodies1 ! times ( _! fall det]m9$ by ! !ory come out ! same1 z by obs]vation1 to a surpriz+ exactness2 9 ! p5dulums1 ! rod1 by :i* ! ball ( ! p5dulum hangs1 suff]s resi/ance z well z ! ball1 & ! motion ( ! ball be+ reciprocal1 x communicates su* a motion to ! fluid1 z increases ! resi/ance1 b ! deviation f ! !ory is no m1 ?an :at may reasonably foll[ f ^! causes4 #bg4 ,,by ?is !ory ( ! resi/ance ( fluids1 & ^! exp]im5ts1 our au?or decides ! "q s long agitat$ among natural philosoph]s1 :e!r all space is absolutely full ( matt]4 ,! ,ari/otelians & ,c>tesians bo? ass]t ?is pl5itude2 ! ,atomi/s h ma9ta9$ ! contr>y4 ,our au?or has *ose to det]m9e ?is "q by 8 !ory ( resi/ance1 z %all be expla9$ 9 ! foll[+ *apt]4 ,illu/ration ,illu/ration ,,book ,,ii4 ,,conc]n+ ,,! ,,sy/em ( ! ,,_w4 ,,*ap4 ,i4 ,t ! ,planets move 9 a space empty ( all s5sible matt]4 ,i ,,h n[ gone ?r\gh ! fir/ "p ( my design1 & h expla9$1 z f> z ! nature ( my und]tak+ w\ld p]mit1 :at ,sir ,,isaac ,,newton has deliv]$ 9 g5]al conc]n+ ! motion ( bodies4 ,x foll[s n[ to speak ( ! discov]ies1 he has made 9 ! sy/em ( ! _w2 & to %ew f him :at cause keeps ! heav5ly bodies 9 _! c\rses4 ,b x w be necess>y = ! use ( su*1 z are n skill$ 9 a/ronomy1 to premise a brief description ( ! planet>y sy/em4 #b4 ,,?is sy/em is dispos$ 9 ! foll[+ mann]4 ,9 ! middle is plac$ ! sun4 ,ab\t him six globes cont9ually roll4 ,^! are ! prim>y planets2 t :i* is ne>e/ to ! sun is call$ ,m]cury1 ! next ,v5us1 next to ?is is our e>?1 ! next beyond is ,m>s1 aft] him ,jupit]1 & ! out]mo/ ( all ,saturn4 ,besides ^! !re are discov]$ 9 ?is sy/em t5 o!r bodies1 :i* move ab\t "s ( ^! prim>y planets 9 ! same mann]1 z !y move r\nd ! sun4 ,^! are call$ second>y planets4 ,! mo/ conspicu\s ( !m is ! moon1 :i* moves r\nd our e>?2 f\r bodies move 9 l mann] r\nd ,jupit]2 & five r\nd ,saturn4 ,^? :i* move ab\t ,jupit] & ,saturn1 are usually call$ satellites2 & _c any ( !m be se5 )\t a telescope4 ,x is n impossible1 b !re may be m second>y planets1 beside ^!2 ?\gh our in/rum5ts h n yet discov]$ any o!r4 ,?is disposition ( ! planet>y or sol> sy/em is repres5t$ 9 fig4 #hi4 #c4 ,,! same planet is n always equally di/ant f ! sun4 ,b ! middle di/ance ( ,m]cury is betwe5 & ( ! di/ance ( ! e>? f ! sun2 ,v5us is di/ant f ! sun almo/ ( ! di/ance ( ! e>?2 ! middle di/ance ( ,m>s is some?+ m ?an half z mu* aga91 z ! di/ance ( ! e>?2 ,jupit]'s middle di/ance exce$s five times ! di/ance ( ! e>?1 by betwe5 & #a_/f "p ( ?is di/ance2 ,saturn's middle di/ance is sc>ce m ?an #i times ! di/ance betwe5 ! e>? & sun2 b ! middle di/ance betwe5 ! e>? & sun is ab\t #bag times ! sun's semidiamet]4 ,illu/ration #d4 ,,all ^! planets move "o way1 f we/ to ea/2 & ( ! prim>y planets ! mo/ remote is longe/ 9 f9i%+ its c\rse r\nd ! sun4 ,! p]iod ( ,saturn falls %ort only sixte5 days ( #bi ye>s & a half4 ,! p]iod ( ,jupit] is twelve ye>s want+ ab\t #ej days4 ,! p]iod ( ,m>s falls %ort ( two ye>s by ab\t #dc days4 ,! revolution ( ! e>? con/itutes ! ye>4 ,v5us p]=ms h] p]iod 9 ab\t #bbd days1 & ,m]cury 9 ab\t #hh days4 #e4 ,,! c\rse ( ea* planet lies ?r\gh\t 9 "o plane or flat surface1 9 :i* ! sun is plac$2 b !y d n all move 9 ! same plane1 ?\gh ! diff]5t planes1 9 :i* !y move1 cross ea* o!r 9 v small angles4 ,!y all cross ea* o!r 9 l9es1 :i* pass ?r\gh ! sun2 because ! sun lies 9 ! plane ( ea* orbit4 ,?is incl9ation ( ! sev]al orbits to ea* o!r is repres5t$ 9 fig4 #ij4 ,! l9e1 9 :i* ! plane ( any orbit crosses ! plane ( ! e>?'s motion1 is call$ ! l9e ( ! nodes ( t orbit4 #f4 ,,ea* planet moves r\nd ! sun 9 ! l9e1 :i* we h m5tion$ above#adc "u ! "n ( ellipsis2 :i* ,i %all "h %ew m p>ticul>ly h[ to describe4 ,i h !re said h[ x is produc$ 9 ! cone4 ,i %all n[ %ew h[ to =m x ^u a plane4 ,fix ^u any plane two p9s1 z at ,a & ,b 9 fig4 #ia4 ,to ^! tye a /r+ ,a ,c ,b ( any l5g?4 ,!n apply a ?ird p9 ,d s to ! /r+1 z to hold x /ra9$2 & 9 t mann] c>ry+ ?is p9 ab\t1 ! po9t ( x w describe an ellipsis4 ,if ?r\gh ! po9ts ,a1 ,b ! /raight l9e ,e ,a ,b ,f be drawn1 to be t]m9at$ at ! ellipsis 9 ! po9ts ,e & ,f1 ?is is ! longe/ l9e ( any1 t c be drawn )9 ! figure1 & is call$ ! great] axis ( ! ellipsis4 ,! l9e ,g ,h1 drawn p]p5dicul> to ?is axis ,e ,f1 s z to pass ?r\gh ! middle ( x1 is call$ ! less] axis4 ,! two po9ts ,a & ,b are call$ focus's4 ,n[ ea* planet moves r\nd ! sun 9 a l9e ( ?is k9d1 s t ! sun is f\nd 9 "o focus4 ,suppose ,a to be ! place ( ! sun4 ,!n ,e is ! po9t1 :]e9 ! planet w be ne>e/ ( all to ! sun1 & at ,f x w be mo/ remote4 ,! po9t ,e is call$ ! p]ihelion ( ! planet1 & ,f ! aphelion4 ,9 ,g & ,h ! planet is said to be 9 its middle or mean di/ance2 because ! di/ance ,a ,g or ,a ,h is truly ! middle betwe5 ,a ,e ! lea/1 & ,a ,f ! greate/ di/ance4 ,9 fig4 #ib4 is repres5t$ h[ ! great] axis ( ea* orbit is situat$ 9 respect ( ! re/4 ,! proportion betwe5 ! greate/ & lea/ di/ances ( ! planet f ! sun is v diff]5t 9 ! diff]5t planets4 ,illu/ration ,9 ,saturn ! proportion ( ! greate/ di/ance to ! lea/ is some?+ less1 ?an ! proportion ( #i to #h1 b mu* ne>] to ?is1 ?an to ! proportion ( #aj to #i4 ,9 ,jupit] ?is proportion is a little great]1 ?an t ( #aa to #aj4 ,9 ,m>s x exce$s ! proportion ( #f to #e4 ,9 ! e>? x is ab\t ! proportion ( #cj to #bi4 ,9 ,v5us x is ne> to t ( #gj to #fi4 ,& 9 ,m]cury x comes n a great deal %ort ( ! proportion ( #c to #b4 ,illu/ration #g4 ,,ea* ( ^! planets s moves ?r\gh its ellipsis1 t ! l9e drawn f ! sun to ! planet1 by accompany+ ! planet 9 its motion1 w describe ab\t ! sun equal spaces 9 equal times1 aft] ! mann] spoke ( 9 ! *apt] ( c5tripetal =ces#add4 ,!re is also a c]ta9 relation betwe5 ! great] axis's ( ^! ellipsis's1 & ! times1 9 :i* ! planets p]=m _! revolutions ?r\gh !m4 ,:i* relation may be express$ ?us4 ,let ! p]iod ( "o planet be d5ot$ by ! lett] ,a1 ! great] axis ( its orbit by ,d2 let ! p]iod ( ano!r planet be d5ot$ by ,b1 & ! great] axis ( ?is planet's orbit by ,e4 ,!n if ,c be tak5 to be> ! same proportion to ,b1 z ,b be>s to ,a2 likewise if ,f be tak5 to be> ! same proportion to ,e1 z ,e be>s to ,d2 & ,g tak5 to be> ! same proportion likewise to ,f1 z ,e be>s to ,d2 !n ,a %all be> ! same proportion to ,c1 z ,d be>s to ,g4 #h4 ,,! second>y planets move r\nd _! respective prim>y1 mu* 9 ! same mann] z ! prim>y d r\nd ! sun4 ,b ! motions ( ^! %all be m fully expla9$ h]eaft]#ade4 ,& !re is1 besides ! planets1 ano!r sort ( bodies1 :i* 9 all probability move r\nd ! sun2 ,i mean ! comets4 ,! f>!r description ( :i* bodies ,i also leave to ! place1 :]e !y are to be p>ticul>ly treat$ on#adf4 #i4 ,,f> )\t ?is sy/em ! fix$ />s are plac$4 ,^! are all s remote f u1 t we seem almo/ incapable ( contriv+ any means to e/imate _! di/ance4 ,_! numb] is exce$+ great4 ,besides two or ?ree ?\s&1 :i* we see ) ! nak$ eye1 telescopes op5 to our view va/ numb]s2 & ! f>!r improv$ ^! in/rum5ts are1 we /ill discov] m & m4 ,)\t d\bt ^! are lum9\s globes1 l our sun1 & rang$ ?r\gh ! wide ext5t ( space2 ea* ( :i*1 x is to be suppos$1 p]=m ! same (fice1 z our sun1 af=d+ light & heat to c]ta9 planets mov+ ab\t !m4 ,b ^! conjectures are n to be pursu$ 9 ?is place4 #aj4 ,i ,,%all !re=e n[ proce$ to ! p>ticul> design ( ?is *apt]1 & %ew1 t !re is no s5sible matt] lodg$ 9 ! space :]e ! planets move4 #aa4 ,,t !y suff] no s5sible resi/ance f any su* matt]1 is evid5t f ! agreem5t betwe5 ! obs]vations ( a/ronom]s 9 diff]5t ages1 ) reg>d to ! "t1 9 :i* ! planets h be5 f\nd to p]=m _! p]iods4 ,b x 0 ! op9ion ( ,,des ,,c>tes#adg1 t ! planets might be kept 9 _! c\rses by ! means ( a fluid matt]1 :i* cont9ually circulat+ r\nd %\ld c>ry ! planets along ) x4 ,!re is "o appe>ance t may seem to fav\r ?is op9ion2 :i* is1 t ! sun turns r\nd its own axis ! same way1 z ! planets move4 ,! e>? also turns r\nd its axis ! same way1 z ! moon moves r\nd ! e>?4 ,& ! planet ,jupit] turns ^u its axis ! same way1 z 8 satellites revolve r\nd him4 ,x might !re=e be suppos$1 t if ! :ole planet>y region 7 fill$ ) a fluid matt]1 ! sun1 by turn+ r\nd on its own axis1 might communicate motion fir/ to t "p ( ! fluid1 :i* 0 contigu\s1 & by degrees propagate ! l motion to ! p>ts m remote4 ,aft] ! same mann] ! e>? might communicate motion to ?is fluid1 to a di/ance suffici5t to c>ry r\nd ! moon1 & ,jupit] communicate ! l to ! di/ance ( its satellites4 ,sir ,,isaac ,,newton has p>ticul>ly exam9$ :at might be ! result ( su* a motion z ?is#adh2 & he f9ds1 t ! velocities1 ) :i* ! p>ts ( ?is fluid w move 9 diff]5t di/ances f ! c5t] ( ! motion1 w n agree ) ! motion obs]v$ 9 diff]5t planets3 = in/ance1 t ! "t ( "o intire circulation ( ! fluid1 :]e9 ,jupit] %\ld swim1 w\ld be> a great] proportion to ! "t ( "o intire circulation ( ! fluid1 :]e ! e>? is2 ?an ! p]iod ( ,jupit] be>s to ! p]iod ( ! e>?4 ,b he also proves#adi1 t ! planet _c circulate 9 su* a fluid1 s z to keep long 9 ! same c\rse1 unless ! planet & ! contigu\s fluid are ( ! same d5sity1 & ! planet be c>ri$ along ) ! same degree ( motion1 z ! fluid4 ,!re is also ano!r rem>k made ^u ?is motion by our au?or2 :i* is1 t "s vivify+ =ce w be cont9ually necess>y at ! c5t] ( ! motion#aej4 ,! sun 9 p>ticul>1 by communicat+ motion to ! ambi5t fluid1 w lose f x self z mu* motion1 z x imp>ts to ! fluid2 unless "s act+ pr9ciple reside 9 ! sun to r5ew its motion cont9ually4 ,if ! fluid be inf9ite1 ?is gradual loss ( motion w\ld cont9ue till ! :ole %\ld /op#aea2 & if ! fluid 7 limit$1 ?is loss ( motion w\ld cont9ue1 till !re w\ld rema9 no swift] a revolution 9 ! sun1 ?an 9 ! utmo/ "p ( ! fluid2 s t ! :ole w\ld turn toge!r ab\t ! axis ( ! sun1 l "o solid globe#aeb4 #ab4 ,,x is f>!r to be obs]v$1 t z ! planets d n move 9 p]fect circles r\nd ! sun2 !re is a great] di/ance betwe5 _! orbits 9 "s places1 ?an 9 o!rs4 ,= in/ance1 ! di/ance betwe5 ! orbit ( ,m>s & ,v5us is ne> half z great aga9 9 "o "p ( _! orbits1 z 9 ! opposite place4 ,n[ "h ! fluid1 9 :i* ! e>? %\ld swim1 mu/ move ) a less rapid motion1 :]e !re is ?is great] int]val betwe5 ! contigu\s orbits2 b on ! contr>y1 :]e ! space is /raite/1 ! e>? moves m sl[ly1 ?an :]e x is wide/#aec4 #ac4 ,,f>!r1 if ?is our globe ( e>? swam 9 a fluid ( equal d5sity ) ! e>? x self1 t is1 9 a fluid m d5se ?an wat]2 all bodies put 9 motion "h ^u ! e>?'s surface mu/ suff] a great resi/ance f x2 :]e z1 by ,sir ,,isaac ,,newton's exp]im5ts m5tion$ 9 ! prec$+ *apt]1 bodies1 t fell p]p5dicul>ly d[n ?r\gh ! air1 felt ab\t #a_/hfj "p only ( ! resi/ance1 :i* bodies suff]$ t fell 9 l mann] ?r\gh wat]4 #ad4 ,sir ,,isaac ,,newton applies ^! exp]im5ts yet f>!r1 & exam9es by !m ! g5]al "q conc]n+ ! absolute pl5itude ( space4 ,accord+ to ! ,ari/otelians1 all space 0 full )\t any ! lea/ vacuities :atev]4 ,,desc>tes embrac$ ! same op9ion1 & !re=e suppos$ a subtile fluid matt]1 :i* %\ld p]vade all bodies1 & adequately fill up _! pores4 ,! ,atomical philosoph]s1 :o suppose all bodies bo? fluid & solid to be compos$ ( v m9ute b solid atoms1 ass]t t no fluid1 h[ subtile soev] ! p>ticles or atoms :]e( x is compos$ %\ld be1 c ev] cause an absolute pl5itude2 because x is impossible t any body c pass ?r\gh ! fluid )\t putt+ ! p>ticles ( x into su* a motion1 z to sep>ate !m1 at lea/ 9 "p1 f "o ano!r1 & s p]petually to cause small vacuities2 by :i* ^! ,atomi/s endeav\r to prove1 t a vacuum1 or "s space empty ( all matt]1 is absolutely necess>y to be 9 nature4 ,sir ,,isaac ,,newton objects aga9/ ! fill+ ( space ) su* a subtile fluid1 t all bodies 9 motion mu/ be unmeasurably resi/$ by a fluid s d5se1 z absolutely to fill up all ! space1 ?r\gh :i* x is spread4 ,& le/ x %\ld be ?\ght1 t ?is objection might be evad$ by ascrib+ to ?is fluid su* v m9ute & smoo? p>ts1 z might remove all adhesion or friction betwe5 !m1 :]eby all resi/ance w\ld be lo/1 :i* ?is fluid might o!rwise give to bodies mov+ 9 x2 ,sir ,,isaac ,,newton proves1 9 ! mann] above relat$1 t fluids resi/ f ! p[] ( inactivity ( _! p>ticles2 & t wat] & ! air resi/ almo/ entirely on ?is acc\nt3 s t 9 ?is subtile fluid1 h[ev] m9ute & lubricat$ ! p>ticles1 :i* compose x1 might be2 yet if ! :ole fluid 0 z d5se z wat]1 x w\ld resi/ v ne> z mu* z wat] does2 & :]eas su* a fluid1 ^: p>ts are absolutely close toge!r )\t any int]v5+ spaces1 mu/ be a great deal m d5se ?an wat]1 x mu/ resi/ m ?an wat] 9 proportion to its great] d5sity2 unless we w suppose ! matt]1 ( :i* ?is fluid is compos$1 n to be endu$ ) ! same degree ( inactivity z o!r matt]4 ,b if y deprive any sub/ance ( ! prop]ty s univ]sally belong+ to all o!r matt]1 )\t impropriety ( spee* x c sc>ce be call$ by ?is "n4 #ae4 ,sir ,,isaac ,,newton made also an exp]im5t to try 9 p>ticul>1 :e!r ! int]nal p>ts ( bodies suff]$ any resi/ance4 ,& ! result did inde$ appe> to fav\r "s small degree ( resi/ance2 b s v little1 z to leave x d\btful1 :e!r ! effect did n arise f "s o!r lat5t cause#aed4 ,,*ap4 ,,ii4 ,conc]n+ ! cause1 :i* keeps 9 motion ! prim>y planets4 ,,s9ce ! planets move 9 a void space & are free f resi/ance2 !y1 l all o!r bodies1 :5 once 9 motion1 w\ld move on 9 a /raight l9e )\t end1 if left to !mselves4 ,& x is n[ to be expla9$ :at k9d ( action ^u !m c>ries !m r\nd ! sun4 ,"h ,i %all treat ( ! prim>y planets only1 & disc\rse ( ! second>y ap>t 9 ! next *apt]4 ,x has be5 j n[ decl>$1 t ^! prim>y planets move s ab\t ! sun1 t a l9e ext5d$ f ! sun to ! planet1 w1 by accompany+ ! planet 9 its motion1 pass ov] equal spaces 9 equal portions ( "t#aee4 ,& ?is "o prop]ty 9 ! motion ( ! planets proves1 t !y are cont9ually act$ on by a p[] direct$ p]petually to ! sun z a c5t]4 ,?is !re=e is "o prop]ty ( ! cause1 :i* keeps ! planets 9 _! c\rses1 t x is a c5tripetal p[]1 ^: c5t] is ! sun4 #b4 ,,aga91 9 ! *apt] ^u c5tripetal =ces#aef x 0 obs]v'd1 t if ! /r5g? ( ! c5tripetal p[] 0 suitably accommodat$ e :]e to ! motion ( any body r\nd a c5t]1 ! body might be c>ri$ 9 any b5t l9e :atev]1 ^: concavity %\ld be e :]e turn$ t[>ds ! c5t] ( ! =ce4 ,x 0 f>!r rem>k$1 t ! /r5g? ( ! c5tripetal =ce1 9 ea* place1 0 to be collect$ f ! nature ( ! l9e1 :]e9 ! body mov$#aeg4 ,n[ s9ce ea* planet moves 9 an ellipsis1 & ! sun is plac$ 9 "o focus2 ,sir ,,isaac ,,newton d$uces f h5ce1 t ! /r5g? ( ?is p[] is reciprocally 9 ! duplicate proportion ( ! di/ance f ! sun4 ,?is is d$uc$ f ! prop]ties1 :i* ! geomet]s h discov]$ 9 ! ellipsis4 ,! process ( ! reason+ is n prop] to be enl>g$ ^u "h2 b ,i %all endeav\r to expla9 :at is meant by ! reciprocal duplicate proportion4 ,ea* ( ! t]ms reciprocal proportion1 & duplicate proportion1 has be5 already def9$#aeh4 ,_! s5se :5 ?us unit$ is z foll[s4 ,suppose ! planet mov$ 9 ! orbit ,a ,b ,c 79 fig4 #ic47 ab\t ! sun 9 ,s4 ,!n1 :5 x is said1 t ! c5tripetal p[]1 :i* acts on ! planet 9 ,a1 be>s to ! p[] act+ on x 9 ,b a proportion1 :i* is ! reciprocal ( ! duplicate proportion ( ! di/ance ,s ,a to ! di/ance ,s ,b2 x is meant t ! p[] 9 ,a be>s to ! p[] 9 ,b ! duplicate ( ! proportion ( ! di/ance ,s ,b to ! di/ance ,s ,a4 ,! reciprocal duplicate proportion may be expla9$ also by numb]s z foll[s4 ,suppose sev]al di/ances to be> to ea* o!r proportions express$ by ! numb]s #a1 #b1 #c1 #d1 #e2 t is1 let ! second di/ance be d\ble ! fir/1 ! ?ird be ?ree times1 ! f\r? f\r times1 & ! fif? five times z great z ! fir/4 ,multiply ea* ( ^! numb]s by x self1 & #a multipli$ by #a produces /ill #a1 #b multipli$ by #b produces #d1 #c by #c makes #i1 #d by #d makes #af1 & #e by #e gives #be4 ,?is be+ done1 ! fractions 1 #a_/i1 #a_/af1 #a_/be1 w respectively express ! proportion1 :i* ! c5tripetal p[] 9 ea* ( ! foll[+ di/ances be>s to ! p[] at ! fir/ di/ance3 = 9 ! second di/ance1 :i* is d\ble ! fir/1 ! c5tripetal p[] w be "o f\r? "p only ( ! p[] at ! fir/ di/ance2 at ! ?ird di/ance ! p[] w be "o n9? "p only ( ! fir/ p[]2 at ! f\r? di/ance1 ! p[] w be b "o sixte5? "p ( ! fir/2 & at ! fif? di/ance1 "o tw5ty fif? "p ( ! fir/ p[]4 #c4 ,,?us is f\nd ! proportion1 9 :i* ?is c5tripetal p[] decreases1 z ! di/ance f ! sun increases1 )9 ! compass ( "o planet's motion4 ,h[ x comes to pass1 t ! planet c be c>ri$ ab\t ! sun by ?is c5tripetal p[] 9 a cont9ual r\nd1 sometimes ris+ f ! sun1 !n desc5d+ aga9 z l[1 & f !nce be c>ri$ up aga9 z f> remote z be=e1 alt]nately ris+ & fall+ )\t end2 appe>s f :at has be5 writt5 above conc]n+ c5tripetal =ces3 = ! orbits ( ! planets resemble 9 %ape ! curve l9e propos$ 9 #ag ( ! *apt] on ^! =ces#aei4 #d4 ,,b f>!r1 9 ord] to "k :e!r ?is c5tripetal =ce ext5ds 9 ! same proportion ?r\gh\t1 & consequ5tly :e!r all ! planets are influ5c$ by ! v same p[]1 our au?or proce$s ?us4 ,he inquires :at relation !re ought to be betwe5 ! p]iods ( ! diff]5t planets1 provid$ !y 7 act$ ^u by ! same p[] decreas+ ?r\gh\t 9 ! =em5tion$ proportion2 & he f9ds1 t ! p]iod ( ea* 9 ?is case w\ld h t v relation to ! great] axis ( its orbit1 z ,i h decl>$ above#afj to be f\nd 9 ! planets by ! obs]vations ( a/ronom]s4 ,& ?is puts x beyond "q1 t ! diff]5t planets are press$ t[>ds ! sun1 9 ! same proportion to _! di/ances1 z "o planet is 9 its sev]al di/ances4 ,& !nce 9 ! la/ place x is ju/ly conclud$1 t !re is su* a p[] act+ t[>ds ! sun 9 ! =esaid proportion at all di/ances f x4 #e4 ,,?is p[]1 :5 ref]r$ to ! planets1 our au?or calls c5tripetal1 :5 to ! sun attractive2 he gives x likewise ! "n ( gravity1 because he f9ds x to be ( ! same nature ) t p[] ( gravity1 :i* is obs]v$ 9 our e>?1 z w appe> h]eaft]#afa4 ,by all ^! names he designs only to signify a p[] endu$ ) ! prop]ties be=e m5tion$2 b by no means w\ld he h x und]/ood1 z if ^! names ref]r$ any way to ! cause ( x4 ,9 p>ticul> 9 "o place :]e he uses ! "n ( attraction1 he cautions u expressly aga9/ imply+ any ?+ b a p[] direct+ a body to a c5t] )\t any ref]5ce to ! cause ( x1 :e!r resid+ 9 t c5t]1 or aris+ f any ext]nal impulse#afb4 #f4 ,,b n[1 9 ^! demon/rations "s v m9ute inequalities 9 ! motion ( ! planets are neglect$2 :i* is done ) a great deal ( judgm5t2 = :atev] be _! cause1 ! effects are v inconsid]able1 !y be+ s exce$+ small1 t "s a/ronom]s h ?\ght fit :olly to pass !m by#afc4 ,h[ev] ! excell5cy ( ?is philosophy1 :5 9 ! h&s ( s great a geomet] z our au?or1 is su*1 t x is able to trace ! lea/ v>iations ( ?+s up to _! causes4 ,! only inequalities1 :i* h be5 obs]v$ common to all ! planets1 are ! motion ( ! aphelion & ! nodes4 ,! transv]se axis ( ea* orbit does n always rema9 fix$1 b moves ab\t ! sun ) a v sl[ progressive motion3 nor d ! planets keep con/antly ! same plane1 b *ange !m1 & ! l9es 9 :i* ^? planes int]sect ea* o!r by ins5sible degrees4 ,! fir/ ( ^! inequalities1 :i* is ! motion ( ! aphelion1 may be acc\nt$ =1 by suppos+ ! gravitation ( ! planets t[>ds ! sun to diff] a little f ! =em5tion$ reciprocal duplicate proportion ( ! di/ances2 b ! second1 :i* is ! motion ( ! nodes1 _c be acc\nt$ = by any p[] direct$ t[>ds ! sun2 = no su* c give ! planet any lat]al impulse to div]t x f ! plane ( its motion into any new plane1 b ( necessity mu/ be d]iv$ f "s o!r c5t]4 ,:]e t p[] is lodg$1 rema9s to be discov]$4 ,n[ x is prov$1 z %all be expla9$ 9 ! foll[+ *apt]1 t ! ?ree prim>y planets ,saturn1 ,jupit]1 & ! e>?1 :i* h satellites revolv+ ab\t !m1 are endu$ ) a p[] ( caus+ bodies1 9 p>ticul> ^? satellites1 to gravitate t[>ds !m ) a =ce1 :i* is reciprocally 9 ! duplicate proportion ( _! di/ances2 & ! planets are 9 all respects1 9 :i* !y come "u our exam9ation1 s simil> & alike1 t !re is no reason to "q1 b !y h all ! same prop]ty4 ,?\gh x be suffici5t = ! pres5t purpose to h x prov$ ( ,jupit] & ,saturn only2 = ^! planets conta9 mu* great] quantities ( matt] ?an ! re/1 & proportionally exce$ ! o!rs 9 p[]#afd4 ,b ! influ5ce ( ^! two planets be+ all[$1 x is evid5t h[ ! planets come to %ift cont9ually _! planes3 = ea* ( ! planets mov+ 9 a diff]5t plane1 ! action ( ,jupit] & ,saturn ^u ! re/ w be oblique to ! planes ( _! motion2 & !re=e w gradually draw !m into new ones4 ,! same action ( ^! two planets ^u ! re/ w cause likewise a progressive motion ( ! aphelion2 s t !re w be no necessity ( hav+ rec\rse to ! o!r cause = ?is motion1 :i* 0 be=e h9t$ at#afe2 viz1 ! gravitation ( ! planets t[>ds ! sun diff]+ f ! exact reciprocal duplicate proportion ( ! di/ances4 ,& 9 ! la/ place1 ! action ( ,jupit] & ,saturn ^u ea* o!r w produce 9 _! motions ! same inequalities1 z _! jo9t action produces 9 ! re/4 ,all ?is is effect$ 9 ! same mann]1 z ! sun produces ! same k9d ( inequalities & _m o!rs 9 ! motion ( ! moon & ! o!r second>y planets2 & !re=e w be be/ appreh5d$ by :at %all be said 9 ! next *apt]4 ,^? o!r irregul>ities 9 ! motion ( ! second>y planets h place likewise "h2 b are too m9ute to be obs]vable3 because !y are produc$ & rectifi$ alt]nately1 = ! mo/ "p 9 ! "t ( a s+le revolution2 :]eas ! motion ( ! aphelion & nodes1 :i* cont9ually increase1 become s5sible 9 a long s]ies ( ye>s4 ,yet "s ( ^! o!r inequalities are disc]nible 9 ,jupit] & ,saturn1 9 ,saturn *iefly2 = :5 ,jupit]1 :o moves fa/] ?an ,saturn1 approa*es ne> to a conjunction ) him1 8 action ^u ,saturn w a little ret>d ! motion ( t planet1 & by ! reciprocal action ( ,saturn he w himself be accel]at$4 ,aft] conjunction1 ,jupit] w aga9 accel]ate ,saturn1 & be likewise ret>d$ 9 ! same degree1 z be=e ! fir/ 0 ret>d$ & ! latt] accel]at$4 ,:atev] inequalities besides are produc$ 9 ! motion ( ,saturn by ! action ( ,jupit] ^u t planet1 w be suffici5tly rectifi$1 by plac+ ! focus ( ,saturn's ellipsis1 :i* %\ld o!rwise be 9 ! sun1 9 ! common c5t] ( gravity ( ! sun & ,jupit]4 ,& all ! inequalities 9 ! motion ( ,jupit]1 caus$ by ,saturn's action ^u him1 are mu* less consid]able ?an ! irregul>ities ( ,saturn's motion#aff4 #g4 ,,?is "o pr9ciple !re=e ( ! planets hav+ a p[]1 z well z ! sun1 to cause bodies to gravitate t[>ds !m1 :i* is prov$ by ! motion ( ! second>y planets to obta9 9 fact1 expla9s all ! irregul>ities relat+ to ! planets ev] obs]v$ by a/ronom]s4 #h4 ,sir ,,isaac ,,newton aft] ?is proce$s to make an improvem5t 9 a/ronomy by apply+ ?is !ory to ! f>!r correction ( _! motions4 ,= z we h "h obs]v$ ! planets to possess a pr9ciple ( gravitation1 z well z ! sun2 s x w be expla9$ at l>ge h]eaft]1 t ! ?ird law ( motion1 :i* makes action & reaction equal1 is to be appli$ 9 ?is case#afg2 & t ! sun does n only attract ea* planet1 b is x self also attract$ by !m2 ! =ce1 :]e) ! planet is act$ on1 be>+ to ! =ce1 :]e) ! sun x self is act$ on at ! same "t1 ! proportion1 :i* ! quantity ( matt] 9 ! sun be>s to ! quantity ( matt] 9 ! planet4 ,f ! action betwe5 ! sun & planet be+ ?us mutual ,sir ,,isaac ,,newton proves t ! sun & planet w describe ab\t _! common c5t] ( gravity simil> ellipsis's2 & !n t ! transv]se axis ( ! ellipsis describ$ ?us ab\t ! moveable sun1 w be> to ! transv]se axis ( ! ellipsis1 :i* w\ld be describ$ ab\t ! sun at re/ 9 ! same "t1 ! same proportion z ! quantity ( solid matt] 9 ! sun & planet toge!r be>s to ! fir/ ( two mean proportionals betwe5 ?is quantity & ! quantity ( matt] 9 ! sun only#afh4 #i4 ,,above1 :]e ,i %ew$ h[ to f9d a cube1 t %\ld be> any proportion to ano!r cube#afi1 ! l9es ,f ,t & ,t ,s are two mean proportionals betwe5 ,e ,f & ,f ,g2 & c\nt+ f ,e ,f1 ,f ,t is call$ ! fir/1 & ,f ,s ! second ( ^? means4 ,9 numb]s ^! mean proportionals are ?us f\nd4 ,illu/ration ,suppose ,a & ,b two numb]s1 & x be requir$ to f9d ,c ! fir/1 & ,d ! second ( ! two mean proportionals betwe5 !m4 ,fir/ multiply ,a by x self1 & ! product multiply by ,b2 !n ,c w be ! numb] :i* 9 ari?metic is call$ ! cubic root ( ?is la/ product2 t is1 ! numb] ,c be+ multipli$ by x self1 & ! product aga9 multipli$ by ! same numb] ,c1 w produce ! product above m5tion$4 ,9 l mann] ,d is ! cubic root ( ! product ( ,b multipli$ by x self1 & ! produce ( t multiplication multipli$ aga9 by ,a4 #aj4 ,,x w be ask$1 p]haps1 h[ ?is correction c be admitt$1 :5 ! cause ( ! motions ( ! planets 0 be=e f\nd by suppos+ ! sun ! c5t] ( ! p[]1 :i* act$ ^u !m3 = accord+ to ! pres5t correction ?is p[] appe>s r to be direct$ to _! common c5t] ( gravity4 ,b :]eas ! sun 0 at fir/ conclud$ to be ! c5t]1 to :i* ! p[] act+ on ! planets 0 direct$1 because ! spaces describ$ r\nd ! sun 9 equal times 7 f\nd to be equal2 s ,sir ,,isaac ,,newton proves1 t if ! sun & planet move r\nd _! common c5t] ( gravity1 yet to an eye plac$ 9 ! planet1 ! spaces1 :i* w appe> to be describ$ ab\t ! sun1 w h ! same relation to ! times ( _! description1 z ! real spaces w\ld h1 if ! sun 7 at re/#agj4 ,i f>!r ass]t$1 t1 suppos+ ! planets to move r\nd ! sun at re/1 & to be attract$ by a p[]1 :i* e :]e %\ld act ) degrees ( /r5g? reciprocally 9 ! duplicate proportion ( ! di/ances2 !n ! p]iods ( ! planets mu/ obs]ve ! same relation to _! di/ances1 z a/ronom]s f9d !m to d4 ,b "h x mu/ n be suppos$1 t ! obs]vations ( a/ronom]s absolutely agree )\t any ! lea/ diff]5ce2 & ! pres5t correction w n cause a deviation f any "o a/ronom]'s obs]vations1 s mu* z !y diff] f "o ano!r4 ,= 9 ,jupit]1 :]e ?is correction is greate/1 x h>dly am\nts to ! #cjjj? "p ( ! :ole axis4 #aa4 ,,^u ?is head ,i ?9k x n improp] to m5tion a reflection made by our excell5t au?or ^u ^! small inequalities 9 ! planets motions2 :i* conta9s "u x a v /rong philosophical argum5t aga9/ ! et]nity ( ! _w4 ,x is ?is1 t ^! inequalities mu/ cont9ually increase by sl[ degrees1 till !y r5d] at l5g? ! pres5t frame ( nature unfit = ! purposes1 x n[ s]ves#aga4 ,& a m conv9c+ pro( _c be desir$ aga9/ ! pres5t con/itution's hav+ exi/$ f et]nity ?an ?is1 t a c]ta9 p]iod ( ye>s w br+ x to an end4 ,i am aw>e ?is ?\ght ( our au?or has be5 repres5t$ ev5 z impi\s1 & z no less ?an ca/+ a reflection ^u ! wisdom ( ! au?or ( nature1 = fram+ a p]i%able "w4 ,b ,i ?9k s bold an ass]tion ought to h be5 made ) s+ul> caution4 ,= if ?is rem>k ^u ! increas+ irregul>ities ( ! heav5ly motions be true 9 fact1 z x really is1 ! imputation mu/ return ^u ! ass]t]1 t ?is does detract f ! div9e wisdom4 ,c]ta9ly we _c pret5d to "k all ! omnisci5t ,creator's purposes 9 mak+ ?is _w1 & !re=e _c und]take to det]m9e h[ long he design$ x %\ld la/4 ,& x is suffici5t1 if x endure ! "t int5d$ by ! au?or4 ,! body ( e animal %ews ! unlimit$ wisdom ( its au?or no less1 nay 9 _m respects m1 ?an ! l>g] frame ( nature2 & yet we see1 !y are all design$ to la/ b a small space ( "t4 #ab4 ,,!re ne$ no?+ m be said ( ! prim>y planets2 ! motions ( ! second>y %all be next consid]$4 ,,*ap4 ,,iii4 ,( ! motion ( ! ,,moon & ! o!r ,,second>y ,,planets4 ,,! excell5cy ( ?is philosophy suffici5tly appe>s f its ext5d+ 9 ! mann]1 :i* has be5 relat$1 to ! m9ute/ circum/ances ( ! prim>y planets motions2 :i* nev]!less be>s no proportion to ! va/ success ( x 9 ! motions ( ! second>y2 = x n only acc\nts = all ! irregul>ities1 by :i* _! motions 7 kn[n to be di/urb$1 b has discov]$ o!rs s complicat$1 t a/ronom]s 7 nev] able to di/+ui% !m1 & r$uce !m "u prop] heads2 b ^! 7 only to be f\nd out f _! causes1 :i* ?is philosophy has br\ght to light1 & has %ewn ! dep5d5ce ( ^! inequalities ^u su* causes 9 s p]fect a mann]1 t we n only le>n f !nce 9 g5]al1 :at ^? inequalities are1 b are able to compute ! degree ( !m4 ,( ?is ,sir ,,is4 ,,newton has giv5 sev]al specim5s1 & has moreov] f\nd means to r$uce ! moon's motion s completely to rule1 t he has fram$ a !ory1 f :i* ! place ( t planet may at all times be comput$1 v ne>ly or altoge!r z exactly1 z ! places ( ! prim>y planets !mselves1 :i* is mu* beyond :at ! greate/ a/ronom]s c\ld ev] effect4 #b4 ,,! fir/ ?+ demon/rat$ ( ^! second>y planets is1 t !y are drawn t[>ds _! respective prim>y 9 ! same mann] z ! prim>y planets are attract$ by ! sun4 ,t ea* second>y planet is kept 9 its orbit by a p[] po9t$ t[>ds ! c5t] ( ! prim>y planet1 ab\t :i* ! second>y revolves2 & t ! p[]1 by :i* ! second>ies ( ! same prim>y are influ5c$1 be>s ! same relation to ! di/ance f ! prim>y1 z ! p[]1 by :i* ! prim>y planets are guid$1 does 9 reg>d to ! di/ance f ! sun#agb4 ,?is is prov$ 9 ! satellites ( ,jupit] & ,saturn1 because !y move 9 circles1 z f> z we c obs]ve1 ab\t _! respective prim>y ) an equable c\rse1 ! respective prim>y be+ ! c5t] ( ea* orbit3 & by comp>+ ! times1 9 :i* ! diff]5t satellites ( ! same prim>y p]=m _! p]iods1 !y are f\nd to obs]ve ! same relation to ! di/ances f _! prim>y1 z ! prim>y planets obs]ve 9 respect ( _! mean di/ances f ! sun#agc4 ,"h ^! bodies mov+ 9 circles ) an equable motion1 ea* satellite passes ov] equal p>ts ( its orbit 9 equal portions ( "t2 consequ5tly ! l9e drawn f ! c5t] ( ! orbit1 t is1 f ! prim>y planet1 to ! satellite1 w pass ov] equal spaces along ) ! satellite 9 equal portions ( "t2 :i* proves ! p[]1 by :i* ea* satellite is held 9 its orbit1 to be po9t$ t[>ds ! prim>y z a c5t]#agd4 ,x is also manife/ t ! c5tripetal p[]1 :i* c>ries a body 9 a circle conc5trical ) ! p[]1 acts ^u ! body at all times ) ! same /r5g?4 ,b ,sir ,,isaac ,,newton demon/rates t1 :5 bodies are c>ri$ 9 diff]5t circles by c5tripetal p[]s direct$ to ! c5t]s ( ^? circles1 !n1 ! degrees ( /r5g? ( ^? p[]s are to be comp>$ by consid]+ ! relation betwe5 ! times1 9 :i* ! bodies p]=m _! p]iods ?r\gh ^? circles#age2 & 9 p>ticul> he %ews1 t if ! p]iodical times be> t relation1 :i* ,i h j n[ ass]t$ ! satellites ( ! same prim>y to obs]ve2 !n ! c5tripetal p[]s are reciprocally 9 ! duplicate proportion ( ! semidiamet]s ( ! circles1 or 9 t proportion to ! di/ances ( ! bodies f ! c5t]s#agf4 ,h5ce x foll[s t 9 ! planets ,jupit] & ,saturn1 ! c5tripetal p[] 9 ea* decreases ) ! increase ( di/ance1 9 ! same proportion z ! c5tripetal p[] app]ta9+ to ! sun decreases ) ! increase ( di/ance4 ,i d n "h mean t ?is proportion ( ! c5tripetal p[]s holds betwe5 ! p[] ( ,jupit] at any di/ance comp>$ ) ! p[] ( ,saturn at any o!r di/ance2 b only 9 ! *ange ( /r5g? ( ! p[] belong+ to ! same planet at diff]5t di/ances f him4 ,moreov] :at is "h discov]$ ( ! planets ,jupit] & ,saturn by means ( ! diff]5t satellites1 :i* revolve r\nd ea* ( !m1 appe>s 9 ! e>? by ! moon alone2 because %e is f\nd to move r\nd ! e>? 9 an ellipsis aft] ! same mann] z ! prim>y planets d ab\t ! sun2 except+ only "s small irregul>ities 9 h] motion1 ! cause ( :i* w be p>ticul>ly expla9$ 9 :at foll[s1 :]eby x w appe>1 t !y are no objection aga9/ ! e>?'s act+ on ! moon 9 ! same mann] z ! sun acts on ! prim>y planets2 t is1 z ! o!r prim>y planets ,jupit] & ,saturn act ^u _! satellites4 ,c]ta9ly s9ce ^! irregul>ities c be o!rwise acc\nt$ =1 we ought n to dep>t f t rule ( induction s necess>y 9 philosophy1 t to l bodies l prop]ties are to be attribut$1 :]e no reason to ! contr>y appe>s4 ,we _c !re=e b ascribe to ! e>? ! same k9d ( action ^u ! moon1 z ! o!r prim>y planets ,jupit] & ,saturn h ^u _! satellites2 :i* is kn[n to be v exactly 9 ! proportion assign$ by ! me?od ( comp>+ ! p]iodical times & di/ances ( all ! satellites :i* move ab\t ! same planet2 ?is abundantly comp5sat+ our n be+ ne> en\gh to obs]ve ! exact figure ( _! orbits4 ,= if ! little deviation ( ! moon's orbit orbit f a true p]man5t ellipsis arose f ! action ( ! e>? ^u ! moon n be+ 9 ! exact reciprocal duplicate proportion ( ! di/ance1 7 ano!r moon to revolve ab\t ! e>?1 ! proportion betwe5 ! p]iodical times ( ?is new moon1 & ! pres5t1 w\ld discov] ! deviation f ! m5tion$ proportion mu* m manife/ly4 #c4 ,,by ! numb] ( satellites1 :i* move r\nd ,jupit] & ,saturn1 ! p[] ( ea* ( ^! planets is measur$ 9 a great div]sity ( di/ance2 = ! di/ance ( ! out]mo/ satellite 9 ea* ( ^! planets exce$s sev]al times ! di/ance ( ! inn]mo/4 ,9 ,jupit] ! a/ronom]s h usually plac$ ! inn]mo/ satellite at a di/ance f ! c5t] ( t planet equal to ab\t #e ( ! semidiamet]s ( ,jupit]'s body1 & ?is satellite p]=ms its revolution 9 ab\t #a day #ah h\rs4 ,! next satellite1 :i* revolves r\nd ,jupit] 9 ab\t #c days #ac h\rs1 !y place at ! di/ance f ,jupit] ( ab\t #i ( t planet's semidiamet]s4 ,to ! ?ird satellite1 :i* p]=ms its p]iod ne>ly 9 #g days #c h\rs1 !y assign ! di/ance ( ab\t #ad semidiamet]s4 ,b ! out]mo/ satellite !y remove to #be semidiamet]s1 & ?is satellite makes its p]iod 9 ab\t #af days #af h\rs#agg4 ,9 ,saturn !re is /ill a great] div]sity 9 ! di/ance ( ! sev]al satellites4 ,by ! obs]vations ( ! late ,,cass9i1 a celebrat$ a/ronom] 9 ,france1 :o fir/ discov]$ all ^! satellites1 except "o kn[n be=e1 ! inn]mo/ is di/ant ab\t #d ( ,saturn's semidiamet]s f 8 c5t]1 & revolves r\nd 9 ab\t #a day #ba h\rs4 ,! next satellite is di/ant ab\t #e semidiamet]s1 & makes its p]iod 9 ab\t #b days #ag h\rs4 ,! ?ird is remov$ to ! di/ance ( ab\t #h semidiamet]s1 & p]=ms its revolution 9 ne> #d days #ab h\rs4 ,! f\r? satellite discov]$ fir/ by ! great ,,huyg5s1 is ne> #ah semidiamet]s1 & moves r\nd ,saturn 9 ab\t #ae days #bb h\rs4 ,! out]mo/ is di/ant #ef semidiamet]s1 & makes its revolution 9 ab\t #gi days #g h\rs#agh4 ,besides ^! satellites1 !re belongs to ! planet ,saturn ano!r body ( a v s+ul> k9d4 ,?is is a %9+1 broad1 & flat r+1 :i* encompasses ! planet r\nd4 ,! diamet] ( ! out]mo/ v]ge ( ?is r+ is m ?an d\ble ! diamet] ( ,saturn4 ,,huyg5s1 :o fir/ describ$ ?is r+1 makes ! :ole diamet] !re( to be> to ! diamet] ( ,saturn ! proportion ( #i to #d4 ,! late rev]5d ,mr4 ,,p\nd makes ! proportion some?+ great]1 viz4 t ( #g to #c4 ,! di/ances ( ! satellites ( ?is planet ,saturn are comp>$ by ,,cass9i to ! diamet] ( ! r+4 ,8 numb]s ,i h r$uc$ to ^? above1 accord+ to ,mr4 ,,p\nd's proportion betwe5 ! diamet]s ( ,saturn & ( 8 r+4 ,z ?is r+ appe>s to adh]e no :]e to ,saturn1 s ! di/ance ( ,saturn f ! inn] edge ( ! r+ seems r great] ?an ! bread? ( ! r+4 ,! di/ances1 :i* h "h be5 giv51 ( ! sev]al satellites1 bo? = ,jupit] & ,saturn1 may be m dep5d$ on 9 relation to ! proportion1 :i* ^? belong+ to ! same prim>y planet be> "o to ano!r1 ?an 9 respect to ! v numb]s1 t h be5 "h set d[n1 by reason ( ! difficulty !re is 9 measur+ to ! greate/ exactness ! diamet]s ( ! prim>y planets2 z w be expla9$ h]eaft]1 :5 we come to treat ( telescopes#agi4 ,by ! obs]vations ( ! =em5tion$ ,mr4 ,,p\nd1 9 ,jupit] ! di/ance ( ! inn]mo/ satellite %\ld r be ab\t #f semidiamet]s1 ( ! second #i-1 ( ! ?ird #ae1 & ( ! out]mo/ #bfahj2 & 9 ,saturn ! di/ance ( ! inn]mo/ satellite #d semidiamet]s1 ( ! next #f1 ( ! ?ird #h1 ( ! f\r? #bj1 & ( ! fif? #eiaha4 ,h[ev] ! proportion betwe5 ! di/ances ( ! satellites 9 ! same prim>y is ! only ?+ necess>y to ! po9t we are "h ^u4 #d4 ,,b moreov] ! =ce1 :]e) ! e>? acts 9 diff]5t di/ances1 is confirm$ f ! foll[+ consid]ation1 yet m expresly ?an by ! prec$+ analogical reason+4 ,x w appe>1 t if ! p[] ( ! e>?1 by :i* x reta9s ! moon 9 h] orbit1 be suppos$ to act at all di/ances betwe5 ! e>? & moon1 accord+ to ! =em5tion$ rule2 ?is p[] w be suffici5t to produce ^u bodies1 ne> ! surface ( ! e>?1 all ! effects ascrib$ to ! pr9ciple ( gravity4 ,?is is discov]$ by ! foll[+ me?od4 ,let ,a 79 fig4 #id47 repres5t ! e>?1 ,b ! moon1 ,b ,c ,d ! moon's orbit1 :i* diff]s little f a circle1 ( :i* ,a is ! c5t]4 ,if ! moon 9 ,b 7 left to x self to move ) ! velocity1 x has 9 ! po9t ,b1 x w\ld leave ! orbit1 & proce$ "r =w>d 9 ! l9e ,b ,e1 :i* t\*es ! orbit 9 ,b4 ,suppose ! moon w\ld ^u ?is condition move f ,b to ,e 9 ! space ( "o m9ute ( "t4 ,by ! action ( ! e>? ^u ! moon1 :]eby x is reta9$ 9 its orbit1 ! moon w really be f\nd at ! end ( ?is m9ute 9 ! po9t ,f1 f :5ce a /raight l9e drawn to ,a %all make ! space ,b ,f ,a 9 ! circle equal to ! triangul> space ,b ,e ,a2 s t ! moon 9 ! "t :]e9 x w\ld h mov$ f ,b to ,e1 if left to x self1 has be5 impell$ t[>ds ! e>? f ,e to ,f4 ,& :5 ! "t ( ! moon's pass+ f ,b to ,f is small1 z "h x is only "o m9ute1 ! di/ance betwe5 ,e & ,f sc>ce diff]s f ! space1 ?r\gh :i* ! moon w\ld desc5d 9 ! same "t1 if x 7 to fall directly d[n f ,b t[>d ,a )\t any o!r motion4 ,a ,b ! di/ance ( ! e>? & moon is ab\t #fj ( ! e>?'s semidiamet]s1 & ! moon completes h] revolution r\nd ! e>? 9 ab\t #bg days #g h\rs & #dc m9utes3 !re=e ! space ,e ,f w "h be f\nd by computation to be ab\t #af feet4 ,consequ5tly1 if ! p[]1 by :i* ! moon is reta9$ 9 its orbit1 be ne> ! surface ( ! e>? great]1 ?an at ! di/ance ( ! moon 9 ! duplicate proportion ( t di/ance2 ! numb] ( feet1 a body w\ld desc5d ne> ! surface ( ! e>? by ! action ( ?is p[] ^u x 9 "o m9ute ( "t1 w\ld be equal to #af multipli$ twice into ! numb] #fj1 t is1 equal to #ehjej4 ,b h[ fa/ bodies fall ne> ! surface ( ! e>? may be kn[n by ! p5dulum#ahb2 & by ! exacte/ exp]im5ts !y are f\nd to desc5d ! space ( #af feet 9 a second ( "t2 & ! spaces describ$ by fall+ bodies be+ 9 ! duplicate proportion ( ! times ( _! fall#ahc1 ! numb] ( feet1 a body w\ld describe 9 its fall ne> ! surface ( ! e>? 9 "o m9ute ( "t1 w be equal to #af twice multipli$ by #fj1 ! same z w\ld be caus$ by ! p[] :i* acts ^u ! moon4 #e4 ,,9 ?is computation ! e>? is suppos$ to be at re/1 :]eas x w\ld h be5 m exact to h suppos$ x to move1 z well z ! moon1 ab\t _! common c5t] ( gravity2 z w easily be und]/ood1 by :at has be5 said 9 ! prec$+ *apt]1 :]e x 0 %ewn1 t ! sun is subject$ to ! l motion ab\t ! common c5t] ( gravity ( x self & ! planets4 ,! action ( ! sun ^u ! moon1 :i* is to be expla9'd 9 :at foll[s1 is likewise "h neglect$3 & ,sir ,,isaac ,,newton %ews1 if y take 9 bo? ^! consid]ations1 ! pres5t computation w be/ agree to a some:at great] di/ance ( ! moon & e>?1 viz4 to #fj semidiamet]s ( ! e>?1 :i* di/ance is m con=mable to a/ronomical obs]vations4 #f4 ,,^! computations af=d an additional pro(1 t ! action ( ! e>? obs]ves ! same proportion to ! di/ance1 :i* is "h cont5d$ =4 ,be=e ,i said1 x 0 reasonable to conclude s by induction f ! planets ,jupit] & ,saturn2 because !y act 9 t mann]4 ,b n[ ! same ?+ w be evid5t by draw+ no o!r consequ5ce f :at is se5 9 ^? planets1 ?an t ! p[]1 by :i* ! prim>y planets act on _! second>y1 is ext5d$ f ! prim>y ?r\gh ! :ole int]val betwe51 s t x w\ld act 9 e "p ( ! int]m$iate space4 ,9 ,jupit] & ,saturn ?is p[] is s f> f be+ conf9$ to a small ext5t ( di/ance1 t x n only rea*es to sev]al satellites at v diff]5t di/ances1 b also f "o planet to ! o!r1 nay ev5 ?r\gh ! :ole planet>y sy/em#ahd4 ,consequ5tly !re is no appe>ance ( reason1 :y ?is p[] %\ld n act at all di/ances1 ev5 at ! v surfaces ( ^! planets z well z f>!r (f4 ,b f h5ce x foll[s1 t ! p[]1 :i* reta9s ! moon 9 h] orbit1 is ! same1 z causes bodies ne> ! surface ( ! e>? to gravitate4 ,= s9ce ! p[]1 by :i* ! e>? acts on ! moon1 w cause bodies ne> ! surface ( ! e>? to desc5d ) all ! velocity !y are f\nd to d1 x is c]ta9 no o!r p[] c act ^u !m besides2 because if x did1 !y mu/ ( necessity desc5d swift]4 ,n[ f all ?is x is at l5g? v evid5t1 t ! p[] 9 ! e>?1 :i* we call gravity1 ext5ds up to ! moon1 & decreases 9 ! duplicate proportion ( ! increase ( ! di/ance f ! e>?4 #g4 ,,?is f9i%es ! discov]ies made 9 ! action ( ! prim>y planets ^u _! second>y4 ,! next ?+ to be %ewn is1 t ! sun acts ^u !m likewise3 = ?is purpose x is to be obs]v$1 t if to ! motion ( ! satellite1 :]eby x w\ld be c>ri$ r\nd its prim>y at re/1 be sup]add$ ! same motion bo? 9 reg>d to velocity & direction1 z ! prim>y x self has1 x w describe ab\t ! prim>y ! same orbit1 ) z great regul>ity1 z if ! prim>y 0 inde$ at re/4 ,! cause ( ?is is t law ( motion1 :i* makes a body ne> ! surface ( ! e>?1 :5 let fall1 to desc5d p]p5dicul>ly1 ?\gh ! e>? be 9 s swift a motion1 t if ! fall+ body did n p>take ( x1 its desc5t w\ld be rem>kably oblique2 & t a body project$ describes 9 ! mo/ regul> mann] ! same p>abola1 :e!r project$ 9 ! direction1 9 :i* ! e>? moves1 or 9 ! opposite direction1 if ! project+ =ce be ! same#ahe4 ,f ?is we le>n1 t if ! satellite mov$ ab\t its prim>y ) p]fect regul>ity1 besides its motion ab\t ! prim>y1 x w\ld p>ticipate ( all ! motion ( its prim>y2 h ! same progressive velocity1 ) :i* ! prim>y is c>ri$ ab\t ! sun2 & be impell$ ) ! same velocity z ! prim>y t[>ds ! sun1 9 a direction p>allel to t impulse ( its prim>y4 ,& on ! contr>y1 ! want ( ei!r ( ^!1 9 p>ticul> ( ! impulse t[>ds ! sun1 w occasion great inequalities 9 ! motion ( ! second>y planet4 ,! inequalities1 :i* w\ld arise f ! abs5ce ( ?is impulse t[>ds ! sun are s great1 t by ! regul>ity1 :i* appe>s 9 ! motion ( ! second>y planets1 x is prov$1 t ! sun communicates1 ! same velocity to !m by its action1 z x gives to _! prim>y at ! same di/ance4 ,= ,sir ,,isaac ,,newton in=ms u1 t ^u exam9ation he f\nd1 t if any ( ! satellites ( ,jupit] 7 attract$ by ! sun m or less1 ?an ,jupit] himself at ! same di/ance1 ! orbit ( t satellite1 in/ead ( be+ conc5trical to ,jupit]1 mu/ h its c5t] at a great] or less di/ance1 ?an ! c5t] ( ,jupit] f ! sun1 ne>ly 9 ! subduplicate proportion ( ! diff]5ce betwe5 ! sun's action ^u ! satellite1 & ^u ,jupit]2 & !re=e if any satellite 7 attract$ by ! sun b #a_/ajjj "p m or less1 ?an ,jupit] is at ! same di/ance1 ! c5t] ( ! orbit ( t satellite w\ld be di/ant f ! c5t] ( ,jupit] no less ?an a fif? "p ( ! di/ance ( ! out]mo/ satellite f ,jupit]#ahf2 :i* is almo/ ! :ole di/ance ( ! inn]mo/ satellite4 ,by ! l argum5t ! satellites ( ,saturn gravitate t[>ds ! sun1 z mu* z ,saturn x self at ! same di/ance2 & ! moon z mu* z ! e>?4 #h4 ,,?us is prov$1 t ! sun acts ^u ! second>y planets1 z mu* z ^u ! prim>y at ! same di/ance3 b x 0 f\nd 9 ! la/ *apt]1 t ! action ( ! sun ^u bodies is reciprocally 9 ! duplicate proportion ( ! di/ance2 !re=e ! second>y planets be+ sometimes ne>] to ! sun ?an ! prim>y1 & sometimes m remote1 !y are n alway act$ ^u 9 ! same degree ) _! prim>y1 b :5 ne>] to ! sun1 are attract$ m1 & :5 f>!r di/ant1 are attract$ less4 ,h5ce arise v>i\s inequalities 9 ! motion ( ! second>y planets#ahg4 #i4 ,,"s ( ^! inequalities w\ld take place1 ?\gh ! moon1 if undi/urb$ by ! sun1 w\ld h mov$ 9 a circle conc5trical to ! e>?1 & 9 ! plane ( ! e>?'s motion2 o!rs dep5d on ! elliptical figure1 & ! oblique situation ( ! moon's orbit4 ,"o ( ! fir/ k9d is1 t ! moon is caus$ s to move1 z n to describe equal spaces 9 equal times1 b is cont9ually accel]at$1 z %e passes f ! qu>t] to ! new or full1 & is ret>d$ aga9 by ! l degrees 9 return+ f ! new & full to ! next qu>t]4 ,"h we consid] n s mu* ! absolute1 z ! app>5t motion ( ! moon 9 respect to u4 #aj4 ,,! pr9ciples ( a/ronomy tea* h[ to di/+ui% ^! two motions4 ,let ,s 79 fig4 #ie47 repres5t ! sun1 ,a ! e>? mov+ 9 its orbit ,b ,c1 ,d ,e ,f ,g ! moon's orbit1 ! place ( ! moon ,h4 ,suppose ! e>? to h mov$ f ,a to ,i4 ,because x has be5 %ewn1 t ! moon p>takes ( all ! progressive motion ( ! e>?2 & likewise t ! sun attracts bo? ! e>? & moon equally1 :5 !y are at ! same di/ance f x1 or t ! mean action ( ! sun ^u ! moon is equal to its action ^u ! e>?3 we mu/ !re=e consid] ! e>? z c>ry+ ab\t ) x ! moon's orbit2 s t :5 ! e>? is remov$ f ,a to ,i1 ! moon's orbit %all likewise be remov$ f its =m] situation into t d5ot$ by ,k ,l ,m ,n4 ,b n[ ! e>? be+ 9 ,i1 if ! moon 7 f\nd 9 ,o1 s t ,o ,i %\ld be p>allel to ,h ,a1 ?\gh ! moon w\ld really h mov$ f ,h to ,o1 yet x w\ld n h appe>$ to a spectator ^u ! e>? to h mov$ at all1 because ! e>? has mov$ z mu* x self2 s t ! moon w\ld /ill appe> 9 ! same place ) respect to ! fix$ />s4 ,b if ! moon be obs]v$ 9 ,p1 x w !n appe> to h mov$1 its app>5t motion be+ measur$ by ! angle "u ,o ,i ,p4 ,& if ! angle "u ,p ,i ,s be less ?an ! angle "u ,h ,a ,s1 ! moon w h approa*$ ne>] to its conjunction ) ! sun4 #aa4 ,,to come n[ to ! explication ( ! m5tion$ inequality 9 ! moon's motion3 let ,s 79 fig4 #if47 repres5t ! sun1 ,a ! e>?1 ,b ,c ,d ,e ! moon's orbit1 ,c ! place ( ! moon1 :5 9 ! latt] qu>t]4 ,"h x w be ne>ly at ! same di/ance f ! sun1 z ! e>? is4 ,9 ?is case !re=e !y w bo? be equally attract$1 ! e>? 9 ! direction ,a ,s1 & ! moon 9 ! direction ,c ,s4 ,:5ce z ! e>? 9 mov+ r\nd ! sun is cont9ually desc5d+ t[>d x1 s ! moon 9 ?is situation mu/ 9 any equal portion ( "t desc5d z mu*2 & !re=e ! position ( ! l9e ,a ,c 9 respect ( ,a ,s1 & ! *ange1 :i* ! moon's motion produces 9 ! angle "u ,c ,a ,s1 w n be alt]$ by ! sun4 #ab4 ,,b n[ z soon z ev] ! moon is advanc$ f ! qu>t] t[>d ! new or conjunction1 suppose to ,g1 ! action ( ! sun ^u x w h a diff]5t effect4 ,"h1 7 ! sun's action ^u ! moon to be appli$ 9 ! direction ,g ,h p>allel to ,a ,s1 if its action on ! moon 7 equal to its action on ! e>?1 no *ange w\ld be wr\ght by ! sun on ! app>5t motion ( ! moon r\nd ! e>?4 ,b ! moon receiv+ a great] impulse 9 ,g ?an ! e>? receives 9 ,a1 7 ! sun to act 9 ! direction ,g ,h1 yet x w\ld accel]ate ! description ( ! space ,d ,a ,g1 & cause ! angle "u ,g ,a ,d to decrease fa/]1 ?an o!rwise x w\ld4 ,! sun's action w h ?is effect ^u acc\nt ( ! obliquity ( its direction to t1 9 :i* ! e>? attracts ! moon4 ,= ! moon by ?is means is drawn by two =ces oblique to ea* o!r1 "o draw+ f ,g t[>d ,a1 ! o!r f ,g t[>d ,h1 !re=e ! moon mu/ necess>ily be impell$ t[>d ,d4 ,aga91 because ! sun does n act 9 ! direction ,g ,h p>allel to ,s ,a1 b 9 ! direction ,g ,s oblique to x1 ! sun's action on ! moon w by reason ( ?is obliquity f>!r contribute to ! moon's accel]ation4 ,suppose ! e>? 9 any %ort space ( "t w\ld h mov$ f ,a to ,i1 if n attract$ by ! sun2 ! po9t ,i be+ 9 ! /raight l9e ,c ,e1 :i* t\*es ! e>?'s orbit 9 ,a4 ,suppose ! moon 9 ! same "t w\ld h mov$ 9 h] orbit f ,g to ,k1 & besides h p>took ( all ! progressive motion ( ! e>?4 ,!n if ,k ,l be drawn p>allel to ,a ,i1 & tak5 equal to x1 ! moon1 if n attract$ by ! sun1 w\ld be f\nd 9 ,l4 ,b ! e>? by ! sun's action is remov$ f ,i4 ,suppose x 7 mov$ d[n to ,m 9 ! l9e ,i ,m ,n p>allel to ,s ,a1 & if ! moon 7 attract$ b z mu*1 & 9 ! same direction1 z ! e>? is "h suppos$ to be attract$1 s z to h desc5d$ dur+ ! same "t 9 ! l9e ,l ,o1 p>allel also to ,a ,s1 d[n z f> z ,p1 till ,l ,p 7 equal to ,i ,m2 ! angle "u ,p ,m ,n w\ld be equal to t "u ,l ,i ,n1 t is1 ! moon w appe> advanc$ no f>!r =w>d1 ?an if nei!r x nor ! e>? _h be5 subject to ! sun's action4 ,b ?is is ^u ! supposition1 t ! action ( ! sun ^u ! moon & e>? 7 equal2 :]eas ! moon be+ act$ ^u m ?an ! e>?1 did ! sun's action draw ! moon 9 ! l9e ,l ,o p>allel to ,a ,s1 x w\ld draw x d[n s f> z to make ,l ,p great] ?an ,i ,m2 :]eby ! angle "u ,p ,m ,n w be r5dr$ less1 ?an t "u ,l ,i ,n4 ,b moreov]1 z ! sun draws ! e>? 9 a direction oblique to ,i ,n1 ! e>? w be f\nd 9 its orbit some:at %ort ( ! po9t ,m2 h[ev] ! moon is attract$ by ! sun /ill m out ( ! l9e ,l ,o1 ?an ! e>? is out ( ! l9e ,i ,n2 !re=e ?is obliquity ( ! sun's action w yet f>!r dim9i% ! angle "u ,p ,m ,n4 #ac4 ,,?us ! moon at ! po9t ,g receives an impulse f ! sun1 :]eby h] motion is accel]at$4 ,& ! sun produc+ ?is effect 9 e place betwe5 ! qu>t] & ! conjunction1 ! moon w move f ! qu>t] ) a motion cont9ually m & m accel]at$2 & !re=e by acquir+ f "t to "t additional degrees ( velocity 9 its orbit1 ! spaces1 :i* are describ$ 9 equal times by ! l9e drawn f ! e>? to ! moon1 w n be e :]e equal1 b ^? t[>d ! conjunction w be great]1 ?an ^? t[>d ! qu>t]4 ,b n[ 9 ! moon's passage f ! conjunction ,d to ! next qu>t] ! sun's action w aga9 ret>d ! moon1 till at ! next qu>t] 9 ,e x be re/or$ to ! fir/ velocity1 :i* x _h 9 ,c4 #ad4 ,,aga9 z ! moon moves f ,e to ! full or opposition to ! sun 9 ,b1 x is aga9 accel]at$1 ! defici5cy ( ! sun's action ^u ! moon1 f :at x has ^u ! e>?1 produc+ "h ! same effect z be=e ! excess ( its action4 ,consid] ! moon 9 ,q1 mov+ f ,e t[>ds ,b4 ,"h if ! moon 7 attract$ by ! sun 9 a direction p>allel to ,a ,s1 yet be+ act$ on less ?an ! e>?1 z ! e>? desc5ds t[>d ! sun1 ! moon w 9 "s measure be left beh9d4 ,!re=e ,q ,f be+ drawn p>allel to ,s ,b1 a spectator on ! e>? w\ld see ! moon move1 z if attract$ f ! po9t ,q 9 ! direction ,q ,f ) a degree ( =ce equal to t1 :]eby ! sun's action on ! moon falls %ort ( its action on ! e>?4 ,b ! obliquity ( ! sun's action has also "h an effect4 ,9 ! "t ! e>? w\ld h mov$ f ,a to ,i )\t ! influ5ce ( ! sun1 let ! moon h mov$ 9 its orbit f ,q to ,r4 ,draw+ !re=e ,r ,t p>allel to ,a ,i1 & equal to ! same1 = ! l reason z be=e1 ! moon by ! motion ( its orbit1 if n at all attract$ by ! sun1 mu/ be f\nd 9 ,t2 & !re=e1 if attract$ 9 a direction p>allel to ,s ,a1 w\ld be 9 ! l9e ,t ,v p>allel to ,a ,s2 suppose 9 ,w4 ,b ! moon 9 ,q be+ f>!r (f ! sun ?an ! e>?1 x w be less attract$1 t is1 ,t ,w w be less ?an ,i ,m1 & if ! l9e ,s ,m be prolong$ t[>d ,x1 ! angle "u ,x ,m ,w w be less ?an t "u ,x ,i ,t4 ,?us by ! sun's action ! moon's passage f ! qu>t] to ! full w\ld be accel]at$1 if ! sun 7 to act on ! e>? & moon 9 a direction p>allel to ,a ,s3 & ! obliquity ( ! sun's action w /ill m increase ?is accel]ation4 ,= ! action ( ! sun on ! moon is oblique to ! l9e ,s ,a ! :ole "t ( ! moon's passage f ,q to ,t1 & w c>ry ! moon out ( ! l9e ,t ,v t[>d ! e>?4 ,"h ,i suppose ! "t ( ! moon's passage f ,q to ,t s %ort1 t x %all n pass beyond ! l9e ,s ,a4 ,! e>? also w come a little %ort ( ! l9e ,i ,n1 z 0 said be=e4 ,f ^! causes ! angle "u ,x ,m ,w w be /ill f>!r less5$4 #ae4 ,,! moon 9 pass+ f ! opposition ,b to ! next qu>t] w be ret>d$ aga9 by ! same degrees1 z x is accel]at$ be=e its appulse to ! opposition4 ,because ?is action ( ! sun1 :i* 9 ! moon's passage f ! qu>t] to ! opposition causes x to be extraord9>ily accel]at$1 & dim9i%es ! angle1 :i* measures its di/ance f ! opposition2 w make ! moon slack5 its pace aft]w>ds1 & ret>d ! augm5tation ( ! same angle 9 its passage f ! opposition to ! foll[+ qu>t]2 t is1 w prev5t t angle f increas+ s fa/1 z o!rwise x w\ld4 ,& ?us ! moon1 by ! sun's action ^u x1 is twice accel]at$ & twice re/or$ to its fir/ velocity1 e circuit x makes r\nd ! e>?4 ,?is inequality ( ! moon's motion ab\t ! e>? is call$ by a/ronom]s its v>iation4 #af4 ,,! next effect ( ! sun ^u ! moon is1 t x gives ! orbit ( ! moon 9 ! qu>t]s a great] degree ( curvature1 ?an x w\ld receive f ! action ( ! e>? alone2 & on ! contr>y 9 ! conjunction & opposition ! orbit is less inflect$4 #ag4 ,,:5 ! moon is 9 conjunction ) ! sun 9 ! po9t ,d1 ! sun attract+ ! moon m =cibly ?an x does ! e>?1 ! moon by t means is impell$ less t[>d ! e>?1 ?an o!rwise x w\ld be1 & s ! orbit is less incurvat$2 = ! p[]1 by :i* ! moon is impell$ t[>d ! e>?1 be+ t1 by :i* x is inflect$ f a rectil9e> c\rse1 ! less t p[] is1 ! less x w be inflect$4 ,aga91 :5 ! moon is 9 ! opposition 9 ,b1 f>!r remov$ f ! sun ?an ! e>? is2 x foll[s !n1 ?\gh ! e>? & moon are bo? cont9ually desc5d+ to ! sun1 t is1 are drawn by ! sun t[>d x self out ( ! place !y w\ld o!rwise move into1 yet ! moon desc5ds ) less velocity ?an ! e>?2 insomu* t ! moon 9 any giv5 space ( "t f its pass+ ! po9t ( opposition w h less approa*$ ! e>?1 ?an o!rwise x w\ld h done1 t is1 its orbit 9 respect ( ! e>? w approa* ne>] to a /raight l9e4 ,9 ! la/ place1 :5 ! moon is 9 ! qu>t] 9 ,f1 & equally di/ant f ! sun z ! e>?1 we obs]v$ be=e1 t ! e>? & moon w\ld desc5d ) equal pace t[>d ! sun1 s z to make no *ange by t desc5t 9 ! angle "u ,f ,a ,s2 b ! l5g? ( ! l9e ,f ,a mu/ ( necessity be %ortn$4 ,!re=e ! moon 9 mov+ f ,f t[>d ! conjunction ) ! sun w be impell$ m t[>d ! e>? by ! sun's action1 ?an x w\ld h be5 by ! e>? alone1 if nei!r ! e>? nor moon _h be5 act$ on by ! sun2 s t by ?is additional impulse ! orbit is r5dr$ m curve1 ?an x w\ld o!rwise be4 ,! same effect w also be produc$ 9 ! o!r qu>t]4 #ah4 ,,ano!r effect ( ! sun's action1 consequ5t ^u ?is we h n[ expla9$1 is1 t ?\gh ! moon undi/urb$ by ! sun might move 9 a circle hav+ ! e>? = its c5t]2 by ! sun's action1 if ! e>? 7 to be 9 ! v middle or c5t] ( ! moon's orbit1 yet ! moon w\ld be ne>] ! e>? at ! new & full1 ?an 9 ! qu>t]s4 ,9 ?is probably w at fir/ appe> "s difficulty1 t ! moon %\ld come ne>e/ to ! e>?1 :]e x is lea/ attract$ to x1 & be f>!/ (f :5 mo/ attract$4 ,:i* yet w appe> evid5tly to foll[ f t v cause1 by consid]+ :at 0 la/ %ewn1 t ! orbit ( ! moon 9 ! conjunction & opposition is r5dr$ less curve2 = ! less curve ! orbit ( ! moon is1 ! less w ! moon h desc5d$ f ! place x w\ld move into1 )\t ! action ( ! e>?4 ,n[ if ! moon 7 to move f any place )\t f>!r di/urbance f t action1 s9ce x w\ld proce$ 9 ! l9e1 :i* w\ld t\* its orbit 9 t place1 x w\ld rec$e cont9ually f ! e>?2 & !re=e if ! p[] ( ! e>? ^u ! moon1 be suffici5t to reta9 x at ! same di/ance1 ?is dim9ution ( t p[] w cause ! di/ance to increase1 ?\gh 9 a less degree4 ,b on ! o!r h& 9 ! qu>t]s1 ! moon1 be+ press$ m t[>ds ! e>? ?an by ! e>?'s s+le action1 w be made to approa* x2 s t 9 pass+ f ! conjunction or opposition to ! qu>t]s ! moon asc5ds f ! e>?1 & 9 pass+ f ! qu>t]s to ! conjunction & opposition x desc5ds aga91 becom+ ne>] 9 ^! la/ m5tion$ places ?an 9 ! o!r4 #ai4 ,,all ^! =em5tion$ inequalities are ( diff]5t degrees1 accord+ z ! sun is m or less di/ant f ! e>?2 great] :5 ! e>? is ne>e/ ! sun1 & less :5 x is f>!/ (f4 ,= 9 ! qu>t]s1 ! ne>] ! moon is to ! sun1 ! great] is ! addition to ! e>?'s action ^u x by ! p[] ( ! sun2 & 9 ! conjunction & opposition1 ! diff]5ce betwe5 ! sun's action ^u ! e>? & ^u ! moon is likewise s mu* ! great]4 #bj4 ,?is diff]5ce 9 ! di/ance betwe5 ! e>? & ! sun produces a f>!r effect ^u ! moon's motion2 caus+ ! orbit to dilate :5 less remote f ! sun1 & become great]1 ?an :5 at a f>!r di/ance4 ,= x is prov$ by ,sir ,,isaac ,,newton1 t ! action ( ! sun1 by :i* x dim9i%es ! e>?'s p[] ov] ! moon1 9 ! conjunction or opposition1 is ab\t twice z great1 z ! addition to ! e>?'s action by ! sun 9 ! qu>t]s#ahh2 s t ^u ! :ole1 ! p[] ( ! e>? ^u ! moon is dim9i%$ by ! sun1 & !re=e is mo/ dim9i%$1 :5 ! action ( ! sun is /ronge/3 b z ! e>? by its approa* to ! sun has its influ5ce less5$1 ! moon be+ less attract$ w gradually rec$e f ! e>?2 & z ! e>? 9 its recess f ! sun recov]s by degrees its =m] p[]1 ! orbit ( ! moon mu/ aga9 contract4 ,two consequ5ces foll[ f h5ce3 ! moon w be mo/ remote f ! e>?1 :5 ! e>? is ne>e/ ! sun2 & also w take up a long] "t 9 p]=m+ its revolution ?r\gh ! dilat$ orbit1 ?an ?r\gh ! m contract$4 #ba4 ,,^! irregul>ities ! sun w\ld produce 9 ! moon1 if ! moon1 )\t be+ act$ on unequally by ! sun1 w\ld describe a p]fect circle ab\t ! e>?1 & 9 ! plane ( ! e>?'s motion2 b ?\gh nei!r ( ^! suppositions obta9 9 ! motion ( ! moon1 yet ! =em5tion$ inequalities w take place1 only ) "s diff]5ce 9 respect to ! degree ( !m2 b ! moon by n mov+ 9 ?is mann] is subject to "s o!r inequalities also4 ,= z ! moon describes1 in/ead ( a circle conc5trical to ! e>?1 an ellipsis1 ) ! e>? 9 "o focus1 t ellipsis w be subject$ to v>i\s *anges4 ,x c nei!r pres]ve con/antly ! same position1 nor yet ! same figure2 & because ! plane ( ?is ellipsis is n ! same ) t ( ! e>?'s orbit1 ! situation ( ! plane1 :]e9 ! moon moves1 w cont9ually *ange2 nei!r ! l9e 9 :i* x int]sects ! plane ( ! e>?'s orbit1 nor ! incl9ation ( ! planes to ea* o!r1 w rema9 = any "t ! same4 ,all ^! alt]ations (f] !mselves n[ to be expla9$4 #bb4 ,i ,,%all fir/ consid] ! *anges :i* are made 9 ! plane ( ! moon's orbit4 ,! moon n mov+ 9 ! same plane ) ! e>?1 ! sun is seldom 9 ! plane ( ! moon's orbit1 viz4 only :5 ! l9e made by ! common int]section ( ! two planes1 if produc$1 w pass ?r\gh ! sun1 z is repres5t$ 9 fig4 #ig4 :]e ,s d5otes ! sun2 ,t ! e>?2 ,a ,t ,b ! e>?'s orbit describ$ ^u ! plane ( ?is s*eme2 ,c ,d ,e ,f ! moon's orbit1 ! "p ,c ,d ,e be+ rais$ above1 & ! "p ,c ,f ,e depress$ "u ! plane ( ?is s*eme4 ,"h ! l9e ,c ,e1 9 :i* ! plane ( ?is s*eme1 t is1 ! plane ( ! e>?'s orbit & ! plane ( ! moon's orbit int]sect ea* o!r1 be+ cont9u$ passes ?r\gh ! sun 9 ,s4 ,:5 ?is happ5s1 ! action ( ! sun is direct$ 9 ! plane ( ! moon's orbit1 & _c draw ! moon out ( ?is plane1 z w evid5tly appe> to any "o t %all consid] ! pres5t s*eme3 = suppose ! moon 9 ,g1 & let a /raight l9e be drawn f ,g to ,s1 ! sun draws ! moon 9 ! direction ( ?is l9e f ,g t[>d ,s3 b ?is l9e lies 9 ! plane ( ! orbit2 & if x be prolong$ f ,s beyond ,g1 ! cont9uation ( x w lie on ! plane ,c ,d ,e2 = ! plane itself1 if suffici5tly ext5d$1 w pass ?r\gh ! sun4 ,b 9 o!r cases ! obliquity ( ! sun's action to ! plane ( ! orbit w cause ?is plane cont9ually to *ange4 #bc4 ,,suppose 9 ! fir/ place1 ! l9e1 9 :i* ! two planes int]sect ea* o!r1 to be p]p5dicul> to ! l9e :i* jo9s ! e>? & sun4 ,let ,t 79 fig4 #ih1 #ii1 #ajj1 #aja47 repres5t ! e>?2 ,s ! sun2 ! plane ( ?is s*eme ! plane ( ! e>?'s motion1 9 :i* bo? ! sun & e>? are plac$4 ,let ,a ,c be p]p5dicul> to ,s ,t1 :i* jo9s ! e>? & sun2 & let ! l9e ,a ,c be t1 9 :i* ! plane ( ! moon's orbit int]sects ! plane ( ! e>?'s motion4 ,to ! c5t] ,t describe 9 ! plane ( ! e>?'s motion ! circle ,a ,b ,c ,d4 ,& 9 ! plane ( ! moon's orbit describe ! circle ,a ,e ,c ,f1 "o half ( :i* ,a ,e ,c w be elevat$ above ! plane ( ?is s*eme1 ! o!r half ,a ,f ,c z mu* depress$ bel[ x4 #bd4 ,,n[ suppose ! moon to set =? f ! po9t ,a 79 fig4 #ih47 9 ! direction ( ! plane ,a ,e ,c4 ,"h %e w be cont9ually drawn out ( ?is plane by ! action ( ! sun3 = ?is plane ,a ,e ,c1 if ext5d$1 w n pass ?r\gh ! sun1 b above x2 s t ! sun1 by draw+ ! moon directly t[>d x self1 w =ce x cont9ually m & m f t plane t[>ds ! plane ( ! e>?'s motion1 9 :i* x self is2 caus+ x to describe ! l9e ,a ,k ,g ,h ,i1 :i* w be convex to ! plane ,a ,e ,c1 & concave to ! plane ( ! e>?'s motion4 ,b "h ?is p[] ( ! sun1 :i* is said to draw ! moon t[>d ! plane ( ! e>?'s motion1 mu/ be und]/ood pr9cipally ( s mu* only ( ! sun's action ^u ! moon1 z x exce$s ! action ( ! same ^u ! e>?4 ,= suppose ! prec$+ figure to be view$ by ! eye1 plac$ 9 ! plane ( t s*eme1 & 9 ! l9e ,c ,t ,a on ! side ( ,a1 ! plane ,a ,b ,c ,d w appe> z ! /raight l9e ,d ,t ,b1 79 fig4 #ajb47 & ! plane ,a ,e ,c ,f z ano!r /raight l9e ,f ,e2 & ! curve l9e ,a ,k ,g ,h ,i "u ! =m ( ! l9e ,t ,k ,g ,h ,i4 ,illu/ration ,n[ x is pla91 t ! e>? & moon be+ bo? attract$ by ! sun1 if ! sun's action ^u bo? 0 equally /rong1 ! e>? ,t1 & ) x ! plane ,a ,e ,c ,f or l9e ,f ,t ,e 9 ?is s*eme1 w\ld be c>ri$ t[>d ! sun ) z great a pace z ! moon1 & !re=e ! moon n drawn out ( x by ! sun's action1 except+ only f ! small obliquity ( ! direction ( ?is action ^u ! moon to t ( ! sun's action ^u ! e>?1 :i* arises f ! moon's be+ out ( ! plane ( ! e>?'s motion1 & is n v consid]able2 b ! action ( ! sun ^u ! moon be+ great] ?an ^u ! e>?1 all ! "t ! moon is ne>] to ! sun ?an ! e>? is1 x w be drawn f ! plane ,a ,e ,c or ! l9e ,t ,e by t excess1 & made to describe ! curve l9e ,a ,g ,i or ,t ,g ,i4 ,b x is ! cu/om ( a/ronom]s1 in/ead ( consid]+ ! moon z mov+ 9 su* a curve l9e1 to ref] its motion cont9ually to ! plane1 :i* t\*es ! true l9e :]e9 x moves1 at ! po9t :]e at any "t ! moon is4 ,?us :5 ! moon is 9 ! po9t ,a1 its motion is consid]$ z be+ 9 ! plane ,a ,e ,c1 9 ^: direction x !n essaies to move2 & :5 9 ! po9t ,k 79 fig4 #ii47 its motion is ref]r$ to ! plane1 :i* passes ?r\gh ! e>?1 & t\*es ! l9e ,a ,k ,g ,h ,i 9 ! po9t ,k4 ,?us ! moon 9 pass+ f ,a to ,i w cont9ually *ange ! plane ( h] motion4 ,9 :at mann] ?is *ange proce$s1 ,i %all n[ p>ticul>ly expla94 #be4 ,,let ! plane1 :i* t\*es ! l9e ,a ,k ,i 9 ! po9t ,k 79 fig4 #ii47 int]sect ! plane ( ! e>?'s orbit 9 ! l9e ,l ,t ,m4 ,!n1 because ! l9e ,a ,k ,i is concave to ! plane ,a ,b ,c1 x falls :olly betwe5 t plane1 & ! plane :i* t\*es x 9 ,k2 s t ! plane ,m ,k ,l w cut ! plane ,a ,e ,c1 be=e x meets ) ! plane ( ! e>?'s motion2 suppose 9 ! l9e ,y ,t1 & ! po9t ,a w fall betwe5 ,k & ,l4 ,) a semidiamet] equal to ,t ,y or ,t ,l describe ! semicircle ,l ,y ,m4 ,n[ to a spectator on ! e>? ! moon1 :5 9 ,a1 w appe> to move 9 ! circle ,a ,e ,c ,f1 &1 :5 9 ,k1 w appe> to be mov+ 9 ! semicircle ,l ,y ,m4 ,! e>?'s motion is p]=m$ 9 ! plane ( ?is s*eme1 & to a spectator on ! e>? ! sun w appe> always mov+ 9 t plane4 ,we may !re=e ref] ! app>5t motion ( ! sun to ! circle ,a ,b ,c ,d1 describ$ 9 ?is plane ab\t ! e>?4 ,b ! po9ts :]e ?is circle1 9 :i* ! sun seems to move1 int]sects ! circle 9 :i* ! moon is se5 at any "t to move1 are call$ ! nodes ( ! moon's orbit at t "t4 ,:5 ! moon is se5 mov+ 9 ! circle ,a ,e ,c ,d1 ! po9ts ,a & ,c are ! nodes ( ! orbit2 :5 %e appe>s 9 ! semicircle ,l ,y ,m1 !n ,l & ,m are ! nodes4 ,n[ "h x appe>s1 f :at has be5 said1 t :ile ! moon has mov$ f ,a to ,k1 "o ( ! nodes has be5 c>ri$ f ,a to ,l1 & ! o!r z mu* f ,c to ,m4 ,b ! motion f ,a to ,l1 & f ,c to ,m1 is backw>d 9 reg>d to ! motion ( ! moon1 :i* is ! o!r way f ,a to ,k1 & f !nce t[>d ,c4 #bf4 ,,f>!r ! angle1 :i* ! plane1 :]e9 ! moon at any "t appe>s1 makes ) ! plane ( ! e>?'s motion1 is call$ ! incl9ation ( ! moon's orbit at t "t4 ,& ,i %all n[ proce$ to %ew1 t ?is incl9ation ( ! orbit1 :5 ! moon is 9 ,k1 is less ?an :5 %e 0 9 ,a2 or1 t ! plane ,l ,y ,m1 :i* t\*es ! l9e ( ! moon's motion 9 ,k1 makes a less angle ) ! plane ( ! e>?'s motion or ) ! circle ,a ,b ,c ,d1 ?an ! plane ,a ,e ,c makes ) ! same4 ,! semicircle ,l ,y ,m int]sects ! semicircle ,a ,e ,c 9 ,y2 & ! ar* ,a ,y is less ?an ,l ,y1 & bo? toge!r less ?an half a circle4 ,b x is demon/rat$ by ! writ]s on t "p ( a/ronomy1 :i* is call$ ! doctr9e ( ! sph]e1 t :5 a triangle is made1 z "h1 by ?ree ar*es ( circles ,a ,l1 ,a ,y1 & ,y ,l1 ! angle "u ,y ,a ,b )\t ! triangle is great] ?an ! angle "u ,y ,l ,a )91 if ! two ar*es ,a ,y1 ,y ,l tak5 toge!r d n am\nt to a semicircle2 if ! two ar*es make a complete semicircle1 ! two angles w be equal2 b if ! two ar*es tak5 toge!r exce$ a semicircle1 ! inn] angle "u ,y ,l ,a is great] ?an ! o!r#ahi4 ,"h !re=e ! two ar*es ,a ,y & ,l ,y toge!r be+ less ?an a semicircle1 ! angle "u ,a ,l ,y is less1 ?an ! angle "u ,b ,a ,e4 ,b f ! doctr9e ( ! sph]e x is also evid5t1 t ! angle "u ,a ,l ,y is equal to t1 9 :i* ! plane ( ! circle ,l ,y ,k ,m1 t is1 ! plane :i* t\*es ! l9e ,a ,k ,g ,h ,i 9 ,k1 is incl9$ to ! plane ( ! e>?'s motion ,a ,b ,c2 & ! angle "u ,b ,a ,e is equal to t1 9 :i* ! plane ,a ,e ,c is incl9$ to ! same plane4 ,!re=e ! incl9ation ( ! =m] plane is less ?an ! incl9ation ( ! latt]4 #bg4 ,,suppose n[ ! moon to be advanc$ to ! po9t ,g 79 fig4 #ajj47 & 9 ?is po9t to be di/ant f its node a qu>t] "p ( ! :ole circle2 or 9 o!r words1 to be 9 ! midway betwe5 its two nodes4 ,& 9 ?is case ! nodes w h rec$$ yet m1 & ! incl9ation ( ! orbit be /ill m dim9i%$3 = suppose ! l9e ,a ,k ,g ,h ,i to be t\*$ 9 ! po9t ,g by a plane pass+ ?r\gh ! e>? ,t3 let ! int]section ( ?is plane ) ! plane ( ! e>?'s motion be ! l9e ,w ,t ,o1 & ! l9e ,t ,p its int]section ) ! plane ,l ,k ,m4 ,9 ?is plane let ! circle ,n ,g ,o be describ$ ) ! semidiamet] ,t ,p or ,n ,t cutt+ ! o!r circle ,l ,k ,m 9 ,p4 ,n[ ! l9e ,a ,k ,g ,i is convex to ! plane ,l ,k ,m1 :i* t\*es x 9 ,k2 & !re=e ! plane ,n ,g ,o1 :i* t\*es x 9 ,g1 w int]sect ! o!r t\*+ plane betwe5 ,g & ,k2 t is1 ! po9t ,p w fall betwe5 ^? two po9ts1 & ! plane cont9u$ to ! plane ( ! e>?'s motion w pass beyond ,l2 s t ! po9ts ,n & ,o1 or ! places ( ! nodes1 :5 ! moon is 9 ,g1 w be f>!r f ,a & ,c ?an ,l & ,m1 t is1 w h mov$ f>!r backw>d4 ,besides1 ! incl9ation ( ! plane ,n ,g ,o to ! plane ( ! e>?'s motion ,a ,b ,c is less1 ?an ! incl9ation ( ! plane ,l ,k ,m to ! same2 = "h also ! two ar*es ,l ,p & ,n ,p tak5 toge!r are less ?an a semicircle1 ea* ( ^! ar*es be+ less ?an a qu>t] ( a circle2 z appe>s1 because ,g ,n1 ! di/ance ( ! moon 9 ,g f its node ,n1 is "h suppos$ to be a qu>t] "p ( a circle4 #bh4 ,,aft] ! moon is pass$ beyond ,g1 ! case is alt]$2 = !n ^! ar*es w be great] ?an qu>t]s ( ! circle1 by :i* means ! incl9ation w be aga9 increas$1 ?o' ! nodes /ill g on to move ! same way4 ,suppose ! moon 9 ,h1 79 fig4 #aja47 & t ! plane1 :i* t\*es ! l9e ,a ,k ,g ,i 9 ,h1 int]sects ! plane ( ! e>?'s motion 9 ! l9e ,q ,t ,r1 & ! plane ,n ,g ,o 9 ! l9e ,t ,v1 & besides t ! circle ,q ,h ,r be describ$ 9 t plane2 !n1 = ! same reason z be=e1 ! po9t ,v w fall betwe5 ,h & ,g1 & ! plane ,r ,v ,q w pass beyond ! la/ plane ,o ,v ,n1 caus+ ! po9ts ,q & ,r to fall f>!r f ,a & ,c ?an ,n & ,o4 ,b ! ar*es ,n ,v1 ,v ,q are ea* great] ?an a qu>t] ( a circle1 ,n ,v ! lea/ ( !m be+ great] ?an ,g ,n1 :i* is a qu>t] ( a circle2 & !re=e ! two ar*es ,n ,v & ,v ,q toge!r exce$ a semicircle2 consequ5tly ! angle "u ,b ,q ,v w be great]1 ?an t "u ,b ,n ,v4 #bi4 ,,9 ! la/ place1 :5 ! moon is by ?is attraction ( ! sun1 drawn at l5g? into ! plane ( ! e>?'s motion1 ! node w h rec$$ yet m1 & ! incl9ation be s mu* increas$1 z to become some:at m ?an at fir/3 = ! l9e ,a ,k ,g ,h ,i be+ convex to all ! planes1 :i* t\* x1 ! "p ,h ,i w :olly fall betwe5 ! plane ,q ,v ,r & ! plane ,a ,b ,c2 s t ! po9t ,i w fall betwe5 ,b & ,r2 & draw+ ,i ,t ,w1 ! po9t ,w w be f>!r remov'd f ,a ?an ,q4 ,b x is evid5t1 t ! plane1 :i* passes ?r\gh ! e>? ,t1 & t\*es ! l9e ,a ,g ,i 9 ! po9t ,i1 w cut ! plane ( ! e>?'s motion ,a ,b ,c ,d 9 ! l9e ,i ,t ,w1 & be incl9$ to ! same 9 ! angle "u ,h ,i ,b2 s t ! node1 :i* 0 fir/ 9 ,a1 aft] hav+ pass$ into ,l1 ,n & ,q1 comes at la/ into ! po9t ,w2 z ! node :i* 0 at fir/ 9 ,c has pass$ successively f !nce ?r\gh ! po9ts ,m1 ,o & ,r to ,i3 b ! angle "u ,h ,i ,b1 :i* is n[ ! incl9ation ( ! orbit to ! plane ( ! ecliptic1 is manife/ly n less ?an ! angle "u ,e ,c ,b or ,e ,a ,b1 b r some?+ great]4 #cj4 ,,?us ! moon 9 ! case be=e u1 :ile x passes f ! plane ( ! e>?'s motion 9 ! qu>t]1 till x comes aga9 into ! same plane1 has ! nodes ( its orbit cont9ually mov$ backw>d1 & ! incl9ation ( its orbit is at fir/ dim9i%$1 viz4 till x comes to ,g 9 fig4 #ajj1 :i* is ne> to its conjunction ) ! sun1 b aft]w>ds is increas$ aga9 almo/ by ! same degrees1 till ^u ! moon's arrival aga9 to ! plane ( ! e>?'s motion1 ! incl9ation ( ! orbit is re/or$ to some?+ m ?an its fir/ magnitude1 ?\gh ! diff]5ce is n v great1 because ! po9ts ,i & ,c are n f> di/ant f ea* o!r#aij4 #ca4 ,,aft] ! same mann]1 if ! moon _h dep>t$ f ! qu>t] 9 ,c1 x %\ld h describ$ ! curve l9e ,c ,x ,w 79 fig4 #ih47 betwe5 ! planes ,a ,f ,c & ,a ,d ,c1 :i* w\ld be convex to ! =m] ( ^? planes1 & concave to ! latt]2 s t1 "h also1 ! nodes %\ld cont9ually rec$e1 & ! incl9ation ( ! orbit gradually dim9i% m & m1 till ! moon arriv$ ne> its opposition to ! sun 9 ,x2 b f t "t ! incl9ation %\ld aga9 increase1 till x became a little great] ?an at fir/4 ,?is w easily appe>1 by consid]+1 t z ! action ( ! sun ^u ! moon1 by exce$+ its action ^u ! e>?1 drew x out ( ! plane ,a ,e ,c t[>ds ! sun1 :ile ! moon pass$ f ,a to ,i2 s1 dur+ its passage f ,c to ,w1 ! moon be+ all t "t f>!r f ! sun ?an ! e>?1 x w be attract$ less2 & ! e>?1 toge!r ) ! plane ,a ,e ,c ,f1 w z x 7 be drawn f ! moon1 9 su* sort1 t ! pa? ! moon describes %all appe> f ! e>?1 z x did 9 ! =m] case by ! moon's be+ drawn away4 #cb4 ,,^! are ! *anges1 :i* ! nodes & ! incl9ation ( ! moon's orbit und]go1 :5 ! nodes are 9 ! qu>t]s2 b :5 ! nodes by _! motion1 & ! motion ( ! sun toge!r1 come to be situat$ betwe5 ! qu>t] & conjunction or opposition1 _! motion & ! *ange made 9 ! incl9ation ( ! orbit are some:at diff]5t4 #cc4 ,,let ,a ,g ,c ,h 79 fig4 #ajc47 be a circle describ$ 9 ! plane ( ! e>?'s motion1 hav+ ! e>? 9 ,t = its c5t]4 ,let ! po9t opposite to ! sun be ,a1 & ! po9t ,g a f\r? "p ( ! circle di/ant f ,a4 ,let ! nodes ( ! moon's orbit be situat$ 9 ! l9e ,b ,t ,d1 & ,b ! node1 fall+ betwe5 ,a1 ! place :]e ! moon w\ld be 9 ! full1 & ,g ! place :]e ! moon w\ld be 9 ! qu>t]4 ,suppose ,b ,e ,d ,f to be ! plane1 9 :i* ! moon essays to move1 :5 x proce$s f ! po9t ,b4 ,because ! moon 9 ,b is m di/ant f ! sun ?an ! e>?1 x %all be less attract$ by ! sun1 & %all n desc5d t[>ds ! sun s fa/ z ! e>?3 consequ5tly x %all quit ! plane ,b ,e ,d ,f1 :i* we suppose to accompany ! e>?1 & describe ! l9e ,b ,i ,k convex !reto1 till su* "t z x comes to ! po9t ,k1 :]e x w be 9 ! qu>t]3 b f !nce=? be+ m attract$ ?an ! e>?1 ! moon %all *ange its c\rse1 & ! foll[+ "p ( ! pa? x describes %all be concave to ! plane ,b ,e ,d or ,b ,g ,d1 & %all cont9ue concave to ! plane ,b ,g ,d1 till x crosses t plane 9 ,l1 j z 9 ! prec$+ case4 ,n[ ,i say1 :ile ! moon is pass+ f ,b to ,k1 ! nodes1 contr>y to :at 0 f\nd 9 ! =ego+ case1 w proce$ =w>d1 or move ! same way ) ! moon#aia2 & at ! same "t ! incl9ation ( ! orbit w increase#aib4 ,illu/ration #cd4 ,,:5 ! moon is 9 ! po9t ,i1 let ! plane ,m ,i ,n pass ?r\gh ! e>? ,t1 & t\* ! pa? ( ! moon 9 ,i1 cutt+ ! plane ( ! e>?'s motion1 9 ! l9e ,m ,t ,n1 & ! plane ,b ,e ,d 9 ! l9e ,t ,o4 ,because ! l9e ,b ,i ,k is convex to ! plane ,b ,e ,d1 :i* t\*es x 9 ,b1 ! plane ,n ,i ,m mu/ cross ! plane ,d ,e ,b1 be=e x meets ! plane ,c ,g ,b2 & !re=e ! po9t ,m w fall f ,b t[>ds ,g1 & ! node ( ! moon's orbit be+ translat$ f ,b to ,m is mov$ =w>d4 #ce4 ,i ,,say f>!r1 ! angle "u ,o ,m ,g1 :i* ! plane ,m ,o ,n makes ) ! plane ,b ,g ,c1 is great] ?an ! angle "u ,o ,b ,g1 :i* ! plane ,b ,o ,d makes ) ! same4 ,?is appe>s f :at has be5 already expla9$2 because ! ar*es ,b ,o1 ,o ,m are ea* less ?an ! qu>t] ( a circle1 & !re=e tak5 bo? toge!r are less ?an a semicircle4 #cf4 ,,aga91 :5 ! moon is come to ! po9t ,k 9 its qu>t]1 ! nodes w be advanc$ yet f>!r =w>d1 & ! incl9ation ( ! orbit also m augm5t$4 ,hi!rto ! moon's motion has be5 ref]r$ to ! plane1 :i* pass+ ?r\gh ! e>? t\*es ! pa? ( ! moon 9 ! po9t1 :]e ! moon is1 accord+ to :at 0 ass]t$ at ! beg9n+ ( ?is disc\rse ^u ! nodes1 t x is ! cu/om ( a/ronom]s s to d4 ,b "h 9 ! po9t ,k no su* plane c be f\nd2 on ! contr>y1 see+ ! l9e ( ! moon's motion on "o side ! po9t ,k is convex to ! plane ,b ,e ,d1 & on ! o!r side concave to ! same1 no plane c pass ?r\gh ! po9ts ,t & ,k b w cut ! l9e ,b ,k ,l 9 t po9t4 ,!re=e in/ead ( su* a t\*+ plane1 we mu/ "h make use ( :at is equival5t1 ! plane ,p ,k ,q1 ) :i* ! l9e ,b ,k ,l %all make a less angle ?an ) any o!r plane2 = ?is plane does z x 7 t\* ! l9e ,b ,k 9 ! po9t ,k1 s9ce x s cuts x1 t no o!r plane c be drawn s1 z to pass betwe5 ! l9e ,b ,k & ! plane ,p ,k ,q4 ,b n[ x is evid5t1 t ! po9t ,p1 or ! node1 is remov$ f ,m t[>ds ,g1 t is1 has mov$ yet f>!r =w>d2 & x is likewise z manife/1 t ! angle "u ,k ,p ,g1 or ! incl9ation ( ! moon's orbit 9 ! po9t ,k1 is great] ?an ! angle "u ,i ,m ,g1 = ! reason s (t5 assign$4 #cg4 ,,aft] ! moon has pass$ ! qu>t]1 ! pa? ( ! moon be+ concave to ! plane ,a ,g ,c ,h1 ! nodes1 z 9 ! prec$+ case1 %all rec$e1 till ! moon arrives at ! po9t ,l2 :i* %ews1 t consid]+ ! :ole "t ( ! moon's pass+ f ,b to ,l1 at ! end ( t "t ! nodes %all be f\nd to h rec$$1 or to be plac$ backw>d]1 :5 ! moon is 9 ,l1 ?an :5 x 0 9 ,b4 ,= ! moon takes a long] "t 9 pass+ f ,k to ,l1 ?an 9 pass+ f ,b to ,k2 & !re=e ! nodes cont9ue to rec$e a long] "t1 ?an !y mov$ =w>ds2 s t _! recess mu/ surm\nt _! advance4 #ch4 ,,9 ! same mann]1 :ile ! moon is 9 its passage f ,k to ,l1 ! incl9ation ( ! orbit %all dim9i%1 till ! moon comes to ! po9t1 9 :i* x is "o qu>t] "p ( a circle di/ant f its node2 suppose 9 ! po9t ,r2 & f t "t ! incl9ation %all aga9 increase4 ,s9ce !re=e ! incl9ation ( ! orbit increases1 :ile ! moon is pass+ f ,b to ,k1 & dim9i%es itself aga9 only1 :ile ! moon is pass+ f ,k to ,r1 & !n augm5ts aga91 till ! moon arrive 9 ,l2 :ile ! moon is pass+ f ,b to ,l1 ! incl9ation ( ! orbit is mu* m increas$ ?an dim9i%$1 & w be di/+ui%ably great]1 :5 ! moon is come to ,l1 ?an :5 x set out f ,b4 #ci4 ,,9 l mann]1 :ile ! moon is pass+ f ,l on ! o!r side ! plane ,a ,g ,c ,h1 ! node %all advance =w>d1 z long z ! moon is betwe5 ! po9t ,l & ! next qu>t]2 b aft]w>ds x %all rec$e1 till ! moon come to pass ! plane ,a ,g ,c ,h aga9 9 ! po9t ,v1 betwe5 ,b & ,a3 & because ! "t betwe5 ! moon's pass+ f ,l to ! next qu>t] is less1 ?an ! "t betwe5 t qu>t] & ! moon's com+ to ! po9t ,v1 ! node %all h m rec$$ ?an advanc$2 s t ! po9t ,v w be ne>] to ,a1 ?an ,l is to ,c4 ,s also ! incl9ation ( ! orbit1 :5 ! moon is 9 ,v1 w be great]1 ?an :5 ! moon 0 at ,l2 = ?is incl9ation increases all ! "t ! moon is betwe5 ,l & ! next qu>t]2 x decreases only :ile ! moon is pass+ f ?is qu>t] to ! mid way betwe5 ! two nodes1 & f !nce increases aga9 dur+ ! :ole passage ?r\gh ! o!r half ( ! way to ! next node4 #dj4 ,,?us we h trac$ ! moon f h] node 9 ! qu>t]1 & %ewn1 t at e p]iod ( ! moon ! nodes w h rec$$1 & !reby w h approa*$ t[>d a conjunction ) ! sun4 ,b ?is conjunction w be mu* =w>d$ by ! visible motion ( ! sun itself4 ,9 ! la/ s*eme ! sun w appe> to move f ,s t[>d ,w4 ,suppose x appe>$ to h mov$ f ,s to ,w1 :ile ! moon's node has rec$$ f ,b to ,v1 !n draw+ ! l9e ,w ,t ,x1 ! ar* ,v ,x w repres5t ! di/ance ( ! l9e drawn betwe5 ! nodes f ! sun1 :5 ! moon is 9 ,v2 :]eas ! ar* ,b ,a repres5t$ t di/ance1 :5 ! moon 0 9 ,b4 ,?is visible motion ( ! sun is mu* great]1 ?an t ( ! node2 = ! sun appe>s to revolve q r\nd ea* ye>1 & ! node is ne> #ai ye>s 9 mak+ "o revolution4 ,we h also se51 t :5 ! node 0 9 ! quadrature1 ! incl9ation ( ! moon's orbit decreas$1 till ! moon came to ! conjunction1 or opposition1 accord+ to :i* node x set out f2 b t aft]w>ds x aga9 increas$1 till x became at ! next node r great] ?an at ! =m]4 ,:5 ! node is once remov$ f ! qu>t] ne>] to a conjunction ) ! sun1 ! incl9ation ( ! moon's orbit1 :5 ! moon comes into ! node1 is m s5sibly great]1 ?an x 0 9 ! node prec$+2 ! incl9ation ( ! orbit by ?is means m & m increas+ till ! node comes into conjunction ) ! sun2 at :i* "t x has be5 %ewn above1 t ! sun has no p[] to *ange ! plane ( ! moon's motion2 & consequ5tly has no effect ei!r on ! nodes1 or on ! incl9ation ( ! orbit4 #da4 ,,z soon z ! nodes1 by ! action ( ! sun1 are got out ( conjunction t[>d ! o!r qu>t]s1 !y beg9 aga9 to rec$e z be=e2 b ! incl9ation ( ! orbit 9 ! appulse ( ! moon to ea* succe$+ node is less ?an at ! prec$+1 till ! nodes come aga9 into ! qu>t]s4 ,?is w appe> z foll[s4 ,let ,a 79 fig4 #ajd47 repres5t "o ( ! moon's nodes plac$ betwe5 ! po9t ( opposition ,b & ! qu>t] ,c4 ,let ! plane ,a ,d ,e pass ?r\gh ! e>? ,t1 & t\* ! pa? ( ! moon 9 ,a4 ,let ! l9e ,a ,f ,g ,h be ! pa? ( ! moon 9 h] passage f ,a to ,h1 :]e %e crosses aga9 ! plane ( ! e>?'s motion4 ,?is l9e w be convex t[>d ! plane ,a ,d ,e1 till ! moon comes to ,g1 :]e %e is 9 ! qu>t]2 & aft] ?is1 betwe5 ,g & ,h1 ! same l9e w be concave t[>d ?is plane4 ,all ! "t ?is l9e is convex t[>d ! plane ,a ,d ,e1 ! nodes w rec$e2 & on ! contr>y proce$1 :ile x is concave to t plane4 ,all ?is w easily be conceiv$ f :at has be5 be=e s l>gely expla9$4 ,b ! moon is long] 9 pass+ f ,a to ,g1 ?an f ,g to ,h2 !re=e ! nodes rec$e a long] "t1 ?an !y proce$2 consequ5tly ^u ! :ole1 :5 ! moon is arriv$ at ,h1 ! nodes w h rec$$1 t is1 ! po9t ,h w fall betwe5 ,b & ,e4 ,! incl9ation ( ! orbit w decrease1 till ! moon is arriv$ to ! po9t ,f1 9 ! middle betwe5 ,a & ,h4 ,?r\gh ! passage betwe5 ,f & ,g ! incl9ation w increase1 b decrease aga9 9 ! rema9+ "p ( ! passage f ,g to ,h1 & consequ5tly at ,h mu/ be less ?an at ,a4 ,! l effects1 bo? 9 respect to ! nodes & incl9ation ( ! orbit1 w take place 9 ! foll[+ passage ( ! moon on ! o!r side ( ! plane ,a ,b ,e ,c1 f ,h1 till x comes ov] t plane aga9 9 ,i4 #db4 ,,?us ! incl9ation ( ! orbit is greate/1 :5 ! l9e drawn betwe5 ! moon's nodes w pass ?r\gh ! sun2 & lea/1 :5 ?is l9e lies 9 ! qu>t]s1 especially if ! moon at ! same "t be 9 conjunction ) ! sun1 or 9 ! opposition4 ,9 ! fir/ ( ^! cases ! nodes h no motion1 9 all o!rs1 ! nodes w ea* mon? h rec$$3 & ?is regressive motion w be greate/1 :5 ! nodes are 9 ! qu>t]s2 = 9 t case ! nodes h no progressive motion dur+ ! :ole mon?1 b 9 all o!r cases ! nodes d at "s times proce$ =w>d1 viz4 :5ev] ! moon is betwe5 ei!r qu>t]1 & ! node :i* is less di/ant f t qu>t] ?an a f\r? "p ( a circle4 #dc4 ,,x n[ rema9s only to expla9 ! irregul>ities 9 ! moon's motion1 :i* foll[ f ! elliptical figure ( ! orbit4 ,by :at has be5 said at ! beg9n+ ( ?is *apt] x appe>s1 t ! p[] ( ! e>? on ! moon acts 9 ! reciprocal duplicate proportion ( ! di/ance3 !re=e ! moon1 if undi/urb$ by ! sun1 w\ld move r\nd ! e>? 9 a true ellipsis1 & ! l9e drawn f ! e>? to ! moon w\ld pass ov] equal spaces 9 equal portions ( "t4 ,t ?is description ( ! spaces is alt]$ by ! sun1 has be5 already decl>$4 ,x has also be5 %[n1 t ! figure ( ! orbit is *ang$ ea* mon?2 t ! moon is ne>] ! e>? at ! new & full1 & m remote 9 ! qu>t]s1 ?an x w\ld be )\t ! sun4 ,n[ we mu/ pass by ^! mon?ly *anges1 & consid] ! effect1 :i* ! sun w h 9 ! diff]5t situations ( ! axis ( ! orbit 9 respect ( t lum9>y4 #dd4 ,,! action ( ! sun v>ies ! =ce1 :]e) ! moon is drawn t[>d ! e>?2 9 ! qu>t]s ! =ce ( ! e>? is directly increas$ by ! sun2 at ! new & full ! same is dim9i%$2 & 9 ! int]m$iate places ! influ5ce ( ! e>? is sometimes aid$1 & sometimes less5$ by ! sun4 ,9 ^! int]m$iate places betwe5 ! qu>t]s & ! conjunction or opposition1 ! sun's action is s oblique to ! action ( ! e>? on ! moon1 z to produce t alt]nate accel]ation & ret>dm5t ( ! moon's motion1 :i* ,i obs]v$ above to be /il$ ! v>iation4 ,b besides ?is effect1 ! p[]1 by :i* ! e>? attracts ! moon t[>d itself1 w n be at full lib]ty to act ) ! same =ce1 z if ! sun act$ n at all on ! moon4 ,& ?is effect ( ! sun's action1 :]eby x corroborates or weak5s ! action ( ! e>?1 is "h only to be consid]$4 ,& by ?is influ5ce ( ! sun x comes to pass1 t ! p[]1 by :i* ! moon is impell$ t[>d ! e>?1 is n p]fectly 9 ! reciprocal duplicate proportion ( ! di/ance4 ,consequ5tly ! moon w n describe a p]fect ellipsis4 ,"o p>ticul>1 :]e9 ! moon's orbit w diff] f an ellipsis1 consi/s 9 ! places1 :]e ! motion ( ! moon is p]p5dicul> to ! l9e drawn f itself to ! e>?4 ,9 an ellipsis1 aft] ! moon %\ld h set out 9 ! direction p]p5dicul> to ?is l9e drawn f itself to ! e>?1 & at its greate/ di/ance f ! e>?1 its motion w\ld aga9 become p]p5dicul> to ?is l9e drawn betwe5 itself & ! e>?1 & ! moon be at its ne>e/ di/ance f ! e>?1 :5 x %\ld h p]=m$ half its p]iod2 aft] p]=m+ ! o!r half ( its p]iod its motion w\ld aga9 become p]p5dicul> to ! =em5tion$ l9e1 & ! moon return into ! place :5ce x set out1 & h recov]$ aga9 its greate/ di/ance4 ,b ! moon 9 its real motion1 aft] sett+ out z be=e1 sometimes makes m ?an half a revolution1 be=e its motion comes aga9 to be p]p5dicul> to ! l9e drawn f itself to ! e>?1 & ! moon is at its ne>e/ di/ance2 & !n p]=ms m ?an ano!r half ( an intire revolution be=e its motion c a second "t recov] its p]p5dicul> direction to ! l9e drawn f ! moon to ! e>?1 & ! moon arrive aga9 to its greate/ di/ance f ! e>?4 ,at o!r times ! moon w desc5d to its ne>e/ di/ance1 be=e x has made half a revolution1 & recov] aga9 its greate/ di/ance1 be=e x has made an intire revolution4 ,! place1 :]e ! moon is at its greate/ di/ance f ! e>?1 is call$ ! moon's apogeon1 & ! place ( ! lea/ di/ance ! p]igeon4 ,?is *ange ( ! place1 :]e ! moon successively comes to its greate/ di/ance f ! e>?1 is call$ ! motion ( ! apogeon4 ,9 :at mann] ! sun causes ! apogeon to move1 ,i %all n[ endeav\r to expla94 #de4 ,,our au?or %ews1 t if ! moon 7 attract$ t[>d ! e>? by a composition ( two p[]s1 "o ( :i* 7 reciprocally 9 ! duplicate proportion ( ! di/ance f ! e>?1 & ! o!r reciprocally 9 ! triplicate proportion ( ! same di/ance2 !n1 ?\gh ! l9e describ$ by ! moon w\ld n be 9 reality an ellipsis1 yet ! moon's motion might be p]fectly expla9$ by an ellipsis1 ^: axis %\ld be made to move r\nd ! e>?2 ?is motion be+ 9 consequ5ce1 z a/ronom]s express !mselves1 t is1 ! same way z ! moon itself moves1 if ! moon be attract$ by ! sum ( ! two p[]s2 b ! axis mu/ move 9 antec$5ce1 or ! contr>y way1 if ! moon be act$ on by ! diff]5ce ( ^! p[]s4 ,:at is meant by duplicate proportion has be5 (t5 expla9$2 namely1 t if ?ree magnitudes1 z ,a1 ,b1 & ,c1 are s relat$1 t ! second ,b be>s ! same proportion to ! ?ird ,c1 z ! fir/ ,a be>s to ! second ,b1 !n ! proportion ( ! fir/ ,a to ! ?ird ,c1 is ! duplicate ( ! proportion ( ! fir/ ,a to ! second ,b4 ,n[ if a f\r? magnitude1 z ,d1 be assum$1 to :i* ,c %all be> ! same proportion z ,a be>s to ,b1 & ,b to ,c1 !n ! proportion ( ,a to ,d is ! triplicate ( ! proportion ( ,a to ,b4 #df4 ,,! way ( repres5t+ ! moon's motion 9 ?is case is ?us4 ,t d5ot+ ! e>? 79 fig4 #aje1 #ajf47 suppose ! moon 9 ! po9t ,a1 its apogeon1 or greate/ di/ance f ! e>?1 mov+ 9 ! direction ,a ,f p]p5dicul> to ,a ,b1 & act$ ^u f ! e>? by two su* =ces z h be5 nam$4 ,by t p[] alone1 :i* is reciprocally 9 ! duplicate proportion ( ! di/ance1 if ! moon let out f ! po9t ,a ) a prop] degree ( velocity1 ! ellipsis ,a ,m ,b may be describ$4 ,b if ! moon be act$ ^u by ! sum ( ! =em5tion$ p[]s1 & ! velocity ( ! moon 9 ! po9t ,a be augm5t$ 9 a c]ta9 proportion#aic2 or if t velocity be dim9i%$ 9 a c]ta9 proportion1 & ! moon be act$ ^u by ! diff]5ce ( ^? p[]s2 9 bo? ^! cases ! l9e ,a ,e1 :i* %all be describ$ by ! moon1 is ?us to be det]m9$4 ,let ! po9t ,m be t1 into :i* ! moon w\ld h arriv$ 9 any giv5 space ( "t1 _h x mov$ 9 ! ellipsis ,a ,m ,b4 ,draw ,m ,t1 & likewise ,c ,t ,d 9 su* sort1 t ! angle "u ,a ,t ,m %all be> ! same proportion to ! angle "u ,a ,t ,c1 z ! velocity1 ) :i* ! ellipsis ,a ,m ,b mu/ h be5 describ$1 be>s to ! diff]5ce betwe5 ?is velocity1 & ! velocity1 ) :i* ! moon mu/ set out f ! po9t ,a 9 ord] to describe ! pa? ,a ,e4 ,let ! angle ,a ,t ,c be tak5 t[>d ! moon 7z 9 fig4 #aje47 if ! moon be attract$ by ! sum ( ! p[]s2 b ! contr>y way 7z 9 fig4 #ajf47 if by _! diff]5ce4 ,!n let ! l9e ,a ,b be mov$ into ! position ,c ,d1 & ! ellipsis ,a ,m ,b into ! situation ,c ,n ,d1 s t ! po9t ,m be translat$ to ,l3 !n ! po9t ,l %all fall ^u ! pa? ( ! moon ,a ,e4 #dg4 ,,! angul> motion ( ! l9e ,a ,t1 w]eby x is remov$ into ! situation ,c ,t1 repres5ts ! motion ( ! apogeon2 by ! means ( :i* ! motion ( ! moon might be fully explicat$ by ! ellipsis ,a ,m ,b1 if ! action ( ! sun ^u x 0 direct$ to ! c5t] ( ! e>?1 & reciprocally 9 ! triplicate proportion ( ! moon's di/ance f x4 ,b t n be+ s1 ! apogeon w n move 9 ! regul> mann] n[ describ$4 ,h[ev]1 x is to be obs]v$ "h1 t 9 ! fir/ ( ! two prec$+ cases1 :]e ! apogeon moves =w>d1 ! :ole c5tripetal p[] increases fa/]1 ) ! decrease ( di/ance1 ?an if ! intire p[] 7 reciprocally 9 ! duplicate proportion ( ! di/ance2 because "o "p only is 9 t proportion1 & ! o!r "p1 :i* is add$ to ?is to make up ! :ole p[]1 increases fa/] ) ! decrease ( di/ance4 ,on ! o!r h&1 :5 ! c5tripetal p[] is ! diff]5ce betwe5 ^! two1 x increases less ) ! decrease ( ! di/ance1 ?an if x 7 simply 9 ! reciprocal duplicate proportion ( ! di/ance4 ,!re=e if we *use to expla9 ! moon's motion by an ellipsis 7z is mo/ conv5i5t = a/ronomical uses to be done1 & by reason ( ! small effect ( ! sun's p[]1 ! do+ s w n be att5d$ ) any s5sible error27 we may collect 9 g5]al1 t :5 ! p[]1 by :i* ! moon is attract$ to ! e>?1 by v>y+ ! di/ance1 increases 9 a great] ?an 9 ! duplicate proportion ( ! di/ance dim9i%$1 a motion 9 consequ5ce mu/ be ascrib$ to ! apogeon2 b t :5 ! attraction increases 9 a less proportion ?an t nam$1 ! apogeon mu/ h giv5 to x a motion 9 antec$5ce#aid4 ,x is !n obs]v$ by ,sir ,,is4 ,,newton1 t ! fir/ ( ^! cases obta9s1 :5 ! moon is 9 ! conjunction & opposition2 & ! latt]1 :5 ! moon is 9 ! qu>t]s3 s t 9 ! fir/ ! apogeon moves accord+ to ! ord] ( ! signs2 9 ! o!r1 ! contr>y way#aie4 ,b1 z 0 said be=e1 ! di/urbance giv5 to ! action ( ! e>? by ! sun 9 ! conjunction & opposition be+ ne> twice z great z 9 ! qu>t]s#aif1 ! apogeon w advance ) a great] velocity ?an rec$e1 & 9 ! compass ( a :ole revolution ( ! moon w be c>ri$ 9 consequ5ce#aig4 #dh4 ,,x is %ewn 9 ! next place by our au?or1 t :5 ! l9e ,a ,b co9cides ) t1 :i* jo9s ! e>? & ! sun1 ! progressive motion ( ! apogeon1 :5 ! moon is 9 ! conjunction or opposition1 exce$s ! regressive 9 ! quadratures m ?an 9 any o!r situation ( ! l9e ,a ,b#aih4 ,on ! contr>y1 :5 ! l9e ,a ,b makes "r angles ) t1 :i* jo9s ! e>? & sun1 ! retrograde motion w be m consid]able#aii1 nay is f\nd s great z to exce$ ! progressive2 s t 9 ?is case ! apogeon 9 ! compass ( an intire revolution ( ! moon is c>ri$ 9 antec$5ce4 ,yet f ! consid]ations 9 ! la/ p>agraph ! progressive motion exce$s ! o!r2 s t 9 ! :ole ! mean motion ( ! apogeon is 9 consequ5ce1 accord+ z a/ronom]s f9d4 ,moreov]1 ! l9e ,a ,b *anges its situation ) t1 :i* jo9s ! e>? & sun1 by su* sl[ degrees1 t ! inequalities 9 ! motion ( ! apogeon aris+ f ?is la/ consid]ation1 are mu* great] ?an :at arises f ! o!r#bjj4 #di4 ,,f>!r1 ?is un/eady motion 9 ! apogeon is att5d$ ) ano!r inequality 9 ! motion ( ! moon1 t x _c be expla9$ at all times by ! same ellipsis4 ,! ellipsis 9 g5]al is call$ by a/ronom]s an ecc5tric orbit4 ,! po9t1 9 :i* ! two axis's cross1 is call$ ! c5t] ( ! figure2 because all l9es drawn ?r\gh ?is po9t )9 ! ellipsis1 f side to side1 are divid$ 9 ! middle by ?is po9t4 ,b ! c5t]1 ab\t :i* ! heav5ly bodies revolve1 ly+ out ( ?is c5t] ( ! figure 9 "o focus1 ^! orbits are said to be ecc5tric2 & :]e ! di/ance ( ! focus f ?is c5t] be>s ! greate/ proportion to ! :ole axis1 t orbit is call$ ! mo/ ecc5tric3 & 9 su* an orbit ! di/ance f ! focus to ! remot] extremity ( ! axis be>s ! greate/ proportion to ! di/ance ( ! ne>] extremity4 ,n[ :5ev] ! apogeon ( ! moon moves 9 consequ5ce1 ! moon's motion mu/ be ref]r$ to an orbit m ecc5tric1 ?an :at ! moon w\ld describe1 if ! :ole p[]1 by :i* ! moon 0 act$ on 9 its pass+ f ! apogeon1 *ang$ accord+ to ! reciprocal duplicate proportion ( ! di/ance f ! e>?1 & by t means ! moon did describe an immoveable ellipsis2 & :5 ! apogeon moves 9 antec$5ce1 ! moon's motion mu/ be ref]r$ to an orbit less ecc5tric4 ,9 ! fir/ ( ! two figures la/ ref]r$ to1 ! true place ( ! moon ,l falls )\t ! orbit ,a ,m ,b1 to :i* its motion is ref]r$3 :5ce ! orbit ,a ,l ,e1 truly describ$ by ! moon1 is less incurvat$ 9 ! po9t ,a1 ?an is ! orbit ,a ,m ,b2 !re=e ! orbit ,a ,m ,b is m oblong1 & diff]s f>!r f a circle1 ?an ! ellipsis w\ld1 ^: curvature 9 ,a 7 equal to t ( ! l9e ,a ,l ,b1 t is1 ! proportion ( ! di/ance ( ! e>? ,t f ! c5t] ( ! ellipsis to its axis w be great] 9 ! ellipsis ,a ,m ,b1 ?an 9 ! o!r2 b t o!r is ! ellipsis1 :i* ! moon w\ld describe1 if ! p[] act+ ^u x 9 ! po9t ,a 7 alt]$ 9 ! reciprocal duplicate proportion ( ! di/ance4 ,9 ! second figure1 :5 ! apogeon rec$es1 ! place ( ! moon ,l falls )9 ! orbit ,a ,m ,b1 & !re=e t orbit is less ecc5tric1 ?an ! immoveable orbit :i* ! moon %\ld describe4 ,! tru? ( ?is is evid5t2 =1 :5 ! apogeon moves =w>d1 ! p[]1 by :i* ! moon is influ5c$ 9 its desc5t f ! apogeon1 increases fa/] ) ! decrease ( di/ance1 ?an 9 ! duplicate proportion ( ! di/ance2 & consequ5tly ! moon be+ drawn m =cibly t[>d ! e>?1 x w desc5d ne>] to x4 ,on ! o!r h&1 :5 ! apogeon rec$es1 ! p[] act+ on ! moon increases ) ! decrease ( di/ance 9 less ?an ! duplicate proportion ( ! di/ance2 & !re=e ! moon is less impell$ t[>d ! e>?1 & w n desc5d s l[4 #ej4 ,,n[ suppose 9 ! fir/ ( ^! figures1 t ! apogeon ,a is 9 ! situation1 :]e x is approa*+ t[>d ! conjunction or opposition ( ! sun4 ,9 ?is case ! progressive motion ( ! apogeon is m & m accel]at$4 ,"h suppose t ! moon1 aft] hav+ desc5d$ f ,a ?r\gh ! orbit ,a ,e z f> z ,f1 :]e x is come to its ne>e/ di/ance f ! e>?1 asc5ds aga9 up ! l9e ,f ,g4 ,because ! motion ( ! apogeon is "h cont9ually m & m accel]at+1 ! cause ( its motion is con/antly ^u ! increase2 t is1 ! p[]1 :]eby ! moon is drawn to ! e>?1 w decrease ) ! increase ( di/ance1 9 ! moon's asc5t f ,f1 9 a great] proportion ?an t :]e) x increas$ ) ! decrease ( di/ance 9 ! moon's desc5t to ,f4 ,consequ5tly ! moon w asc5d high] ?an to ! di/ance ,a ,t1 f :5ce x desc5d$2 !re=e ! proportion ( ! greate/ di/ance ( ! moon to ! lea/ is increas$4 ,& :5 ! moon desc5ds aga91 ! p[] w yet m increase ) ! decrease ( di/ance1 ?an 9 ! la/ asc5t x decreas$ ) ! augm5tation ( di/ance2 ! moon !re=e mu/ desc5d ne>] to ! e>? ?an x did be=e1 & ! proportion ( ! greate/ di/ance to ! lea/ yet be m increas$4 ,?us z long z ! apogeon is advanc+ t[>d ! conjunction or opposition1 ! proportion ( ! greate/ di/ance ( ! moon f ! e>? to ! lea/ w cont9ually increase2 & ! elliptical orbit1 to :i* ! moon's motion is ref]r$1 w be r5d]$ m & m ecc5tric4 #ea4 ,,z soon z ! apogeon is pass$ ! conjunction ) ! sun or ! opposition1 ! progressive motion !re( abates1 & ) x ! proportion ( ! greate/ di/ance ( ! moon f ! e>? to ! lea/ di/ance w also dim9i%2 & :5 ! apogeon becomes regressive1 ! dim9ution ( ?is proportion w be /ill f>!r cont9u$ on1 till ! apogeon comes into ! qu>t]2 f !nce ?is proportion1 & ! ecc5tricity ( ! orbit w increase aga94 ,?us ! orbit ( ! moon is mo/ ecc5tric1 :5 ! apogeon is 9 conjunction ) ! sun1 or 9 opposition to x1 & lea/ ( all :5 ! apogeon is 9 ! qu>t]s4 #eb4 ,,^! *anges 9 ! nodes1 9 ! incl9ation ( ! orbit to ! plane ( ! e>?'s motion1 9 ! apogeon1 & 9 ! ecc5tricity1 are v>i$ l ! o!r inequalities 9 ! motion ( ! moon1 by ! diff]5t di/ance ( ! e>? f ! sun2 be+ greate/1 :5 _! cause is greate/1 t is1 :5 ! e>? is ne>e/ to ! sun4 #ec4 ,i ,,said at ! beg9n+ ( ?is *apt]1 t ,sir ,,isaac ,,newton has comput$ ! v quantity ( _m ( ! moon's inequalities4 ,t accel]ation ( ! moon's motion1 :i* is call$ ! v>iation1 :5 greate/1 removes ! moon out ( ! place1 9 :i* x w\ld o!rwise be f\nd1 some?+ m ?an half a degree#bja4 ,9 ! phrase ( a/ronom]s1 a degree is #a_/cfj "p ( ! :ole circuit ( ! moon or any planet4 ,if ! moon1 )\t di/urbance f ! sun1 w\ld h describ$ a circle conc5trical to ! e>?1 ! sun w cause ! moon to approa* ne>] to ! e>? 9 ! conjunction & opposition1 ?an 9 ! qu>t]s1 ne>ly 9 ! proportion ( #fi to #gjbjb4 ,we _h occasion to m5tion above1 t ! nodes p]=m _! p]iod 9 almo/ #ai ye>s4 ,?is ! a/ronom]s f\nd by obs]vation2 & our au?or's computations assign to !m ! same p]iod#bjc4 ,! incl9ation ( ! moon's orbit :5 lea/1 is an angle ab\t #a_/ah "p ( t angle1 :i* con/itutes a p]p5dicul>2 & ! diff]5ce betwe5 ! greate/ & lea/ incl9ation ( ! orbit is det]m9$ by our au?or's computation to be ab\t #a_/ah ( ! lea/ incl9ation#bjd4 ,& ?is also is agreeable to ! obs]vations ( a/ronom]s4 ,! motion ( ! apogeon1 & ! *anges 9 ! ecc5tricity1 ,sir ,,isaac ,,newton has n comput$4 ,! apogeon p]=ms its revolution 9 ab\t eight ye>s & t5 mon?s4 ,:5 ! moon's orbit is mo/ ecc5tric1 ! greate/ di/ance ( ! moon f ! e>? be>s to ! lea/ di/ance ne>ly ! proportion ( #h to #g2 :5 ! orbit is lea/ ecc5tric1 ?is proportion is h>dly s great z t ( #ab to #aa4 #ed4 ,,sir ,,isaac ,,newton %ews f>!r1 h[1 by comp>+ ! p]iods ( ! motion ( ! satellites1 :i* revolve r\nd ,jupit] & ,saturn1 ) ! p]iod ( our moon r\nd ! e>?1 & ! p]iods ( ^? planets r\nd ! sun ) ! p]iod ( our e>?'s motion1 ! inequalities 9 ! motion ( ^? satellites may be d]iv$ f ! inequalities 9 ! moon's motion2 except+ only 9 reg>d to t motion ( ! axis ( ! orbit1 :i* 9 ! moon makes ! motion ( ! apogeon2 = ! orbits ( ^? satellites1 z f> z c be disc]n$ by u at ?is di/ance1 appe>+ little or no?+ ecc5tric1 ?is motion1 z d$uc$ f ! moon1 mu/ be dim9i%$4 ,,*ap4 ,,iv4 ,( ,comets4 ,,9 ! =m] ( ! two prec$+ *apt]s ! p[]s h be5 expla9$1 :i* keep 9 motion ^? cele/ial bodies1 ^: c\rses _h be5 well det]m9$ by ! a/ronom]s4 ,9 ! la/ *apt] we h %ewn1 h[ ^? p[]s h be5 appli$ by our au?or to ! mak+ a m p]fect discov]y ( ! motion ( ^? bodies1 ! c\rses ( :i* 7 b imp]fectly und]/ood2 = "s ( ! inequalities1 :i* we h be5 describ+ 9 ! moon's motion1 7 unkn[n to ! a/ronom]s4 ,9 ?is *apt] we are to treat ( a ?ird species ( ! heav5ly bodies1 ! true motion ( :i* 0 n at all appreh5d$ be=e our au?or writ2 9 s mu*1 t "h ,sir ,,isaac ,,newton has n only expla9$ ! causes ( ! motion ( ^! bodies1 b has p]=m$ also ! "p ( an a/ronom]1 by discov]+ :at _! motions are4 #b4 ,,t ^! bodies are n meteors 9 our air1 is manife/2 because !y rise & set 9 ! same mann]1 z ! sun & />s4 ,! a/ronom]s _h gone s f> 9 _! inquiries conc]n+ !m1 z to prove by _! obs]vations1 t !y mov$ 9 ! e!rial spaces f> beyond ! moon2 b !y _h no true notion at all ( ! pa?1 :i* !y describ$4 ,! mo/ prevail+ op9ion be=e our au?or 01 t !y mov$ 9 /raight l9es2 b 9 :at "p ( ! heav5s 0 n det]m9$4 ,,desc>tes#bje remov$ !m f> beyond ! sph]e ( ,saturn1 z f9d+ ! /raight motion attribut$ to !m1 inconsi/5t ) ! vortical fluid1 by :i* he expla9s ! motions ( ! planets1 z we h above relat$#bjf4 ,b ,sir ,,isaac ,,newton di/9ctly proves f a/ronomical obs]vation1 t ! comets pass ?r\gh ! region ( ! planets1 & are mo/ly invisible at a less di/ance1 ?an t ( ,jupit]#bjg4 #c4 ,,& f h5ce f9d+ ! comets to be evid5tly )9 ! sph]e ( ! sun's action1 he concludes !y mu/1 necess>ily move ab\t ! sun1 z ! planets d#bjh4 ,! planets move 9 ellipsis's2 b x is n necess>y t e body1 :i* is influ5c$ by ! sun1 %\ld move 9 t p>ticul> k9d ( l9e4 ,h[ev] our au?or proves1 t ! p[] ( ! sun be+ reciprocally 9 ! duplicate proportion ( ! di/ance1 e body act$ on by ! sun mu/ ei!r fall directly d[n1 or move 9 "s conic section2 ( :i* l9es ,i h above obs]v$1 t !re are ?ree species1 ! ellipsis1 p>abola1 & hyp]bola#bji4 ,if a body1 :i* desc5ds t[>d ! sun z l[ z ! orbit ( any planet1 move ) a swift] motion ?an ! planet does1 t body w describe an orbit ( a m oblong figure1 ?an t ( ! planet1 & h a long] axis at lea/4 ,! velocity ( ! body may be s great1 t x %all move 9 a p>abola1 & hav+ once pass$ ab\t ! sun1 %all asc5d = ev] )\t return+ any m3 b ! sun w be plac$ 9 ! focus ( ?is p>abola4 ,) a velocity /ill great] ! body w move 9 an hyp]bola4 ,b x is mo/ probable1 t ! comets move 9 elliptical orbits1 ?\gh ( a v oblong1 or 9 ! phrase ( a/ronom]s1 ( a v ecc5tric =m1 su* z is repres5t$ 9 fig4 #ajg1 :]e ,s is ! sun1 ,c ! comet1 & ,a ,b ,d ,e its orbit1 :]e9 ! di/ance ( ,s & ,d f> exce$s t ( ,s & ,a4 ,:5ce x is1 t !y sometimes are f\nd at a mod]ate di/ance f ! sun1 & appe> )9 ! planet>y regions2 at o!r times !y asc5d to va/ di/ances1 f> beyond ! v orbit ( ,saturn1 & s become invisible4 ,t ! comets d move 9 ?is mann] is prov$ by our au?or1 f computations built ^u ! obs]vations1 :i* a/ronom]s _h made on _m comets4 ,^! computations 7 p]=m$ by ,sir ,,isaac ,,newton himself ^u ! comet1 :i* appe>$ t[>d ! latt] end ( ! ye> #afhj1 & at ! beg9n+ ( ! ye> foll[+#baj2 b ! le>n$ ,dr4 ,,halley prosecut$ ! l computations m at l>ge 9 ?is1 & also 9 _m o!r comets#baa4 ,:i* computations are made ^u propositions highly wor?y ( our au?or's unp>allel'd g5ius1 su* z c\ld sc>ce h be5 discov]$ by any "o n possess$ ( ! utmo/ =ce ( inv5tion2 #d4 ,,^? computations dep5d ^u ?is pr9ciple1 t ! ecc5tricity ( ! orbits ( ! comets is s great1 t if !y are really elliptical1 yet !y approa* s ne> to p>abolas 9 t "p ( !m1 :]e !y come "u our view1 t !y may be tak5 = su* )\t s5sible error#bab3 z 9 ! prec$+ figure ! p>abola ,f ,a ,g diff]s 9 ! l[] "p ( x ab\t ,a v little f ! ellipsis ,d ,e ,a ,b4 ,^u :i* gr\nd our great au?or tea*es a me?od ( f9d+ by ?ree obs]vations made ^u any comet ! p>abola1 :i* ne>e/ agrees ) its orbit#bac4 #e4 ,,n[ :at confirms ?is :ole !ory beyond ! lea/ room = d\bt is1 t ! places ( ! comets comput$ 9 ! orbits1 :i* ! me?od "h m5tion$ assigns !m1 agree to ! obs]vations ( a/ronom]s ) ! same degree ( exactness1 z ! computations ( ! prim>y planets places usually d2 & ?is 9 comets1 ^: motions are v extraord9>y#bad4 #f4 ,,our au?or aft]w>ds %ews h[ to make use ( any small deviation f ! p>abola1 t %all be obs]v$1 to det]m9e :e!r ! orbits ( ! comets are elliptical or n1 & s to discov] if ! same comet returns at c]ta9 p]iods#bae4 ,& ^u exam9+ ! comet 9 #afhj1 by ! rule laid d[n = ?is purpose1 he f9ds its orbit to agree m exactly to an ellipsis ?an to a p>abola1 ?\gh ! ellipsis be s v ecc5tric1 t ! comet _c p]=m its p]iod ?r\gh x 9 ! space ( #ejj ye>s#baf4 ,^u ?is ,dr4 ,,halley obs]v$1 t m5tion is made 9 hi/ory ( a comet1 ) ! l em95t tail z ?is1 hav+ appe>$ ?ree sev]al times be=e2 ! fir/ ( :i* appe>ances 0 at ! dea? ( ,,julius ,,ces>1 & ea* appe>ance 0 at ! di/ance ( #ege ye>s f ! next prec$+4 ,he !re=e comput$ ! motion ( ?is comet 9 su* an elliptic orbit1 z w\ld require ?is numb] ( ye>s = ! body to revolve ?r\gh x2 & ^! computations agree yet m p]fectly ) ! obs]vations made on ?is comet1 ?an any p>abolical orbit w d#bag4 #g4 ,,! comp>+ toge!r diff]5t appe>ances ( ! same comet1 is ! only way to discov] c]ta9ly ! true =m ( ! orbit3 = x is impossible to det]m9e ) exactness ! figure ( an orbit s exce$+ly ecc5tric1 f s+le obs]vations tak5 9 "o "p ( x2 & !re=e ,sir ,,isaac ,,newton#bah proposes to comp>e ! orbits1 ^u ! supposition t !y are p>abolical1 ( su* comets z appe> at diff]5t times2 = if ! same orbit be f\nd to be describ$ by a comet at diff]5t times1 9 all probability x w be ! same comet :i* describes x4 ,& "h he rem>ks f ,dr4 ,,halley1 t ! same orbit v ne>ly agrees to two appe>ances ( a comet ab\t ! space ( #ge ye>s di/ance#bai2 s t if ^? two appe>ances 7 really ( ! same comet1 ! transv]se axis ( ! orbit ( ! comet w\ld be ne> #ah times ! axis ( ! e>?'s orbit2 & ! comet1 :5 at its greate/ di/ance f ! sun1 w be remov$ n less ?an #ce times z f> z ! middle di/ance ( ! e>?4 #h4 ,,& ?is seems to be ! %orte/ p]iod ( any ( ! comets4 ,b x w be f>!r confirm$1 if ! same comet %\ld return a ?ird "t aft] ano!r p]iod ( #ge ye>s4 ,h[ev] x is n to be expect$1 t comets %\ld pres]ve ! same regul>ity 9 _! p]iods1 z ! planets2 because ! great ecc5tricity ( _! orbits makes !m liable to suff] v consid]able alt]ations f ! action ( ! planets1 & o!r comets1 ^u !m4 #i4 ,,x is !re=e to prev5t too great di/urbances 9 _! motions f ^! causes1 z our au?or obs]ves1 t :ile ! planets revolve all ( !m ne>ly 9 ! same plane1 ! comets are dispos$ 9 v diff]5t ones2 & di/ribut$ ov] all p>ts ( ! heav5s2 t1 :5 9 _! greate/ di/ance f ! sun1 & mov+ sl[e/1 !y might be remov$ z f> z possible out ( ! rea* ( ea* o!r's action#bbj4 ,! same end is likewise f>!r answ]$ 9 ^? comets1 :i* by mov+ sl[e/ 9 ! aphelion1 or remote/ di/ance f ! sun1 desc5d ne>e/ to x1 by plac+ ! aphelion ( ^! at ! greate/ height f ! sun#bba4 #aj4 ,,our philosoph] be+ l$ by 8 pr9ciples to expla9 ! motions ( ! comets1 9 ! mann] n[ relat$1 takes occasion f !nce to give u 8 ?\ghts ^u _! nature & use4 ,= :i* end he proves 9 ! fir/ place1 t !y mu/ necess>ily be solid & compact bodies1 & by no means any sort ( vap\r or light sub/ance exhal$ f ! planets or />s3 because at ! ne> di/ance1 to :i* "s comets approa* ! sun1 x c\ld n be1 b ! imm5se heat1 to :i* !y are expos$1 %\ld in/antane\sly disp]se & scatt] any su* light volatile sub/ance#bbb4 ,9 p>ticul> ! =em5tion$ comet ( #afhj desc5d$ s ne> ! sun1 z to come )9 a six? "p ( ! sun's diamet] f ! surface ( x4 ,9 :i* situation x mu/ h be5 expos$1 z appe>s by computation1 to a degree ( heat exce$+ ! heat ( ! sun ^u our e>? no less ?an #bhjjj times2 & !re=e might h contract$ a degree ( heat #bjjj times great]1 ?an t ( r$ hot iron#bbc4 ,n[ a sub/ance1 :i* c\ld endure s int5se a heat1 )\t be+ disp]s$ 9 vapor1 mu/ ne$s be firm & solid4 #aa4 ,,x is %ewn likewise1 t ! comets are opake sub/ances1 %9+ by a reflect$ light1 borr[$ f ! sun#bbd4 ,?is is prov$ f ! obs]vation1 t comets1 ?\gh !y are approa*+ ! e>?1 yet dim9i% 9 lu/re1 if at ! same "t !y rec$e f ! sun2 & on ! contr>y1 are f\nd to encrease daily 9 brightness1 :5 !y advance t[>ds ! sun1 ?\gh at ! same "t !y move f ! e>?#bbe4 #ab4 ,,! comets !re=e 9 ^! respects resemble ! planets2 t bo? are durable opake bodies1 & bo? revolve ab\t ! sun 9 conic sections4 ,b f>!r ! comets1 l our e>?1 are surr\nd$ by an atmosph]e4 ,! air we brea? is call$ ! e>?'s atmosph]e2 & x is mo/ probable1 t all ! o!r planets are inve/$ ) ! l fluid4 ,inde$ "h a diff]5ce is f\nd betwe5 ! planets & comets4 ,! atmosph]es ( ! planets are ( s f9e & subtile a sub/ance1 z h>dly to be disc]n$ at any di/ance1 by reason ( ! small quantity ( light :i* !y reflect1 except only 9 ! planet ,m>s4 ,9 him !re is "s little appe>ance ( su* a sub/ance surr\nd+ him1 z />s :i* h be5 cov]$ by him are said to look some:at dim a small space be=e 8 body comes "u !m1 z if _! light1 :5 he is ne>1 7 ob/ruct$ by 8 atmosph]e4 ,b ! atmosph]es :i* surr\nd ! comets are s gross & ?ick1 z to reflect light v copi\sly4 ,!y are also mu* great] 9 proportion to ! body !y surr\nd1 ?an ^? ( ! planets1 if we may judge ( ! re/ f our air2 = x has be5 obs]v$ ( comets1 t ! bright light appe>+ 9 ! middle ( !m1 :i* is reflect$ f ! solid body1 is sc>ce a n9? or t5? "p ( ! :ole comet1 #ac4 ,i ,,speak only ( ! heads ( ! comets1 ! mo/ lucid "p ( :i* is surr\nd$ by a fa9t] light1 ! mo/ lucid "p be+ usually n above a n9? or t5? "p ( ! :ole 9 bread?#bbf4 ,_! tails are an appe>ance v peculi>1 no?+ ( ! same nature app]ta9+ 9 ! lea/ degree to any o!r ( ! cele/ial bodies4 ,( t appe>ance !re are sev]al op9ions2 our au?or r$uces !m to ?ree#bbg4 ,! two fir/1 :i* he proposes1 are reject$ by him2 b ! ?ird he approves4 ,! fir/ is1 t !y arise f a beam ( light transmitt$ ?r\gh ! head ( ! comet1 9 l mann] z a /ream ( light is disc]n$1 :5 ! sun %9es into a d>k5$ room ?r\gh a small hole4 ,?is op9ion1 z ,sir ,,isaac ,,newton obs]ves1 implies ! au?ors ( x :olly unskill$ 9 ! pr9ciples ( optics2 = t /ream ( light1 se5 9 a d>k5$ room1 arises f ! reflection ( ! sun beams by ! du/ & motes float+ 9 ! air3 = ! rays ( light !mselves are n se51 b by _! be+ reflect$ to ! eye f "s sub/ance1 ^u :i* !y fall#bbh4 ,! next op9ion exam9$ by our au?or is t ( ! celebrat$ ,,desc>tes1 :o imag9s ^! tails to be ! light ( ! comet refract$ 9 its passage to u1 & !nce af=d+ an oblong repres5tation2 z ! light ( ! sun does1 :5 refract$ by ! prism 9 t not$ exp]im5t1 :i* w h a great %>e 9 ! ?ird book ( ?is disc\rse#bbi4 ,b ?is op9ion is at once ov]turn$ f ?is consid]ation only1 t ! planets c\ld be no m free f ?is refraction ?an ! comets2 nay ought to h l>g] or bright] tails1 ?an !y1 because ! light ( ! planets is /ronge/4 ,h[ev] our au?or has ?\ght prop] to add "s f>!r objections aga9/ ?is op9ion3 = in/ance1 t ^! tails are n v>iegat$ ) col\rs1 z is ! image produc$ by ! prism1 & :i* is insep>able f t unequal refraction1 :i* produces t disproportion$ l5g? ( ! image4 ,& besides1 :5 ! light 9 its passage f diff]5t comets to ! e>? describes ! same pa? ?r\gh ! heav5s1 ! refraction ( x %\ld ( necessity be 9 all respects ! same4 ,b ?is is contr>y to obs]vation2 = ! comet 9 #afhj1 ! #bh? day ( ,decemb]1 & a =m] comet 9 ! ye> #aegg1 ! #bi? day ( ,decemb]1 appe>'d 9 ! same place ( ! heav5s1 t is1 7 se5 adjac5t to ! same fix$ />s1 ! e>? likewise be+ 9 ! same place at bo? times2 yet ! tail ( ! latt] comet deviat$ f ! opposition to ! sun a little to ! nor?w>d1 & ! tail ( ! =m] comet decl9$ f ! opposition ( ! sun five times z mu* s\?w>d#bcj4 #ad4 ,,!re are "s o!r false op9ions1 ?\gh less reg>d$ ?an ^!1 :i* h be5 advanc$ ^u ?is argum5t4 ,^! our excell5t au?or passes ov]1 ha/5+ to expla91 :at he takes to be ! true cause ( ?is appe>ance4 ,he ?9ks x is c]ta9ly ow+ to /eams & vap\rs exhal$ f ! body1 & gross atmosph]e ( ! comets1 by ! heat ( ! sun2 because all ! appe>ances agree p]fectly to ?is s5tim5t4 ,! tails are b small1 :ile ! comet is desc5d+ to ! sun1 b enl>ge !mselves to an imm5se degree1 z soon z ev] ! comet has pass$ its p]ihelion2 :i* %ews ! tail to dep5d ^u ! degree ( heat1 :i* ! comet receives f ! sun4 ,& t ! int5se heat to :i* comets1 :5 ne>e/ ! sun1 are expos$1 %\ld exhale f !m a v copi\s vap\r1 is a mo/ reasonable supposition2 especially if we consid]1 t 9 ^? free & empty regions /eams w m easily asc5d1 ?an "h ^u ! surface ( ! e>?1 :]e !y are suppress$ & h9d]$ f ris+ by ! weight ( ! incumb5t air3 z we f9d by exp]im5ts made 9 vessels exhau/$ ( ! air1 :]e ^u removal ( ! air sev]al sub/ances w fume & dis*>ge /eams pl5tifully1 :i* emit none 9 ! op5 air4 ,! tails ( comets1 l su* a vap\r1 are always 9 ! plane ( ! comet's orbit1 & opposite to ! sun1 except t ! upp] "p !re( incl9es t[>ds ! p>ts1 :i* ! comet has left by its motion2 resembl+ p]fectly ! smoak ( a burn+ coal1 :i*1 if ! coal rema9 fix$1 asc5ds f x p]p5dicul>ly2 b1 if ! coal be 9 motion1 asc5ds obliquely1 incl9+ f ! motion ( ! coal4 ,& besides1 ! tails ( comets may be comp>$ to ?is smoak 9 ano!r respect1 t bo? ( !m are d5s] & m compact on ! convex side1 ?an on ! concave4 ,! diff]5t appe>ance ( ! head ( ! comet1 aft] x has pa/ its p]ihelion1 f :at x _h be=e1 confirms greatly ?is op9ion ( _! tails3 = smoke rais$ by a /rong heat is black] & gross]1 ?an :5 rais$ by a less2 & accord+ly ! heads ( comets1 at ! same di/ance f ! sun1 are obs]v$ less bright & %9+ aft] ! p]ihelion1 ?an be=e1 z if obscur$ by su* a gross smoke4 #ae4 ,,! obs]vations ( ,,hevelius ^u ! atmosph]es ( comets /ill f>!r illu/rate ! same2 :o relates1 t ! atmosph]es1 especially t "p ( !m next ! sun1 are rem>kably contract$ :5 ne> ! sun1 & dilat$ aga9 aft]w>ds4 #af4 ,,to give a m full idea ( ^! tails1 a rule is laid d[n by our au?or1 :]eby to det]m9e at any "t1 :5 ! vap\r 9 ! extremity ( ! tail fir/ rose f ! head ( ! comet4 ,by ?is rule x is f\nd1 t ! tail does n consi/ ( a fleet+ vap\r1 dissipat$ soon aft] x is rais$1 b is ( long cont9uance2 t almo/ all ! vap\r1 :i* rose ab\t ! "t ( ! p]ihelion f ! comet ( #afhj1 cont9u$ to accompany x1 asc5d+ by degrees1 be+ succe$$ con/antly by fre% matt]1 :i* r5d]$ ! tail contigu\s to ! comet4 ,f ?is computation ! tails are f\nd to p>ticipate ( ano!r prop]ty ( asc5d+ vap\rs1 t1 :5 !y asc5d ) ! greate/ velocity1 !y are lea/ incurvat$4 #ag4 ,,! only objection t c be made aga9/ ?is op9ion is ! difficulty ( expla9+1 h[ a suffici5t quantity ( vap\r c be rais$ f ! atmosph]e ( a comet to fill ^? va/ spaces1 ?r\gh :i* _! tails are sometimes ext5d$4 ,?is our au?or removes by ! foll[+ computation3 our air be+ an ela/ic fluid1 z has be5 said be=e#bca1 is m d5se "h ne> ! surface ( ! e>?1 :]e x is press$ ^u by ! :ole air above2 ?an x is at a di/ance f ! e>?1 :]e x has a less weight incumb5t4 ,i h obs]v$1 t ! d5sity ( ! air is reciprocally proportional to ! compress+ weight4 ,f h5ce our au?or computes to :at degree ( r>ity ! air mu/ be exp&$1 accord+ to ?is rule1 at an height equal to a semidiamet] ( ! e>?3 & he f9ds1 t a globe ( su* air1 z we brea? "h on ! surface ( ! e>?1 :i* %all be "o in* only 9 diamet]1 if x 7 exp&$ to ! degree ( r>ity1 :i* ! air mu/ h at ! height n[ m5tion$1 w\ld fill all ! planet>y regions ev5 to ! v sph]e ( ,saturn1 & f> beyond4 ,n[ s9ce ! air at a great] height w be /ill imm5sly m r>ifi$1 & ! surface ( ! atmosph]es ( comets is usually ab\t t5 times ! di/ance f ! c5t] ( ! comet1 z ! surface ( ! comet x self1 & ! tails are yet va/ly f>!r remov$ f ! c5t] ( ! comet2 ! vap\r1 :i* composes ^? tails1 may v well be all[$ to be s exp&$1 z t a mod]ate quantity ( matt] may fill all t space1 !y are se5 to take up4 ,?\gh inde$ ! atmosph]es ( comets be+ v gross1 !y w h>dly be r>ifi$ 9 _! tails to s great a degree1 z our air "u ! same circum/ances2 especially s9ce !y may be some?+ cond5s$1 z well by _! gravitation to ! sun1 z t ! p>ts w gravitate to "o ano!r2 :i* w h]eaft] be %ewn to be ! univ]sal prop]ty ( all matt]#bcb4 ,! only scruple left is1 h[ s mu* light c be reflect$ f a vap\r s r>e1 z ?is computation implies4 ,= ! removal ( :i* our au?or obs]ves1 t ! mo/ refulg5t ( ^! tails h>dly appe> bright]1 ?an a beam ( ! sun's light transmitt$ into a d>k5$ room ?r\gh a hole ( a s+le in* diamet]2 & t ! smalle/ fix$ />s are visible ?r\gh !m )\t any s5sible dim9ution ( _! lu/re4 #ah4 ,,all ^! consid]ations put x beyond d\bt1 :at is ! true nature ( ! tails ( comets4 ,!re has inde$ no?+ be5 said1 :i* w acc\nt = ! irregul> figures1 9 :i* ^? tails are sometimes report$ to h appe>$2 b s9ce none ( ^? appe>ances h ev] be5 record$ by a/ronom]s1 :o on ! contr>y ascribe ! same lik5ess to ! tails ( all comets1 our au?or ) great judgm5t ref]s all ^? to accid5tal refractions by int]v5+ cl\ds1 or to p>ts ( ! milky way contigu\s to ! comets#bcc4 #ai4 ,,! discussion ( ?is appe>ance 9 comets has l$ ,sir ,,isaac ,,newton into "s speculations relat+ to _! use1 :i* ,i _c b extreamly admire1 z repres5t+ 9 ! /ronge/ light imag9able ! ext5sive provid5ce ( ! great au?or ( nature1 :o1 besides ! furni%+ ?is globe ( e>?1 & )\t d\bt ! re/ ( ! planets1 s abundantly ) e ?+ necess>y = ! support & cont9uance ( ! num]\s races ( plants & animals1 !y are /ock$ )1 has ov] & above provid$ a num]\s tra9 ( comets1 f> exce$+ ! numb] ( ! planets1 to rectify cont9ually1 & re/ore _! gradual decay1 :i* is our au?or's op9ion conc]n+ !m#bcd4 ,= s9ce ! comets are subject to su* unequal degrees ( heat1 be+ sometimes burnt ) ! mo/ int5se degree ( x1 at o!r times sc>ce receiv+ any s5sible influ5ce f ! sun2 x c h>dly be suppos$1 !y are design$ = any su* con/ant use1 z ! planets4 ,n[ ! tails1 :i* !y emit1 l all o!r k9ds ( vap\r1 dilate !mselves z !y asc5d1 & by consequ5ce are gradually disp]s$ & scatt]$ ?r\gh all ! planet>y regions1 & !nce _c b be ga!r$ up by ! planets1 z !y pass ?r\gh _! orbs3 = ! planets hav+ a p[] to cause all bodies to gravitate t[>ds !m1 z w 9 ! sequel ( ?is disc\rse be %ewn#bce2 ^! vap\rs w be drawn 9 process ( "t into ?is or ! o!r planet1 :i* happ5s to act /ronge/ ^u !m4 ,& by ent]+ ! atmosph]es ( ! e>? & o!r planets1 !y may well be suppos$ to contribute to ! r5ovation ( ! face ( ?+s1 9 p>ticul> to supply ! dim9ution caus$ 9 ! humid p>ts by vegetation & putrefaction4 ,= vegetables are n\ri%$ by moi/ure1 & by putrefaction are turn$ 9 great "p into dry e>?2 & an e>?y sub/ance always subsides 9 f]m5t+ liquors2 by :i* means ! dry p>ts ( ! planets mu/ cont9ually increase1 & ! fluids dim9i%1 nay 9 a suffici5t l5g? ( "t be exhau/$1 if n suppli$ by "s su* means4 ,x is f>!r our great au?or's op9ion1 t ! mo/ subtile & active p>ts ( our air1 ^u :i* ! life ( ?+s *iefly dep5ds1 is d]iv$ to u1 & suppli$ by ! comets4 ,s f> are !y f port5d+ any hurt or mis*ief to u1 :i* ! natural fe>s ( m5 are s apt to sugge/ f ! appe>ance ( any ?+ uncommon & a/oni%+4 #bj4 ,,t ! tails ( comets h "s su* important use seems reasonable1 if we consid]1 t ^? bodies d n s5d out ^? fumes m]ely by _! ne> approa* to ! sun2 b are fram$ ( a texture1 :i* disposes !m 9 a p>ticul> mann] to fume 9 t sort3 = ! e>?1 )\t emitt+ any su* /eam1 is m ?an half ! ye> at a less di/ance f ! sun1 ?an ! comet ( #affd & #affe approa*$ x1 :5 ne>e/2 likewise ! comets ( #afhb & #afhc nev] approa*$ ! sun mu* above a sev5? "p ne>] ?an ,v5us1 & 7 m ?an half z f> aga9 f ! sun z ,m]cury2 yet all ^! emitt$ tails4 #ba4 ,,f ! v ne> approa* ( ! comet ( #afhj our au?or draws ano!r speculation2 = if ! sun h an atmosph]e ab\t x1 ! comet m5tion$ seems to h desc5d$ ne> en\gh to ! sun to ent] )9 x4 ,if s1 x mu/ h be5 some?+ ret>d$ by ! resi/ance x w\ld meet )1 & consequ5tly 9 its next desc5t to ! sun w fall ne>] ?an n[2 by :i* means x w meet ) a great] resi/ance1 & be aga9 m ret>d$4 ,! ev5t ( :i* mu/ be1 t at l5g? x w imp+e ^u ! sun's surface1 & !reby supply any decrease1 :i* may h happ5$ by s long an emission ( light1 or o!rwise4 ,& some?+ l ?is our au?or conjectures may be ! case ( ^? fix$ />s :i* by an additional increase ( _! lu/re h = a c]ta9 "t become visible to u1 ?\gh usually !y are out ( sight4 ,!re is inde$ a k9d ( fix$ />s1 :i* appe> & disappe> at regul> & equal int]vals3 "h "s m /eady cause mu/ be s\ght =2 p]haps ^! />s turn r\nd _! own axis's1 z our sun does#bcf1 & h "s "p ( _! body m lum9\s ?an ! o!r1 :]eby !y are se51 :5 ! mo/ lucid "p is next to u1 & :5 ! d>k] "p is turn$ t[>d u1 !y vani% out ( sight4 #bb4 ,,:e!r ! sun does really dim9i%1 z has be5 "h sugge/$1 is difficult to prove2 yet t x ei!r does s1 or t ! e>? increases1 if n bo?1 is r5d]$ probable f ,dr4 ,,halley's obs]vation#bcg1 t by comp>+ ! proportion1 :i* ! p]iodical "t ( ! moon bore to t ( ! sun 9 =m] times1 ) ! proportion betwe5 !m at pres5t1 ! moon is f\nd to be some?+ accel]at$ 9 respect ( ! sun4 ,b if ! sun dim9i%1 ! p]iods ( ! prim>y planets w be l5g!n$2 & if ! e>? be encreas$1 ! p]iod ( ! moon w be %ort5$3 z w appe> by ! next *apt]1 :]e9 x %all be %ewn1 t ! p[] ( ! sun & e>? is ! result ( ! same p[] be+ lodg'd 9 all _! p>ts1 & t ?is pr9ciple ( produc+ gravitation 9 o!r bodies is proportional to ! solid matt] 9 ea* body4 ,,*ap4 ,v4 ,( ! ,,bodies ( ! ,,sun & ,,planets4 ,,our au?or1 aft] hav+ discov]$ t ! cele/ial motions are p]=m$ by a =ce ext5d$ f ! sun & prim>y planets1 foll[s ?is p[] into ! deepe/ recesses ( ^? bodies !mselves1 & proves ! same to accompany ! smalle/ p>ticle1 ( :i* !y are compos$4 #b4 ,,prep>ative h]eto he %ews fir/1 t ea* ( ! heav5ly bodies attracts ! re/1 & all bodies1 ) su* diff]5t degrees ( =ce1 z t ! =ce ( ! same attract+ body is ex]t$ on o!rs exactly 9 proportion to ! quantity ( matt] 9 ! body attract$#bch4 #c4 ,,( ?is ! fir/ pro( he br+s is f exp]im5ts made "h ^u ! e>?4 ,! p[] by :i* ! moon is influ5c$ 0 above %ewn to be ! same1 ) t p[] "h on ! surface ( ! e>?1 :i* we call gravity#bci4 ,n[ "o ( ! effects ( ! pr9ciple ( gravity is1 t all bodies desc5d by ?is =ce f ! same height 9 equal times4 ,:i* has be5 long tak5 notice (2 p>ticul> me?ods hav+ be5 inv5t$ to %ew t ! only cause1 :y "s bodies 7 obs]v$ to fall f ! same height soon] ?an o!rs1 0 ! resi/ance ( ! air4 ,?is we h above relat$#bdj2 & prov$ f h5ce1 t s9ce bodies resi/ to any *ange ( _! /ate f re/ to motion1 or f motion to re/1 9 proportion to ! quantity ( matt] conta9$ 9 !m2 ! p[] t c move diff]5t quantities ( matt] equally1 mu/ be proportional to ! quantity4 ,! only objection "h is1 t x c h>dly be made c]ta91 :e!r ?is proportion 9 ! effect ( gravity on diff]5t bodies holds p]fectly exact or n f ^! exp]im5ts2 by reason t ! great swiftness1 ) :i* bodies fall1 prev5ts our be+ able to det]m9e ! times ( _! desc5t ) all ! exactness requisite4 ,!re=e to rem$y ?is inconv5i5ce1 our au?or sub/itutes ano!r m c]ta9 exp]im5t 9 ! room ( ^! made ^u fall+ bodies4 ,p5dulums are caus$ to vibrate by ! same pr9ciple1 z makes bodies desc5d2 ! p[] ( gravity putt+ !m 9 motion1 z well z ! o!r4 ,b if ! ball ( any p5dulum1 ( ! same l5g? ) ano!r1 7 m or less attract$ 9 proportion to ! quantity ( solid matt] 9 ! ball1 t p5dulum mu/ accord+ly move fa/] or sl[] ?an ! o!r4 ,n[ ! vibrations ( p5dulums cont9ue = a great l5g? ( "t1 & ! numb] ( vibrations !y make may easily be det]m9$ )\t suspicion ( error2 s t ?is exp]im5t may be ext5d$ to :at exactness "o pleases3 & our au?or assures u1 t he exam9$ 9 ?is way sev]al sub/ances1 z gold1 silv]1 lead1 glass1 s&1 common salt1 wood1 wat]1 & :eat2 9 all :i* he f\nd n ! lea/ deviation f ! proportion m5tion$1 ?\gh he made ! exp]im5t 9 su* a mann]1 t 9 bodies ( ! same weight a diff]5ce 9 ! quantity ( _! matt] less ?an a ?\s&? "p ( ! :ole w\ld h discov]$ x self#bda4 ,x appe>s !re=e1 t all bodies are made to desc5d by ! p[] ( gravity "h1 ne> ! surface ( ! e>?1 ) ! same degree ( swiftness4 ,we h above obs]v$ ?is desc5t to be aft] ! rate ( #af feet 9 ! fir/ second ( "t f ! beg9n+ ( _! fall4 ,moreov] x 0 also obs]v$1 t if any body1 :i* fell "h at ! surface ( ! e>? aft] ?is rate1 7 to be convey$ up to ! height ( ! moon1 x w\ld desc5d f !nce j ) ! same degree ( velocity1 z t ) :i* ! moon is attract$ t[>d ! e>?2 & !re=e ! p[] ( ! e>? ^u ! moon be>s ! same proportion to ! p[] x w\ld h ^u ^? bodies at ! same di/ance1 z ! quantity ( matt] 9 ! moon be>s to ! quantity 9 ^? bodies4 #d4 ,,?us ! ass]tion laid d[n is prov$ 9 ! e>?1 t ! p[] ( ! e>? on e body x attracts is1 at ! same di/ance f ! e>?1 proportional to ! quantity ( solid matt] 9 ! body act$ on4 ,z to ! sun1 x has be5 %ewn1 t ! p[] ( ! sun's action ^u ! same prim>y planet is reciprocally 9 ! duplicate proportion ( ! di/ance2 & t ! p[] ( ! sun decreases ?r\gh\t 9 ! same proportion1 ! motion ( comets trav]s+ ! :ole planet>y region te/ifies4 ,?is proves1 t if any planet 7 remov$ f ! sun to any o!r di/ance :atev]1 ! degree ( its accel]ation t[>d ! sun w\ld yet rema9 reciprocally 9 ! duplicate proportion ( its di/ance4 ,b x has likewise be5 %ewn1 t ! degree ( accel]ation1 :i* ! sun gives to e "o ( ! planets1 is reciprocally 9 ! duplicate proportion ( _! respective di/ances4 ,all :i* comp>$ toge!r puts x out ( d\bt1 t ! p[] ( ! sun ^u any planet1 remov$ into ! place ( any e!r1 w\ld give x ! same velocity ( desc5t1 z x gives t o!r2 & consequ5tly1 t ! sun's action ^u diff]5t planets at ! same di/ance w\ld be proportional to ! quantity ( matt] 9 ea*4 ,x has f>!r be5 %ewn1 t ! sun attracts ! prim>y planets1 & _! respective second>y1 :5 at ! same di/ance1 s z to communicate to bo? ! same degree ( velocity2 & !re=e ! =ce1 :]e) ! sun acts on ! second>y planet1 be>s ! same proportion to ! =ce1 :]e) at ! same di/ance x attracts ! prim>y1 z ! quantity ( solid matt] 9 ! second>y planet be>s to ! quantity ( matt] 9 ! prim>y4 #e4 ,,?is prop]ty !re=e is prov$ ( bo? k9ds ( planets1 9 respect ( ! sun4 ,!re=e ! sun possesses ! quality f\nd 9 ! e>?1 ( act+ on bodies ) a degree ( =ce proportional to ! quantity ( matt] 9 ! body1 :i* receives ! influ5ce4 #f4 ,,t ! p[] ( attraction1 ) :i* ! o!r planets are endu$1 %\ld diff] f t ( ! e>?1 c h>dly be suppos$1 if we consid] ! similitude betwe5 ^? bodies2 & t x does n 9 ?is respect1 is f>!r prov$ f ! satellites ( ,saturn & ,jupit]1 :i* are attract$ by _! respective prim>y accord+ to ! same law1 t is1 9 ! same proportion to _! di/ances1 z ! prim>y are attract$ by ! sun3 s t :at has be5 conclud$ ( ! sun 9 relation to ! prim>y planets1 may be ju/ly conclud$ ( ^! prim>y 9 respect ( _! second>y1 & 9 consequ5ce ( t1 9 reg>d likewise to all o!r bodies1 viz4 t !y w attract e body 9 proportion to ! quantity ( solid matt] x conta9s4 #g4 ,,h5ce x foll[s1 t ?is attraction ext5ds itself to e p>ticle ( matt] 9 ! attract$ body3 & t no portion ( matt] :atev] is exempt$ f ! influ5ce ( ^? bodies1 to :i* we h prov$ ?is attractive p[] to belong4 #h4 ,,be=e we proce$ f>!r1 we may "h rem>k1 t ?is attractive p[] bo? ( ! sun & planets n[ appe>s to be q ( ! same nature 9 all2 = x acts 9 ea* 9 ! same proportion to ! di/ance1 & 9 ! same mann] acts alike ^u e p>ticle ( matt]4 ,?is p[] !re=e 9 ! sun & o!r planets is n ( a diff]5t nature f ?is p[] 9 ! e>?2 :i* has be5 already %ewn to be ! same ) t1 :i* we call gravity#bdb4 #i4 ,,& ?is lays op5 ! way to prove1 t ! attract+ p[] lodg$ 9 ! sun & planets1 belongs likewise to e "p ( !m3 & t _! respective p[]s ^u ! same body are proportional to ! quantity ( matt]1 ( :i* !y are compos$2 = in/ance1 t ! =ce ) :i* ! e>? attracts ! moon1 is to ! =ce1 ) :i* ! sun w\ld attract x at ! same di/ance1 z ! quantity ( solid matt] conta9$ 9 ! e>?1 to ! quantity conta9$ 9 ! sun#bdc4 #aj4 ,,! fir/ ( ^! ass]tions is a v evid5t consequ5ce f ! latt]4 ,& be=e we proce$ to ! pro(1 x mu/ fir/ be %ewn1 t ! ?ird law ( motion1 :i* makes action & reaction equal1 holds 9 ^! attractive p[]s4 ,! mo/ rem>kable attractive =ce1 next to ! p[] ( gravity1 is t1 by :i* ! load/one attracts iron4 ,n[ if a load/one 7 laid ^u wat]1 & support$ by "s prop] sub/ance1 z wood or cork1 s t x might swim2 & if a piece ( iron 7 caus$ to swim ^u ! wat] 9 l mann]3 z soon z ! load/one beg9s to attract ! iron1 ! iron %all move t[>d ! /one1 & ! /one %all also move t[>d ! iron2 :5 !y meet1 !y %all /op ea* o!r1 & rema9 fix$ toge!r )\t any motion4 ,?is %ews1 t ! velocities1 :]e) !y meet1 are reciprocally proportional to ! quantities ( solid matt] 9 ea*2 & t by ! /one's attract+ ! iron1 ! /one itself receives z mu* motion1 9 ! /rict philosophic s5se ( t ^w#bdd1 z x communicates to ! iron3 = x has be5 decl>$ above to be an effect ( ! p]cussion ( two bodies1 t if !y meet ) velocities reciprocally proportional to ! respective bodies1 !y %all be /opp$ by ! conc\rse1 unless _! ela/icity put !m into fre% motion2 b if !y meet ) any o!r velocities1 !y %all reta9 "s motion aft] meet+#bde4 ,amb]1 glass1 seal+-wax1 & _m o!r sub/ances acquire by rubb+ a p[]1 :i* f its hav+ be5 rem>kable1 p>ticul>ly 9 amb]1 is call$ electrical4 ,by ?is p[] !y w = "s "t aft] rubb+ attract light bodies1 t %all be br\ght )9 ! sph]e ( _! activity4 ,on ! o!r h& ,mr4 ,,boyle f\nd1 t if a piece ( amb] be hung 9 a p]p5dicul> position by a /r+1 x %all be drawn itself t[>d ! body :]eon x 0 rubb$1 if t body be br\ght ne> x4 ,bo? 9 ! load/one & 9 electrical bodies we usually ascribe ! p[] to ! p>ticul> body1 ^: pres5ce we f9d necess>y = produc+ ! effect4 ,! load/one & any piece ( iron w draw ea* o!r1 b 9 two pieces ( iron no su* effect is ord9>ily obs]v$2 !re=e we call ?is attractive p[] ! p[] ( ! load/one3 ?\gh ne> a load/one two pieces ( iron w also draw ea* o!r4 ,9 l mann] ! rubb+ ( amb]1 glass1 or any su* body1 till x is gr[n w>m1 be+ necess>y to cause any action betwe5 ^? bodies & o!r sub/ances1 we ascribe ! electrical p[] to ^? bodies4 ,b 9 all ^! cases if we w\ld speak m correctly1 & n ext5d ! s5se ( our expressions beyond :at we see2 we c only say t ! neighb\rhood ( a load/one & a piece ( iron is att5d$ ) a p[]1 :]eby ! load/one & ! iron are drawn t[>d ea* o!r2 & ! rubb+ ( electrical bodies gives rise to a p[]1 :]eby ^? bodies & o!r sub/ances are mutually attract$4 ,?us we mu/ also und]/& 9 ! p[] ( gravity1 t ! two bodies are mutually made to approa* by ! action ( t p[]4 ,:5 ! sun draws any planet1 t planet also draws ! sun2 & ! motion1 :i* ! planet receives f ! sun1 be>s ! same proportion to ! motion1 :i* ! sun x self receives1 z ! quantity ( solid matt] 9 ! sun be>s to ! quantity ( solid matt] 9 ! planet4 ,hi!rto1 = brevity sake 9 speak+ ( ^! =ces1 we h g5]ally ascrib$ !m to ! body1 :i* is lea/ mov$2 z :5 we call$ ! p[]1 :i* ex]ts itself betwe5 ! sun & any planet1 ! attractive p[] ( ! sun2 b to speak m correctly1 we %\ld r call ?is p[] 9 any case ! =ce1 :i* acts betwe5 ! sun & e>?1 betwe5 ! sun & ,jupit]1 betwe5 ! e>? & moon1 c4 = bo? ! bodies are mov$ by ! p[] act+ betwe5 !m1 9 ! same mann]1 z :5 two bodies are ti$ toge!r by a rope1 if t rope %r9k by be+ wet1 or o!rwise1 & !reby cause ! bodies to approa*1 by draw+ bo?1 x w communicate to bo? ! same degree ( motion1 & cause !m to approa* ) velocities reciprocally proportional to ! respective bodies4 ,f ?is mutual action betwe5 ! sun & planet x foll[s1 z has be5 obs]v$ above#bdf1 t ! sun & planet d ea* move ab\t _! common c5t] ( gravity4 ,let ,a 79 fig4 #ajh47 repres5t ! sun1 ,b a planet1 ,c _! common c5t] ( gravity4 ,if ^! bodies 7 once at re/1 by _! mutual attraction !y w\ld directly approa* ea* o!r ) su* velocities1 t _! common c5t] ( gravity w\ld rema9 at re/1 & ! two bodies w\ld at l5g? meet 9 t po9t4 ,if ! planet ,b 7 to receive an impulse1 z 9 ! direction ( ! l9e ,d ,e1 ?is w\ld prev5t ! two bodies f fall+ toge!r2 b _! common c5t] ( gravity w\ld be put into motion 9 ! direction ( ! l9e ,c ,f equidi/ant f ,b ,e4 ,9 ?is case ,sir ,,isaac ,,newton proves#bdg1 t ! sun & planet w\ld describe r\nd _! common c5t] ( gravity simil> orbits1 :ile t c5t] w\ld proce$ ) an uni=m motion 9 ! l9e ,c ,f2 & s ! sy/em ( ! two bodies w\ld move on ) ! c5t] ( gravity )\t end4 ,9 ord] to keep ! sy/em 9 ! same place1 x is necess>y1 t :5 ! planet receiv$ its impulse 9 ! direction ,b ,e1 ! sun %\ld also receive su* an impulse ! contr>y way1 z might keep ! c5t] ( gravity ,c )\t motion2 = if ^! began once to move )\t giv+ any motion to _! common c5t] ( gravity1 t c5t] w\ld always rema9 fix$4 #aa4 ,,by ?is may be und]/ood 9 :at mann] ! action betwe5 ! sun & planets is mutual4 ,b f>!r1 we h %ewn above#bdh1 t ! p[]1 :i* acts betwe5 ! sun & prim>y planets1 is altoge!r ( ! same nature ) t1 :i* acts betwe5 ! e>? & ! bodies at its surface1 or betwe5 ! e>? & its p>ts1 & ) t :i* acts betwe5 ! prim>y planets & _! second>y2 !re=e all ^! actions mu/ be ascrib$ to ! same cause#bdi4 ,aga91 x has be5 already prov$1 t 9 diff]5t planets ! =ce ( ! sun's action ^u ea* at ! same di/ance w\ld be proportional to ! quantity ( solid matt] 9 ! planet#bej2 !re=e ! reaction ( ea* planet on ! sun at ! same di/ance1 or ! motion1 :i* ! sun w\ld receive f ea* planet1 w\ld also be proportional to ! quantity ( matt] 9 ! planet2 t is1 ^! planets at ! same di/ance w\ld act on ! same body ) degrees ( /r5g? proportional to ! quantity ( solid matt] 9 ea*4 ,illu/ration #ab4 ,,9 ! next place1 f :at has be5 n[ prov$1 our great au?or has d$uc$ ?is f>!r consequ5ce1 no less surpriz+ ?an elegant2 t ea* ( ! p>ticles1 out ( :i* ! bodies ( ! sun & planets are fram$1 ex]t _! p[] ( gravitation by ! same law1 & 9 ! same proportion to ! di/ance1 z ! great bodies :i* !y compose4 ,= ?is purpose he fir/ demon/rates1 t if a globe 7 comp\nd$ ( p>ticles1 :i* w attract ! p>ticles ( any o!r body reciprocally 9 ! duplicate proportion ( _! di/ances1 ! :ole globe w attract ! same 9 ! reciprocal duplicate proportion ( _! di/ances f ! c5t] ( ! globe2 provid$ ! globe be ( uni=m d5sity ?r\gh\t#bea4 ,& f ?is our au?or d$uces ! rev]se1 t if a globe acts ^u di/ant bodies by ! law j n[ specifi$1 & ! p[] ( ! globe is d]iv$ f its be+ compos$ ( attractive p>ticles2 ea* ( ^? p>ticles w attract aft] ! same proportion#beb4 ,! mann] ( d$uc+ ?is is n set d[n at l>ge by our au?or1 b is z foll[s4 ,! globe is suppos$ to act ^u ! p>ticles ( a body )\t x con/antly 9 ! reciprocal duplicate proportion ( _! di/ances f its c5t]2 & !re=e at ! same di/ance f ! globe1 on :i* side soev] ! body be plac$1 ! globe w act equally ^u x4 ,n[ because1 if ! p>ticles1 ( :i* ! globe is compos$1 act$ ^u ^? )\t 9 ! reciprocal duplicate proportion ( _! di/ances1 ! :ole globe w\ld act ^u !m 9 ! same mann] z x does2 !re=e1 if ! p>ticles ( ! globe h n all ( !m t prop]ty1 "s mu/ act /rong] ?an 9 t proportion1 :ile o!rs act weak]3 & if ?is be ! condition ( ! globe1 x is pla91 t :5 ! body attract$ is 9 su* a situation 9 respect ( ! globe1 t ! great] numb] ( ! /ronge/ p>ticles are ne>e/ to x1 ! body w be m =cibly attract$2 ?an :5 by turn+ ! globe ab\t1 ! great] quantity ( weak p>ticles %\ld be ne>e/1 ?\gh ! di/ance ( ! body %\ld rema9 ! same f ! c5t] ( ! globe4 ,:i* is contr>y to :at 0 at fir/ rem>k$1 t ! globe on all sides ( x acts ) ! same /r5g? at ! same di/ance4 ,:5ce x appe>s1 t no o!r con/itution ( ! globe c agree to x4 #ac4 ,,f ^! propositions x is f>!r collect$1 t if all ! p>ticles ( "o globe attract all ! p>ticles ( ano!r 9 ! proportion s (t5 m5tion$1 ! attract+ globe w act ^u ! o!r 9 ! same proportion to ! di/ance betwe5 ! c5t] ( ! globe :i* attracts1 & ! c5t] ( t :i* is attract$#bec3 & f>!r1 t ?is proportion holds true1 ?\gh ei!r or bo? ! globes be compos$ ( dissimil> p>ts1 "s r>] & "s m d5se2 provid$ only1 t all ! p>ts 9 ! same globe equally di/ant f ! c5t] be homog5e\s#bed4 ,& also1 if bo? ! globes attract ea* o!r#bee4 ,all :i* place x beyond contradiction1 t ?is proportion obta9s ) z mu* exactness ne> & contigu\s to ! surface ( attract+ globes1 z at great] di/ances f !m4 #ad4 ,,?us our au?or1 )\t ! pomp\s pret5ce ( expla9+ ! cause ( gravity1 has made "o v important /ep t[>d x1 by %ew+ t ?is p[] 9 ! great bodies ( ! univ]se1 is d]iv$ f ! same p[] be+ lodg$ 9 e p>ticle ( ! matt] :i* composes !m3 & consequ5tly1 t ?is prop]ty is no less ?an univ]sal to all matt] :atev]1 ?\gh ! p[] be too m9ute to produce any visible effects on ! small bodies1 :]e) we conv]se1 by _! action on ea* o!r#bef4 ,9 ! fix$ />s inde$ we h no p>ticul> pro( t !y h ?is p[]2 = we f9d no app]ance to demon/rate t !y ei!r act1 or are act$ ^u by x4 ,b s9ce ?is p[] is f\nd to belong to all bodies1 :]eon we c make obs]vation2 & we see t x is n to be alt]$ by any *ange 9 ! =m ( bodies1 b always accompanies !m 9 e %ape )\t dim9ution1 rema9+ ev] proportional to ! quantity ( solid matt] 9 ea*2 su* a p[] mu/ )\t d\bt belong univ]sally to all matt]4 #ae4 ,,?is !re=e is ! univ]sal law ( matt]2 :i* recomm5ds x self no less = its great pla9ness & simplicity1 ?an = ! surpriz+ discov]ies x leads u to4 ,by ?is pr9ciple we le>n ! diff]5t weight1 :i* ! same body w h ^u ! surfaces ( ! sun & ( div]se planets2 & by ! same we c judge ( ! composition ( ^? cele/ial bodies1 & "k ! d5sity ( ea*2 :i* is =m$ ( ! mo/ compact1 & :i* ( ! mo/ r>e sub/ance4 ,let ! adv]s>ies ( ?is philosophy reflect "h1 :e!r load+ ?is pr9ciple ) ! appellation ( an occult quality1 or p]petual miracle1 or any o!r reproa*ful "n1 be suffici5t to dissuade u f cultivat+ x2 s9ce ?is quality1 :i* !y call occult1 leads to ! k ( su* ?+s1 t x w\ld h be5 reput$ no less ?an madness = any "o1 be=e !y _h be5 discov]$1 ev5 to h conjectur$ t our faculties %\ld ev] h rea*$ s f>4 #af4 ,,see h[ all ?is naturally foll[s f ! =ego+ pr9ciples 9 ^? planets1 :i* h satellites mov+ ab\t !m4 ,by ! times1 9 :i* ^! satellites p]=m _! revolutions1 comp>$ ) _! di/ances f _! respective prim>y1 ! proportion betwe5 ! p[]1 ) :i* "o prim>y attracts 8 satellites1 & ! =ce ) :i* any o!r attracts 8 w be kn[n2 & ! proportion ( ! p[] ) :i* any planet attracts its second>y1 to ! p[] ) :i* x attracts a body at its surface is f\nd1 by comp>+ ! di/ance ( ! second>y planet f ! c5t] ( ! prim>y1 to ! di/ance ( ! prim>y planet's surface f ! same3 & f h5ce is d$uc$ ! proportion betwe5 ! p[] ( gravity ^u ! surface ( "o planet1 to ! gravity ^u ! surface ( ano!r4 ,by ! l me?od ( comp>+ ! p]iodical "t ( a prim>y planet ab\t ! sun1 ) ! revolution ( a satellite ab\t its prim>y1 may be f\nd ! proportion ( gravity1 or ( ! weight ( any body ^u ! surface ( ! sun1 to ! gravity1 or to ! weight ( ! same body ^u ! surface ( ! planet1 :i* c>ries ab\t ! satellite4 #ag4 ,,by ^! k9ds ( computation x is f\nd1 t ! weight ( ! same body ^u ! surface ( ! sun w be ab\t #bc times z great1 z "h ^u ! surface ( ! e>?2 ab\t #aj times z great1 z ^u ! surface ( ,jupit]2 & ne> #ai times z great1 z ^u ! surface ( ,saturn#beg4 #ah4 ,,! quantity ( matt]1 :i* composes ea* ( ^! bodies1 is proportional to ! p[] x has ^u a body at a giv5 di/ance4 ,by ?is means x is f\nd1 t ! sun conta9s #ajfg times z mu* matt] z ,jupit]2 ,jupit] #aeh times z mu* z ! e>?1 & #b-e_/f times z mu* z ,saturn#beh4 ,! diamet] ( ! sun is ab\t #ib times1 t ( ,jupit] ab\t #i times1 & t ( ,saturn ab\t #g times ! diamet] ( ! e>?4 #ai4 ,,by mak+ a comp>ison betwe5 ! quantity ( matt] 9 ^! bodies & _! magnitudes1 to be f\nd f _! diamet]s1 _! respective d5sities are readily d$uc$2 ! d5sity ( e body be+ measur$ by ! quantity ( matt] conta9$ "u ! same bulk1 z has be5 above rem>k$#bei4 ,?us ! e>? is f\nd #d times m d5se ?an ,jupit]2 ,saturn has betwe5 & ( ! d5sity ( ,jupit]2 b ! sun has "o f\r? "p only ( ! d5sity ( ! e>?#bfj4 ,f :i* ?is obs]vation is drawn by our au?or2 t ! sun is r>ifi$ by its great heat1 & t ( ! ?ree planets nam$1 ! m d5se is ne>] ! sun ?an ! m r>e2 z 0 highly reasonable to expect1 ! d5se/ bodies requir+ ! greate/ heat to agitate & put _! p>ts 9 motion2 z on ! contr>y1 ! planets :i* are m r>e1 w\ld be r5d]$ unfit = _! (fice1 by ! int5se heat to :i* ! d5s] are expos$4 ,?us ! wat]s ( our seas1 if remov$ to ! di/ance ( ,saturn f ! sun1 w\ld rema9 p]petually froz52 & if z ne> ! sun z ,m]cury1 w\ld con/antly boil#bfa4 #bj4 ,,! d5sities ( ! ?ree planets ,m]cury1 ,v5us1 & ,m>s1 :i* h no satellites1 _c be expresly assign$2 b f :at is f\nd 9 ! o!rs1 x is v probable1 t !y also are ( su* diff]5t degrees ( d5sity1 t univ]sally ! planet :i* is ne>e/ to ! sun1 is =m$ ( ! mo/ compact sub/ance4 ,,*ap4 ,,vi4 ,( ! ,,fluid ,,p>ts ( ! ,,planets4 ,,?is globe1 t we inhabit1 is compos$ ( two p>ts2 ! solid e>?1 :i* af=ds u a f\ndation to dwell ^u2 & ! seas & o!r wat]s1 t furni% ra9s & vap\rs necess>y to r5d] ! e>? fruitful1 & productive ( :at is requisite = ! support ( life4 ,& t ! moon1 ?\gh b a second>y planet1 is compos$ 9 l mann]1 is g5]ally ?\ght1 f ! diff]5t degrees ( light :i* appe> on its surface2 ! p>ts ( t planet1 :i* reflect a dim light1 be+ suppos$ to be fluid1 & to imbibe ! sun's rays1 :ile ! solid p>ts reflect !m m copi\sly4 ,"s inde$ d n all[ ?is to be a conclusive argum5t3 b :e!r we c di/+ui% ! fluid "p ( ! moon's surface f ! re/ or n2 yet x is mo/ probable t !re are two su* diff]5t p>ts1 & ) /ill great] reason we may ascribe ! l to ! o!r prim>y planets1 :i* yet m ne>ly resemble our e>?4 ,! e>? is also encompass$ by ano!r fluid ! air1 & we h be=e rem>k$1 t probably ! re/ ( ! planets are surr\nd$ by ! l4 ,^! fluid p>ts 9 p>ticul> engage our au?or's att5tion1 bo? by reason ( "s rem>kable appe>ances peculi> to !m1 & likewise ( "s effects !y h ^u ! :ole bodies to :i* !y belong4 #b4 ,,fluids h be5 already treat$ ( 9 g5]al1 ) respect to ! effect !y h ^u solid bodies mov+ 9 !m#bfb2 n[ we mu/ consid] !m 9 ref]5ce to ! op]ation ( ! p[] ( gravity ^u !m4 ,by ?is p[] !y are r5d]$ weighty1 l all o!r bodies1 9 proportion to ! quantity ( matt]1 :i* is conta9$ 9 !m4 ,& 9 any quantity ( a fluid ! upp] p>ts press ^u ! l[] z mu*1 z any solid body w\ld press on ano!r1 :]eon x %\ld lie4 ,b !re is an effect ( ! pressure ( fluids on ! bottom ( ! vessel1 :]e9 !y are conta9$1 :i* ,i %all p>ticul>ly expla94 ,! =ce support$ by ! bottom ( su* a vessel is n simply ! weight ( ! quantity ( ! fluid 9 ! vessel1 b is equal to ! weight ( t quantity ( ! fluid1 :i* w\ld be conta9$ 9 a vessel ( ! same bottom & ( equal wid? ?r\gh\t1 :5 ?is vessel is fill$ up to ! same height1 z t to :i* ! vessel propos$ is fill$4 ,suppose wat] 7 conta9$ 9 ! vessel ,a ,b ,c ,d 79 fig4 #aji47 fill$ up to ,e ,f4 ,"h x is evid5t1 t if a "p ( ! bottom1 z ,g ,h1 :i* is directly "u any "p ( ! space ,e ,f1 be consid]$ sep>ately2 x w appe> at once1 t ?is "p su/a9s ! weight ( z mu* ( ! fluid1 z /&s p]p5dicul>ly ov] x up to ! height ( ,e ,f2 t is1 ! two p]p5dicul>s ,g ,i & ,h ,k be+ drawn1 ! "p ,g ,h ( ! bottom w su/a9 ! :ole weight ( ! fluid includ$ betwe5 ^! two p]p5dicul>s4 ,aga91 ,i say1 e o!r "p ( ! bottom equally broad ) ?is1 w su/a9 z great a pressure4 ,let ! "p ,l ,m be ( ! same bread? ) ,g ,h4 ,"h ! p]p5dicul>s ,l ,o & ,m ,n be+ drawn1 ! quantity ( wat] conta9$ betwe5 ^! p]p5dicul>s is n s great1 z t conta9$ betwe5 ! p]p5dicul>s ,g ,i & ,h ,k2 yet1 ,i say1 ! pressure on ,l ,m w be equal to t on ,g ,h4 ,?is w appe> by ! foll[+ consid]ations4 ,x is evid5t1 t if ! "p ( ! vessel betwe5 ,o & ,n 7 remov$1 ! wat] w\ld imm$iately fl[ out1 & ! surface ,e ,f w\ld subside2 = all p>ts ( ! wat] be+ equally heavy1 x mu/ soon =m itself to a level surface1 if ! =m ( ! vessel1 :i* conta9s x1 does n prev5t4 ,!re=e s9ce ! wat] is prev5t$ f ris+ by ! side ,n ,o ( ! vessel1 x is manife/1 t x mu/ press aga9/ ,n ,o ) "s degree ( =ce4 ,9 o!r words1 ! wat] betwe5 ! p]p5dicul>s ,l ,o & ,m ,n endeav\rs to ext5d itself ) a c]ta9 degree ( =ce2 or m correctly1 ! ambi5t wat] presses ^u ?is1 & endeav\rs to =ce ?is pill> or column ( wat] into a great] l5g?4 ,b s9ce ?is column ( wat] is su/a9$ betwe5 ,n ,o & ,l ,m1 ea* ( ^! p>ts ( ! vessel w be equally press$ aga9/ by ! p[]1 :]e) ?is column endeav\rs to ext5d4 ,consequ5tly ,l ,m be>s ?is =ce ov] & above ! weight ( ! column ( wat] betwe5 ,l ,o & ,m ,n4 ,to "k :at ?is expansive =ce is1 let ! "p ,o ,n ( ! vessel be remov$1 & ! p]p5dicul>s ,l ,o & ,m ,n be prolong$2 !n by means ( "s pipe fix$ ov] ,n ,o let wat] be fill$ betwe5 ^! p]p5dicul>s up to ,p ,q an equal height ) ,e ,f4 ,"h ! wat] betwe5 ! p]p5dicul>s ,l ,p & ,m ,q is ( an equal height ) ! highe/ "p ( ! wat] 9 ! vessel2 !re=e ! wat] 9 ! vessel _c by its pressure =ce x up high]1 nor c ! wat] 9 ?is column subside2 because1 if x %\ld1 x w\ld raise ! wat] 9 ! vessel to a great] height ?an itself4 ,b x foll[s f h5ce1 t ! weight ( wat] conta9$ betwe5 ,p ,o & ,q ,n is a j balance to ! =ce1 :]e) ! column betwe5 ,l ,o & ,m ,n endeav\rs to ext5d4 ,s ! "p ,l ,m ( ! bottom1 :i* su/a9s bo? ?is =ce & ! weight ( ! wat] betwe5 ,l ,o & ,m ,n1 is press$ ^u by a =ce equal to ! unit$ weight ( ! wat] betwe5 ,l ,o & ,m ,n1 & ! weight ( ! wat] betwe5 ,p ,o & ,q ,n2 t is1 x is press$ on by a =ce equal to ! weight ( all ! wat] conta9$ betwe5 ,l ,p & ,m ,q4 ,& ?is weight is equal to t ( ! wat] conta9$ betwe5 ,g ,i & ,h ,k1 :i* is ! weight su/a9$ by ! "p ,g ,h ( ! bottom4 ,n[ ?is be+ true ( e "p ( ! bottom ,b ,c1 x is evid5t1 t if ano!r vessel ,r ,s ,t ,v be =m$ ) a bottom ,r ,v equal to ! bottom ,b ,c1 & be ?r\gh\t its :ole height ( "o & ! same bread?2 :5 ?is vessel is fill$ ) wat] to ! same height1 z ! vessel ,a ,b ,c ,d is fill$1 ! bottoms ( ^! two vessels %all be press$ ^u ) equal =ce4 ,if ! vessel be broad] at ! top ?an at ! bottom1 x is evid5t1 t ! bottom w be> ! pressure ( s mu* ( ! fluid1 z is p]p5dicul>ly ov] x1 & ! sides ( ! vessel w support ! re/4 ,?is prop]ty ( fluids is a coroll>y f a proposition ( our au?or#bfc2 f :5ce also he d$uces ! effects ( ! pressure ( fluids on bodies re/+ 9 !m4 ,^! are1 t any body heavi] ?an a fluid w s9k to ! bottom ( ! vessel1 :]e9 ! fluid is conta9$1 & 9 ! fluid w weigh z mu* z its own weight exce$s ! weight ( an equal quantity ( ! fluid2 any body uncompressible ( ! same d5sity ) ! fluid1 w re/ any :]e 9 ! fluid )\t suff]+ ! lea/ *ange ei!r 9 its place or figure f ! pressure ( su* a fluid1 b w rema9 z undi/urb$ z ! p>ts ( ! fluid !mselves2 b e body ( less d5sity ?an ! fluid w swim on its surface1 a "p only be+ receiv$ )9 ! fluid4 ,:i* "p w be equal 9 bulk to a quantity ( ! fluid1 ^: weight is equal to ! weight ( ! :ole body2 = by ?is means ! p>ts ( ! fluid "u ! body w suff] z great a pressure z any o!r p>ts ( ! fluid z mu* bel[ ! surface z ^!4 #c4 ,,9 ! next place1 9 relation to ! air1 we h above made m5tion1 t ! air surr\nd+ ! e>? be+ an ela/ic fluid1 ! p[] ( gravity w h ?is effect on x1 to make ! l[] p>ts ne> ! surface ( ! e>? m compact & compress$ toge!r by ! weight ( ! air incumb5t1 ?an ! high] p>ts1 :i* are press$ ^u by a less quantity ( ! air1 & !re=e su/a9 a less weight#bfd4 ,x has be5 also obs]v$1 t our au?or has laid d[n a rule = comput+ ! exact degree ( d5sity 9 ! air at all heights f ! e>?#bfe4 ,b !re is a f>!r effect f ! air's be+ compress$ by ! p[] ( gravity1 :i* he has di/9ctly consid]$4 ,! air be+ ela/ic & 9 a /ate ( compression1 any tremul\s body w propagate its motion to ! air1 & excite !re9 vibrations1 :i* w spread f ! body t occasions !m to a great di/ance4 ,?is is ! effici5t cause ( s\nd3 = t s5sation is produc$ by ! air1 :i*1 z x vibrates1 /rikes aga9/ ! organ ( he>+4 ,z ?is subject 0 extremely difficult1 s our great au?or's success is surpriz+4 #d4 ,,our au?or's doctr9e ^u ?is head ,i %all endeav\r to expla9 some:at at l>ge4 ,b prelim9>y !reto mu/ be %ewn1 :at he has deliv]$ 9 g5]al ( pressure propagat$ ?r\gh fluids2 & also :at he has set d[n relat+ to t wave-l motion1 :i* appe>s ^u ! surface ( wat]1 :5 agitat$ by ?r[+ any ?+ into x1 or by ! reciprocal motion ( ! f+]1 c4 #e4 ,,conc]n+ ! fir/1 x is prov$1 t pressure is spread ?r\gh fluids1 n only "r =w>d 9 a /reight l9e1 b also lat]ally1 ) almo/ ! same ease & =ce4 ,( :i* a v obvi\s exemplification by exp]im5t is propos$3 t is1 to agitate ! surface ( wat] by ! reciprocal motion ( ! f+] =w>ds & backw>ds only2 = ?\gh ! f+] h no circul> motion giv5 x1 yet ! waves excit$ 9 ! wat] w diffuse !mselves on ea* h& ( ! direction ( ! motion1 & soon surr\nd ! f+]4 ,nor is :at we obs]ve 9 s\nds unlike to ?is1 :i* d n proce$ 9 /raight l9es only1 b are he>d ?\gh a m\nta9 int]v5e1 & :5 !y ent] a room 9 any "p ( x1 !y spread !mselves into e corn]2 n by reflection f ! walls1 z "s h imag9$1 b z f> z ! s5se c judge1 directly f ! place :]e !y ent]4 #f4 ,,h[ ! waves are excit$ 9 ! surface ( /agnant wat]1 may be ?us conceiv$4 ,suppose 9 any place1 ! wat] rais$ above ! re/ 9 =m ( a small hillock2 t wat] w imm$iately subside1 & raise ! circumambi5t wat] above ! level ( ! p>ts m remote1 to :i* ! motion _c be communicat$ "u long] "t4 ,& aga91 ! wat] 9 subsid+ w acquire1 l all fall+ bodies1 a =ce1 :i* w c>ry x bel[ ! level surface1 till at l5g? ! pressure ( ! ambi5t wat] prevail+1 x w rise aga91 & ev5 ) a =ce l to t :]e) x desc5d$1 :i* w c>ry x aga9 above ! level4 ,b 9 ! mean "t ! ambi5t wat] be=e rais$ w subside1 z ?is did1 s9k+ bel[ ! level2 & 9 s do+1 w n only raise ! wat]1 :i* fir/ subsid$1 b also ! wat] next )\t itself4 ,s t n[ beside ! fir/ hillock1 we %all h a r+ inve/+ x1 at "s di/ance rais$ above ! pla9 surface likewise2 & betwe5 !m ! wat] w be sunk bel[ ! re/ ( ! surface4 ,aft] ?is1 ! fir/ hillock1 & ! new made annul> ris+1 w desc5d2 rais+ ! wat] betwe5 !m1 :i* 0 be=e depress$1 & likewise ! adjac5t "p ( ! surface )\t4 ,?us w ^! annul> waves be successively spread m & m4 ,=1 z ! hillock subsid+ produces "o r+1 & t r+ subsid+ raises aga9 ! hillock1 & a second r+2 s ! hillock & second r+ subsid+ toge!r raise ! fir/ r+1 & a ?ird2 !n ?is fir/ & ?ird r+ subsid+ toge!r raise ! fir/ hillock1 ! second r+1 & a f\r?2 & s on cont9ually1 till ! motion by degrees ceases4 ,n[ x is demon/rat$1 t ^! r+s asc5d & desc5d 9 ! mann] ( a p5dulum2 desc5d+ ) a motion cont9ually accel]at$1 till !y become ev5 ) ! pla9 surface ( ! fluid1 :i* is half ! space !y desc5d2 & !n be+ ret>d$ aga9 by ! same degrees z ^?1 :]eby !y 7 accel]at$1 till !y are depress$ bel[ ! pla9 surface1 z mu* z !y 7 be=e rais$ above x3 & t ?is augm5tation & dim9ution ( _! velocity proce$s by ! same degrees1 z t ( a p5dulum vibrat+ 9 a cycloid1 & ^: l5g? %\ld be a f\r? "p ( ! di/ance betwe5 any two adjac5t waves3 & f>!r1 t a new r+ is produc$ e "t a p5dulum1 ^: l5g? is f\r times ! =m]1 t is1 equal to ! int]val betwe5 ! summits ( two waves1 makes "o oscillation or sw+#bff4 #g4 ,,?is n[ op5s ! way = und]/&+ ! motion consequ5t ^u ! tremors ( ! air1 excit$ by ! vibrations ( sonor\s bodies3 :i* we mu/ conceive to be p]=m$ 9 ! foll[+ mann]4 #h4 ,,let ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 ,h 79 fig4 #aaj47 repres5t a s]ies ( ! p>ticles ( ! air1 at equal di/ances f ea* o!r4 ,i ,k ,l a musical *ord1 :i* ,i %all use = ! tremul\s & sonor\s body1 to make ! conception z simple z may be4 ,suppose ?is *ord /ret*$ ^u ! po9ts ,i & ,l1 & =cibly drawn into ! situation ,i ,k ,l1 s t x become contigu\s to ! p>ticle ,a 9 its middle po9t ,k3 & let ! *ord f ?is situation beg9 to recoil1 press+ aga9/ ! p>ticle ,a1 :i* w !reby be put into motion t[>ds ,b3 b ! p>ticles ,a1 ,b1 ,c be+ equidi/ant1 ! ela/ic p[]1 by :i* ,b avoids ,a1 is equal to1 & balanc$ by ! p[]1 by :i* x avoids ,c2 !re=e ! ela/ic =ce1 by :i* ,b is repell$ f ,a1 w n put ,b into any degree ( motion1 till ,a is by ! motion ( ! *ord br\ght ne>] to ,b1 ?an ,b is to ,c3 b z soon z t is done1 ! p>ticle ,b w be mov$ t[>ds ,c2 & be+ made to approa* ,c1 w 9 ! next place move t2 :i* w ^u t advance1 put ,d likewise into motion1 & s on3 !re=e ! p>ticle ,a be+ mov$ by ! *ord1 ! foll[+ p>ticles ( ! air ,b1 ,c1 ,d1 c4 w successively be mov$4 ,f>!r1 if ! po9t ,k ( ! *ord moves =w>d ) an accel]at$ velocity1 s t ! p>ticle ,a %all move aga9/ ,b ) an advanc+ pace1 & ga9 gr\nd ( x1 approa*+ ne>] & ne>] cont9ually2 ,a by approa*+ w press m ^u ,b1 & give x a great] velocity likewise1 by reason t z ! di/ance betwe5 ! p>ticles dim9i%es1 ! ela/ic p[]1 by :i* !y fly ea* o!r1 increases4 ,h5ce ! p>ticle ,b1 z well z ,a1 w h its motion gradually accel]at$1 & by t means w m & m approa* to ,c4 ,& f ! same cause ,c w m & m approa* ,d2 & s ( ! re/4 ,suppose n[1 s9ce ! agitation ( ^! p>ticles has be5 %ewn to be successive1 & to foll[ "o ano!r1 t ,e be ! remote/ p>ticle mov$1 :ile ! *ord is mov+ f its curve situation ,i ,k ,l into t ( a /reight l9e1 z ,i k ,l2 & ,f ! fir/ :i* rema9s unaffect$1 ?\gh j ^u ! po9t ( be+ put into motion4 ,!n %all ! p>ticles ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 :5 ! po9t ,k is mov$ into k1 h acquir$ ! rangem5t repres5t$ by ! adjac5t po9ts a1 b1 c1 d1 e1 f1 g3 9 :i* a is ne>] to b ?an b to c1 & b ne>] to c ?an c to d1 & c ne>] to d ?an d to e & d ne>] to e ?an e to f1 & la/ly e ne>] to f ?an f to g4 #i4 ,,b n[ ! *ord hav+ recov]$ its rectil9e> situation ,i k ,l1 ! foll[+ motion w be *ang$1 = ! po9t ,k1 :i* be=e advanc$ ) a motion m & m accel]at$1 ?\gh by ! =ce x has acquir$ x w g on to move ! same way z be=e1 till x has advanc$ ne> z f> =w>ds1 z x 0 at fir/ drawn backw>ds2 yet ! motion ( x w h5ce=? be gradually less5$4 ,! effect ( :i* ^u ! p>ticles a1 b1 c1 d1 e1 f1 g w be1 t by ! "t ! *ord has made its utmo/ advance1 & is ^u ! return1 ^! p>ticles w be put into a contr>y rangem5t2 s t f %all be ne>] to g1 ?an e to f1 & e ne>] to f ?an d to e2 & ! l ( ! re/1 till y come to ! fir/ p>ticles a1 b1 ^: di/ance w !n be ne>ly or q :at x 0 at fir/4 ,all :i* w appe> z foll[s4 ,! pres5t di/ance betwe5 a & b is su*1 t ! ela/ic p[]1 by :i* a repels b1 is /rong en\gh to ma9ta9 t di/ance1 ?\gh a advance ) ! velocity1 ) :i* ! /r+ resumes its rectil9e> figure2 & ! motion ( ! p>ticle a be+ aft]w>ds sl[]1 ! pres5t ela/icity betwe5 a & b w be m ?an suffici5t to pres]ve ! di/ance betwe5 !m4 ,!re=e :ile x accel]ates b x w ret>d a4 ,! di/ance b c w /ill dim9i%1 till b come ab\t z ne> to c1 z x is f a at pres5t2 = aft] ! di/ances a b & b c are become equal1 ! p>ticle b w cont9ue its velocity sup]ior to t ( c by its own p[] ( inactivity1 till su* "t z ! increase ( ela/icity betwe5 b & c m ?an %all be betwe5 a & b %all suppress its motion3 = z ! p[] ( inactivity 9 b made a great] ela/icity necess>y on ! side ( a ?an on ! side ( c to pu% b =w>d1 s :at motion b has acquir$ x w reta9 by ! same p[] ( inactivity1 till x be suppress$ by a great] ela/icity on ! side ( c1 ?an on ! side ( a4 ,b z soon z b beg9s to slack5 its pace ! di/ance ( b f c w wid5 z ! di/ance a b has already done4 ,n[ z a acts on b1 s w b on c1 c on d1 c4 s t ! di/ances betwe5 all ! p>ticles b1 c1 d1 e1 f1 g w be successively contract$ into ! di/ance ( a f b1 & !n dilat$ aga94 ,n[ because ! "t1 9 :i* ! *ord describes ?is pres5t half ( its vibration1 is ab\t equal to t x took up 9 describ+ ! =m]2 ! p>ticles a1 b w be z long 9 dilat+ _! di/ance1 z be=e 9 contract+ x1 & w return ne>ly to _! orig9al di/ance4 ,& f>!r1 ! p>ticles b1 c1 :i* did n beg9 to approa* s soon z a1 b1 are n[ ab\t z mu* long]1 be=e !y beg9 to rec$e2 & likewise ! p>ticles c1 d1 :i* began to approa* aft] b1 c1 beg9 to sep>ate lat]4 ,:5ce x appe>s t ! p>ticles1 ^: di/ance began to be less5$1 :5 t ( a1 b 0 fir/ enl>g$1 viz4 ! p>ticles f1 g1 %\ld be ab\t _! ne>e/ di/ance1 :5 a & b h recov]$ _! prime int]val4 ,?us w ! p>ticles a1 b1 c1 d1 e1 f1 g h *ang$ _! situation 9 ! mann] ass]t$4 ,b f>!r1 z ! p>ticles f1 g or ,f1 ,g gradually approa* ea* o!r1 !y w move by degrees ! succe$+ p>ticles to z great a l5g?1 z ! p>ticles ,a1 ,b did by a l approa*4 ,s t1 :5 ! *ord has made its greate/ advance1 be+ arriv$ into ! situation ,i ,l1 ! p>ticles mov$ by x w h ! rangem5t not$ by ! po9ts 1 1 1 1 1 1 1 1 1 1 1 4 ,:]e 1 are at ! orig9al di/ance ( ! p>ticles 9 ! l9e ,a ,h2 1 are ! ne>e/ ( all1 & ! di/ance is equal to t betwe5 & 4 #aj4 ,,by ?is "t ! *ord ,i ,l beg9s to return1 & ! di/ance betwe5 ! p>ticles & be+ enl>g$ to its orig9al magnitude1 has lo/ all t =ce x _h acquir$ by its motion1 be+ n[ at re/2 & !re=e w return ) ! *ord1 mak+ ! di/ance betwe5 & great] ?an ! natural2 = w n return s soon1 because its motion =w>d is n yet q suppress$1 ! di/ance n be+ already enl>g$ to its prime dim5sion3 b ! recess ( 1 by dim9i%+ ! pressure ^u by its ela/icity1 w occasion ! motion ( to be /opt 9 a little "t by ! action ( 1 & !n %all beg9 to return3 at :i* "t ! di/ance betwe5 & %all by ! sup]ior action ( above be enl>g$ to ! dim5sion ( ! di/ance 1 & !re=e soon aft] to t ( 4 ,?us x appe>s1 t ea* ( ^! p>ticles goes on to move =w>d1 till its di/ance f ! prec$+ "o be equal to its orig9al di/ance2 ! :ole *a9 1 1 1 1 1 1 1 hav+ an undulat+ motion =w>d1 :i* is /opt gradually by ! excess ( ! expansive p[] ( ! prec$+ p>ts above t ( ! h9d]4 ,?us are ^! p>ts successively /opt1 z be=e !y 7 mov$2 s t :5 ! *ord has rega9$ its rectil9e> situation1 ! expansion ( ! p>ts ( ! air w h advanc$ s f>1 t ! int]val betwe5 1 :i* at pres5t is mo/ contract$1 w !n be re/or$ to its natural size3 ! di/ances betwe5 & 1 & 1 & 1 & 1 & 1 be+ successively contract$ into ! pres5t di/ance ( f 1 & aga9 enl>g$2 s t ! same effect %all be produc$ ^u ! p>ts beyond 1 by ! enl>gem5t ( ! di/ance betwe5 ^? two p>ticles1 z 0 occasion$ ^u ! p>ticles 1 1 1 1 1 1 1 1 1 1 1 1 by ! enl>gem5t ( ! di/ance to its natural ext5t4 ,& !re=e ! motion 9 ! air w be ext5d$ half z mu* f>!r z at pres5t1 & ! di/ance betwe5 & contract$ into t1 :i* is at pres5t betwe5 & 1 all ! p>ticles ( ! air 9 motion tak+ ! rangem5t express$ 9 figure #aaa4 by ! po9ts 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :]e9 ! p>ticles f to h _! di/ances f ea* o!r gradually dim9i%$1 ! di/ances betwe5 ! p>ticles 1 be+ contract$ ! mo/ f ! natural di/ance betwe5 ^? p>ticles1 & ! di/ance betwe5 1 z mu* augm5t$1 & ! di/ance betwe5 ! middle p>ticles 1 becom+ equal to ! natural4 ,! p>ticles 1 1 1 :i* foll[ 1 h _! di/ances gradually great] & great]1 ! p>ticles 1 1 1 1 1 1 be+ rang$ l ! p>ticles a1 b1 c1 d1 e1 f1 g1 or l ! p>ticles 1 1 1 1 1 1 9 ! =m] figure4 ,"h x w be und]/ood1 by :at has be5 be=e expla9$1 t ! p>ticles 1 be+ at _! natural di/ance f ea* o!r1 ! p>ticle is at re/1 ! p>ticles 1 1 1 1 betwe5 !m & ! /r+ be+ 9 motion backw>d1 & ! re/ ( ! p>ticles 1 1 1 1 1 1 1 1 1 9 motion =w>d3 ea* ( ! p>ticles betwe5 & mov+ fa/] ?an t1 :i* imm$iately foll[s x2 b ( ! p>ticles f to 1 on ! contr>y1 ^? beh9d mov+ on fa/] ?an ^?1 :i* prec$e4 #aa4 ,,b n[ ! /r+ hav+ recov]$ its rectil9e> figure1 ?\gh x %all g on recoil+1 till x return ne> to its fir/ situation ,i ,k ,l1 yet !re w be a *ange 9 its motion2 s t :]eas x return$ f ! situation ,i ,l ) an accel]at$ motion1 its motion %all f h5ce be ret>d$ aga9 by ! same degrees1 z accel]at$ be=e4 ,! effect ( :i* *ange ^u ! p>ticles ( ! air w be ?is4 ,z by ! accel]at$ motion ( ! *ord contigu\s to x mov$ fa/] ?an 1 1 s z to make ! int]val great] ?an ! int]val 1 & f !nce 0 made likewise to move fa/] ?an 1 & ! di/ance betwe5 & r5d]$ great] ?an ! di/ance betwe5 & 1 & s ( ! re/2 n[ ! motion ( be+ dim9i%$1 %all ov]take x1 & ! di/ance betwe5 & be r$uc$ into t1 :i* is at pres5t betwe5 & 1 ! int]val betwe5 & be+ inl>g$ into ! pres5t di/ance betwe5 & 2 b :5 ! int]val is increas$ to t1 :i* is at pres5t betwe5 & ! di/ance betwe5 & %all be enl>g$ to ! pres5t di/ance betwe5 & 1 & ! di/ance betwe5 & inl>g$ into ! pres5t di/ance betwe5 & 2 & ! same ( ! re/4 ,b ! *ord m & m slack5+ its pace1 ! di/ance betwe5 & %all be m & m dim9i%$2 & 9 consequ5ce ( t ! di/ance betwe5 & %all be aga9 contract$1 fir/ into its pres5t dim5sion1 & aft]w>ds into a n>r[] space2 :ile ! int]val %all dilate into t at pres5t betwe5 & 1 & z soon z x is s mu* enl>g$1 x %all contract aga94 ,?us by ! reciprocal expansion & contraction ( ! air betwe5 & 1 by t "t ! *ord is got into ! situation ,i ,k ,l1 ! int]val %all be exp&$ into ! pres5t di/ance betwe5 & 2 & by t "t likewise ! pres5t di/ance ( f w be contract$ into _! natural int]val3 = ?is di/ance w be ab\t ! same "t 9 contract+ x self1 z has be5 tak5 up 9 its dilatation2 see+ ! /r+ w be z long 9 return+ f its rectil9e> figure1 z x has be5 9 recov]+ x f its situation ,i ,l4 ,?is is ! *ange :i* w be made 9 ! p>ticles betwe5 & 4 ,z = ^? betwe5 & 1 because ea* prec$+ p>ticle advances fa/] ?an t1 :i* imm$iately foll[s x1 _! di/ances w successively be dilat$ into t1 :i* is at pres5t betwe5 & 4 ,& z soon z any two p>ticles are arriv$ at _! natural di/ance1 ! h9d]mo/ ( !m %all be /opt1 & imm$iately aft] return1 ! di/ances betwe5 ! return+ p>ticles be+ great] ?an ! natural4 ,& ?is dilatation ( ^! di/ances %all ext5d s f>1 by t "t ! *ord is return$ into its fir/ situation ,i ,k ,l1 t ! p>ticles %all be remov$ to _! natural di/ance4 ,b ! dilatation ( %all contract ! int]val into t at pres5t betwe5 & 1 & ! contraction ( ! di/ance betwe5 ^? two p>ticles & w agitate a "p ( ! air beyond2 s t :5 ! *ord is return$ into ! situation ,i ,k ,l1 hav+ made an intire vibration1 ! mov$ p>ticles ( ! air w take ! rangem5t express$ by ! po9ts1 l1 m1 n1 o1 p1 q1 r1 s1 t1 u1 w1 x1 y1 z1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h3 9 :i* l m1 are at ! natural di/ance ( ! p>ticles1 ! di/ance m n great] ?an l m & n o great] ?an m n1 & s on1 till y come to q r1 ! wide/ ( all3 & !n ! di/ances gradually dim9i% n only to ! natural di/ance1 z w x1 b till !y are contract$ z mu* z 0 be=e2 :i* falls out 9 ! po9ts #b1 #c1 f :5ce ! di/ances augm5t aga91 till y come to ! "p ( ! air unt\*$4 #ab4 ,,?is is ! motion1 into :i* ! air is put1 :ile ! *ord makes "o vibration1 & ! :ole l5g? ( air ?us agitat$ 9 ! "t ( "o vibration ( ! *ord our au?or calls ! l5g? ( "o pulse4 ,:5 ! *ord goes on to make ano!r vibration1 x w n only cont9ue to agitate ! air at pres5t 9 motion1 b spread ! pulsation ( ! air z mu* f>!r1 & by ! same degrees1 z be=e4 ,= :5 ! *ord returns into its rectil9e> situation ,i k ,l1 l m %all be br\ght into its mo/ contract$ /ate1 q r n[ 9 ! /ate ( greate/ dilatation %all be r$uc$ to its natural di/ance1 ! po9ts w1 x n[ at _! natural di/ance %all be at _! greate/ di/ance1 ! po9ts #b1 #c n[ mo/ contract$ enl>g$ to _! natural di/ance1 & ! po9ts #g1 #h r$uc$ to _! mo/ contract$ /ate3 & ! contraction ( !m w c>ry ! agitation ( ! air z f> beyond !m1 z t motion 0 c>ri$ f ! *ord1 :5 x fir/ mov$ out ( ! situation ,i ,k ,l into its rectil9e> figure4 ,:5 ! *ord is got into ! situation ,i ,l1 l m %all recov] its natural dim5sions1 q r be r$uc$ to its /ate ( greate/ contraction1 w x br\ght to its natural dim5sion1 ! di/ance #b #c enl>g$ to ! utmo/1 & ! po9ts #g1 #h %all h recov]$ _! natural di/ance2 & by ?us recov]+ !mselves !y %all agitate ! air to z great a l5g? beyond !m1 z x 0 mov$ beyond ! *ord1 :5 x fir/ came into ! situation ,i ,l4 ,:5 ! *ord is return$ back aga9 into its rectil9e> situation1 l m %all be 9 its utmo/ dilatation1 q r re/or$ aga9 to its natural di/ance1 w x r$uc$ into its /ate ( greate/ contraction1 #b #c %all recov] its natural dim5sion1 & #g #h be 9 its /ate ( greate/ dilatation4 ,by :i* means ! air %all be mov$ z f> beyond ! po9ts #g1 #h1 z x 0 mov$ beyond ! *ord1 :5 x be=e made its return back to its rectil9e> situation2 = ! p>ticles #g1 #h h be5 *ang$ f _! /ate ( re/ & _! natural di/ance into a /ate ( contraction1 & !n h proce$$ to ! recov]y ( _! natural di/ance1 & aft] t to a dilatation ( x1 9 ! same mann] z ! p>ticles contigu\s to ! *ord 7 agitat$ be=e4 ,9 ! la/ place1 :5 ! *ord is return$ into ! situation ,i ,k ,l1 ! p>ticles ( air f l to %all acquire _! pres5t rangem5t1 & ! motion ( ! air be ext5d$ z mu* f>!r4 ,& ! l w happ5 aft] e compleat vibration ( ! /r+4 #ac4 ,,conc]n+ ?is motion ( s\nd1 our au?or %ews h[ to compute ! velocity !re(1 or 9 :at "t x w rea* to any propos$ di/ance f ! sonor\s body4 ,= ?is he requires to "k ! height ( air1 hav+ ! same d5sity ) ! p>ts "h at ! surface ( ! e>?1 :i* we brea?1 t w\ld be equival5t 9 weight to ! :ole incumb5t atmosph]e4 ,?is is to be f\nd by ! b>omet]1 or common wea!rglass4 ,9 t in/rum5t quicksilv] is includ$ 9 a holl[ glass cane firmly clos$ at ! top4 ,! bottom is op51 b imm]g$ into quicksilv] conta9$ 9 a vessel op5 to ! air4 ,c>e is tak5 :5 ! l[] end ( ! cane is imm]g$1 t ! :ole cane be full ( quicksilv]1 & t no air ins9uate itself4 ,:5 ! in/rum5t is ?us fix$1 ! quicksilv] 9 ! cane be+ high] ?an t 9 ! vessel1 if ! top ( ! cane 7 op51 ! fluid w\ld soon s9k out ( ! glass cane1 till x came to a level ) t 9 ! vessel4 ,b ! top ( ! cane be+ clos$ up1 s t ! air1 :i* has free lib]ty to press on ! quicksilv] 9 ! vessel1 _c be> at all on t1 :i* is )9 ! cane1 ! quicksilv] 9 ! cane w be susp5d$ to su* a height1 z to balance ! pressure ( ! air on ! quicksilv] 9 ! vessel4 ,"h x is evid5t1 t ! weight ( ! quicksilv] 9 ! glass cane is equival5t to ! pressure ( s mu* ( ! air1 z is p]p5dicul>ly ov] ! holl[ ( ! cane2 = if ! cane be op5$ t ! air may ent]1 !re w be no f>!r use ( ! quicksilv] to su/a9 ! pressure ( ! air )\t2 = ! quicksilv] 9 ! cane1 z has already be5 obs]v$1 w !n subside to a level ) t )\t4 ,h5ce !re=e if ! proportion betwe5 ! d5sity ( quicksilv] & ( ! air we brea? be kn[n1 we may "k :at height ( su* air w\ld =m a column equal 9 weight to ! column ( quicksilv] )9 ! glass cane4 ,:5 ! quicksilv] is su/a9$ 9 ! b>omet] at ! height ( #cj in*es1 ! height ( su* a column ( air w be ab\t #bigbe feet2 = 9 ?is case ! air has ab\t #a_/hgj ( ! d5sity ( wat]1 & ! d5sity ( quicksilv] exce$s t ( wat] ab\t #ac times1 s t ! d5sity ( quicksilv] exce$s t ( ! air ab\t #aahij times2 & s _m times #cj in*es make #bigbe feet4 ,n[ ,sir ,,isaac ,,newton det]m9es1 t :ile a p5dulum ( ! l5g? ( ?is column %\ld make "o vibration or sw+1 ! space1 :i* any s\nd w h mov$1 %all be> to ?is l5g? ! same proportion1 z ! circumf]5ce ( a circle be>s to ! diamet] !re(2 t is1 ab\t ! proportion ( #cee to #aacbfg4 ,only our au?or "h consid]s s+ly ! gradual progress ( s\nd 9 ! air f p>ticle to p>ticle 9 ! mann] we h expla9$1 )\t tak+ into consid]ation ! magnitude ( ^? p>ticles4 ,& ?\gh !re requires "t = ! motion to be propagat$ f "o p>ticle to ano!r1 yet x is communicat$ to ! :ole ( ! same p>ticle 9 an in/ant3 !re=e :atev] proportion ! ?ickness ( ^! p>ticles be>s to _! di/ance f ea* o!r1 9 ! same proportion w ! motion ( s\nd be swift]4 ,aga9 ! air we brea? is n simply compos$ ( ! ela/ic "p1 by :i* s\nd is convey$1 b p>tly ( vap\rs1 :i* are ( a diff]5t nature2 & 9 ! computation ( ! motion ( s\nd we ought to f9d ! height ( a column ( ?is pure air only1 ^: weight %\ld be equal to ! weight ( ! quicksilv] 9 ! cane ( ! b>omet]1 & ?is pure air be+ a "p only ( t we brea?1 ! column ( ?is pure air w be high] ?an #bigbe feet4 ,on bo? ^! acc\nts ! motion ( s\nd is f\nd to be ab\t #aadb feet 9 "o second ( "t1 or ne> #ac miles 9 a m9ute1 :]eas by ! computation propos$ above1 x %\ld move b #igi feet 9 "o second4 #ad4 ,,we may obs]ve "h1 t f ^! demon/rations ( our au?or x foll[s1 t all s\nds :e!r acute or grave move equally swift1 & t s\nd is swifte/1 :5 ! quicksilv] /&s highe/ 9 ! b>omet]4 #ae4 ,,?us mu* ( ! appe>ances1 :i* are caus$ 9 ^! fluids f _! gravitation t[>d ! e>?4 ,!y also gravitate t[>d ! moon2 = 9 ! la/ *apt] x has be5 prov$1 t ! gravitation betwe5 ! e>? & moon is mutual1 & t ?is gravitation ( ! :ole bodies arises f t p[] act+ 9 all _! p>ts2 s t e p>ticle ( ! moon gravitates t[>d ! e>?1 & e p>ticle ( ! e>? t[>d ! moon4 ,b ?is gravitation ( ^! fluids t[>d ! moon produces no s5sible effect1 except only 9 ! sea1 :]e x causes ! tides4 #af4 ,,t ! tides dep5d ^u ! influ5ce ( ! moon has be5 ! receiv'd op9ion ( all antiquity2 nor is !re inde$ ! lea/ %ad[ ( reason to suppose o!rwise1 consid]+ h[ /eadily !y accompany ! moon's c\rse4 ,?\gh h[ ! moon caus$ !m1 & by :at pr9ciple x 0 enabl$ to produce s di/+ui%'d an appe>ance1 0 a secret left = ?is philosophy to unfold3 :i* tea*es1 t ! moon is n "h alone conc]n$1 b t ! sun likewise has a consid]able %>e 9 _! production2 ?\gh !y h be5 g5]ally ascrib$ to ! o!r lum9>y1 because its effect is greate/1 & by t means ! tides m imm$iately suit !mselves to its motion2 ! sun discov]+ its influ5ce m by enl>g+ or re/ra9+ ! moon's p[]1 ?an by any di/9ct effects4 ,our au?or f9ds ! p[] ( ! moon to be> to ! p[] ( ! sun ab\t ! proportion ( #d to #a4 ,?is he d$uces f ! obs]vations made at ! m\? ( ! riv] ,avon1 ?ree miles f ,bri/ol1 by ,capta9 ,,/urmey1 & at ,plym\? by ,mr4 ,,colepresse1 ( ! height to :i* ! wat] is rais$ 9 ! conjunction & opposition ( ! lum9>ies1 comp>$ ) ! elevation ( x1 :5 ! moon is 9 ei!r qu>t]2 ! fir/ be+ caus$ by ! unit$ actions ( ! sun & moon1 & ! o!r by ! diff]5ce ( !m1 z %all h]eaft] be %ewn4 #ag4 ,,t ! sun %\ld h a l effect on ! sea1 z ! moon1 is v manife/2 s9ce ! sun likewise attracts e s+le p>ticle1 ( :i* ?is e>? is compos$4 ,& 9 bo? lum9>ies s9ce ! p[] ( gravity is reciprocally 9 ! duplicate proportion ( ! di/ance1 !y w n draw all ! p>ts ( ! wat]s 9 ! same mann]2 b mu/ act ^u ! ne>e/ p>ts /rong]1 ?an ^u ! remote/1 produc+ by ?is inequality an irregul> motion4 ,we %all n[ attempt to %ew h[ ! actions ( ! sun & moon on ! wat]s1 by be+ comb9$ toge!r1 produce all ! appe>ances obs]v$ 9 ! tides4 #ah4 ,,to beg9 !re=e1 ! read] w rememb] :at has be5 said above1 t if ! moon )\t ! sun w\ld h describ$ an orbit conc5trical to ! e>?1 ! action ( ! sun w\ld make ! orbit oval1 & br+ ! moon ne>] to ! e>? at ! new & full1 ?an at ! qu>t]s#bfh4 ,n[ our excell5t au?or obs]ves1 t if in/ead ( "o moon1 we suppose a r+ ( moons1 contigu\s & occupy+ ! :ole orbit ( ! moon1 8 demon/ration w\ld /ill take place1 & prove t ! p>ts ( ?is r+ 9 pass+ f ! qu>t] to ! conjunction or opposition w\ld be accel]at$1 & be ret>d$ aga9 9 pass+ f ! conjunction or opposition to ! next qu>t]4 ,& z ?is effect does n dep5d on ! magnitude ( ! bodies1 :]e( ! r+ is compos$1 ! same w\ld hold1 ?\gh ! magnitude ( ^! moons 7 s f> to be dim9i%$1 & _! numb] increas$1 till !y %\ld =m a fluid#bfi4 ,n[ ! e>? turns r\nd cont9ually ^u its own c5t]1 caus+ !reby ! alt]nate *ange ( day & night1 :ile by ?is revolution ea* "p ( ! e>? is successively br\ght t[>d ! sun1 & c>ri$ (f aga9 9 ! space ( #bd h\rs4 ,& z ! sea revolves r\nd along ) ! e>? itself 9 ?is diurnal motion1 x w repres5t 9 "s sort su* a fluid r+4 #ai4 ,,b z ! wat] ( ! sea does n move r\nd ) s mu* swiftness1 z w\ld c>ry x ab\t ! c5t] ( ! e>? 9 ! circle x n[ describes1 )\t be+ support$ by ! body ( ! e>?2 x w be necess>y to consid] ! wat] "u ?ree di/9ct cases4 ,! fir/ case %all suppose ! wat] to move ) ! degree ( swiftness1 requir$ to c>ry a body r\nd ! c5t] ( ! e>? dis+ag$ f x 9 a circle at ! di/ance ( ! e>?'s semidiamet]1 l ano!r moon4 ,! second case is1 t ! wat]s make b "o turn ab\t ! axis ( ! e>? 9 ! space ( a mon?1 keep+ pace ) ! moon2 s t all p>ts ( ! wat] %\ld pres]ve cont9ually ! same situation 9 respect ( ! moon4 ,! ?ird case %all be ! real "o ( ! wat]s mov+ ) a velocity betwe5 ^! two1 nei!r s swift z ! fir/ case requires1 nor s sl[ z ! second4 #bj4 ,,9 ! fir/ case ! wat]s1 l ! body :i* !y equall$ 9 velocity1 by ! action ( ! moon w\ld be br\ght ne>] ! c5t] "u & opposite to ! moon1 ?an 9 ! p>ts 9 ! middle betwe5 ^! ea/w>d or we/w>d4 ,t su* a body w\ld s alt] its di/ance by ! moon's action ^u x1 is cle> f :at has be5 m5tion$ ( ! l *anges 9 ! moon's motion caus$ by ! sun#bgj4 ,& computation %ews1 t ! diff]5ce betwe5 ! greate/ & lea/ di/ance ( su* a body w\ld n be mu* above #d feet4 ,b 9 ! second case1 :]e all ! p>ts ( ! wat] pres]ve ! same situation cont9ually 9 respect ( ! moon1 ! weight ( ^? p>ts "u & opposite to ! moon w be dim9i%$ by ! moon's action1 & ! p>ts 9 ! middle betwe5 ^! w h _! weight increas$3 ?is be+ effect$ j 9 ! same mann]1 z ! sun dim9i%es ! attraction ( ! moon t[>ds ! e>? 9 ! conjunction & opposition1 b increases t attraction 9 ! qu>t]s4 ,= z ! fir/ ( ^! consequ5ces f ! sun's action on ! moon is occasion$ by ! moon's be+ attract$ by ! sun 9 ! conjunction m ?an ! e>?1 & 9 ! opposition less ?an x1 & !re=e 9 ! common motion ( ! e>? & moon1 ! moon is made to advance t[>d ! sun 9 "o case too fa/1 & 9 ! o!r is left z x 7 beh9d2 s ! e>? w n h its middle p>ts drawn t[>ds ! moon s /rongly z ! ne>] p>ts1 & yet m =cibly ?an ! remote/3 & !re=e s9ce ! e>? & moon move ea* mon? r\nd _! common c5t] ( gravity#bga1 :ile ! e>? moves r\nd ?is c5t]1 ! same effect w be produc$1 on ! p>ts ( ! wat] ne>e/ to t c5t] or to ! moon1 z ! moon feels f ! sun :5 9 conjunction1 & ! wat] on ! contr>y side ( ! e>? w be affect$ by ! moon1 z ! moon is by ! sun1 :5 9 opposition#bgb2 t is1 9 bo? cases ! weight ( ! wat]1 or its prop5sity t[>ds ! c5t] ( ! e>?1 w be dim9i%$4 ,! p>ts 9 ! middle betwe5 ^! w h _! weight increas$1 by be+ press$ t[>ds ! c5t] ( ! e>? ?r\gh ! obliquity ( ! moon's action ^u !m to its action ^u ! e>?'s c5t]1 j z ! sun increases ! gravitation ( ! moon 9 ! qu>t]s f ! same cause#bgc4 ,b n[ x is manife/1 t :]e ! weight ( ! same quantity ( wat] is lea/1 !re x w be accumulat$2 :ile ! p>ts1 :i* h ! greate/ weight1 w subside4 ,!re=e 9 ?is case !re w\ld be no tide or alt]nate ris+ & fall+ ( ! wat]1 b ! wat] w\ld =m x self into an oblong figure1 ^: axis prolong$ w\ld pass ?r\gh ! moon4 ,by ,sir ,,isaac ,,newton's computation ! excess ( ?is axis above ! diamet]s p]p5dicul> to x1 t is1 ! height ( ! wat]s "u & opposite to ! moon above _! height 9 ! middle betwe5 ^! places ea/w>d or we/w>d caus$ by ! moon1 is ab\t #h feet4 #ba4 ,,?us ! diff]5ce ( height 9 ?is latt] supposition is little %ort ( twice t diff]5ce 9 ! prec$+4 ,b ! case ( ! sea is a middle betwe5 ^! two3 = a body1 :i* %\ld revolve r\nd ! c5t] ( ! e>? at ! di/ance ( a semidiamet] )\t press+ on ! e>?'s surface1 mu/ p]=m its p]iod 9 less ?an an h\r & half1 :]eas ! e>? turns r\nd b once 9 a day2 & 9 ! case ( ! wat]s keep+ pace ) ! moon x %\ld turn r\nd b once 9 a mon?3 s t ! real motion ( ! wat] is betwe5 ! motions requir$ 9 ^! two cases4 ,aga91 if ! wat]s mov$ r\nd z swiftly z ! fir/ case requir$1 _! weight w\ld be :olly tak5 (f by _! motion2 = ?is case supposes ! body to move s1 z to be kept revolv+ 9 a circle r\nd ! e>? by ! p[] ( gravity )\t press+ on ! e>? at all1 s t its motion j supports its weight4 ,b if ! p[] ( gravity _h be5 only #a_/bhi "p ( :at x is1 ! body c\ld h mov$ ?us )\t press+ on ! e>?1 & h be5 z long 9 mov+ r\nd1 z ! e>? x self is4 ,consequ5tly ! motion ( ! e>? takes (f f ! weight ( ! wat] 9 ! middle betwe5 ! poles1 :]e its motion is swifte/1 #a_/bhi "p ( its weight & no m4 ,s9ce !re=e 9 ! fir/ case ! weight ( ! wat]s mu/ be intirely tak5 (f by _! motion1 & by ! real motion ( ! e>? !y lose only #a_/bhi "p !re(1 ! motion ( ! wat] w s little dim9i% _! weight1 t _! figure w mu* ne>] resemble ! case ( _! keep+ pace ) ! moon ?an ! o!r4 ,^u ! :ole1 if ! wat]s mov$ ) ! velocity necess>y to c>ry a body r\nd ! c5t] ( ! e>? at ! di/ance ( ! e>?'s semidiamet] )\t be>+ on its surface1 ! wat] w\ld be l[e/ "u ! moon1 & rise gradually z x mov$ on ) ! e>? ea/w>d1 till x came half way t[>d ! place opposite to ! moon2 f !nce x w\ld subside aga91 till x came to ! opposition1 :]e x w\ld become z l[ z at fir/2 aft]w>ds x w\ld rise aga91 till x came half way to ! place "u ! moon2 & f h5ce x w\ld subside1 till x came a second "t "u ! moon4 ,b 9 case ! wat] kept pace ) ! moon1 x w\ld be highe/ :]e 9 ! o!r case x is l[e/1 & l[e/ :]e 9 ! o!r x is highe/2 !re=e ! diurnal motion ( ! e>? be+ betwe5 ! motions ( ^! two cases1 x w cause ! highe/ place ( ! wat] to fall betwe5 ! places ( ! greate/ height 9 ^! two cases4 ,! wat] z x passes f "u ! moon %all = "s "t rise1 b desc5d aga9 be=e x arrives half way to ! opposite place1 & %all come to its lea/ height be=e x becomes opposite to ! moon2 !n x %all rise aga91 cont9u+ s to d till x has pass$ ! place opposite to ! moon1 b subside be=e x comes to ! middle betwe5 ! places opposite to & "u ! moon2 & la/ly x %all come to its l[e/1 be=e x comes a second "t "u ! moon4 ,if ,a 79 fig4 #aab1 #aac1 #aad47 repres5t ! moon1 ,b ! c5t] ( ! e>?1 ! oval ,c ,d ,e ,f 9 fig4 #aab4 w repres5t ! situation ( ! wat] 9 ! fir/ case2 b if ! wat] kept pace ) ! moon1 ! l9e ,c ,d ,e ,f 9 fig4 #aac4 w\ld repres5t ! situation ( ! wat]2 b ! l9e ,c ,d ,e ,f 9 fig4 #aad4 w repres5t ! same 9 ! real motion ( ! wat]1 z x accompanies ! e>? 9 its diurnal rotation3 9 all ^! figures ,c & ,e be+ ! places :]e ! wat] is l[e/1 & ,d & ,f ! places :]e x is highe/4 ,pursuant to ?is det]m9ation x is f\nd1 t on ! %ores1 :i* lie expos$ to ! op5 sea1 ! high wat] usually falls out ab\t ?ree h\rs aft] ! moon has pass$ ! m]idian ( ea* place4 #bb4 ,,let ?is suffice 9 g5]al = expla9+ ! mann]1 9 :i* ! moon acts ^u ! seas4 ,x is f>!r to be not$1 t ^! effects are greate/1 :5 ! moon is ov] ! e>?'s equator#bgd1 t is1 :5 x %9es p]p5dicul>ly ^u ! p>ts ( ! e>? 9 ! middle betwe5 ! poles4 ,= if ! moon 7 plac$ ov] ei!r ( ! poles1 x c\ld h no effect ^u ! wat] to make x asc5d & desc5d4 ,s t :5 ! moon decl9es f ! equator t[>d ei!r pole1 x's action mu/ be some?+ dim9i%$1 & t ! m1 ! f>!r x decl9es4 ,! tides likewise w be greate/1 :5 ! moon is ne>e/ to ! e>?1 x's action be+ !n ! /ronge/4 #bc4 ,,?us mu* ( ! action ( ! moon4 ,t ! sun %\ld produce ! v same effects1 ?\gh 9 a less degree1 is too obvi\s to require a p>ticul> explanation3 b z 0 rem>k$ be=e1 ?is action ( ! sun be+ weak] ?an t ( ! moon1 w cause ! tides to foll[ m ne>ly ! moon's c\rse1 & pr9cipally %ew x self by height5+ or dim9i%+ ! effects ( ! o!r lum9>y4 ,:i* is ! occasion1 t ! highe/ tides are f\nd ab\t ! conjunction & opposition ( ! lum9>ies1 be+ !n produc$ by _! unit$ action1 & ! weake/ tides ab\t ! qu>t]s ( ! moon2 because ! moon 9 ?is case rais+ ! wat] :]e ! sun depresses x1 & depress+ x :]e ! sun raises x1 ! /rong] action ( ! moon is 9 "p retund$ & weak5$ by t ( ! sun4 ,our au?or computes t ! sun w add ne> two feet to ! height ( ! wat] 9 ! fir/ case1 & 9 ! o!r take f x z mu*4 ,h[ev] ! tides 9 bo? comply ) ! same h\r ( ! moon4 ,b at o!r times1 betwe5 ! conjunction or opposition & qu>t]s1 ! "t deviates f t =em5tion$1 t[>ds ! h\r 9 :i* ! sun w\ld make high wat]1 ?\gh /ill x keeps mu* ne>] to ! moon's h\r ?an to ! sun's4 #bd4 ,,aga9 ! tides h "s f>!r v>ieties f ! situation ( ! places :]e !y happ5 nor?w>d or s\?w>d4 ,let p ,p 79 fig4 #aae47 repres5t ! axis1 on :i* ! e>? daily revolves1 let h p ,h ,p repres5t ! figure ( ! wat]1 & let n ,b ,n ,d be a globe inscrib$ )9 ?is figure4 ,suppose ! moon to be advanc$ f ! equator t[>d ! nor? pole1 s t h ,h ! axis ( ! figure ( ! wat] p ,a ,h ,p ,e h %all decl9e t[>ds ! nor? pole ,n2 take any place ,g ne>] to ! nor? pole ?an to ! s\?1 & f ! c5t] ( ! e>? ,c draw ,c ,g ,f2 !n w ,g ,f d5ote ! altitude to :i* ! wat] is rais$ by ! tide1 :5 ! moon is above ! horizon3 9 ! space ( twelve h\rs1 ! e>? hav+ turn$ half r\nd its axis1 ! place ,g w be remov$ to g2 b ! axis h ,h w h kept its place pres]v+ its situation 9 respect ( ! moon1 at lea/ w h mov$ no m ?an ! moon has done 9 t "t1 :i* x is n necess>y "h to take into consid]ation4 ,n[ 9 ?is case ! height ( ! wat] w be equal to g f1 :i* is n s great z ,g ,f4 ,b :]eas ,g ,f is ! altitude at high wat]1 :5 ! moon is above ! horizon1 g f w be ! altitude ( ! same1 :5 ! moon is "u ! horizon4 ,! contr>y happ5s t[>d ! s\? pole1 = ,k ,l is less ?an k l4 ,h5ce is prov$1 t :5 ! moon decl9es f ! equator1 9 ^? places1 :i* are on ! same side ( ! equator z ! moon1 ! tides are great]1 :5 ! moon is above ! horizon1 ?an :5 "u x2 & ! contr>y happ5s on ! o!r side ( ! equator4 #be4 ,,n[ f ^! pr9ciples may be expla9$ all ! kn[n appe>ances 9 ! tides2 only by ! assi/ance ( ?is additional rem>k1 t ! fluctuat+ motion1 :i* ! wat] has 9 fl[+ & ebb+1 is ( a durable nature1 & w\ld cont9ue = "s "t1 ?\gh ! action ( ! lum9>ies %\ld cease2 = ?is prev5ts ! diff]5ce betwe5 ! tide :5 ! moon is above ! horizon1 & ! tide :5 ! moon is bel[ x f be+ s great1 z ! rule laid d[n requires4 ,?is likewise makes ! greate/ tides n exactly ^u ! new & full moon1 b to be a tide or two aft]2 z at ,bri/ol & ,plym\? !y are f\nd ! ?ird aft]4 #bf4 ,,?is doctr9e f>!r %ews u1 :y n only ! spr+ tides fall out ab\t ! new & full moon1 & ! neap tides ab\t ! qu>t]s2 b likewise h[ x comes to pass1 t ! greate/ spr+ tides happ5 ab\t ! equ9oxes2 because ! lum9>ies are !n "o ( !m ov] ! equator1 & ! o!r n f> f x4 ,x appe>s too1 :y ! neap tides1 :i* accompany ^!1 are ! lea/ ( all1 = ! sun /ill cont9u+ ov] ! equator cont9ues to h ! greate/ p[] ( less5+ ! moon's action1 & ! moon 9 ! qu>t]s be+ f> remov$ t[>d "o ( ! poles1 has its p[] !reby weakn$4 #bg4 ,,moreov] ! action ( ! moon be+ /rong]1 :5 ne> ! e>?1 ?an :5 m remote2 if ! moon1 :5 new suppose1 be at its ne>e/ di/ance f ! e>?1 x %all :5 at ! full be f>!/ (f2 :5ce x is1 t two ( ! v l>ge/ spr+ tides d nev] imm$iately succe$ ea* o!r4 #bh4 ,,because ! sun 9 its passage f ! w9t] sol/ice to ! summ] rec$es f ! e>?1 & pass+ f ! summ] sol/ice to ! w9t] approa*es x1 & is !re=e ne>] ! e>? be=e ! v]nal equ9ox ?an aft]1 b ne>] aft] ! autumnal equ9ox ?an be=e2 ! greate/ tides (tn] prec$e ! v]nal equ9ox ?an foll[ x1 & 9 ! autumnal equ9ox on ! contr>y !y (tn] foll[ x ?an come be=e x4 #bi4 ,,! altitude1 to :i* ! wat] is rais$ 9 ! op5 ocean1 corresponds v well to ! =em5tion$ calculations2 = z x 0 %ewn1 t ! wat] 9 spr+ tides %\ld rise to ! height ( #aj or #aa feet1 & ! neap tides to #f or #g2 accord+ly 9 ! ,pacific1 ,atlantic & ,e?iopic oceans 9 ! p>ts )\t ! tropics1 ! wat] is obs]v$ to rise ab\t #f1 #i1 #ab or #ae feet4 ,9 ! ,pacific ocean ?is elevation is said to be great] ?an 9 ! o!r1 z x ought to be by reason ( ! wide ext5t ( t sea4 ,= ! same reason 9 ! ,e?iopic ocean betwe5 ! tropics ! asc5t ( ! wat] is less ?an )\t1 by reason ( ! n>r[ness ( ! sea betwe5 ! coa/s ( ,africa & ! s\!rn p>ts ( ,am]ica4 ,& isl&s 9 su* n>r[ seas1 if f> f %ore1 h less tides ?an ! coa/s4 ,b n[ 9 ^? ports :]e ! wat] fl[s 9 ) great viol5ce ^u =ds & %oals1 ! =ce x acquires by t means w c>ry x to a mu* great] height1 s z to make x asc5d & desc5d to #cj1 #dj or ev5 #ej feet & m2 in/ances ( :i* we h at ,plym\?1 & 9 ! ,sev]n ne> ,*ep/[2 at ,/4 ,mi*ael's & ,auran*es 9 ,norm&y2 at ,cambay & ,pegu 9 ! ,ea/ ,indies4 #cj4 ,,aga9 ! tides take a consid]able "t 9 pass+ ?r\gh long /raits1 & %all[ places4 ,?us ! tide1 :i* is made on ! we/ coa/ ( ,irel& & on ! coa/ ( ,spa9 at ! ?ird h\r aft] ! moon's com+ to ! m]idian1 9 ! ports ea/w>d t[>d ! ,briti% *annel falls out lat]1 & z ! flood passes up t *annel /ill lat] & lat]1 s t ! tide takes up full twelve h\rs 9 com+ up to ,london bridge4 #ca4 ,,9 ! la/ place tides may come to ! same port f diff]5t seas1 & z !y may int]f]e ) ea* o!r1 !y w produce p>ticul> effects4 ,suppose ! tide f "o sea come to a port at ! ?ird h\r aft] ! moon's pass+ ! m]idian ( ! place1 b f ano!r sea to take up six h\rs m 9 its passage4 ,"h "o tide w make high wat]1 :5 by ! o!r x %\ld be l[e/2 s t :5 ! moon is ov] ! equator1 & ! two tides are equal1 !re w be no ris+ & fall+ ( ! wat] at all2 = z mu* z ! wat] is c>ri$ (f by "o tide1 x w be suppli$ by ! o!r4 ,b :5 ! moon decl9es f ! equator1 ! same way z ! port is situat$1 we h %ewn t ( ! two tides ( ! ocean1 :i* are made ea* day1 t tide1 :i* is made :5 ! moon is above ! horizon1 is great] ?an ! o!r4 ,!re=e 9 ?is case1 z f\r tides come to ?is port ea* day ! two greate/ w come on ! ?ird1 & on ! n9? h\r aft] ! moon's pass+ ! m]idian1 & ! two lea/ at ! fifte5? & at ! tw5ty fir/ h\r4 ,?us f ! ?ird to ! n9? h\r m wat] w be 9 ?is port by ! two greate/ tides ?an f ! n9? to ! fifte5?1 or f ! tw5ty fir/ to ! foll[+ ?ird h\r1 :]e ! wat] is br\ght by "o great & "o small tide2 b yet !re w be m wat] br\ght by ^! tides1 ?an :at w be f\nd betwe5 ! two lea/ tides1 t is1 betwe5 ! fifte5? & tw5ty fir/ h\r4 ,!re=e 9 ! middle betwe5 ! ?ird & n9? h\r1 or ab\t ! moon's sett+1 ! wat] w be at its greate/ height2 9 ! middle betwe5 ! n9? & fifte5?1 z also betwe5 ! tw5ty fir/ & foll[+ ?ird h\r x w h its mean height2 & be l[e/ 9 ! middle betwe5 ! fifte5? & tw5ty fir/ h\r1 t is1 at ! moon's ris+4 ,?us "h ! wat] w h b "o flood & "o ebb ea* day4 ,:5 ! moon is on ! o!r side ( ! equator1 ! flood w be turn$ into ebb1 & ! ebb into flood2 ! high wat] fall+ out at ! ris+ ( ! moon1 & ! l[ wat] at ! sett+4 ,n[ ?is is ! case ( ! port ( ,bat%am 9 ! k+dom ( ,tunqu9 9 ! ,ea/ ,indies2 to :i* port !re are two inlets1 "o betwe5 ! cont95t & ! isl&s :i* are call$ ! ,manillas1 & ! o!r betwe5 ! cont95t & ,borneo4 #cb4 ,,! next ?+ to be consid]$ is ! effect1 :i* ^! fluids ( ! planets h ^u ! solid "p ( ! bodies to :i* !y belong4 ,& 9 ! fir/ place ,i %all %ew1 t x 0 necess>y ^u acc\nt ( ^! fluid p>ts to =m ! bodies ( ! planets into a figure some?+ diff]5t f t ( a p]fect globe4 ,because ! diurnal rotation1 :i* our e>? p]=ms ab\t its axis1 & ! l motion we see 9 "s ( ! o!r planets1 7:i* is an ample conviction t !y all d ! l7 w dim9i% ! =ce1 ) :i* bodies are attract$ ^u all ! p>ts ( _! surfaces1 except at ! v poles1 ^u :i* !y turn4 ,?us a /one or o!r weighty sub/ance re/+ ^u ! surface ( ! e>?1 by ! =ce :i* x receives f ! motion communicat$ to x by ! e>?1 if its weight prev5t$ n1 w\ld cont9ue t motion 9 a /raight l9e f ! po9t :]e x receiv$ x1 & accord+ to ! direction1 9 :i* x 0 giv51 t is1 9 a l9e :i* t\*es ! surface at t po9t2 insomu* t x w\ld move (f f ! e>? 9 ! same mann]1 z a weight fa/5'd to a /r+ & :irl$ ab\t endeav\rs cont9ually to rec$e f ! c5t] ( motion1 & w\ld =?) remove x self to a great] di/ance f x1 if loos$ f ! /r+ :i* reta9s x4 ,& f>!r1 z ! c5trifugal =ce1 ) :i* su* a weight presses f ! c5t] ( its motion1 is great]1 by h[ mu* great] ! velocity is1 ) :i* x moves2 s su* a body1 z ,i h be5 suppos+ to lie on ! e>?1 w\ld rec$e f x ) ! great] =ce1 ! great] ! velocity is1 ) :i* ! "p ( ! e>?'s surface x re/s ^u is mov$1 t is1 ! f>!r di/ant x is f ! poles4 ,b n[ ! p[] ( gravity is great en\gh to prev5t bodies 9 any "p ( ! e>? f be+ c>ri$ (f f x by ?is means2 h[ev] x is pla9 t bodies hav+ an ef=t contr>y to t ( gravity1 ?\gh mu* weak] ?an x1 _! weight1 t is1 ! degree ( =ce1 ) :i* !y are press$ to ! e>?1 w be dim9i%$ !reby1 & be ! m dim9i%$1 ! great] ?is contr>y ef=t is2 or 9 o!r words1 ! same body w weigh heavi] at ei!r ( ! poles1 ?an ^u any o!r "p ( ! e>?2 & if any body be remov$ f ! pole t[>ds ! equator1 x w lose ( its weight m & m1 & be lighte/ ( all at ! equator1 t is1 9 ! middle betwe5 ! poles4 #cc4 ,,?is n[ is easily appli$ to ! wat]s ( ! seas1 & %ews t ! wat] "u ! poles w press m =cibly to ! e>?1 ?an at or ne> ! equator3 & consequ5tly t :i* presses lea/1 mu/ give place1 till by asc5d+ x makes room = receiv+ a great] quantity1 :i* by its additional weight may place ! :ole ^u a ballance4 ,to illu/rate ?is m p>ticul>ly ,i %all make use ( fig4 #aaf ,9 :i* let ,a ,c ,b ,d be a circle1 by ^: revolution ab\t ! diamet] ,a ,b a globe %\ld be =m$1 repres5t+ a globe ( solid e>?4 ,suppose ?is globe cov]$ on all sides ) wat] to ! same height1 suppose t ( ,e ,a or ,b ,f1 at :i* di/ance ! circle ,e ,g ,f ,h surr\nds ! circle ,a ,c ,b ,d2 !n x is evid5t1 if ! globe ( e>? be at re/1 ! wat] :i* surr\nds x w re/ 9 t situation4 ,b if ! globe be turn$ incessantly ab\t its axis ,a ,b1 & ! wat] h likewise ! same motion1 x is also evid5t1 f :at has be5 expla9$1 t ! wat] betwe5 ! circles ,e ,h ,f ,g & ,a ,d ,b ,c w rema9 no long] 9 ! pres5t situation1 ! p>ts ( x betwe5 ,h & ,d1 & betwe5 ,g & ,c be+ by ?is rotation become light]1 ?an ! p>ts betwe5 ,e & ,a & betwe5 ,b & ,f2 s t ! wat] ov] ! poles ,a & ,b mu/ ( necessity subside1 & ! wat] be accumulat$ ov] ,d & ,c1 till ! great] quantity 9 ^! latt] places supply ! defect ( its weight4 ,?is w\ld be ! case1 7 ! globe all cov]$ ) wat]4 ,& ! same figure ( ! surface w\ld also be pres]v$1 if "s "p ( ! wat] adjo9+ to ! globe 9 any "p ( x 7 turn$ into solid e>?1 z is too evid5t to ne$ any pro(2 because ! p>ts ( ! wat] rema9+ at re/1 x is ! same ?+1 :e!r !y cont9ue 9 ! /ate ( be+ easily sep>able1 :i* d5om9ates !m fluid1 or 7 to be consolidat$ toge!r1 s z to make a h>d body3 & ?is1 ?\gh ! wat] %\ld 9 "s places be ?us consolidat$1 ev5 to ! surface ( x4 ,:i* %ews t ! =m ( ! solid "p ( ! e>? makes no alt]ation 9 ! figure ! wat] w take3 & by consequ5ce 9 ord] to ! prev5t+ "s p>ts ( ! e>? f be+ entirely ov]fl[$1 & o!r p>ts q des]t$1 ! solid p>ts ( ! e>? mu/ h giv5 !m mu* ! same figure1 z if ! :ole e>? 7 cov]$ on all sides ) wat]4 #cd4 ,,f>!r1 ,i say1 ?is figure ( ! e>? is ! same1 z x w\ld receive1 7 x entirely a globe ( wat]1 provid$ t wat] 7 ( ! same d5sity z ! sub/ance ( ! globe4 ,= suppose ! globe ,a ,c ,b ,d to be liquifi$1 & t ! globe ,e ,h ,f ,g1 n[ entirely wat]1 by its rotation ab\t its axis %\ld receive su* a figure z we h be5 describ+1 & !n ! globe ,a ,c ,b ,d %\ld be consolidat$ aga91 ! figure ( ! wat] w\ld pla9ly n be alt]$1 by su* a consolidation4 #ce4 ,,b f ?is la/ obs]vation our au?or is enabl$ to det]m9e ! proportion betwe5 ! axis ( ! e>? drawn f pole to pole1 & ! diamet] ( ! equator1 ^u ! supposition t all ! p>ts ( ! e>? are ( equal d5sity2 :i* he does by comput+ 9 ! fir/ place ! proportion ( ! c5trifugal =ce ( ! p>ts "u ! equator to ! p[] ( gravity2 & !n by consid]+ ! e>? z a sph]oid1 made by ! revolution ( an ellipsis ab\t its less] axis1 t is1 suppos+ ! l9e ,m ,i ,l ,k to be an exact ellipsis1 f :i* x c diff] b little1 by reason t ! diff]5ce betwe5 ! less] axis ,m ,l & ! great] ,i ,k is b v small4 ,f ?is supposition1 & :at 0 prov$ be=e1 t all ! p>ticles :i* compose ! e>? h ! attract+ p[] expla9$ 9 ! prec$+ *apt]1 he f9ds at :at di/ance ! p>ts "u ! equator ought to be remov$ f ! c5t]1 t ! =ce1 ) :i* !y %all be attract$ to ! c5t]1 dim9i%$ by _! c5trifugal =ce1 %all be suffici5t to keep ^? p>ts 9 a ballance ) ^? :i* lie "u ! poles4 ,& ^u ! supposition ( all ! p>ts ( ! e>? hav+ ! same degree ( d5sity1 ! e>?'s surface at ! equator mu/ be above #ag miles m di/ant f ! c5t]1 ?an at ! poles#bge4 #cf4 ,,aft] ?is x is %ewn1 f ! proportion ( ! equatorial diamet] ( ! e>? to its axis1 h[ ! same may be det]m9$ ( any o!r planet1 ^: d5sity 9 comp>ison ( ! d5sity ( ! e>?1 & ! "t ( its revolution ab\t its axis1 are kn[n4 ,& by ! rule deliv]$ = ?is1 x is f\nd1 t ! diamet] ( ! equator 9 ,jupit] %\ld be> to its axis ab\t ! proportion ( #aj to #ibgf1 & accord+ly ?is planet appe>s ( an oval =m to ! a/ronom]s4 ,! mo/ consid]able effects ( ?is sph]oidical figure our au?or takes likewise into consid]ation2 "o ( :i* is t bodies are n equally heavy 9 all di/ances f ! poles2 b ne> ! equator1 :]e ! di/ance f ! c5t] is greate/1 !y are light] ?an t[>ds ! poles3 & ne>ly 9 ?is proportion1 t ! actual p[]1 by :i* !y are drawn to ! c5t]1 result+ f ! diff]5ce betwe5 _! absolute gravity & c5trifugal =ce1 is reciprocally z ! di/ance f ! c5t]4 ,t ?is may n appe> to contradict :at has be=e be5 said ( ! alt]ation ( ! p[] ( gravity1 9 proportion to ! *ange ( ! di/ance f ! c5t]1 x is prop] c>efully to rem>k1 t our au?or has demon/rat$ ?ree ?+s relat+ h]eto3 ! fir/ is1 t decrease ( ! p[] ( gravity z we rec$e f ! c5t]1 :i* has be5 fully expla9$ 9 ! la/ *apt]1 ^u supposition t ! e>? & planets are p]fect sph]es1 f :i* _! diff]5ce is by _m degrees too little to require notice = ! purposes !re int5d$3 ! next is1 t :e!r !y be p]fect sph]es1 or exactly su* sph]oids z h n[ be5 m5tion$1 ! p[] ( gravity1 z we desc5d 9 ! same l9e to ! c5t]1 is at all di/ances z ! di/ance f ! c5t]1 ! p>ts ( ! e>? above ! body by draw+ ! body t[>ds !m less5+ its gravitation t[>ds ! c5t]#bgg2 & bo? ^! ass]tions relate to gravity alone3 ! ?ird is :at we m5tion$ 9 ?is place1 t ! actual =ce on diff]5t p>ts ( ! surface1 ) :i* bodies are drawn to ! c5t]1 is 9 ! proportion "h assign$#bgh4 #ch4 ,,! next effect ( ?is figure ( ! e>? is an obvi\s consequ5ce ( ! =m]3 t p5dulums ( ! same l5g? d n 9 diff]5t di/ances f ! pole make _! vibrations 9 ! same "t2 b t[>ds ! poles1 :]e ! gravity is /ronge/1 !y move quick] ?an ne> ! equator1 :]e !y are less impell$ to ! c5t]2 & accord+ly p5dulums1 t measure ! same "t by _! vibrations1 mu/ be %ort] ne> ! poles ?an at a great] di/ance4 ,bo? :i* d$uctions are f\nd true 9 fact2 ( :i* our au?or has rec\nt$ p>ticul>ly sev]al exp]im5ts1 9 :i* x 0 f\nd1 t clocks exactly adju/$ to ! true measure ( "t at ,p>is1 :5 transport$ ne>] to ! equator1 became errone\s & mov$ too sl[1 b 7 r$uc$ to _! true motion by contract+ _! p5dulums4 ,our au?or is p>ticul> 9 rem>k+1 h[ mu* !y lo/ ( _! motion1 :ile ! p5dulums rema9$ unalt]$2 & :at l5g? ! obs]v]s are said to h %ort5$ !m1 to br+ !m to "t4 ,& ! exp]im5ts1 :i* appe> to be mo/ c>efully made1 %ew ! e>? to be rais$ 9 ! middle betwe5 ! poles1 z mu* z our au?or f\nd x by 8 computation#bgi4 #ci4 ,,^! exp]im5ts on ! p5dulum our au?or has be5 v exact 9 exam9+1 inquir+ p>ticul>ly h[ mu* ! ext5sion ( ! rod ( ! p5dulum by ! great heats 9 ! torrid zone might make x necess>y to %ort5 x4 ,= by an exp]im5t made by ,,pic>t1 & ano!r made by ,,de ,,la ,,hire1 heat1 ?\gh n v int5se1 0 f\nd to increase ! l5g? ( rods ( iron4 ,! exp]im5t ( ,,pic>t 0 made ) a rod "o foot long1 :i* 9 w9t]1 at ! "t ( fro/1 0 f\nd to increase 9 l5g? by be+ heat$ at ! fire4 ,9 ! exp]im5t ( ,,de ,,la ,,hire a rod ( six foot 9 l5g? 0 f\nd1 :5 heat$ by ! summ] sun only1 to gr[ to a great] l5g?1 ?an x _h 9 ! a=esaid cold season4 ,f :i* obs]vations a d\bt has be5 rais$1 :e!r ! rod ( ! p5dulums 9 ! a=em5tion$ exp]im5ts 0 n ext5d$ by ! heat ( ^? w>m climates to all t excess ( l5g?1 ! obs]v]s f\nd !mselves oblig$ to less5 !m by4 ,b ! exp]im5ts n[ m5tion$ %ew ! contr>y4 ,= 9 ! fir/ ( !m ! rod ( a foot long 0 l5g!n$ no m ?an #a_/i "p ( :at ! p5dulum "u ! equator mu/ be dim9i%$2 & !re=e a rod ( ! l5g? ( ! p5dulum w\ld n h be5 ext5d$ above ( t l5g?4 ,9 ! exp]im5t ( ,,de ,,la ,,hire1 :]e ! heat 0 less1 ! rod ( six foot long 0 ext5d$ no m ?an #c_/aj ( :at ! p5dulum mu/ be %ort5$2 s t a rod ( ! l5g? ( ! p5dulum w\ld n h ga9$ above #c_/bj or #a_/g ( t l5g?4 ,& ! heat 9 ?is latt] exp]im5t1 ?\gh less ?an 9 ! =m]1 0 yet great] ?an ! rod ( a p5dulum c ord9>ily contract 9 ! hotte/ c\ntry2 = metals receive a great heat :5 expos$ to ! op5 sun1 c]ta9ly mu* great] ?an t ( a human body4 ,b p5dulums are n usually s expos$1 & )\t d\bt 9 ^! exp]im5ts 7 kept cool en\gh to appe> s to ! t\*2 :i* !y w\ld d 9 ! hotte/ place1 if lodg$ 9 ! %ade4 ,our au?or !re=e ?9ks x en\gh to all[ ab\t #a_/aj ( ! diff]5ce obs]v$ ^u acc\nt ( ! great] w>m? ( ! p5dulum4 #dj4 ,,!re is a ?ird effect1 :i* ! wat] has on ! e>? by *ang+ its figure1 t is tak5 notice ( by our au?or2 = ! expla9+ ( :i* we %all fir/ prove1 t bodies desc5d p]p5dicul>ly to ! surface ( ! e>? 9 all places4 ,! mann] ( collect+ ?is f obs]vation1 is z foll[s4 ,! surfaces ( all fluids re/ p>allel to t "p ( ! surface ( ! sea1 :i* is 9 ! same place ) !m1 to ! figure ( :i*1 z has be5 p>ticul>ly %ewn1 ! figure ( ! :ole e>? is =m$4 ,= if any holl[ vessel1 op5 at ! bottom1 be imm]s$ into ! sea2 x is evid5t1 t ! surface ( ! sea )9 ! vessel w reta9 ! same figure x _h1 be=e ! vessel inclos$ x2 s9ce its communication ) ! ext]nal wat] is n cut (f by ! vessel4 ,b all ! p>ts ( ! wat] be+ at re/1 x is z cle>1 t if ! bottom ( ! vessel 7 clos$1 ! figure ( ! wat] c\ld receive no *ange !reby1 ev5 ?\gh ! vessel 7 rais$ out ( ! sea2 any m ?an f ! ins5sible alt]ation ( ! p[] ( gravity1 consequ5t ^u ! augm5tation ( ! di/ance f ! c5t]4 ,b n[ x is cle>1 t bodies desc5d 9 l9es p]p5dicul> to ! surfaces ( quiesc5t fluids2 = if ! p[] ( gravity did n act p]p5dicul>ly to ! surface ( fluids1 bodies :i* swim on !m c\ld n re/1 z !y are se5 to d2 because1 if ! p[] ( gravity drew su* bodies 9 a direction oblique to ! surface :]eon !y lay1 !y w\ld c]ta9ly be put 9 motion1 & be c>ri$ to ! side ( ! vessel1 9 :i* ! fluid 0 conta9$1 t way ! action ( gravity incl9$4 #da4 ,,h5ce x foll[s1 t z we /&1 our bodies are p]p5dicul> to ! surface ( ! e>?4 ,!re=e 9 go+ f nor? to s\? our bodies d n keep 9 a p>allel direction4 ,n[ 9 all di/ances f ! pole ! same l5g? gone on ! e>? w n make ! same *ange 9 ! position ( our bodies1 b ! ne>] we are to ! poles1 we mu/ g great] l5g? to cause ! same v>iation h]e94 ,let ,m ,i ,l ,k 79 fig4 #aag7 repres5t ! figure ( ! e>?1 ,m1 ,l ! poles1 ,i1 ,k two opposite po9ts 9 ! middle betwe5 ^! poles4 ,let ,t ,v & ,p ,o be two ar*es1 ,t ,v be+ mo/ remote f ! pole ,l2 draw ,t ,w1 ,v ,x1 ,p ,q1 ,o ,r1 ea* p]p5dicul> to ! surface ( ! e>?1 & let ,t ,w1 ,v ,x meet 9 ,y1 & ,p ,q1 ,o ,r 9 ,s4 ,"h x is evid5t1 t 9 pass+ f ,v to ,t ! position ( a man's body w\ld be *ang$ by ! angle "u ,t ,y ,v1 = at ,v he w\ld /& 9 ! l9e ,y ,v cont9u$ upw>d1 & at ,t 9 ! l9e ,y ,t2 b 9 pass+ f ,o to ,p ! position ( 8 body w\ld be *ang$ by ! angle "u ,o ,s ,p4 ,n[ ,i say1 if ^! two angles are equal ! ar* ,o ,p is long] ?an ,t ,v3 = ! figure ,m ,i ,l ,k be+ oblong1 & ,i ,k long] ?an ,m ,l1 ! figure w be m incurvat$ t[>d ,i ?an t[>d ,l2 s t ! l9es ,t ,w & ,v ,x w meet 9 ,y be=e !y are drawn out to s great a l5g? z ! l9es ,p ,q & ,o ,r mu/ be cont9u$ to1 be=e !y w meet 9 ,s4 ,s9ce !re=e ,y ,t & ,y ,v are %ort] ?an ,p ,s & ,s ,v1 ,t ,v mu/ be less ?an ,o ,p4 ,if ^! angles "u ,t ,y ,v & ,o ,s ,p are ea* #a_/ij "p ( ! angle made by a p]p5dicul> l9e1 !y are said ea* to conta9 "o degree4 ,& ! unequal l5g? ( ^! ar*es ,o ,p & ,v ,t gives occasion to ! ass]tion1 t 9 pass+ f nor? to s\? ! degrees on ! e>?'s surface are n ( an equal l5g?1 b ^? ne> ! pole long] ?an ^? t[>d ! equator4 ,= ! l5g? ( ! ar* on ! e>? ly+ betwe5 ! two p]p5dicul>s1 :i* make an angle ( a degree ) ea* o!r1 is call$ ! l5g? ( a degree on ! e>?'s surface4 #db4 ,,?is figure ( ! e>? has "s effect on eclipses4 ,x has be5 obs]v$ above1 t sometimes ! nodes ( ! moon's orbit lie 9 a /raight l9e drawn f ! sun to ! e>?2 9 :i* case ! moon w cross ! plane ( ! e>?'s motion at ! new & full4 ,b :5ev] ! moon passes ne> ! plane at ! full1 "s "p ( ! e>? w int]cept ! sun's light1 & ! moon %9+ only ) light borr['d f ! sun1 :5 t light is prev5t$ f fall+ on any "p ( ! moon1 s mu* ( h] body w be d>k5$4 ,also :5 ! moon at ! new is ne> ! plane ( ! e>?'s motion1 ! inhabitants on "s "p ( ! e>? w see ! moon come "u ! sun1 & ! sun !reby be cov]$ f !m ei!r :olly or 9 "p4 ,n[ ! figure1 :i* we h %ewn to belong to ! e>?1 w occasion ! %ad[ ( ! e>? on ! moon n to be p]fectly r\nd1 b cause ! diamet] f ea/ to we/ to be some:at long] ?an ! diamet] f nor? to s\?4 ,9 eclipse ( ! sun ?is figure ( ! e>? w make "s little diff]5ce 9 ! place1 :]e ! sun %all appe> :olly or 9 any giv5 "p cov]$4 ,let ,a ,b ,c ,d 79 fig4 #aah47 repres5t ! e>?1 ,a ,c ! axis :]eon x turns daily1 ,e ! c5t]4 ,let ,f ,a ,g ,c repres5t a p]fect globe inscrib$ )9 ! e>?4 ,let ,h ,i be a l9e drawn ?r\gh ! c5t]s ( ! sun & moon1 cross+ ! surface ( ! e>? 9 ,k1 & ! surface ( ! globe inscrib$ 9 ,l4 ,draw ,e ,l1 :i* w be p]p5dicul> to ! surface ( ! globe 9 ,l3 & draw likewise ,k ,m1 s t x %all be p]p5dicul> to ! surface ( ! e>? 9 ,k4 ,n[ :]eas ! eclipse w\ld appe> c5tral at ,l1 if ! e>? 7 ! globe ,a ,g ,c ,f1 & does really appe> s at ,k2 ,i say1 ! latitude ( ! place ,k on ! real e>? is diff]5t f ! latitude ( ! place ,l on ! globe ,f ,a ,g ,c4 ,:at is call$ ! latitude ( any place is det]m9$ by ! angle :i* ! l9e p]p5dicul> to ! surface ( ! e>? at t place makes ) ! axis2 ! diff]5ce betwe5 ?is angle1 & t made by a p]p5dicul> l9e or squ>e be+ call$ ! latitude ( ea* place4 ,b x might "h be prov$1 t ! angle :i* ,k ,m makes ) ,m ,c is less1 ?an ! angle made betwe5 ,l ,e & ,e ,c3 consequ5tly ! latitude ( ! place ,k is great]1 ?an ! latitude1 :i* ! place ,l w\ld h4 #dc4 ,,! next effect1 :i* foll[s f ?is figure ( ! e>?1 is t gradual *ange 9 ! di/ance ( ! fix$ />s f ! equ9octial po9ts1 :i* a/ronom]s obs]ve4 ,b be=e ?is c be expla9$1 x is necess>y to say some?+ m p>ticul>1 ?an has yet be5 done1 conc]n+ ! mann] ( ! e>?'s motion r\nd ! sun4 #dd4 ,,x has already be5 said1 t ! e>? turns r\nd ea* day on its own axis1 :ile its :ole body is c>ri$ r\nd ! sun once 9 a ye>4 ,h[ ^! two motions are jo9$ toge!r may be conceiv$ 9 "s degree by ! motion ( a b[l on ! gr\nd1 :]e ! b[l 9 r\l+ on cont9ually turns ^u its axis1 & at ! same "t ! :ole body !re( is c>ri$ /raight on4 ,b to be m express let ,a 79 fig4 #aai7 repres5t ! sun ,b ,c ,d ,e f\r diff]5t situations ( ! e>? 9 its orbit mov+ ab\t ! sun4 ,9 all ^! let ,f ,g repres5t ! axis1 ab\t :i* ! e>? daily turns4 ,! po9ts ,f1 ,g are call$ ! poles ( ! e>?2 & ?is axis is suppos$ to keep always p>allel to x self 9 e situation ( ! e>?2 at lea/ t x w\ld d s1 7 x n = a m9ute deviation1 ! cause :]e( w be expla9$ 9 :at foll[s4 ,:5 ! e>? is 9 ,b1 ! half ,h ,i ,k w be illum9at$ by ! sun1 & ! o!r half ,h ,l ,k w be 9 d>kness4 ,n[ if on ! globe any po9t be tak5 9 ! middle betwe5 ! poles1 ?is po9t %all describe by ! motion ( ! globe ! circle ,m ,n1 half ( :i* is 9 ! enlight5$ "p ( ! globe1 & half 9 ! d>k "p4 ,b ! e>? is suppos$ to move r\nd its axis ) an equable motion2 !re=e on ?is po9t ( ! globe ! sun w be se5 j half ! day1 & be invisible ! o!r half4 ,& ! same w happ5 to e po9t ( ?is circle1 9 all situations ( ! e>? dur+ its :ole revolution r\nd ! sun4 ,?is circle ,m ,n is call$ ! equator1 ( :i* we h be=e made m5tion4 #de4 ,,n[ suppose any o!r po9t tak5 on ! surface ( ! globe t[>d ! pole ,f1 :i* 9 ! diurnal revolution ( ! globe %all describe ! circle ,o ,p4 ,"h x appe>s t m ?an half ?is circle is enlightn$ by ! sun1 & consequ5tly t 9 any p>ticul> po9t ( ?is circle ! sun w be long] se5 ?an lie hid1 t is ! day w be long] ?an ! night4 ,aga9 if we consid] ! same circle ,o ,p on ! globe situat$ 9 ,d ! opposite "p ( ! orbit f ,b1 we %all see1 t "h 9 any place ( ?is circle ! night w be z mu* long] ?an ! day4 #df4 ,,9 ^! situations ( ! globe ( e>? a l9e drawn f ! sun to ! c5t] ( ! e>? w be obliquely incl9$ t[>d ! axis ,f ,g4 ,n[ suppose1 t su* a l9e drawn f ! sun to ! c5t] ( ! e>?1 :5 9 ,c or ,e1 w\ld be p]p5dicul> to ! axis ,f ,g2 9 :i* cases ! sun w %9e p]p5dicul>ly ^u ! equator1 & consequ5tly ! l9e drawn f ! c5t] ( ! e>? to ! sun w cross ! equator1 z x passes ?r\gh ! surface ( ! e>?2 :]eas 9 all o!r situations ( ! globe ?is l9e w pass ?r\gh ! surface ( ! globe at a di/ance f ! equator ei!r nor?w>d or s\?w>d4 ,n[ 9 bo? ^! cases half ! circle ,o ,p w be 9 ! light1 & half 9 ! d>k2 & !re=e to e place 9 ?is circle ! day w be equal to ! night4 ,?us x appe>s1 t 9 ^! two opposite situations ( ! e>? ! day is equal to ! night 9 all p>ts ( ! globe2 b 9 all o!r situations ?is equality w only be f\nd 9 places situat$ 9 ! v middle betwe5 ! poles1 t is1 on ! equator4 #dg4 ,,! times1 :]e9 ?is univ]sal equality betwe5 ! day & night happ5s1 are call$ ! equ9oxes4 ,n[ x has be5 long obs]v$ by a/ronom]s1 t aft] ! e>? ha? set out f ei!r equ9ox1 suppose f ,e 7:i* w be ! spr+ equ9ox1 if ,f be ! nor? pole7 ! same equ9ox %all aga9 return a little be=e ! e>? has made a compleat revolution r\nd ! sun4 ,?is return ( ! equ9ox prec$+ ! intire revolution ( ! e>? is call$ ! precession ( ! equ9ox1 & is caus$ by ! protub]ant figure ( ! e>?4 #di4 ,,s9ce ! sun %9es p]p5dicul>ly ^u ! equator1 :5 ! l9e drawn f ! sun to ! c5t] ( ! e>? is p]p5dicul> to ! e>?'s axis1 9 ?is case ! plane1 :i* %\ld cut ?r\gh ! e>? at ! equator1 may be ext5d$ to pass ?r\gh ! sun2 b x w n d s 9 any o!r position ( ! e>?4 ,n[ let u consid] ! prom95t "p ( ! e>? ab\t ! equator1 z a solid r+ mov+ ) ! e>? r\nd ! sun4 ,at ! "t ( ! equ9oxes1 ?is r+ w h ! same k9d ( situation 9 respect ( ! sun1 z ! orbit ( ! moon has1 :5 ! l9e ( ! nodes is direct$ to ! sun2 & at all o!r times w resemble ! moon's orbit 9 o!r situations4 ,consequ5tly ?is r+1 :i* o!rwise w\ld keep ?r\gh\t its motion p>allel to x self1 w receive "s *ange 9 its position f ! action ( ! sun ^u x1 except only at ! "t ( ! equ9ox4 ,! mann] ( ?is *ange may be und]/ood z foll[s4 ,let ,a ,b ,c ,d 79 fig4 #abj7 repres5t ?is r+1 ,e ! c5t] ( ! e>?1 ,s ! sun1 ,a ,f ,c ,g a circle describ$ 9 ! plane ( ! e>?'s motion to ! c5t] ,e4 ,"h ,a & ,c are ! two po9ts1 9 :i* ! e>?'s equator crosses ! plane ( ! e>?'s motion2 & ! "t ( ! equ9ox falls out1 :5 ! /raight l9e ,a ,c cont9u$ w\ld pass ?r\gh ! sun4 ,n[ let u recollect :at 0 said above conc]n+ ! moon1 :5 h] orbit 0 9 ! same situation ) ?is r+4 ,f !nce x w be und]/ood1 if a body 7 suppos$ to be mov+ 9 any "p ( ?is circle ,a ,b ,c ,d1 :at effect ! action ( ! sun on ! body w\ld h t[>d *ang+ ! position ( ! l9e ,a ,c4 ,9 p>ticul> ,h ,i be+ drawn p]p5dicul> to ,s ,e1 if ! body be 9 any "p ( ?is circle betwe5 ,a & ,h1 or betwe5 ,c & ,i1 ! l9e ,a ,c w\ld be s turn$1 t ! po9t ,a %all move t[>d ,b1 & ! po9t ,c t[>d ,d2 b if x 7 9 any o!r "p ( ! circle1 ei!r betwe5 ,h & ,c1 or betwe5 ,i & ,a1 ! l9e ,a ,c w\ld be turn$ ! contr>y way4 ,h5ce x foll[s1 t z ?is solid r+ turns r\nd ! c5t] ( ! e>?1 ! p>ts ( ?is r+ betwe5 ,a & ,h1 & betwe5 ,c & ,i1 are s influ5c$ by ! sun1 t !y w endeav\r1 s to *ange ! situation ( ! l9e ,a ,c z to cause ! po9t ,a to move t[>d ,b1 & ! po9t ,c to move t[>d ,d2 b all ! p>ts ( ! r+ betwe5 ,h & ,c1 & betwe5 ,i & ,a1 w h ! opposite t5d5cy1 & dispose ! l9e ,a ,c to move ! contr>y way4 ,& s9ce ^! la/ nam$ p>ts are l>g] ?an ! o!r1 !y w prevail ov] ! o!r1 s t by ! action ( ! sun ^u ?is r+1 ! l9e ,a ,c w be s turn$1 t ,a %all cont9ually be m & m mov+ t[>d ,d1 & ,c t[>d ,b4 ,?us no soon] %all ! sun 9 its visible motion h dep>t$ f ,a1 b ! motion ( ! l9e ,a ,c %all ha/5 its meet+ ) ,c1 & f !nce ! motion ( ?is l9e %all aga9 ha/5 ! sun's second conjunction ) ,a2 = z ?is l9e s turns1 t ,a is cont9ually mov+ t[>d ,d1 s ! sun's visible motion is ! same way z f ,s t[>d ,t4 #di4 ,,! moon w h on ?is r+ ! l effect z ! sun1 & op]ate on x m /rongly1 9 ! same proportion z its =ce on ! sea exce$$ t ( ! sun on ! same4 ,b ! effect ( ! action ( bo? lum9>ies w be greatly dim9i%$ by reason ( ?is r+'s be+ connect$ to ! re/ ( ! e>?2 = by ?is means ! sun & moon h n only ?is r+ to move1 b likewise ! :ole globe ( ! e>?1 ^u ^: sph]ical "p !y h no imm$iate influ5ce4 ,beside ! effect is also r5dr$ less1 by reason t ! prom95t "p ( ! e>? is n collect$ all "u ! equator1 b spreads gradually f !nce t[>d bo? poles4 ,^u ! :ole1 ?\gh ! sun alone c>ries ! nodes ( ! moon ?r\gh an intire revolution 9 ab\t #ai ye>s1 ! unit$ =ce ( bo? lum9>ies on ! prom95t p>ts ( ! e>? w h>dly c>ry r\nd ! equ9ox 9 a less space ( "t ?an #bfjjj ye>s4 #ej4 ,,to ?is motion ( ! equ9ox we mu/ add ano!r consequ5ce ( ?is action ( ! sun & moon ^u ! elevat$ p>ts ( ! e>?1 t ?is annul> "p ( ! e>? ab\t ! equator1 & consequ5tly ! e>?'s axis1 w twice a ye> & twice a mon? *ange its incl9ation to ! plane ( ! e>?'s motion1 & be aga9 re/or$1 j z ! incl9ation ( ! moon's orbit by ! action ( ! sun is annually twice dim9i%$1 & z (t5 recov]s its orig9al magnitude4 ,b ?is *ange is v ins5sible4 #ea4 ,i ,,%all n[ f9i% ! pres5t *apt] ) our great au?or's inquiry into ! figure ( ! second>y planets1 p>ticul>ly ( our moon1 ^u ! figure ( :i* its fluid p>ts w h an influ5ce4 ,! moon turns always ! same side t[>ds ! e>?1 & consequ5tly revolves b once r\nd its axis 9 ! space ( an entire mon?2 = a spectator plac$ )\t ! circle1 9 :i* ! moon moves1 w\ld 9 t "t obs]ve all ! p>ts ( ! moon successively to pass once be=e 8 view & no m1 t is1 t ! :ole globe ( ! moon has turn$ once r\nd4 ,n[ ! great sl[ness ( ?is motion w r5d] ! c5trifugal =ce ( ! p>ts ( ! wat]s v weak1 s t ! figure ( ! moon _c1 z 9 ! e>?1 be mu* affect$ by ?is revolution ^u its axis3 b ! figure ( ^? wat]s are made diff]5t f sph]ical by ano!r cause1 viz4 ! action ( ! e>? ^u !m2 by :i* !y w be r$uc$ to an oblong oval =m1 ^: axis prolong$ w\ld pass ?r\gh ! e>?2 = ! same reason1 z we h above obs]v$1 t ! wat]s ( ! e>? w\ld take ! l figure1 if !y _h mov$ s sl[ly1 z to keep pace ) ! moon4 ,& ! solid "p ( ! moon mu/ correspond ) ?is figure ( ! fluid "p3 b ?is elevation ( ! p>ts ( ! moon is no?+ ne> s great z is ! protub]ance ( ! e>? at ! equator1 = x w n exce$ #ic engli% feet4 #eb4 ,! wat]s ( ! moon w h no tide1 except :at w arise f ! motion ( ! moon r\nd ! e>?4 ,= ! conv]sion ( ! moon ab\t h] axis is equable1 :]eby ! inequality 9 ! motion r\nd ! e>? discov]s to u at "s times small p>ts ( ! moon's surface t[>ds ! ea/ or we/1 :i* at o!r times lie hid2 & z ! axis1 :]eon ! moon turns1 is oblique to h] motion r\nd ! e>?1 sometimes small p>ts ( h] surface t[>d ! nor?1 & sometimes ! l t[>d ! s\? are visible1 :i* at o!r times are out ( sight4 ,^! appe>ances make :at is call$ ! libration ( ! moon1 discov]$ by ,,hevelius4 ,b n[ z ! axis ( ! oval figure ( ! wat]s w he po9t$ t[>ds ! e>?1 !re mu/ arise f h5ce "s fluctuation 9 !m2 & beside1 by ! *ange ( ! moon's di/ance f ! e>?1 !y w n always h ! v same height4 ,illu/ration ,illu/ration ,,book ,,iii4 ,,*ap ,i4 ,conc]n+ ! cause ( ,,col\rs inh]5t 9 ! ,,light4 ,,aft] ?is view :i* has be5 tak5 ( ,sir ,,isaac ,,newton',s ma!matical pr9ciples ( philosophy1 & ! use he has made ( !m1 9 expla9+ ! sy/em ( ! _w1 c4 ! c\rse ( my design directs u to turn our eyes to t o!r philosophical "w1 8 treatise ( ,optics1 9 :i* we %all f9d our great au?or's inimitable g5ius discov]+ x self no less1 ?an 9 ! =m]2 nay p]haps ev5 m1 s9ce ?is "w gives z _m in/ances ( 8 s+ul> =ce ( reason+1 & ( 8 unb\nd$ inv5tion1 ?\gh unassi/$ 9 great measure by ^? rules & g5]al precepts1 :i* facilitate ! inv5tion ( ma!matical !orems4 ,nor yet is ?is "w inf]ior to ! o!r 9 usefulness2 = z t has made kn[n to u "o great pr9ciple 9 nature1 by :i* ! cele/ial motions are cont9u$1 & by :i* ! frame ( ea* globe is pres]v$2 s does ?is po9t out to u ano!r pr9ciple no less univ]sal1 ^u :i* dep5ds all ^? op]ations 9 ! small] p>ts ( matt]1 = ^: sake ! great] frame ( ! univ]se is erect$2 all ^? imm5se globes1 ) :i* ! :ole heav5s are fill$1 be+ )\t d\bt only design'd z s _m conv5i5t ap>tm5ts = c>ry+ on ! m noble op]ations ( nature 9 vegetation & animal life4 ,:i* s+le consid]ation gives abundant pro( ( ! excell5cy ( our au?or's *oice1 9 apply+ himself c>efully to exam9e ! action betwe5 light & bodies1 s necess>y 9 all ! v>ieties ( ^! productions1 t none ( !m c be successfully promot$ )\t ! concurr5ce ( heat 9 a great] or less degree4 #b4 ',,tis true1 our au?or has n made s full a discov]y ( ! pr9ciple1 by :i* ?is mutual action betwe5 light & bodies is caus$2 z he has 9 relation to ! p[]1 by :i* ! planets are kept 9 _! c\rses3 yet he has l$ u to ! v entrance ^u x1 & po9t$ out ! pa? s pla9ly :i* mu/ be foll[$ to rea* x2 t "o may be bold to say1 :5ev] mank9d %all be bless$ ) ?is improvem5t ( _! k1 x w be d]iv$ s directly f ! pr9ciples laid d[n by our au?or 9 ?is book1 t ! greate/ %>e ( ! praise due to ! discov]y w belong to him4 #c4 ,,9 speak+ ( ! progress our au?or has made1 ,i %all di/9ctly pursue ?ree ?+s1 ! two fir/ relat+ to ! col\rs ( natural bodies3 = 9 ! fir/ head %all be %ewn1 h[ ^? col\rs are d]iv$ f ! prop]ties ( ! light itself2 & 9 ! second ^u :at prop]ties ( ! bodies !y dep5d3 b ! ?ird head ( my disc\rse %all treat ( ! action ( bodies ^u light 9 refract+1 reflect+1 & inflect+ x4 #d4 ,,! fir/ ( ^!1 :i* %all be ! bus9ess ( ! pres5t *apt]1 is conta9$ 9 ?is "o proposition3 t ! sun's direct light is n uni=m 9 respect ( col\r1 n be+ dispos$ 9 e "p ( x to excite ! idea ( :it5ess1 :i* ! :ole raises2 b on ! contr>y is a composition ( diff]5t k9ds ( rays1 "o sort ( :i* if alone w\ld give ! s5se ( r$1 ano!r ( orange1 a ?ird ( yell[1 a f\r? ( gre51 a fif? ( light blue1 a six? ( indigo1 & a sev5? ( a violet purple2 t all ^! rays toge!r by ! mixture ( _! s5sations impress ^u ! organ ( sight ! s5se ( :it5ess1 ?\gh ea* ray always impr9ts !re its own col\r2 & all ! diff]5ce betwe5 ! col\rs ( bodies :5 view$ 9 op5 day light arises f ?is1 t col\r$ bodies d n reflect all ! sorts ( rays fall+ ^u !m 9 equal pl5ty1 b "s sorts mu* m copi\sly ?an o!rs2 ! body appe>+ ( t col\r1 ( :i* ! light com+ f x is mo/ compos$4 #e4 ,,t ! light ( ! sun is comp\nd$1 z has be5 said1 is prov$ by refract+ x ) a prism4 ,by a prism ,i "h mean a glass or o!r body ( a triangul> =m1 su* z is repres5t$ 9 fig4 #aba4 ,b be=e we proce$ to ! illu/ration ( ! proposition we h j n[ laid d[n1 x w be necess>y to sp5d a few words 9 expla9+ :at is meant by ! refraction ( light2 z ! design ( our pres5t lab\r is to give "s notion ( ! subject1 we are engag$ 91 to su* z are n v]s$ 9 ! ma!matics4 #f4 ,,x is well kn[n1 t :5 a ray ( light pass+ ?r\gh ! air falls obliquely ^u ! surface ( any transp>5t body1 suppose wat] or glass1 & ent]s x1 ! ray w n pass on 9 t body 9 ! same l9e x describ$ ?r\gh ! air1 b be turn$ (f f ! surface1 s z to be less incl9$ to x aft] pass+ x1 ?an be=e4 ,let ,a ,b ,c ,d 79 fig4 #abb47 repres5t a portion ( wat]1 or glass1 ,a ,b ! surface ( x1 ^u :i* ! ray ( light ,e ,f falls obliquely2 ?is ray %all n g "r on 9 ! c\rse del9eat$ by ! l9e ,f ,g1 b be turn$ (f f ! surface ,a ,b into ! l9e ,f ,h1 less incl9$ to ! surface ,a ,b ?an ! l9e ,e ,f is1 9 :i* ! ray is incid5t ^u t surface4 #g4 ,,on ! o!r h&1 :5 ! light passes out ( any su* body into ! air1 x is inflect$ ! contr>y way1 be+ aft] its em]g5ce r5dr$ m oblique to ! surface x passes ?r\gh1 ?an be=e4 ,?us ! ray ,f ,h1 :5 x goes out ( ! surface ,c ,d1 w be turn$ up t[>ds t surface1 go+ out into ! air 9 ! l9e ,h ,i4 #h4 ,,?is turn+ ( ! light out ( its way1 z x passes f "o transp>5t body into ano!r is call$ its refraction4 ,bo? ^! cases may be tri$ by an easy exp]im5t ) a bason & wat]4 ,= ! fir/ case set an empty bason 9 ! sun%9e or ne> a c&le1 mak+ a m>k ^u ! bottom at ! extremity ( ! %ad[ ca/ by ! brim ( ! bason1 !n by p\r+ wat] into ! bason y w obs]ve ! %ad[ to %r9k1 & leave ! bottom ( ! bason enlightn$ to a good di/ance f ! m>k4 ,let ,a ,b ,c 79 fig4 #abc47 d5ote ! empty bason1 ,e ,a ,d ! light %9+ ov] ! brim ( x1 s t all ! "p ,a ,b ,d be %ad$4 ,!n a m>k be+ made at ,d1 if wat] be p\r$ into ! bason 7z 9 fig4 #abd47 to ,f ,g1 y %all obs]ve ! light1 :i* be=e w5t on to ,d1 n[ to come mu* %ort ( ! m>k ,d1 fall+ on ! bottom 9 ! po9t ,h1 & leav+ ! m>k ,d a good way )9 ! enlight5$ "p2 :i* %ews t ! ray ,e ,a1 :5 x ent]s ! wat] at ,i1 goes no long] /raight =w>ds1 b is at t place incurvat$1 & made to g ne>] ! p]p5dicul>4 ,! o!r case may be try$ by putt+ any small body into an empty bason1 plac$ l[] ?an y\r eye1 & !n rec$+ f ! bason1 till y c b j see ! body ov] ! brim4 ,aft] :i*1 if ! bason be fill$ ) wat]1 y %all pres5tly obs]ve ! body to be visible1 ?\gh y g f>!r (f f ! bason4 ,let ,a ,b ,c 79 fig4 #abe47 d5ote ! bason z be=e1 ,d ! body 9 x1 ,e ! place ( y\r eye1 :5 ! body is se5 j ov] ! edge ,a1 :ile ! bason is empty4 ,if x be !n fill$ ) wat]1 y w obs]ve ! body /ill to be visible1 ?\gh y take y\r eye f>!r (f4 ,suppose y see ! body 9 ?is case j ov] ! brim ,a1 :5 y\r eye is at ,f1 x is pla9 t ! rays ( light1 :i* come f ! body to y\r eye h n come /raight on1 b are b5t at ,a1 be+ turn$ d[nw>ds1 & m incl9$ to ! surface ( ! wat]1 betwe5 ,a & y\r eye at ,f1 ?an !y are betwe5 ,a & ! body ,d4 #i4 ,,?is we hope is suffici5t to make all our read]s appreh5d1 :at ! writ]s ( optics mean1 :5 !y m5tion ! refraction ( ! light1 or speak ( ! rays ( light be+ refract$4 ,we %all !re=e n[ g on to prove ! ass]tion advanc$ 9 ! =em5tion$ proposition1 9 relation to ! diff]5t k9ds ( col\rs1 t ! direct light ( ! sun exhibits to our s5se3 :i* may be done 9 ! foll[+ mann]4 #aj4 ,,if a room be d>k5$1 & ! sun p]mitt$ to %9e into x ?r\gh a small hole 9 ! w9d[ %utt]1 & be made imm$iately to fall ^u a glass prism1 ! beam ( light %all 9 pass+ ?r\gh su* a prism be p>t$ into rays1 :i* exhibit all ! =em5tion$ col\rs4 ,9 ?is mann] if ,a ,b 79 fig4 #abf7 repres5t ! w9d[ %utt]2 ,c ! hole 9 x2 ,d ,e ,f ! prism2 ,z ,y a beam ( light com+ f ! sun1 :i* passes ?r\gh ! hole1 & falls ^u ! prism at ,y1 & if ! prism 7 remov$ w\ld g on to ,x1 b 9 entr+ ! surface ,b ,f ( ! glass x %all be turn$ (f1 z has be5 expla9$1 into ! c\rse ,y ,w fall+ ^u ! second surface ( ! prism ,d ,f 9 ,w1 go+ out ( :i* into ! air x %all be aga9 f>!r inflect$4 ,let ! light n[1 aft] x has pass$ ! prism1 be receiv$ ^u a %eet ( pap] held at a prop] di/ance1 & x %all pa9t ^u ! pap] ! picture1 image1 or spectrum ,l ,m ( an oblong figure1 ^: l5g? %all mu* exce$ its bread?2 ?\gh ! figure %all n be oval1 ! ends ,l & ,m be+ semicircul> & ! sides /raight4 ,b n[ ?is figure w be v>iegat$ ) col\rs 9 ?is mann]4 ,f ! extremity ,m to "s l5g?1 suppose to ! l9e n o1 x %all be ( an int5se r$2 f n o to p q x %all be an orange2 f p q to r s x %all be yell[2 f !nce to t u x %all be gre52 f !nce to w x blue2 f !nce to y z indigo2 & f !nce to ! end violet4 #aa4 ,,?us x appe>s t ! sun's :ite light by its passage ?r\gh ! prism1 is s *ang$ z n[ to be divid$ into rays1 :i* exhibit all ^! sev]al col\rs4 ,! "q is1 :e!r ! rays :ile 9 ! sun's beam be=e ?is refraction possess$ ^! prop]ties di/9ctly2 s t "s "p ( t beam w\ld )\t ! re/ h giv5 a r$ col\r1 & ano!r "p alone h giv5 an44orange1 c4 ,t ?is is possible to be ! case1 appe>s f h5ce2 t if a convex glass be plac$ betwe5 ! pap] & ! prism1 :i* may collect all ! rays proce$+ out ( ! prism into its focus1 z a burn+ glass does ! sun's direct rays2 & if t focus fall ^u ! pap]1 ! spot =m$ by su* a glass ^u ! pap] %all appe> :ite1 j l ! sun's direct light4 ,illu/ration ,! re/ rema9+ z be=e1 let ,p ,q4 79 fig4 #abg47 be ! convex glass1 caus+ ! rays to meet ^u ! pap] ,h ,g ,i ,k 9 ! po9t ,n1 ,i say t po9t or r spot ( light %all appe> :ite1 )\t ! lea/ t9cture ( any col\r4 ,b x is evid5t t into ?is spot are n[ ga!r$ all ^? rays1 :i* be=e :5 sep>ate gave all ^? diff]5t col\rs2 :i* %ews t :it5ess may be made by mix+ ^? col\rs3 especially if we consid]1 x c be prov$ t ! glass ,p ,q does n alt] ! col\r ( ! rays :i* pass ?r\gh x4 ,:i* is done ?us3 if ! pap] be made to approa* ! glass ,p ,q1 ! col\rs w manife/ !mselves z f> z ! magnitude ( ! spectrum1 :i* ! pap] receives1 w p]mit4 ,suppose x 9 ! situation h g i k1 & t x !n receive ! spectrum l m1 ?is spectrum %all be mu* small]1 ?an if ! glass ,p ,q 7 remov$1 & !re=e ! col\rs _c be s mu* sep>at$2 b yet ! extremity m %all manife/ly appe> r$1 & ! o!r extremity l %all be blue2 & ^! col\rs z well z ! int]m$iate ones %all discov] !mselves m p]fectly1 ! f>!r ! pap] is remov$ f ,n1 t is1 ! l>g] ! spectrum is3 ! same ?+ happ5s1 if ! pap] be remov$ f>!r (f f ,p ,q ?an ,n4 ,suppose into ! position 1 ! spectrum pa9t$ ^u x %all aga9 discov] its col\rs1 & t m di/9ctly1 ! f>!r ! pap] is remov$1 b only 9 an inv]t$ ord]3 = z be=e1 :5 ! pap] 0 ne>] ! convex glass1 ?an at ,n1 ! upp] "p ( ! image 0 blue1 & ! "u r$2 n[ ! upp] "p %all be r$1 & ! "u blue3 because ! rays cross at ,n4 #ab4 ,,nay f>!r t ! :it5ess at ! focus ,n1 is made by ! union ( ! col\rs may be prov$ )\t remov+ ! pap] out ( ! focus1 by int]cept+ ) any opake body "p ( ! light ne> ! glass2 = if ! "u "p1 t is ! r$1 or m prop]ly ! r$-mak+ rays1 z !y are /yl$ by our au?or1 are int]cept$1 ! spot %all take a blui% hue2 & if m ( ! inf]ior rays are cut (f1 s t nei!r ! r$-mak+ nor orange-mak+ rays1 & if y please ! yell[-mak+ rays likewise1 %all fall ^u ! spot2 !n %all ! spot incl9e m & m to ! rema9+ col\rs4 ,9 l mann] if y cut (f ! upp] "p ( ! rays1 t is ! violet col\r$ or indigo-mak+ rays1 ! spot %all turn r$di%1 & become1 m s1 ! m ( ^? opposite col\rs are int]cept$4 #ac4 ,,?is ,i ?9k abundantly proves t :it5ess may be produc$ by a mixture ( all ! col\rs ( ! spectrum4 ,at lea/ !re is b "o way ( evad+ ! pres5t argum5ts1 :i* is1 by ass]t+ t ! rays ( light aft] pass+ ! prism h no diff]5t prop]ties to exhibit ?is or ! o!r col\r1 b are 9 t respect p]fectly homog5eal1 s t ! rays :i* pass to ! "u & r$ "p ( ! image d n diff] 9 any prop]ties :atev] f ^?1 :i* g to ! upp] & violet "p ( x2 b t ! col\rs ( ! spectrum are produc$ only by "s new modifications ( ! rays1 made at _! incid5ce ^u ! pap] by ! diff]5t t]m9ations ( light & %ad[3 if inde$ ?is ass]tion c be all[$ any place1 aft] :at has be5 said2 = x seems to be suffici5tly obviat$ by ! latt] "p ( ! prec$+ exp]im5t1 t by int]cept+ ! inf]ior "p ( ! light1 :i* comes f ! prism1 ! :ite spot %all receive a blui% ca/1 & by /opp+ ! upp] "p ! spot %all turn r$1 & 9 bo? cases recov] its col\r1 :5 ! int]cept$ light is p]mitt$ to pass aga92 ?\gh 9 all ^! trials !re is ! l t]m9ation ( light & %ad[4 ,h[ev] our au?or has contriv$ "s exp]im5ts expresly to %ew ! absurdity ( ?is supposition2 all :i* he has expla9$ & enl>g$ ^u 9 s di/9ct & expressive a mann]1 t x w\ld be :olly unnecess>y to repeat !m 9 ?is place#bhj4 ,i %all only m5tion t ( !m1 :i* may be tri$ 9 ! exp]im5t be=e u4 ,if y draw ^u ! pap] ,h ,g ,i ,k1 & ?r\gh ! spot ,n1 ! /raight l9e w x p>allel to ! horizon1 & !n if ! pap] be mu* incl9$ into ! situation r s v t ! l9e w x /ill rema9+ p>allel to ! horizon1 ! spot ,n %all lose its :it5ess & receive a blue t9cture2 b if x be incl9$ z mu* ! contr>y way1 ! same spot %all ex*ange its :ite col\r = a r$di% dye4 ,all :i* c nev] be acc\nt$ = by any diff]5ce 9 ! t]m9ation ( ! light & %ad[1 :i* "h is none at all2 b are easily expla9$ by suppos+ ! upp] "p ( ! rays1 :5ev] !y ent] ! eye1 dispos$ to give ! s5sation ( ! d>k col\rs blue1 indigo & violet2 & t ! "u "p is fitt$ to produce ! bright col\rs yell[1 orange & r$3 = :5 ! pap] is 9 ! situation r s t u1 x is pla9 t ! upp] "p ( ! light falls m directly ^u x1 ?an ! "u "p1 & !re=e ^? rays w be mo/ pl5tifully reflect$ f x2 & by _! ab\nd+ 9 ! reflect$ light w cause x to incl9e to _! col\r4 ,j s :5 ! pap] is incl9$ ! contr>y way1 x w receive ! inf]ior rays mo/ directly1 & !re=e t+ ! light x reflects ) _! col\r4 #ad4 ,,x is n[ to be prov$ t ^! dispositions ( ! rays ( light to produce "s "o col\r & "s ano!r1 :i* manife/ !mselves aft] _! be+ refract$1 are n wr\ght by any action ( ! prism ^u !m1 b are orig9ally inh]5t 9 ^? rays2 & t ! prism only af=ds ea* species an occasion ( %ew+ its di/9ct quality by sep>at+ !m "o f ano!r1 :i* be=e1 :ile !y 7 bl5d$ toge!r 9 ! direct beam ( ! sun's light1 lay conceal'd4 ,b t ?is is s1 w be prov$1 if x c be %ewn t no prism has any p[] ^u ! rays1 :i* aft] _! passage ?r\gh "o prism are r5d]$ uncomp\nd$ & conta9 9 !m b "o col\r1 ei!r to divide t col\r into sev]al1 z ! sun's light is divid$1 or s mu* z to *ange x into any o!r col\r4 ,?is w be prov$ by ! foll[+ exp]im5t#bha4 ,! same ?+ rema9+1 z 9 ! fir/ exp]im5t1 let ano!r prism ,n ,o 79 fig4 #abh47 be plac$ ei!r imm$iately1 or at "s di/ance aft] ! fir/1 9 a p]p5dicul> po/ure1 s t x %all refract ! rays issu+ f ! fir/ sideways4 ,n[ if ?is prism c\ld divide ! light fall+ ^u x into col\r$ rays1 z ! fir/ has done1 x w\ld divide ! spectrum bread?wise into col\rs1 z be=e x 0 divid$ l5g?wise2 b no su* ?+ is obs]v$4 ,if ,l ,m 7 ! spectrum1 :i* ! fir/ prism ,d ,e ,f w\ld pa9t ^u ! pap] ,h ,g ,i ,k2 ,p ,q ly+ 9 an oblique po/ure %all be ! spectrum project$ by ! second1 & %all be divid$ l5g?wise into col\rs correspond+ to ! col\rs ( ! spectrum ,l ,m1 & occasion$ l !m by ! refraction ( ! fir/ prism1 b its bread? %all receive no su* division2 on ! contr>y ea* col\r %all be uni=m f side to side1 z mu* z 9 ! spectrum ,l ,m1 :i* proves ! :ole ass]tion4 #ae4 ,,! same is yet mu* f>!r confirm$ by ano!r exp]im5t4 ,our au?or tea*es t ! col\rs ( ! spectrum ,l ,m 9 ! fir/ exp]im5t are yet comp\nd$1 ?\gh n s mu* z 9 ! sun's direct light4 ,he %ews !re=e h[1 by plac+ ! prism at a di/ance f ! hole1 & by ! use ( a convex glass1 to sep>ate ! col\rs ( ! spectrum1 & make !m uncomp\nd$ to any degree ( exactness#bhb4 ,& he %ews :5 ?is is done suffici5tly1 if y make a small hole 9 ! pap] :]eon ! spectrum is receiv$1 ?r\gh :i* any "o sort ( rays may pass1 & !n let t col\r$ ray fall s ^u a prism1 z to be refract$ by x1 x %all 9 no case :atev] *ange its col\r2 b %all always reta9 x p]fectly z at fir/1 h[ev] x be refract$#bhc4 #af4 ,,nor yet w ^! col\rs aft] ?is full sep>ation ( !m suff] any *ange by reflection f bodies ( diff]5t col\rs2 on ! o!r h& !y make all bodies plac$ 9 ^! col\rs appe> ( ! col\r :i* falls ^u !m#bhd3 = m9ium 9 r$ light w appe> z 9 op5 day light2 b 9 yell[ light w appe> yell[2 & :i* is m extraord9>y1 9 gre5 light w appe> gre51 9 blue1 blue2 & 9 ! violet-purple col\r$ light w appe> ( a purple col\r2 9 l mann] v]digrease1 or blue bise1 w put on ! appe>ance ( t col\r1 9 :i* x is plac$2 s t nei!r bise plac$ 9 ! r$ light %all be able to give t light ! lea/ blue t9cture1 or any o!r diff]5t f r$2 nor %all m9ium 9 ! indigo or violet light exhibit ! lea/ appe>ance ( r$1 or any o!r col\r di/9ct f t x is plac$ 94 ,! only diff]5ce is1 t ea* ( ^! bodies appe>s mo/ lum9\s & bright 9 ! col\r1 :i* corresponds ) t x exhibits 9 ! day light1 & dimm$ 9 ! col\rs mo/ remote f t2 t is1 ?\gh m9ium & bise plac$ 9 blue light %all bo? appe> blue1 yet ! bise %all appe> ( a bright blue1 & ! m9ium ( a dusky & obscure blue3 b if m9ium & bise be comp>$ toge!r 9 r$ light1 ! m9ium %all af=d a brisk r$1 ! bise a dull] col\r1 ?\gh ( ! same species4 #ag4 ,,& ?is n only proves ! immutability ( all ^! simple & uncomp\nd$ col\rs2 b likewise unfolds ! :ole my/]y1 :y bodies appe> 9 op5 day-light ( su* diff]5t col\rs1 x consi/+ 9 no?+ m ?an ?is1 t :]eas ! :ite light ( ! day is compos$ ( all sorts ( col\rs1 "s bodies reflect ! rays ( "o sort 9 great] abundance ?an ! rays ( any o!r#bhe4 ,?\gh x appe>s by ! =e-cit$ exp]im5t1 t almo/ all ^! bodies reflect "s portion ( ! rays ( e col\r1 & give ! s5se ( p>ticul> col\rs only by ! pr$om9ancy ( "s sorts ( rays above ! re/4 ,& :at has be=e be5 expla9$ ( compos+ :ite by m+l+ all ! col\rs ( ! spectrum toge!r %ews cle>ly1 t no?+ m is requir$ to make bodies look :ite1 ?an a p[] to reflect indiff]5tly rays ( e col\r4 ,b ?is w m fully appe> by ! foll[+ me?od3 if ne> ! col\r$ spectrum 9 our fir/ exp]im5t a piece ( :ite pap] be s held1 z to be illum9at$ equally by all ! p>ts ( t spectrum1 x %all appe> :ite2 :]eas if x be held ne>] to ! r$ end ( ! image1 ?an to ! o!r1 x %all turn r$di%2 if ne>] ! blue end1 x %all seem blui%#bhf4 #ah4 ,,our indefatigable & circumspect au?or f>!r exam9$ 8 !ory by mix+ ! p[d]s :i* pa9t]s use ( sev]al col\rs1 9 ord] if possible to produce a :ite p[d] by su* a composition#bhg4 ,b 9 ?is he f\nd "s difficulties = ! foll[+ reasons4 ,ea* ( ^! col\r$ p[d]s reflects b "p ( ! light1 :i* is ca/ ^u !m2 ! r$ p[d]s reflect+ little gre5 or blue1 & ! blue p[d]s reflect+ v little r$ or yell[1 nor ! gre5 p[d]s reflect+ ne> s mu* ( ! r$ or indigo & purple1 z ( ! o!r col\rs3 & besides1 :5 any ( ^! are exam9$ 9 homog5eal light1 z our au?or calls ! col\rs ( ! prism1 :5 well sep>at$1 ?\gh ea* appe>s m bright & lum9\s 9 its own day-light col\r1 ?an 9 any o!r2 yet :ite bodies1 suppose :ite pap] = in/ance1 9 ^? v col\rs exce$ ^! col\r$ bodies !mselves 9 brightness2 s t :ite bodies reflect n only m ( ! :ole light ?an col\r$ bodies d 9 ! day-light1 b ev5 m ( t v col\r :i* !y reflect mo/ copi\sly4 ,all :i* consid]ations make x manife/ t a mixture ( ^! w n reflect s great a quantity ( light1 z a :ite body ( ! same size2 & !re=e w compose su* a col\r z w\ld result f a mixture ( :ite & black1 su* z are all grey & dun col\rs1 r ?an a /rong :ite4 ,n[ su* a col\r he comp\nd$ ( c]ta9 +r$i5ts1 :i* he p>ticul>ly sets d[n1 9 s mu* t :5 ! composition 0 /rongly illum9at$ by ! sun's direct beams1 x w\ld appe> mu* :it] ?an ev5 :ite pap]1 if consid]ably %ad$4 ,nay he f\nd by trials h[ to proportion ! degree ( illum9ation ( ! mixture & pap]1 s t to a spectator at a prop] di/ance x c\ld n well be det]m9$ :i* 0 ! m p]fect col\r2 z he exp]i5c$ n only by himself1 b by ! concurr5t op9ion ( a fri5d1 :o *anc$ to visit him :ile he 0 try+ ?is exp]im5t4 ,i mu/ n "h omit ano!r me?od ( try+ ! :it5ess ( su* a mixture1 propos$ 9 "o ( our au?or's lett]s on ?is subject#bhh3 :i* is to enlight5 ! composition by a beam ( ! sun let into a d>k5$ room1 & !n to receive ! light reflect$ f x ^u a piece ( :ite pap]1 obs]v+ :e!r ! pap] appe>s :ite by t reflection2 = if x does1 x gives pro( ( ! composition's be+ :ite2 because :5 ! pap] receives ! reflection f any col\r$ body1 x looks ( t col\r4 ,agreeable to ?is is ! trial he made ^u wat] impregnat$ ) soap1 & agitat$ into a fro?#bhi3 = :5 ?is fro? aft] "s %ort "t exhibit$ ^u ! little bubbles1 :i* compos$ x1 a great v>iety ( col\rs1 ?\gh ^! col\rs to a spectator at a small di/ance discov]'d !mselves di/9ctly2 yet :5 ! eye 0 s f> remov$1 t ea* little bubble c\ld no long] be di/+ui%$1 ! :ole fro? by ! mixture ( all ^! col\rs appe>$ int5sly :ite4 #ai4 ,,our au?or hav+ fully satisfi$ himself by ^! & _m o!r exp]im5ts1 :at ! result is ( mix+ toge!r all ! prismatic col\rs2 he proce$s 9 ! next place to exam9e1 :e!r ?is appe>ance ( :it5ess be rais$ by ! rays ( ^! diff]5t k9ds act+ s1 :5 !y meet1 ^u "o ano!r1 z to cause ea* ( !m to impress ! s5se ( :it5ess ^u ! optic n]ve2 or :e!r ea* ray does n make ^u ! organ ( sight ! same impression1 z :5 sep>ate & alone2 s t ! idea ( :it5ess is n excit$ by ! impression f any "o "p ( ! rays1 b results f ! mixture ( all ^? diff]5t s5sations4 ,& t ! latt] s5tim5t is ! true "o1 he ev9ces by und5iable exp]im5ts4 #bj4 ,,9 p>ticul> ! =ego+ exp]im5t#bij1 :]e9 ! convex glass 0 us$1 furni%es pro(s ( ?is3 9 t :5 ! pap] is br\ght into ! situation 1 beyond1 beyond ,n ! col\rs1 t at ,n disappe>$1 beg9 to em]ge aga92 :i* %ews t by m+l+ at ,n !y did n lose _! colorific qualities1 ?\gh = "s reason !y lay conceal$4 ,?is f>!r appe>s by t "p ( ! exp]im5t1 :5 ! pap]1 :ile 9 ! focus1 0 direct$ to be encl9$ diff]5t ways2 = :5 ! pap] 0 9 su* a situation1 t x mu/ ( necessity reflect ! rays1 :i* be=e _! arrival at ! po9t ,n w\ld h giv5 a blue col\r1 ^? rays 9 ?is v po9t itself by ab\nd+ 9 ! reflect$ light t+$ x ) ! same col\r2 s :5 ! pap] reflects mo/ copi\sly ! rays1 :i* be=e !y come to ! po9t ,n exhibit r$ness1 ^? same rays t9cture ! light reflect$ by ! pap] f t v po9t ) _! own prop] col\r4 #ba4 ,,!re is a c]ta9 condition relat+ to sight1 :i* af=ds an opportunity ( exam9+ ?is /ill m fully3 x is ?is1 t ! impressions ( light rema9 "s %ort space ^u ! eye2 z :5 a burn+ coal is :irl'd ab\t 9 a circle1 if ! motion be v quick1 ! eye %all n be able to di/+ui% ! coal1 b %all see an entire circle ( fire4 ,! reason ( :i* appe>ance is1 t ! impression made by ! coal ^u ! eye 9 any "o situation is n worn out1 be=e ! coal returns aga9 to ! same place1 & r5ews ! s5sation4 ,?is gives our au?or ! h9t to try1 :e!r ^! col\rs might n be transmitt$ successively to ! eye s quick1 t no "o ( ! col\rs %\ld be di/9ctly p]ceiv$1 b ! mixture ( ! s5sations %\ld produce a uni=m :it5ess2 :5 ! rays c\ld n act ^u ea* o!r1 because !y nev] %\ld meet1 b come to ! eye "o aft] ano!r4 ,& ?is ?\ght he execut$ by ! foll[+ exp$i5t#bia4 ,he made an in/rum5t 9 %ape l a comb1 :i* he appli$ ne> ! convex glass1 s t by mov+ x up & d[n sl[ly ! tee? ( x might int]cept sometimes "o & sometimes ano!r col\r2 & accord+ly ! light reflect$ f ! pap]1 plac$ at ,n1 %\ld *ange col\r cont9ually4 ,b n[ :5 ! comb-l in/rum5t 0 mov$ v quick1 ! eye lo/ all preception ( ! di/9ct col\rs1 :i* came to x f "t to "t1 a p]fect :it5ess result+ f ! mixture ( all ^? di/9ct impressions 9 ! s5sorium4 ,n[ 9 ?is case !re c be no suspicion ( ! sev]al col\r$ rays act+ ^u "o ano!r1 & mak+ any *ange 9 ea* o!r's mann] ( affect+ ! eye1 see+ !y d n s mu* z meet toge!r !re4 #bb4 ,,our au?or f>!r tea*es u h[ to view ! spectrum ( col\rs produc$ 9 ! fir/ exp]im5t ) ano!r prism1 s t x %all appe> to ! eye "u ! %ape ( a r\nd spot & p]fectly :ite#bib4 ,& 9 ?is case if ! comb be us$ to int]cept alt]nately "s ( ! col\rs1 :i* compose ! spectrum1 ! r\nd spot %all *ange its col\r accord+ to ! col\rs int]cept$2 b if ! comb be mov$ too swiftly = ^? *anges to be di/9ctly p]ceiv$1 ! spot %all seem always :ite1 z be=e#bic4 #bc4 ,,besides ?is :it5ess1 :i* results f an univ]sal composition ( all sorts ( col\rs1 our au?or p>ticul>ly expla9s ! effects ( o!r less comp\nd$ mixtures2 "s ( :i* comp\nd o!r col\rs l "s ( ! simple ones1 b o!rs produce col\rs diff]5t f any ( !m4 ,= in/ance1 a mixture ( r$ & yell[ comp\nd a col\r l 9 appe>ance to ! orange1 :i* 9 ! spectrum lies betwe5 !m2 z a composition ( yell[ & blue is made use ( 9 all dyes to make a gre54 ,b r$ & violet purple comp\nd$ make purples unlike to any ( ! prismatic col\rs1 & ^! jo9$ ) yell[ or blue make yet new col\rs4 ,besides "o rule is "h to be obs]v$1 t :5 _m diff]5t col\rs are mix$1 ! col\r :i* arises f ! mixture gr[s languid & deg5]ates into :it5ess4 ,s :5 yell[ gre5 & blue are mix$ toge!r1 ! comp\nd w be gre52 b if to ?is y add r$ & purple1 ! col\r %all fir/ gr[ dull & less vivid1 & at l5g? by add+ m ( ^! col\rs x %all turn to :it5ess1 or "s o!r col\r#bid4 #bd4 ,,only "h is "o ?+ rem>kable ( ^? comp\nd$ col\rs1 :i* are l 9 appe>ance to ! simple ones2 t ! simple ones :5 view$ ?r\gh a prism %all /ill reta9 _! col\r1 b ! comp\nd$ col\rs se5 ?r\gh su* a glass %all be p>t$ into ! simple ones ( :i* !y are ! aggregate4 ,& = ?is reason any body illum9at$ by ! simple light %all appe> ?r\gh a prism di/9ctly1 & h its m9ute/ p>ts obs]vable1 z may easily be tri$ ) flies1 or o!r su* little bodies1 :i* h v small p>ts2 b ! same view$ 9 ?is mann] :5 enlight5'd ) comp\nd$ col\rs %all appe> confus$1 _! smalle/ p>ts n be+ di/+ui%able4 ,h[ ! prism sep>ates ^! comp\nd$ col\rs1 z likewise h[ x divides ! light ( ! sun into its col\rs1 has n yet be5 expla9$2 b is res]v$ = our ?ird *apt]4 #be4 ,,9 ! mean "t :at has be5 said1 ,i hope1 w suffice to give a ta/e ( our au?or's way ( argu+1 & 9 "s measure to illu/rate ! proposition laid d[n 9 ?is *apt]4 #bf4 ,,!re are me?ods ( sep>at+ ! het]og5e\s rays ( ! sun's light by reflection1 :i* p]fectly conspire ) & confirm ?is reason+4 ,"o ( :i* ways may be ?is4 ,let ,a ,b 79 fig4 #abi7 repres5t ! w9d[ %utt] ( a d>k5$ room2 ,c a hole to let 9 ! sun's rays2 ,d ,e ,f1 ,g ,h ,i two prisms s appli$ toge!r1 t ! sides ,e ,f & ,g ,i be contigu\s1 & ! sides ,d ,f1 ,g ,h p>allel2 by ?is means ! light w pass ?r\gh !m )\t any sep>ation into col\rs3 b if x be aft]w>ds receiv$ by a ?ird prism ,i ,k ,l1 x %all be divid$ s z to =m ^u any :ite body ,p ,q ! usual col\rs1 violet at m1 blue at n1 gre5 at o1 yell[ at r1 & r$ at s4 ,b because x nev] happ5s t ! two adjac5t surfaces ,e ,f & ,g ,i p]fectly t\*1 "p only ( ! light incid5t ^u ! surface ,e ,f %all be transmitt$1 & "p %all be reflect$4 ,let n[ ! reflect$ "p be receiv$ by a f\r? prism 1 & pass+ ?r\gh x pa9t ^u a :ite body ! col\rs ( ! prism1 r$ at t1 yell[ at u1 gre5 at w1 blue at x1 violet at y4 ,if ! prisms ,d ,e ,f1 ,g ,h ,i be sl[ly turn$ ab\t :ile !y rema9 contigu\s1 ! col\rs ^u ! body ,p ,q %all n s5sibly *ange _! situation1 till su* "t z ! rays become pretty oblique to ! surface ,e ,f2 b !n ! light incid5t ^u ! surface ,e ,f %all beg9 to be :olly reflect$4 ,& fir/ ( all ! violet light %all be :olly reflect$1 & !reupon w disappe> at m1 appe>+ in/ead !re( at y1 & increas+ ! violet light fall+ !re1 ! o!r col\rs rema9+ z be=e4 ,if ! prisms ,d ,e ,f1 ,g ,h ,i be turn$ a little f>!r ab\t1 t ! incid5t rays become yet m incl9$ to ! surface ,e ,f1 ! blue %all be totally reflect$1 & %all disappe> 9 n1 b appe> at x by mak+ ! col\r !re m int5se4 ,& ! same may be cont9u$1 till all ! col\rs are successively remov$ f ! surface ,p ,q to 4 ,b 9 any case1 suppose :5 ! violet & ! blue h =sak5 ! surface ,p ,q1 & appe> ^u ! surface 1 1 ! gre51 yell[1 & r$ only rema9+ ^u ! surface ,p ,q2 if ! light be receiv$ ^u a pap] held any :]e 9 its :ole passage betwe5 ! light's com+ out ( ! prisms ,d ,e ,f1 ,g ,i ,h & its incid5ce ^u ! prism ,i ,k ,l1 x %all appe> ( ! col\r comp\nd$ ( all ! col\rs se5 ^u ,p ,q2 & ! reflect$ ray1 receiv$ ^u a piece ( :ite pap] held any :]e betwe5 ! prisms ,d ,e ,f & %all exhibit ! col\r comp\nd$ ( ^? ! surface ,p ,q is depriv$ ( mix$ ) ! sun's light3 :]eas be=e any ( ! light 0 reflect$ f ! surface ,e ,f1 ! rays betwe5 ! prisms ,g ,h ,i & ,i ,k ,l w\ld appe> :ite2 z w likewise ! reflect$ ray bo? be=e & aft] ! total reflection1 provid$ ! diff]5ce ( refraction by ! surfaces ,d ,f & ,d ,e be inconsid]able4 ,i call "h ! sun's light :ite1 z ,i h all along done2 b x is m exact to ascribe to x some?+ ( a yell[i% t9cture1 occasion$ by ! bright] col\rs ab\nd+ 9 x2 :i* caution is necess>y 9 exam9+ ! col\rs ( ! reflect$ beam1 :5 all ! violet & blue are 9 x3 = ?is yell[i% turn ( ! sun's light causes ! blue n to be q s visible 9 x1 z x %\ld be1 7 ! light p]fectly :ite2 b makes ! beam ( light incl9e r t[>ds a pale :ite4 ,,*ap4 ,,ii4 ,( ! prop]ties ( ,,bodies1 ^u :i* _! ,,col\rs dep5d4 ,,aft] hav+ %ewn 9 ! la/ *apt]1 t ! diff]5ce betwe5 ! col\rs ( bodies view$ 9 op5 day-light is only ?is1 t "s bodies are dispos$ to reflect rays ( "o col\r 9 ! greate/ pl5ty1 & o!r bodies rays ( "s o!r col\r2 ord] n[ requires u to exam9e m p>ticul>ly into ! prop]ty ( bodies1 :i* gives !m ?is diff]5ce4 ,b ?is our au?or %ews to be no?+ m1 ?an ! diff]5t magnitude ( ! p>ticles1 :i* compose ea* body3 ?is ,i "q n w appe> no small p>adox4 ,& inde$ ?is :ole *apt] w conta9 sc>ce any ass]tions1 b :at w be almo/ incr$ible1 ?\gh ! argum5ts = !m are s /rong & conv9c+1 t !y =ce our ass5t4 ,9 ! =m] *apt] h be5 expla9$ prop]ties ( light1 n 9 ! lea/ ?\ght ( be=e our au?or's discov]y ( !m2 yet are !y n difficult to admit1 z soon z exp]im5ts are kn[n to give pro( ( _! reality2 b "s ( ! propositions to be /at$ "h w1 ,i fe>1 be acc\nt$ almo/ pa/ belief2 not)/&+ t ! argum5ts1 by :i* !y are e/abli%$ are unansw]able4 ,= x is prov$ by our au?or1 t bodies are r5d]$ transp>5t by ! m9ut5ess ( _! pores1 & become opake by hav+ !m l>ge2 & m1 t ! mo/ transp>5t body by be+ r$uc$ to a great ?9ness w become less p]vi\s to ! light4 #b4 ,,b :]eas x _h be5 ! receiv$ op9ion1 & yet rema9s s among all :o h n /udi$ ?is philosophy1 t light is reflect$ f bodies by its imp++ aga9/ _! solid p>ts1 reb\nd+ f !m1 z a t5nis ball or o!r ela/ic sub/ance w\ld d1 :5 /ruck aga9/ any h>d & resi/+ surface2 x w be prop] to beg9 ) decl>+ our au?or's s5tim5t conc]n+ ?is1 :o %ews by _m argum5ts t reflection _c be caus$ by any su* means#bie3 "s few ( 8 pro(s ,i %all set d[n1 ref]r+ ! read] to our au?or himself = ! re/4 #c4 ,,x is well kn[n1 t :5 light falls ^u any transp>5t body1 glass = in/ance1 "p ( x is reflect$ & "p transmitt$2 = :i* x is ready to acc\nt1 by say+ t "p ( ! light ent]s ! pores ( ! glass1 & "p imp+es ^u its solid p>ts4 ,b :5 ! transmitt$ light arrives at ! f>!r surface ( ! glass1 9 pass+ out ( glass into air !re is z /rong a reflection caus$1 or r some?+ /rong]4 ,n[ x is n to be conceiv$1 h[ ! light %\ld f9d z _m solid p>ts 9 ! air to /rike aga9/ z 9 ! glass1 or ev5 a great] numb] ( !m4 ,& to augm5t ! difficulty1 if wat] be plac$ beh9d ! glass1 ! reflection becomes mu* weak]4 ,c we !re=e say1 t wat] has few] solid p>ts = ! light to /rike aga9/1 ?an ! air8 ,& if we %\ld1 :at reason c be giv5 = ! reflection's be+ /rong]1 :5 ! air by ! air-pump is remov$ f beh9d ! glass1 ?an :5 ! air receives ! rays ( light4 ,besides ! light may be s incl9$ to ! h9d] surface ( ! glass1 t x %all :olly be reflect$1 :i* happ5s :5 ! angle :i* ! ray makes ) ! surface does n exce$ ab\t #di degrees2 b if ! incl9ation be a v little increas$1 great "p ( ! light w be transmitt$2 & h[ ! light 9 "o case %\ld meet ) no?+ b ! solid p>ts ( ! air1 & by s small a *ange ( its incl9ation f9d pores 9 great pl5ty1 is :olly inconceivable4 ,x _c be said1 t ! light is reflect$ by /rik+ aga9/ ! solid p>ts ( ! surface ( ! glass2 because )\t mak+ any *ange 9 t surface1 only by plac+ wat] contigu\s to x in/ead ( air1 great "p ( t light %all be transmitt$1 :i* c\ld f9d no passage ?r\gh ! air4 ,moreov] 9 ! la/ exp]im5t recit$ 9 ! prec$+ *apt]1 :5 by turn+ ! prisms ,d ,e ,f1 ,g ,h ,i1 ! blue light became :olly reflect$1 :ile ! re/ 0 mo/ly transmitt$1 no possible reason c be assign$1 :y ! blue-mak+ rays %\ld meet ) no?+ b ! solid p>ts ( ! air betwe5 ! prisms1 & ! re/ ( ! light 9 ! v same obliquity f9d pores 9 abundance4 ,nay f>!r1 :5 two glasses t\* ea* o!r1 no reflection at all is made2 ?\gh x does n 9 ! lea/ appe>1 h[ ! rays %\ld avoid ! solid p>ts ( glass1 :5 contigu\s to o!r glass1 any m ?an :5 contigu\s to air4 ,b 9 ! la/ place ^u ?is supposition x is n to be compreh5d$1 h[ ! mo/ poli%$ sub/ances c\ld reflect ! light 9 t regul> mann] we f9d !y d2 = :5 a poli%$ look+ glass is cov]$ ov] ) quicksilv]1 we _c suppose ! p>ticles ( light s mu* l>g] ?an ^? ( ! quicksilv] t !y %\ld n be scatt]$ z mu* 9 reflection1 z a p>cel ( m>bles ?r[n d[n ^u a rugg$ pavem5t4 ,! only cause ( s uni=m & regul> a reflection mu/ be "s m secret cause1 uni=mly spread ov] ! :ole surface ( ! glass4 #d4 ,,b n[1 s9ce ! reflection ( light f bodies does n dep5d ^u its imp++ aga9/ _! solid p>ts1 "s o!r reason mu/ be s\ght =4 ,& fir/ x is pa/ d\bt t ! lea/ p>ts ( almo/ all bodies are transp>5t1 ev5 ! microscope %ew+ z mu*#bif2 besides t x may be exp]i5c$ by ?is me?od4 ,take any ?9 plate ( ! opake/ body1 & apply x to a small hole design$ = ! admission ( light into a d>k5$ room2 h[ev] opake t body may seem 9 op5 day-light1 x %all "u ^! circum/ances suffici5tly discov] its transp>5cy1 provid$ only ! body be v ?94 ,:ite metals inde$ d n easily %ew !mselves transp>5t 9 ^! trials1 !y reflect+ almo/ all ! light incid5t ^u !m at _! fir/ sup]ficies2 ! cause ( :i* w appe> 9 :at foll[s#big4 ,b yet ^! sub/ances1 :5 r$uc$ into p>ts ( extraord9>y m9ut5ess by be+ dissolv$ 9 aqua =tis or ! l corrod+ liquors d also become transp>5t4 #e4 ,,s9ce !re=e ! light f9ds free passage ?r\gh ! lea/ p>ts ( bodies1 let u consid] ! l>g5ess ( _! pores1 & we %all f9d1 t :5ev] a ray ( light has pass$ ?r\gh any p>ticle ( a body1 & is come to its f>!r surface1 if x f9ds !re ano!r p>ticle contigu\s1 x w )\t int]ruption pass into t p>ticle2 j z light w pass ?r\gh "o piece ( glass into ano!r piece 9 contact ) x )\t any imp$im5t1 or any "p be+ reflect$3 b z ! light 9 pass+ out ( glass1 or any o!r transp>5t body1 %all "p ( x be reflect$ back1 if x ent] into air or o!r transp>5t body ( a diff]5t d5sity f t x passes out (2 ! same ?+ w happ5 9 ! light's passage ?r\gh any p>ticle ( a body1 :5ev] at its exit out ( t p>ticle x meets no o!r p>ticle contigu\s1 b mu/ ent] into a pore1 = 9 ?is case x %all n all pass ?r\gh1 b "p ( x be reflect$ back4 ,?us w ! light1 e "t x ent]s a pore1 be 9 "p reflect$2 s t no?+ m seems necess>y to opacity1 ?an t ! p>ticles1 :i* compose any body1 t\* b 9 v few places1 & t ! pores ( x are num]\s & l>ge1 s t ! light may 9 "p be reflect$ f x1 & ! o!r "p1 :i* ent]s too deep to be return$ out ( ! body1 by num]\s reflections may be /ifl$ & lo/#bih2 :i* 9 all probability happ5s1 z (t5 z x imp+es aga9/ ! solid "p ( ! body1 all ! light :i* does s n be+ reflect$ back1 b /opt1 & depriv$ ( any f>!r motion#bii4 #f4 ,,?is notion ( opacity is greatly confirm$ by ! obs]vation1 t opake bodies become transp>5t by fill+ up ! pores ) any sub/ance ( ne> ! same d5sity ) _! p>ts4 ,z :5 pap] is wet ) wat] or oyl2 :5 l9n5 clo? is ei!r dipt 9 wat]1 oyl$1 or v>ni%$2 or ! oculus mundi /one /eep$ 9 wat]#cjj4 ,all :i* exp]im5ts confirm bo? ! fir/ ass]tion1 t light is n reflect$ by /rik+ ^u ! solid p>ts ( bodies2 & also ! second1 t its passage is ob/ruct$ by ! reflections x und]goes 9 ! pores2 s9ce we f9d x 9 ^! trials to pass 9 great] abundance ?r\gh bodies1 :5 ! numb] ( _! solid p>ts is increas$1 only by tak+ away 9 great measure ^? reflections2 :i* fill+ ! pores ) a sub/ance ( ne> ! same d5sity ) ! p>ts ( ! body w d4 ,besides z fill+ ! pores ( a d>k body makes x transp>5t2 s on ! o!r h& evacuat+ ! pores ( a body transp>5t1 or sep>at+ ! p>ts ( su* a body1 r5d]s x opake4 ,z salts or wet pap] by be+ dri$1 glass by be+ r$uc$ to p[d] or ! surface made r\gh2 & x is well kn[n t glass vessels discov] cracks 9 !m by _! opacity4 ,j s wat] itself becomes imp]vi\s to ! light by be+ =m$ into _m small bubbles1 :e!r 9 fro?1 or by be+ mix$ & agitat$ ) any quantity ( a liquor ) :i* x w n incorporate1 su* z oyl ( turp5t9e1 or oyl olive4 #g4 ,a ,,c]ta9 electrical exp]im5t made by ,mr4 ,,hauksbee may n p]haps be useless to cle> up ! pres5t speculation1 by %ew+ t some?+ m is necess>y besides m]e porosity = transmitt+ freely o!r f9e sub/ances4 ,! exp]im5t is ?is2 t a glass cane rubb$ till x put =? its electric quality w\ld agitate leaf brass inclos$ "u a glass vessel1 ?\gh n at s great a di/ance1 z if no body _h int]v5$2 yet ! same cane w\ld lose all its influ5ce on ! leaf brass by ! int]position ( a piece ( ! f9e/ musl91 ^: pores are imm5sely l>g] & m pat5t ?an ^? ( glass4 #h4 ,,?us ,i h endeav\r$ to smoo? my way1 z mu* z ,i c\ld1 to ! unfold+ yet great] secrets 9 nature2 = ,i %all n[ proce$ to %ew ! reason :y bodies appe> ( diff]5t col\rs4 ,my read] no d\bt w be suffici5tly surpriz$1 :5 ,i in=m him t ! k ( ?is is d$uc$ f t ludicr\s exp]im5t1 ) :i* *ildr5 div]t !mselves 9 bl[+ bubbles ( wat] made t5aci\s by ! solution ( soap4 ,& t ^! bubbles1 z !y gradually gr[ ?9n] & ?9n] till !y break1 *ange successively _! col\rs f ! same pr9ciple1 z all natural bodies pres]ve !irs4 #i4 ,,our au?or aft] prep>+ wat] ) soap1 s z to r5d] x v t5aci\s1 blew x up into a bubble1 & plac+ x "u a glass1 t x might n be irregul>ly agitat$ by ! air1 obs]v$ z ! wat] by subsid+ *ang$ ! ?ickness ( ! bubble1 mak+ x gradually less & less till ! bubble broke2 !re successively appe>$ col\rs at ! top ( ! bubble1 :i* spread !mselves into r+s surr\nd+ ! top & desc5d+ m & m1 till !y vani%$ at ! bottom 9 ! same ord] 9 :i* !y appe>$#cja4 ,! col\rs em]g$ 9 ?is ord]3 fir/ r$1 !n blue2 to :i* succe$$ r$ a second "t1 & blue imm$iately foll[$2 aft] t r$ a ?ird "t1 succe$$ by blue2 to :i* foll[$ a f\r? r$1 b succe$$ by gre52 aft] ?is a m num]\s ord] ( col\rs1 fir/ r$1 !n yell[1 next gre51 & aft] t blue1 & at la/ purple2 !n aga9 r$1 yell[1 gre51 blue1 violet foll[$ ea* o!r 9 ord]2 & 9 ! la/ place r$1 yell[1 :ite1 blue2 to :i* succe$$ a d>k spot1 :i* reflect$ sc>ce any light1 ?\gh our au?or f\nd x did make "s v obscure reflection1 = ! image ( ! sun or a c&le might be fa9tly disc]n$ ^u x2 & ?is la/ spot spread itself m & m1 till ! bubble at la/ broke4 ,^! col\rs 7 n simple & uncomp\nd$ col\rs1 l ^? :i* are exhibit$ by ! prism1 :5 due c>e is tak5 to sep>ate !m2 b 7 made by a v>i\s mixture ( ^? simple col\rs1 z w be %ewn 9 ! next *apt]3 :5ce ^! col\rs1 to :i* ,i h giv5 ! "n ( blue1 gre51 or r$1 7 n all alike1 b diff]$ z foll[s4 ,! blue1 :i* appe>$ next ! d>k spot1 0 a pure col\r1 b v fa9t1 resembl+ ! sky-col\r2 ! :ite next to x a v /rong & int5se :ite1 bright] mu* ?an ! :ite1 :i* ! bubble reflect$1 be=e any ( ! col\rs appe>$4 ,! yell[ :i* prec$$ ?is 0 at fir/ pretty good1 b soon grew dilute2 & ! r$ :i* w5t be=e ! yell[ at fir/ gave a t9cture ( sc>let incl9+ to violet1 b soon *ang$ into a bright] col\r2 ! violet ( ! next s]ies 0 deep ) little or no r$ness 9 x2 ! blue a brisk col\r1 b came mu* %ort ( ! blue 9 ! next ord]2 ! gre5 0 b dilute & pale2 ! yell[ & r$ 7 v bright & full1 ! be/ ( all ! yell[s :i* appe>$ among any ( ! col\rs3 9 ! prec$+ ord]s ! purple 0 r$di%1 b ! blue1 z 0 j n[ said1 ! brighte/ ( all2 ! gre5 pretty lively bett] ?an 9 ! ord] :i* appe>$ be=e x1 ?\gh t 0 a good will[ gre52 ! yell[ b small 9 quantity1 ?\gh bright2 ! r$ ( ?is ord] n v pure3 ^? :i* appe>$ be=e yet m obscure1 be+ v dilute & dirty2 z 7 likewise ! ?ree fir/ blues4 #aj4 ,,n[ x is evid5t1 t ^! col\rs arose at ! top ( ! bubble1 z x grew by degrees ?9n] & ?9n]3 b :at ! express ?ickness ( ! bubble 01 :]e ea* ( ^! col\rs appe>$ ^u x1 c\ld n be det]m9$ by ^! exp]im5ts2 b 0 f\nd by ano!r means1 viz4 by tak+ ! object glass ( a long telescope1 :i* is 9 a small degree convex1 & plac+ x ^u a flat glass1 s z to t\* x 9 "o po9t1 & !n wat] be+ put betwe5 !m1 ! same col\rs appe>$ z 9 ! bubble1 9 ! =m ( circles or r+s surr\nd+ ! po9t :]e ! glasses t\*$1 :i* appe>$ black = want ( any reflection f x1 l ! top ( ! bubble :5 ?9ne/#cjb3 next to ?is spot lay a blue circle1 & next )\t t a :ite "o2 & s on 9 ! same ord] z be=e1 reckon+ f ! d>k spot4 ,& h5ce=w>d ,i %all speak ( ea* col\r1 z be+ ( ! fir/1 second1 or any foll[+ ord]1 z x is ! fir/1 second1 or any foll[+ "o1 c\nt+ f ! black spot 9 ! c5t] ( ^! r+s2 :i* is contr>y to ! ord] 9 :i* ,i mu/ h m5tion$ !m1 if ,i %\ld h reput$ !m ! fir/1 second1 or ?ird1 c4 9 ord]1 z !y arise aft] "o ano!r ^u ! top ( ! bubble4 #aa4 ,b n[ by measur+ ! diamet]s ( ea* ( ^! r+s1 & kn[+ ! convexity ( ! telescope glass1 ! ?ickness ( ! wat] at ea* ( ^? r+s may be det]m9$ ) great exactness3 = in/ance ! ?ickness ( x1 :]e ! :ite light ( ! fir/ ord] is reflect$1 is ab\t #c su* p>ts1 ( :i* an in* conta9s #ajjjjjjcjc4 ,& ?is measure gives ! ?ickness ( ! bubble1 :]e x appe>$ ( ?is :ite col\r1 z well z ( ! wat] betwe5 ! glasses2 ?\gh ! transp>5t body :i* surr\nds ! wat] 9 ^! two cases be v diff]5t3 = our au?or f\nd1 t ! condition ( ! ambi5t body w\ld n alt] ! species ( ! col\r at all1 ?\gh x might its /r5g? & brightness2 = pieces ( ,muscovy glass1 :i* 7 s ?9 z to appe> col\r$ by be+ wet ) wat]1 w\ld h _! col\rs fad$ & made less bright !reby2 b he c\ld n obs]ve _! species at all to be *ang$4 ,s t ! ?ickness ( any transp>5t body det]m9es its col\r1 :atev] body ! light passes ?r\gh 9 com+ to x#cjd4 #ab4 ,,b x 0 f\nd t diff]5t transp>5t bodies w\ld n "u ! same ?icknesses exhibit ! same col\rs3 = if ! =em5tion$ glasses 7 laid ^u ea* o!r )\t any wat] betwe5 _! surfaces1 ! air itself w\ld af=d ! same col\rs z ! wat]1 b m exp&$1 insomu* t ea* r+ _h a l>g] diamet]1 & all 9 ! same proportion4 ,s t ! ?ickness ( ! air prop] to ea* col\r 0 9 ! same proportion l>g]1 ?an ! ?ickness ( ! wat] appropriat$ to ! same#cje4 #ac4 ,,if we exam9e ) c>e all ! circum/ances ( ^! col\rs1 :i* w be enum]at$ 9 ! next *apt]1 we %all n be surpriz$1 t our au?or takes !m to be> a great analogy to ! col\rs ( natural bodies#cjf4 ,= ! regul>ity ( ^? v>i\s & /range appe>ances relat+ to !m1 :i* makes ! mo/ my/]i\s "p ( ! action betwe5 light & bodies1 z ! next *apt] w %ew1 is suffici5t to conv9ce u t ! pr9ciple1 f :i* !y fl[1 is ( ! greate/ importance 9 ! frame ( nature2 & !re=e )\t "q is design$ = no less a purpose ?an to give bodies _! v>i\s col\rs1 to :i* end x seems v fitly suit$4 ,= if any su* transp>5t sub/ance ( ! ?ickness prop] to produce any "o col\r %\ld be cut into sl5d] ?reads1 or brok5 into fragm5ts1 x does n appe> b ^! %\ld reta9 ! same col\r2 & a heap ( su* fragm5ts %\ld frame a body ( t col\r4 ,s t ?is is )\t dispute ! cause :y bodies are ( ?is or ! o!r col\r1 t ! p>ticles ( :i* !y are compos$ are ( diff]5t sizes4 ,:i* is f>!r confirm$ by ! analogy betwe5 ! col\rs ( ?9 plates1 & ! col\rs ( _m bodies4 ,= example1 ^! plates d n look ( ! same col\r :5 view$ obliquely1 z :5 se5 direct2 = if ! r+s & col\rs betwe5 a convex & plane glass are view$ fir/ 9 a direct mann]1 & !n at diff]5t degrees ( obliquity1 ! r+s w be obs]v$ to dilate !mselves m & m z ! obliquity is increas$#cjg2 :i* %ews t ! transp>5t sub/ance betwe5 ! glasses does n exhibit ! same col\r at ! same ?ickness 9 all situations ( ! eye3 j s ! col\rs 9 ! v same "p ( a peacock's tail *ange1 z ! tail *anges po/ure 9 respect ( ! sight4 ,also ! col\rs ( silks1 clo?s1 & o!r sub/ances1 :i* wat] or oyl c intimately p5etrate1 become fa9t & dull by ! bodies be+ wet ) su* fluids1 & recov] _! brightness aga9 :5 dry2 j z x 0 be=e said t plates ( ,muscovy glass grew fa9t & dim by wett+4 ,to ?is may be add$1 t ! col\rs :i* pa9t]s use w be a little *ang$ by be+ gr\nd v elaborately1 )\t "q by ! dim9ution ( _! p>ts4 ,all :i* p>ticul>s1 & _m m t might be extract$ f our au?or1 give abundant pro( ( ! pres5t po9t4 ,i %all only subjo9 "o m3 ^! transp>5t plates transmit ?r\gh !m all ! light !y d n reflect2 s t :5 look$ ?r\gh !y exhibit ^? col\rs1 :i* result f ! depriv+ :ite light ( ! col\r reflect$4 ,?is may commodi\sly be try$ by ! glasses s (t5 m5tion$2 :i* if look$ ?r\gh exhibit col\r$ r+s z by reflect$ light1 b 9 a contr>y ord]2 = ! middle spot1 :i* 9 ! o!r view appe>s black = want ( reflect$ light1 n[ looks p]fectly :ite1 opposite to ! blue circle2 next )\t ?is spot ! light appe>s t+$ ) a yell[i% r$2 :]e ! :ite circle appe>$ be=e1 x n[ seems d>k2 & s ( ! re/#cjh4 ,n[ 9 ! same mann]1 ! light transmitt$ ?r\gh foliat$ gold into a d>k5$ room appe>s gre5i% by ! loss ( ! yell[ light1 :i* gold reflects4 #ad4 ,,h5ce x foll[s1 t ! col\rs ( bodies give a v probable gr\nd = mak+ conjecture conc]n+ ! magnitude ( _! con/itu5t p>ticles#cji4 ,my reason = call+ x a conjecture is1 its be+ difficult to fix c]ta9ly ! ord] ( any col\r4 ,! gre5 ( vegetables our au?or judges to be ( ! ?ird ord]1 p>tly because ( ! int5s5ess ( _! col\r2 & p>tly f ! *anges !y suff] :5 !y )]1 turn+ at fir/ into a gre5i% or m p]fect yell[1 & aft]w>ds "s ( !m to an orange or r$2 :i* *anges seem to be effect$ f _! r++ p>ticles gr[+ d5s] by ! exhalation ( _! moi/ure1 & p]haps augm5t$ likewise by ! accretion ( ! e>?y & oily p>ts ( t moi/ure4 ,h[ ! m5tion$ col\rs %\ld arise f increas+ ! bulk ( ^? p>ticles1 is evid5t2 see+ ^? col\rs lie )\t ! r+ ( gre5 betwe5 ! glasses1 & are !re=e =m$ :]e ! transp>5t sub/ance :i* reflects !m is ?ick]4 ,& t ! augm5tation ( ! d5sity ( ! colorific p>ticles w conspire to ! production ( ! same effect1 w be evid5t2 if we rememb] :at 0 said ( ! diff]5t size ( ! r+s1 :5 air 0 includ$ betwe5 ! glasses1 f _! size :5 wat] 0 betwe5 !m2 :i* %ew$ t a sub/ance ( a great] d5sity ?an ano!r gives ! same col\r at a less ?ickness4 ,n[ ! *anges likely to be wr\ght 9 ! d5sity or magnitude ( ! p>ts ( vegetables by )]+ seem n great]1 ?an are suffici5t to *ange _! col\r into ^? ( ! same ord]2 b ! yell[ & r$ ( ! f\r? ord] are n full en\gh to agree ) ^?1 into :i* ^! sub/ances *ange1 nor is ! gre5 ( ! second suffici5tly good to be ! col\r ( vegetables2 s t _! col\r mu/ ( necessity be ( ! ?ird ord]4 #ae4 ,,! blue col\r ( syrup ( violets our au?or supposes to be ( ! ?ird ord]2 = acids1 z v9eg>1 ) ?is syrup *ange x r$1 & salt ( t>t> or o!r alcalies mix$ !re) turn x gre54 ,b if ! blue col\r ( ! syrup 7 ( ! second ord]1 ! r$ col\r1 :i* acids by att5uat+ its p>ts give x1 mu/ be ( ! fir/ ord]1 & ! gre5 giv5 x by alcalies by incrassat+ its p>ticles %\ld be ( ! second2 :]eas nei!r ( ^? col\rs is p]fect en\gh1 especially ! gre51 to answ] ^? produc$ by ^! *anges2 b ! r$ may well en\gh be all[$ to be ( ! second ord]1 & ! gre5 ( ! ?ird2 9 :i* case ! blue mu/ be likewise ( ! ?ird ord]4 #af4 ,,! azure col\r ( ! skies our au?or takes to be ( ! fir/ ord]1 :i* requires ! smalle/ p>ticles ( any col\r1 & !re=e mo/ l to be exhibit$ by vap\rs1 be=e !y h suffici5tly coalesc$ to produce cl\ds ( o!r col\rs4 #ag4 ,,! mo/ int5se & lum9\s :ite is ( ! fir/ ord]1 if less /rong x is a mixture ( ! col\rs ( all ! ord]s4 ,( ! latt] sort he takes ! col\r ( l9n51 pap]1 & su* l sub/ances to be2 b :ite metals to be ( ! =m] sort4 ,! argum5ts = x are ^!4 ,! opacity ( all bodies has be5 %ewn to arise f ! numb] & /r5g? ( ! reflections made )9 !m2 b all exp]im5ts %ew1 t ! /ronge/ reflection is made at ^? surfaces1 :i* int]c$e transp>5t bodies diff]+ mo/ 9 d5sity4 ,among o!r in/ances ( ?is1 ! exp]im5ts be=e u af=d "o2 = :5 air only is includ$ betwe5 ! glasses1 ! col\r$ r+s are n only m dilat$1 z has be=e be5 said1 ?an :5 wat] is betwe5 !m2 b are likewise mu* m lum9\s & bright4 ,x foll[s !re=e1 t :atev] m$ium p]vades ! pores ( bodies1 if s be !re is any1 ^? sub/ances mu/ be mo/ opake1 ! d5sity ( ^: p>ts diff]s mo/ f ! d5sity ( ! m$ium1 :i* fills _! pores4 ,b x has be5 suffici5tly prov$ 9 ! =m] "p ( ?is tract1 t !re is no v d5se m$ium lodg+ 91 at lea/ p]vad+ at lib]ty ! pores ( bodies4 ,& x is f>!r prov$ by ! pres5t exp]im5ts4 ,= :5 air is inclos$ by ! d5s] sub/ance ( glass1 ! r+s dilate !mselves1 z has be5 said1 by be+ view$ obliquely2 ?is !y d s v mu*1 t at diff]5t obliquities ! same ?ickness ( air w exhibit all sorts ( col\rs4 ,! bubble ( wat]1 ?\gh surr\nd$ ) ! ?9n] sub/ance ( air1 does likewise *ange its col\r by be+ view$ obliquely2 b n any ?+ ne> s mu*1 z 9 ! o!r case2 = 9 t ! same col\r might be se51 :5 ! r+s 7 view$ mo/ obliquely1 at m ?an twelve times ! ?ickness x appe>$ at "u a direct view2 :]eas 9 ?is o!r case ! ?ickness 0 nev] f\nd consid]ably above half z mu* aga94 ,n[ ! col\rs ( bodies n dep5d+ only on ! light1 t is incid5t ^u !m p]p5dicul>ly1 b likewise ^u t1 :i* falls on !m 9 all degrees ( obliquity2 if ! m$ium surr\nd+ _! p>ticles 7 d5s] ?an ^? p>ticles1 all sorts ( col\rs mu/ ( necessity be reflect$ f !m s copi\sly1 z w\ld make ! col\rs ( all bodies :ite1 or grey1 or at be/ v dilute & imp]fect4 ,b on ! o!r h&1 if ! m$ium 9 ! pores ( bodies be mu* r>] ?an _! p>ticles1 ! col\r reflect$ w be s little *ang$ by ! obliquity ( ! rays1 t ! col\r produc$ by ! rays1 :i* fall ne> ! p]p5dicul>1 may s mu* ab\nd 9 ! reflect$ light1 z to give ! body _! col\r ) little allay4 ,to ?is may be add$1 t :5 ! diff]5ce ( ! contigu\s transp>5t sub/ances is ! same1 a col\r reflect$ f ! d5s] sub/ance r$uc$ into a ?9 plate & surr\nd$ by ! r>] w be m brisk1 ?an ! same col\r w be1 :5 reflect$ f a ?9 plate =m$ ( ! r>] sub/ance1 & surr\nd$ by ! d5s]2 z our au?or exp]i5c$ by bl[+ glass v ?9 at a lamp furnace1 :i* exhibit$ 9 ! op5 air m vivid col\rs1 ?an ! air does betwe5 two glasses4 ,f ^! consid]ations x is manife/1 t if all o!r circum/ances are alike1 ! d5se/ bodies w be mo/ opake4 ,b x 0 obs]v$ be=e1 t ^! :ite metals c h>dly be made s ?91 except by be+ dissolv$ 9 corrod+ liquors1 z to be r5dr$ transp>5t2 ?\gh none ( !m are s d5se z gold1 :i* proves _! great opacity to h "s o!r cause besides _! d5sity2 & none is m fit to produce ?is1 ?an su* a size ( _! p>ticles1 z qualifies !m to reflect ! :ite ( ! fir/ ord]4 #ah4 ,,= produc+ black ! p>ticles ought to be small] ?an = exhibit+ any ( ! col\rs1 viz4 ( a size answ]+ to ! ?ickness ( ! bubble1 :]e by reflect+ little or no light x appe>s col\rless2 b yet !y mu/ n be too small1 = t w make !m transp>5t ?r\gh defici5cy ( reflections 9 ! inw>d p>ts ( ! body1 suffici5t to /op ! light f go+ ?r\gh x2 b !y mu/ be ( a size bord]+ ^u t dispos$ to reflect ! fa9t blue ( ! fir/ ord]1 :i* af=ds an evid5t reason :y blacks usually p>take a little ( t col\r4 ,we see too1 :y bodies dissolv$ by fire or putrefaction turn black3 & :y 9 gr9d+ glasses ^u copp] plates ! du/ ( ! glass1 copp]1 & s& x is gr\nd )1 become v black3 & 9 ! la/ place :y ^! black sub/ances communicate s easily to o!rs _! hue2 :i* is1 t _! p>ticles by reason ( ! great m9ut5ess ( !m easily ov]spread ! gross] p>ticles ( o!rs4 #ai4 ,i ,,%all n[ f9i% ?is *apt] ) "o rem>k ( ! exce$+ great porosity 9 bodies necess>ily requir$ 9 all t has "h be5 said2 :i*1 :5 duly consid]$1 mu/ appe> v surpriz+2 b p]haps x w be matt] ( great] surprize1 :5 ,i affirm t ! sagacity ( our au?or has discov]$ a me?od1 by :i* bodies may easily become s2 nay h[ any ! lea/ portion ( matt] may be wr\ght into a body ( any assign$ dim5sions h[ great s ev]1 & yet ! pores ( t body none ( !m great]1 ?an any ! smalle/ magnitude propos$ at pleasure2 not)/&+ :i* ! p>ts ( ! body %all s t\*1 t ! body itself %all be h>d & solid#caj4 ,! mann] is ?is3 suppose ! body be comp\nd$ ( p>ticles ( su* figures1 t :5 laid toge!r ! pores f\nd betwe5 !m may be equal 9 bigness to ! p>ticles2 h[ ?is may be effect$1 & yet ! body be h>d & solid1 is n difficult to und]/&2 & ! pores ( su* a body may be made ( any propos$ degree ( smallness4 ,b ! solid matt] ( a body s fram$ w take up only half ! space occupi$ by ! body2 & if ea* con/itu5t p>ticle be compos$ ( o!r less p>ticles accord+ to ! same rule1 ! solid p>ts ( su* a body w be b a f\r? "p ( its bulk2 if e "o ( ^! less] p>ticles aga9 be comp\nd$ 9 ! same mann]1 ! solid p>ts ( ! :ole body %all be b "o eigh? ( its bulk2 & ?us by cont9u+ ! composition ! solid p>ts ( ! body may be made to be> z small a proportion to ! :ole magnitude ( ! body1 z %all be desir$1 not)/&+ ! body w be by ! contiguity ( its p>ts capable ( be+ 9 any degree h>d4 ,:i* %ews t ?is :ole globe ( e>?1 nay all ! kn[n bodies 9 ! univ]se toge!r1 z f> z we "k1 may be comp\nd$ ( no great] a portion ( solid matt]1 ?an might be r$uc$ into a globe ( "o in* only 9 diamet]1 or ev5 less4 ,we see !re=e h[ by ?is means bodies may easily be made r>e en\gh to transmit light1 ) all t fre$om pellucid bodies are f\nd to d4 ,?\gh :at is ! real /ructure ( bodies we yet "k n4 ,,*ap4 ,,iii4 ,( ! ,,refraction1 ,,reflection1 & ,,inflection ( ,,light4 ,,?us mu* ( ! col\rs ( natural bodies2 our me?od n[ leads u to speculations yet great]1 no less ?an to lay op5 ! causes ( all t has hi!rto be5 relat$4 ,= x mu/ 9 ?is *apt] be expla9$1 h[ ! prism sep>ates ! col\rs ( ! sun's light1 z we f\nd 9 ! fir/ *apt]2 & :y ! ?9 transp>5t plates disc\rs$ ( 9 ! la/ *apt]1 & consequ5tly ! p>ticles ( col\r$ bodies1 reflect t div]sity ( col\rs only by be+ ( diff]5t ?icknesses4 #b4 ,,= ! fir/ x is prov$ by our au?or1 t ! col\rs ( ! sun's light are manife/$ by ! prism1 f ! rays und]go+ diff]5t degrees ( refraction2 t ! violet-mak+ rays1 :i* g to ! upp] "p ( ! col\r$ image 9 ! fir/ exp]im5t ( ! fir/ *apt]1 are ! mo/ refract$2 t ! indigo-mak+ rays are refract$1 or turn$ out ( _! c\rse by pass+ ?r\gh ! prism1 some?+ less ?an ! violet-mak+ rays1 b m ?an ! blue-mak+ rays2 & ! blue-mak+ rays m ?an ! gre52 ! gre5-mak+ rays m ?an ! yell[2 ! yell[ m ?an ! orange2 & ! orange-mak+ rays m ?an ! r$-mak+1 :i* are lea/ ( all refract$4 ,! fir/ pro( ( ?is1 t rays ( diff]5t col\rs are refract$ unequally is ?is4 ,if y take any body1 & pa9t "o half ( x r$ & ! o!r half blue1 !n ^u view+ x ?r\gh a prism ^? two p>ts %all appe> sep>at$ f ea* o!r2 :i* c be caus$ no o!rwise ?an by ! prism's refract+ ! light ( "o half m ?an ! light ( ! o!r half4 ,b ! blue half w be mo/ refract$2 = if ! body be se5 ?r\gh ! prism 9 su* a situation1 t ! body %all appe> lift$ upw>ds by ! refraction1 z a body )9 a bason ( wat]1 9 ! exp]im5t m5tion$ 9 ! fir/ *apt]1 appe>$ to be lift$ up by ! refraction ( ! wat]1 s z to be se5 at a great] di/ance ?an :5 ! bason is empty1 !n %all ! blue "p appe> high] ?an ! r$2 b if ! refraction ( ! prism be ! contr>y way1 ! blue "p %all be depress$ m ?an ! o!r4 ,aga91 aft] lay+ f9e ?reads ( black silk across ea* ( ! col\rs1 & ! body well inlight5$1 if ! rays com+ f x be receiv$ ^u a convex glass1 s t x may by refract+ ! rays ca/ ! image ( ! body ^u a piece ( :ite pap] held beyond ! glass2 !n x w be se5 t ! black ?reads ^u ! r$ "p ( ! image1 & ^? ^u ! blue "p1 d n at ! same "t appe> di/9ctly 9 ! image ( ! body project$ by ! glass2 b if ! pap] be held s1 t ! ?reads on ! blue "p may di/9ctly appe>1 ! ?reads _c be se5 di/9ct ^u ! r$ "p2 b ! pap] mu/ be drawn f>!r (f f ! convex glass to make ! ?reads on ?is "p visible2 & :5 ! di/ance is great en\gh = ! ?reads to be se5 9 ?is r$ "p1 !y become indi/9ct 9 ! o!r4 ,:5ce x appe>s t ! rays proce$+ f ea* po9t ( ! blue "p ( ! body are soon] unit$ aga9 by ! convex glass ?an ! rays :i* come f ea* po9t ( ! r$ p>ts#caa4 ,b bo? ^! exp]im5ts prove t ! blue-mak+ rays1 z well 9 ! small refraction ( ! convex glass1 z 9 ! great] refraction ( ! prism1 are m b5t1 ?an ! r$-mak+ rays4 #c4 ,,?is seems already to expla9 ! reason ( ! col\r$ spectrum made by refract+ ! sun's light ) a prism1 ?\gh our au?or proce$s to exam9e t 9 p>ticul>1 & proves t ! diff]5t col\r$ rays 9 t spectrum are 9 diff]5t degrees refract$2 by %ew+ h[ to place ! prism 9 su* a po/ure1 t if all ! rays 7 refract$ 9 ! same mann]1 ! spectrum %\ld ( necessity be r\nd3 :]eas 9 t case if ! angle made by ! two surfaces ( ! prism1 ?r\gh :i* ! light passes1 t is ! angle ,d ,f ,e 9 fig4 #abf1 be ab\t #fc or #fd degrees1 ! image in/ead ( be+ r\nd %all be ne> five times z long z broad2 a diff]5ce en\gh to %ew a great inequality 9 ! refractions ( ! rays1 :i* g to ! opposite extremities ( ! image4 ,to leave no scruple unremov$1 our au?or is v p>ticul> 9 %ew+ by a great numb] ( exp]im5ts1 t ?is inequality ( refraction is n casual1 & t x does n dep5d ^u any irregul>ities ( ! glass2 no nor t ! rays are 9 _! passage ?r\gh ! prism ea* split & divid$2 b on ! contr>y t e ray ( ! sun has its own peculi> degree ( refraction prop] to x1 accord+ to :i* x is m or less refract$ 9 pass+ ?r\gh pellucid sub/ances always 9 ! same mann]#cab4 ,t ! rays are n split & multipli$ by ! refraction ( ! prism1 ! ?ird ( ! exp]im5ts relat$ 9 our fir/ *apt] %ews v cle>ly2 = if !y 71 & ! l5g? ( ! spectrum 9 ! fir/ refraction 7 !reby occasion$1 ! bread? %\ld be no less dilat$ by ! cross refraction ( ! second prism2 :]eas ! bread? is n at all increas$1 b ! image is only ?r[n into an oblique po/ure by ! upp] "p ( ! rays :i* 7 at fir/ m refract$ ?an ! "u "p1 be+ aga9 turn$ f>!/ out ( _! c\rse4 ,b ! exp]im5t mo/ expressly adapt$ to prove ?is regul> div]sity ( refraction is ?is1 :i* foll[s#cac4 ,two bo>ds ,a ,b1 ,c ,d 79 fig4 #acj47 be+ erect$ 9 a d>k5$ room at a prop] di/ance1 "o ( !m ,a ,b be+ ne> ! w9d[-%utt] ,e ,f1 a space only be+ left = ! prism ,g ,h ,i to be plac$ betwe5 !m2 s t ! rays entr+ at ! hole ,m ( ! w9d[-%utt] may aft] pass+ ?r\gh ! prism be traject$ ?r\gh a small] hole ,k made 9 ! bo>d ,a ,b1 & pass+ on f !nce g out at ano!r hole ,l made 9 ! bo>d ,c ,d ( ! same size z ! hole ,k1 & small en\gh to transmit ! rays ( "o col\r only at a "t2 let ano!r prism ,n ,o ,p be plac$ aft] ! bo>d ,c ,d to receive ! rays pass+ ?r\gh ! holes ,k & ,l1 & aft] refraction by t prism let ^? rays fall ^u ! :ite surface ,q ,r4 ,suppose fir/ ! violet light to pass ?r\gh ! holes1 & to be refract$ by ! prism ,n ,o ,p to s1 :i* if ! prism ,n ,o ,p 7 remov$ %\ld h pass$ "r onto ,w4 ,if ! prism ,g ,h ,i be turn$ sl[ly ab\t1 :ile ! bo>ds & prism ,n ,o ,p rema9 fix$1 9 a little "t ano!r col\r w fall ^u ! hole ,l1 :i*1 if ! prism ,n ,o ,p 7 tak5 away1 w\ld proce$ l ! =m] rays to ! same po9t ,w2 b ! refraction ( ! prism ,n ,o ,p %all n c>ry ^! rays to s1 b to "s place less di/ant f ,w z to t4 ,suppose n[ ! rays :i* g to t to be ! indigo-mak+ rays4 ,x is manife/ t ! bo>ds ,a ,b1 ,c ,d1 & prism ,n ,o ,p rema9+ immoveable1 bo? ! violet-mak+ & indigo-mak+ rays are incid5t alike ^u ! prism ,n ,o ,p1 = !y are equally incl9$ to its surface ,o ,p1 & ent] x 9 ! same "p ( t surface2 :i* %ews t ! indigo-mak+ rays are less div]t$ out ( _! c\rse by ! refraction ( ! prism1 ?an ! violet-mak+ rays "u an exact p>ity ( all circum/ances4 ,f>!r1 if ! prism ,g ,h ,i be m turn$ ab\t1 'till ! blue-mak+ rays pass ?r\gh ! hole ,l1 ^! %all fall ^u ! surface ,q ,r bel[ ,i1 z at v1 & !re=e are subject$ to a less refraction ?an ! indigo-mak+ rays4 ,& ?us by proce$+ x w be f\nd t ! gre5-mak+ rays are less refract$ ?an ! blue-mak+ rays1 & s ( ! re/1 accord+ to ! ord] 9 :i* !y lie 9 ! col\r$ spectrum4 #d4 ,,?is disposition ( ! diff]5t col\r$ rays to be refract$ "s m ?an o!rs our au?or calls _! respective degrees ( refrangibility4 ,& s9ce ?is diff]5ce ( refrangibility discov]s x self to be s regul>1 ! next /ep is to f9d ! rule x obs]ves4 #e4 ,,x is a common pr9ciple 9 optics1 t ! s9e ( ! angle ( incid5ce be>s to ! s9e ( ! refract$ angle a giv5 proportion4 ,if ,a ,b 79 fig4 #aca1 #acb7 repres5t ! surface ( any refract+ sub/ance1 suppose ( wat] or glass1 & ,c ,d a ray ( light incid5t ^u t face 9 ! po9t ,d1 let ,d ,e be ! ray1 aft] x has pass$ ! surface ,a ,b2 if ! ray pass out ( ! air into ! sub/ance ^: surface is ,a ,b 7z 9 fig4 #aca7 x %all be turn$ f ! surface1 & if x pass out ( t sub/ance into air x %all be b5t t[>ds x 7z 9 fig4 #acb7 ,b if ,f ,g be drawn ?r\gh ! po9t ,d p]p5dicul> to ! surface ,a ,b1 ! angle "u ,c ,d ,f made by ! incid5t ray & ?is p]p5dicul> is call$ ! angle ( incid5ce2 & ! angle "u ,e ,d ,g1 made by ?is p]p5dicul> & ! ray aft] refraction1 is call$ ! refract$ angle4 ,& if ! circle ,h ,f ,i ,g be describ$ ) any int]val cutt+ ,c ,d 9 ,h & ,d ,e 9 ,i1 !n ! p]p5dicul>s ,h ,k1 ,i ,l be+ let fall ^u ,f ,g1 ,h ,k is call$ ! s9e ( ! angle "u ,c ,d ,f ! angle ( incid5ce1 & ,i ,l ! s9e ( ! angle "u ,e ,d ,g ! refract$ angle4 ,! fir/ ( ^! s9es is call$ ! s9e ( ! angle ( incid5ce1 or m briefly ! s9e ( incid5ce1 ! latt] is ! s9e ( ! refract$ angle1 or ! s9e ( refraction4 ,& x has be5 f\nd by num]\s exp]im5ts t :atev] proportion ! s9e ( incid5ce ,h ,k be>s to ! s9e ( refraction ,i ,l 9 any "o case1 ! same proportion %all hold 9 all cases2 t is1 ! proportion betwe5 ^! s9es w rema9 unalt]ably ! same 9 ! same refract+ sub/ance1 :atev] be ! magnitude ( ! angle "u ,c ,d ,f4 #f4 ,,b n[ because optical writ]s did n obs]ve t e beam ( :ite light 0 divid$ by refraction1 z has be5 "h expla9$1 ?is rule collect$ by !m c only be und]/ood 9 ! gross ( ! :ole beam aft] refraction1 & n s mu* ( any p>ticul> "p ( x1 or at mo/ only ( ! middle "p ( ! beam4 ,x !re=e 0 incumb5t ^u our au?or to f9d by :at law ! rays 7 p>t$ f ea* o!r2 :e!r ea* ray ap>t obta9$ ?is prop]ty1 & t ! sep>ation 0 made by ! proportion betwe5 ! s9es ( incid5ce & refraction be+ 9 ea* species ( rays diff]5t2 or :e!r ! light 0 divid$ by "s o!r rule4 ,b he proves by a c]ta9 exp]im5t t ea* ray has its s9e ( incid5ce proportional to its s9e ( refraction2 & f>!r %ews by ma!matical reason+1 t x mu/ be s ^u condition only t bodies refract ! light by act+ ^u x1 9 a direction p]p5dicul> to ! surface ( ! refract+ body1 & ^u ! same sort ( rays always 9 an equal degree at ! same di/ances#cad4 #g4 ,,our great au?or tea*es 9 ! next place h[ f ! refraction ( ! mo/ refrangible & lea/ refrangible rays to f9d ! refraction ( all ! int]m$iate ones#cae4 ,! me?od is ?is3 if ! s9e ( incid5ce be to ! s9e ( refraction 9 ! lea/ refrangible rays z ,a to ,b ,c1 79 fig4 #acc7 & to ! s9e ( refraction 9 ! mo/ refrangible z ,a to ,b ,d2 if ,c ,e be tak5 equal to ,c ,d1 & !n ,e ,d be s divid$ 9 ,f1 ,g1 ,h1 ,i1 ,k1 ,l1 t ,e ,d1 ,e ,f1 ,e ,g1 ,e ,h1 ,e ,i1 ,e ,k1 ,e ,l1 ,e ,c1 %all be proportional to ! eight l5g?s ( musical *ords1 :i* f\nd ! notes 9 an octave1 ,e ,d be+ ! l5g? ( ! key1 ,e ,f ! l5g? ( ! tone above t key1 ,e ,g ! l5g? ( ! less] ?ird1 ,e ,h ( ! f\r?1 ,e ,i ( ! fif?1 ,e ,k ( ! great] six?1 ,e ,l ( ! sev5?1 & ,e ,c ( ! octave above t key2 t is if ! l9es ,e ,d1 ,e ,f1 ,e ,g1 ,e ,h1 ,e ,i1 ,e ,k1 ,e ,l1 & ,e ,c be> ! same proportion z ! numb]s1 #a1 #i_/h1 #e_/f1 1 1 1 #i_/fa1 1 respectively !n %all ,b ,d1 ,b ,f1 be ! two limits ( ! s9es ( refraction ( ! violet-mak+ rays1 t is ! violet-mak+ rays %all n all ( !m h precisely ! same s9e ( refraction1 b none ( !m %all h a great] s9e ?an ,b ,d1 nor a less ?an ,b ,f1 ?\gh !re are violet-mak+ rays :i* answ] to any s9e ( refraction t c be tak5 betwe5 ^! two4 ,9 ! same mann] ,b ,f & ,b ,g are ! limits ( ! s9es ( refraction ( ! indigo-mak+ rays2 ,b ,g1 ,b ,h are ! limits belong+ to ! blue-mak+ rays2 ,b ,h1 ,b ,i ! limits p]ta9+ to ! gre5-mak+ rays1 ,b ,i1 ,b ,k ! limits = ! yell[-mak+ rays2 ,b ,k1 ,b ,l ! limits = ! orange-mak+ rays2 & la/ly1 ,b ,l & ,b ,c ! extreme limits ( ! s9es ( refraction belong+ to ! r$-mak+ rays4 ,^! are ! proportions by :i* ! het]og5e\s rays ( light are sep>at$ f ea* o!r 9 refraction4 #h4 ,,:5 light passes out ( glass into air1 our au?or f\nd ,a to ,b ,c z #ej to #gg1 & ! same ,a to ,b ,d z #ej to #gh4 ,& :5 x goes out ( any o!r refract+ sub/ance into air1 ! excess ( ! s9e ( refraction ( any "o species ( rays above its s9e ( incid5ce be>s a con/ant proportion1 :i* holds ! same 9 ea* species1 to ! excess ( ! s9e ( refraction ( ! same sort ( rays above ! s9e ( incid5ce into ! air out ( glass2 provid$ ! s9es ( incid5ce bo? 9 glass & ! o!r sub/ance are equal4 ,?is our au?or v]ifi$ by transmitt+ ! light ?r\gh prisms ( glass includ$ )9 a prismatic vessel ( wat]2 & draws f ^? exp]im5ts ! foll[+ obs]vations3 t :5ev] ! light 9 pass+ ?r\gh s _m surfaces p>t+ div]se transp>5t sub/ances is by contr>y refractions made to em]ge into ! air 9 a direction p>allel to t ( its incid5ce1 x w appe> aft]w>ds :ite at any di/ance f ! prisms1 :]e y %all please to exam9e x2 b if ! direction ( its em]g5ce be oblique to its incid5ce1 9 rec$+ f ! place ( em]g5ce its edges %all appe> t+$ ) col\rs3 :i* proves t 9 ! fir/ case !re is no inequality 9 ! refractions ( ea* species ( rays1 b t :5 any "o species is s refract$ z to em]ge p>allel to ! incid5t rays1 e sort ( rays aft] refraction %all likewise be p>allel to ! same incid5t rays1 & to ea* o!r2 :]eas on ! contr>y1 if ! rays ( any "o sort are oblique to ! incid5t light1 ! sev]al species %all be oblique to ea* o!r1 & be gradually sep>at$ by t obliquity4 ,f h5ce he d$uces bo? ! =em5tion$ !orem1 & also ?is o!r2 t 9 ea* sort ( rays ! proportion ( ! s9e ( incid5ce to ! s9e ( refraction1 9 ! passage ( ! ray out ( any refract+ sub/ance into ano!r1 is comp\nd$ ( ! proportion to :i* ! s9e ( incid5ce w\ld h to ! s9e ( refraction 9 ! passage ( t ray out ( ! fir/ sub/ance into any ?ird1 & ( ! proportion :i* ! s9e ( incid5ce w\ld h to ! s9e ( refraction 9 ! passage ( ! ray out ( t ?ird sub/ance into ! second4 ,f s simple & pla9 an exp]im5t has our mo/ judici\s au?or d$uc$ ^! important !orems1 by :i* we may le>n h[ v exact & circumspect he has be5 9 ?is :ole "w ( 8 optics2 t not)/&+ 8 great p>ticul>ity 9 expla9+ 8 doctr9e1 & ! num]\s collection ( exp]im5ts he has made to cle> up e d\bt :i* c\ld arise1 yet at ! same "t he has us$ ! greate/ caution to make out e ?+ by ! simple/ & easie/ means possible4 #i4 ,,our au?or adds b "o rem>k m ^u refraction1 :i* is1 t if refraction be p]=m$ 9 ! mann] he has suppos$ f ! light's be+ press$ by ! refract+ p[] p]p5dicul>ly t[>d ! surface ( ! refract+ body1 & consequ5tly be made to move swift] 9 ! body ?an be=e its incid5ce2 :e!r ?is p[] act equally at all di/ances or o!rwise1 provid$ only its p[] 9 ! same body at ! same di/ances rema9 )\t v>iation ! same 9 "o incl9ation ( ! incid5t rays z well z ano!r2 he obs]ves t ! refract+ p[]s 9 diff]5t bodies w be 9 ! duplicate proportion ( ! tang5ts ( ! lead angles1 :i* ! refract$ light c make ) ! surfaces ( ! refract+ bodies#caf4 ,?is obs]vation may be expla9$ ?us4 ,:5 ! light passes into any refract+ sub/ance1 x has be5 %ewn above t ! s9e ( incid5ce be>s a con/ant proportion to ! s9e ( refraction4 ,suppose ! light to pass to ! refract+ body ,a ,b ,c ,d 79 fig4 #acd7 9 ! l9e ,e ,f1 & to fall ^u x at ! po9t ,f1 & !n to proce$ )9 ! body 9 ! l9e ,f ,g4 ,let ,h ,i be drawn ?r\gh ,f p]p5dicul> to ! surface ,a ,b1 & any circle ,k ,l ,m ,n be describ$ to ! c5t] ,f4 ,!n f ! po9ts ,o & ,p :]e ?is circle cuts ! incid5t & refract$ ray1 ! p]p5dicul>s ,o ,q1 ,p ,r be+ drawn1 ! proportion ( ,o ,q to ,p ,r w rema9 ! same 9 all ! diff]5t obliquities1 9 :i* ! same ray ( light c fall on ! surface ,a ,b4 ,n[ ,o ,q is less ?an ,f ,l ! semidiamet] ( ! circle ,k ,l ,m ,n1 b ! m ! ray ,e ,f is incl9$ d[n t[>d ! surface ,a ,b1 ! great] w ,o ,q be1 & w approa* ne>] to ! magnitude ( ,f ,l4 ,b ! proportion ( ,o ,q to ,p ,r rema9+ always ! same1 :5 ,o ,q1 is l>ge/1 ,p ,r w also be greate/2 s t ! m ! incid5t ray ,e ,f is incl9$ t[>d ! surface ,a ,b1 ! m ! ray ,f ,g aft] refraction w be incl9$ t[>d ! same4 ,n[ if ! l9e ,f ,s ,t be s drawn1 t ,s ,v be+ p]p5dicul> to ,f ,i %all be to ,f ,l ! semidiamet] ( ! circle 9 ! con/ant proportion ( ,p ,r to ,o ,q2 !n ! angle "u ,n ,f ,t is t :i* ,i meant by ! lea/ ( all t c be made by ! refract$ ray ) ?is surface1 = ! ray aft] refraction w\ld proce$ 9 ?is l9e1 if x 7 to come to ! po9t ,f ly+ on ! v surface ,a ,b2 = if ! incid5t ray came to ! po9t ,f 9 any l9e betwe5 ,a ,f & ,f ,h1 ! ray aft] refraction w\ld proce$ =w>d 9 "s l9e betwe5 ,f ,t & ,f ,i4 ,"h if ,n ,w be drawn p]p5dicul> to ,f ,n1 ?is l9e ,n ,w 9 ! circle ,k ,l ,m ,n is call$ ! tang5t ( ! angle "u ,n ,f ,s4 ,?us mu* be+ premis$1 ! s5se ( ! =em5tion$ proposition is ?is4 ,let !re be two refract+ sub/ances 79 fig4 #ace7 ,a ,b ,c ,d1 & ,e ,f ,g ,h4 ,take a po9t1 z ,i1 9 ! surface ,a ,b1 & to ! c5t] ,i ) any semidiamet] describe ! circle ,k ,l ,m4 ,9 l mann] on ! surface ,e ,f take "s po9t ,n1 z a c5t]1 & describe ) ! same semidiamet] ! circle ,o ,p ,q4 ,let ! angle "u ,b ,i ,r be ! lea/ :i* ! refract$ light c make ) ! surface ,a ,b1 & ! angle "u ,f ,n ,s ! lea/ :i* ! refract$ light c make ) ! surface ,e ,f4 ,!n if ,l ,t be drawn p]p5dicul> to ,a ,b1 & ,p ,v p]p5dicul> to ,e ,f2 ! :ole p[]1 :]e) ! sub/ance ,a ,b ,c ,d acts on ! light1 w be> to ! :ole p[] :]e) ! sub/ance ,e ,f ,g ,h acts on1 ! light1 a proportion1 :i* is duplicate ( ! proportion1 :i* ,l ,t be>s to ,p ,v4 #aj4 ,,^u comp>+ accord+ to ?is rule ! refractive p[]s ( a great _m bodies x is f\nd1 t unctu\s bodies :i* ab\nd mo/ ) sulphure\s p>ts refract ! light two or ?ree times m 9 proportion to _! d5sity ?an o!rs3 b t ^? bodies1 :i* seem to receive 9 _! composition l proportions ( sulphure\s p>ts1 h _! refractive p[]s proportional to _! d5sities2 z appe>s beyond contradiction by comp>+ ! refractive p[] ( s r>e a sub/ance z ! air ) t ( common glass or rock cry/al1 ?\gh ^! sub/ances are #bjjj times d5s] ?an air2 nay ! same proportion is f\nd to hold )\t s5sible diff]5ce 9 comp>+ air ) pseudo-top> & glass ( antimony1 ?\gh ! pseudo-top> be #cejj times d5s] ?an air1 & glass ( antimony no less ?an #ddjj times d5s]4 ,?is p[] 9 o!r sub/ances1 z salts1 common wat]1 _s ( w9e1 c4 seems to be> a great] proportion to _! d5sities ?an ^! la/ nam$1 accord+ z !y ab\nd ) sulphurs m ?an ^!2 :i* makes our au?or conclude x probable1 t bodies act ^u ! light *iefly1 if n altoge!r1 by means ( ! sulphurs 9 !m2 :i* k9d ( sub/ances x is likely ent]s 9 "s degree ! composition ( all bodies4 ,( all ! sub/ances exam9$ by our au?or1 none has s great a refractive p[]1 9 respect ( its d5sity1 z a diamond4 #aa4 ,,our au?or f9i%es ^! rem>ks1 & all he (f]s relat+ to refraction1 ) obs]v+1 t ! action betwe5 light & bodies is mutual1 s9ce sulphure\s bodies1 :i* are mo/ readily set on fire by ! sun's light1 :5 collect$ ^u !m ) a burn+ glass1 act m ^u light 9 refract+ x1 ?an o!r bodies ( ! same d5sity d4 ,& f>!r1 t ! d5se/ bodies1 :i* h be5 n[ %ewn to act mo/ ^u light1 contract ! greate/ heat by be+ expos$ to ! summ] sun4 #ab4 ,,hav+ ?us dispat*$ :at relates to refraction1 we mu/ address ourselves to disc\rse ( ! o!r op]ation ( bodies ^u light 9 reflect+ x4 ,:5 light passes ?r\gh a surface1 :i* divides two transp>5t bodies diff]+ 9 d5sity1 "p ( x only is transmitt$1 ano!r "p be+ reflect$4 ,& if ! light pass out ( ! d5s] body into ! r>]1 by be+ mu* incl9$ to ! =esaid surface at l5g? no "p ( x %all pass ?r\gh1 b be totally reflect$4 ,n[ t "p ( ! light1 :i* suff]s ! greate/ refraction1 %all be :olly reflect$ ) a less obliquity ( ! rays1 ?an ! p>ts ( ! light :i* und]go a less degree ( refraction2 z is evid5t f ! la/ exp]im5t recit$ 9 ! fir/ *apt]2 :]e1 z ! prisms ,d ,e ,f1 ,g ,h ,i1 79 fig4 #abi47 7 turn$ ab\t1 ! violet light 0 fir/ totally reflect$1 & !n ! blue1 next to t ! gre51 & s ( ! re/4 ,9 consequ5ce ( :i* our au?or lays d[n ?is proportion2 t ! sun's light diff]s 9 reflexibility1 ^? rays be+ mo/ reflexible1 :i* are mo/ refrangible4 ,& collects f ?is1 9 conjunction ) o!r argum5ts1 t ! refraction & reflection1 ( light are produc$ by ! same cause1 compass+ ^? diff]5t effects only by ! diff]5ce ( circum/ances ) :i* x is att5d$4 ,ano!r pro( ( ?is be+ tak5 by our au?or f :at he has discov]$ ( ! passage ( light ?r\gh ?9 transp>5t plates1 viz4 t any p>ticul> species ( light1 suppose1 = in/ance1 ! r$-mak+ rays1 w ent] & pass out ( su* a plate1 if t plate be ( "s c]ta9 ?icknesses2 b if x be ( o!r ?icknesses1 x w n break ?r\gh x1 b be reflect$ back3 9 :i* is se51 t ! ?ickness ( ! plate det]m9es :e!r ! p[]1 by :i* t plate acts ^u ! light1 %all reflect x1 or suff] x to pass ?r\gh4 #ac4 ,,b ?is la/ m5tion$ surpris+ prop]ty ( ! action betwe5 light & bodies af=ds ! reason ( all t has be5 said 9 ! prec$+ *apt] conc]n+ ! col\rs ( natural bodies2 & mu/ !re=e m p>ticul>ly be illu/rat$ & expla9$1 z be+ :at w pr9cipally unfold ! nature ( ! action ( bodies ^u light4 #ad4 ,,to beg93 ,! object glass ( a long telescope be+ laid ^u a plane glass1 z propos$ 9 ! =ego+ *apt]1 9 op5 day-light !re w be exhibit$ r+s ( v>i\s col\rs1 z 0 !re relat$2 b if 9 a d>k5$ room ! col\r$ spectrum be =m$ by ! prism1 z 9 ! fir/ exp]im5t ( ! fir/ *apt]1 & ! glasses be illum9at$ by a reflection f ! spectrum1 ! r+s %all n 9 ?is case exhibit ! div]sity ( col\rs be=e describ$1 b appe> all ( ! col\r ( ! light :i* falls ^u ! glasses1 hav+ d>k r+s betwe54 ,:i* %ews t ! ?9 plate ( air betwe5 ! glasses at "s ?icknesses reflects ! incid5t light1 at o!r places does n reflect x1 b is f\nd 9 ^? places to give ! light passage2 = by hold+ ! glasses 9 ! light z x passes f ! prism to ! spectrum1 suppose at su* a di/ance f ! prism t ! sev]al sorts ( light mu/ be suffici5tly sep>at$ f ea* o!r1 :5 any p>ticul> sort ( light falls on ! glasses1 y w f9d by hold+ a piece ( :ite pap] at a small di/ance beyond ! glasses1 t at ^? int]vals1 :]e ! d>k l9es appe>$ ^u ! glasses1 ! light is s transmitt$1 z to pa9t ^u ! pap] r+s ( light hav+ t col\r :i* falls ^u ! glasses4 ,?is exp]im5t !re=e op5s to u ?is v /range prop]ty ( reflection1 t 9 ^! ?9 plates x %\ld be> su* a relation to ! ?ickness ( ! plate1 z is "h %ewn4 ,f>!r1 by c>efully measur+ ! diamet]s ( ea* r+ x is f\nd1 t :]eas ! glasses t\* :]e ! d>k spot appe>s 9 ! c5t] ( ! r+s made by reflexion1 :]e ! air is ( twice ! ?ickness at :i* ! light ( ! fir/ r+ is reflect$1 !re ! light by be+ aga9 transmitt$ makes ! fir/ d>k r+2 :]e ! plate has ?ree times t ?ickness :i* exhibits ! fir/ lucid r+1 x aga9 reflects ! light =m+ ! second lucid r+2 :5 ! ?ickness is f\r times ! fir/1 ! light is aga9 transmitt$ s z to make ! second d>k r+2 :]e ! air is five times ! fir/ ?ickness1 ! ?ird lucid r+ is made2 :]e x has six times ! ?ickness1 ! ?ird d>k r+ appe>s1 & s on3 9 s mu* t ! ?icknesses1 at :i* ! light is reflect$1 are 9 proportion to ! numb]s #a1 #c1 #e1 #g1 #i1 c4 & ! ?icknesses1 :]e ! light is transmitt$1 are 9 ! proportion ( ! numb]s #j1 #b1 #d1 #f1 #h1 c4 ,& ^! proportions betwe5 ! ?icknesses :i* reflect & transmit ! light rema9 ! same 9 all situations ( ! eye1 z well :5 ! r+s are view$ obliquely1 z :5 look$ on p]p5dicul>ly4 ,we mu/ f>!r "h obs]ve1 t ! light1 :5 x is reflect$1 z well z :5 x is transmitt$1 ent]s ! ?9 plate1 & is reflect$ f its f>!r surface2 because1 z 0 be=e rem>k$1 ! alt]+ ! transp>5t body beh9d ! f>!r surface alt]s ! degree ( reflection z :5 a ?9 piece ( ,muscovy glass has its f>!r surface wet ) wat]1 & ! col\r ( ! glass made dimm] by be+ s wet2 :i* %ews t ! light rea*es to ! wat]1 o!rwise its reflection c\ld n be influ5c$ by x4 ,b yet ?is reflection dep5ds ^u "s p[] propagat$ f ! fir/ surface to ! second2 = ?\gh made at ! second surface x dep5ds also ^u ! fir/1 because x dep5ds ^u ! di/ance betwe5 ! surfaces2 & besides1 ! body ?r\gh :i* ! light passes to ! fir/ surface influ5ces ! reflection3 = 9 a plate ( ,muscovy glass1 wett+ ! surface1 :i* fir/ receives ! light1 dim9i%es ! reflection1 ?\gh n q s mu* z wett+ ! f>!r surface w d4 ,s9ce !re=e ! light 9 pass+ ?r\gh ^! ?9 plates at "s ?icknesses is reflect$1 b at o!rs transmitt$ )\t reflection1 x is evid5t1 t ?is reflection is caus$ by "s p[] propagat$ f ! fir/ surface1 :i* int]mits & returns successively4 ,?us is e ray ap>t dispos$ to alt]nate reflections & transmissions at equal int]vals2 ! successive returns ( :i* disposition our au?or calls ! fits ( easy reflection1 & ( easy transmission4 ,b ^! fits1 :i* obs]ve ! same law ( return+ at equal int]vals1 :e!r ! plates are view$ p]p5dicul>ly or obliquely1 9 diff]5t situations ( ! eye *ange _! magnitude4 ,= :at 0 obs]v$ be=e 9 respect ( ^? r+s1 :i* appe> 9 op5 day-light1 holds likewise 9 ^! r+s exhibit$ by simple lights2 namely1 t ^! two alt] 9 bigness accord+ to ! diff]5t angle "u :i* !y are se53 & our au?or lays d[n a rule :]eby to det]m9e ! ?icknesses ( ! plate ( air1 :i* %all exhibit ! same col\r "u diff]5t oblique views#cag4 ,& ! ?ickness ( ! a]eal plate1 :i* 9 diff]5t incl9ations ( ! rays w exhibit to ! eye 9 op5 day-light ! same col\r1 is also v>i$ by ! same rule#cah4 ,he contriv$ f>!r a me?od ( comp>+ 9 ! bubble ( wat] ! proportion betwe5 ! ?ickness ( its coat1 :i* exhibit$ any col\r :5 se5 p]p5dicul>ly1 to ! ?ickness ( x1 :]e ! same col\r appe>$ by an oblique view2 & he f\nd ! same rule to obta9 "h likewise#cai4 ,b f>!r1 if ! glasses be enlight5$ successively by all ! sev]al species ( light1 ! r+s w appe> ( diff]5t magnitudes2 9 ! r$ light !y w be l>g] ?an 9 ! orange col\r1 9 t l>g] ?an 9 ! yell[1 9 ! yell[ l>g] ?an 9 ! gre51 less 9 ! blue1 less yet 9 ! indigo1 & lea/ ( all 9 ! violet3 :i* %ew t ! same ?ickness ( ! a]eal plate is n fitt$ to reflect all col\rs1 b t "o col\r is reflect$ :]e ano!r w\ld h be5 transmitt$2 & z ! rays :i* are mo/ /rongly refract$ =m ! lea/ r+s1 a rule is laid d[n by our au?or = det]m9+ ! relation1 :i* ! degree ( refraction ( ea* species ( col\r has to ! ?icknesses ( ! plate :]e x is reflect$4 #ae4 ,,f ^! obs]vations our au?or %ews ! reason ( t great v>iety ( col\rs1 :i* appe>s 9 ^! ?9 plates 9 ! op5 :ite light ( ! day4 ,= :5 ?is :ite light falls on ! plate1 ea* "p ( ! light =ms r+s ( its own col\r2 & ! r+s ( ! diff]5t col\rs n be+ ( ! same bigness are v>i\sly int]mix$1 & =m a great v>iety ( t9ts#cbj4 #af4 ,,9 c]ta9 exp]im5ts1 :i* our au?or made ) ?ick glasses1 he f\nd1 t ^! fits ( easy reflection & transmission return$ = "s ?\s&s ( times1 & !reby f>!r confirm$ 8 reason+ conc]n+ !m#cba4 #ag4 ,,^u ! :ole1 our great au?or concludes f "s ( ! exp]im5ts made by him1 t ! reason :y all transp>5t bodies refract "p ( ! light incid5t ^u !m1 & reflect ano!r "p1 is1 because "s ( ! light1 :5 x comes to ! surface ( ! body1 is 9 a fit ( easy transmission1 & "s "p ( x 9 a fit ( easy reflection2 & f ! durabl5ess ( ^! fits he ?9ks x probable1 t ! light is put into ^! fits f _! fir/ emission out ( ! lum9\s body2 & t ^! fits cont9ue to return at equal int]vals )\t end1 unless ^? int]vals be *ang$ by ! light's entr+ into "s refract+ sub/ance#cbb4 ,he likewise has taught h[ to det]m9e ! *ange :i* is made ( ! int]vals ( ! fits ( easy transmission & reflection1 :5 ! light passes out ( "o transp>5t space or sub/ance into ano!r4 ,8 rule is1 t :5 ! light passes p]p5dicul>ly to ! surface1 :i* p>ts any two transp>5t sub/ances1 ^! int]vals 9 ! sub/ance1 out ( :i* ! light passes1 be> to ! int]vals 9 ! sub/ance1 :]e9to ! light ent]s1 ! same proportion1 z ! s9e ( incid5ce be>s to ! s9e ( refraction#cbc4 ,x is f>!r to be obs]v$1 t ?\gh ! fits ( easy reflection return at con/ant int]vals1 yet ! reflect+ p[] nev] op]ates1 b at or ne> a surface :]e ! light w\ld suff] refraction2 & if ! ?ickness ( any transp>5t body %all be less ?an ! int]vals ( ! fits1 ^? int]vals %all sc>ce be di/urb$ by su* a body1 b ! light %all pass ?r\gh )\t any reflection#cbd4 #ah4 ,,:at ! p[] 9 nature is1 :]eby ?is action betwe5 light & bodies is caus$1 our au?or has n discov]$4 ,b ! effects1 :i* he has discov]$1 ( ?is p[] are v surpris+1 & altoge!r wide f any conjectures t _h ev] be5 fram$ conc]n+ x2 & f ^! discov]ies ( 8 no d\bt ?is p[] is to be d$uc$1 if we ev] c come to ! k ( x4 ,sir ,,isaac ,,newton has 9 g5]al h9t$ at 8 op9ion conc]n+ x2 t probably x is ow+ to "s v subtle & ela/ic sub/ance diffus$ ?r\gh ! univ]se1 9 :i* su* vibrations may be excit$ by ! rays ( light1 z !y pass ?r\gh x1 t %all occasion x to op]ate s diff]5tly ^u ! light 9 diff]5t places z to give rise to ^! alt]nate fits ( reflection & transmission1 ( :i* we h n[ be5 speak+#cbe4 ,he is ( op9ion1 t su* a sub/ance may produce ?is & o!r effects also 9 nature1 ?\gh x be s r>e z n to give any s5sible resi/ance to bodies 9 motion#cbf2 & !re=e n inconsi/5t ) :at has be5 said above1 t ! planets move 9 spaces free f resi/ance#cbg4 #ai4 ,,9 ord] = ! m full discov]y ( ?is action betwe5 light & bodies1 our au?or began ano!r set ( exp]im5ts1 :]e9 he f\nd ! light to be act$ on z x passes ne> ! edges ( solid bodies2 9 p>ticul> all small bodies1 su* z ! hairs ( a man's head or ! l1 held 9 a v small beam ( ! sun's light1 ca/ extremely broad %ad[s4 ,& 9 "o ( ^! exp]im5ts ! %ad[ 0 #ce times ! bread? ( ! body#cbh4 ,^! %ad[s are also obs]v$ to be bord]$ ) col\rs#cbi4 ,?is our au?or calls ! inflection ( light2 b z he in=ms u1 t he 0 int]rupt$ f prosecut+ ^! exp]im5ts to any l5g?1 ,i ne$ n deta9 my read]s ) a m p>ticul> acc\nt ( !m4 ,,*ap4 ,,iv4 ,( ,,optic ,,glasses4 ,,sir ,,isaac ,,newton hav+ d$uc$ f 8 doctr9e ( light & col\rs a surpris+ improvem5t ( telescopes1 ( :i* ,i int5d "h to give an acc\nt1 ,i %all fir/ premise some?+ 9 g5]al conc]n+ ^? in/rum5ts4 #b4 ,,x w be und]/ood f :at has be5 said above1 t :5 light falls ^u ! surface ( glass obliquely1 aft] its entrance into ! glass x is m incl9$ to ! l9e drawn ?r\gh ! po9t ( incid5ce p]p5dicul> to t surface1 ?an be=e4 ,suppose a ray ( light issu+ f ! po9t ,a 79 fig4 #acf7 falls on a piece ( glass ,b ,c ,d ,e1 ^: surface ,b ,c1 :]eon ! ray falls1 is ( a sph]ical or globul> figure1 ! c5t] :]e( is ,f4 ,let ! ray proce$ 9 ! l9e ,a ,g fall+ on ! surface ,b ,c 9 ! po9t ,g1 & draw ,f ,g ,h4 ,"h ! ray aft] its entrance into ! glass w pass on 9 "s l9e1 z ,g ,i1 m incl9$ t[>d ! l9e ,f ,g ,h t ! l9e ,a ,g is incl9$ !reto2 = ! l9e ,f ,g ,h is p]p5dicul> to ! surface ,b ,c 9 ! po9t ,g4 ,by ?is means1 if a numb] ( rays proce$+ f any "o po9t fall on a convex sph]ical surface ( glass1 !y %all be inflect$ 7z is repres5t$ 9 fig4 #acg17 s z to be ga!r$ pretty close toge!r ab\t ! l9e drawn ?r\gh ! c5t] ( ! glass f ! po9t1 :5ce ! rays proce$2 :i* l9e h5ce=w>d we %all call ! axis ( ! glass3 or ! po9t f :5ce ! rays proce$ may be s ne> ! glass1 t ! rays %all aft] entr+ ! glass /ill g on to spread !mselves1 b n s mu* z be=e2 s t if ! rays 7 to be cont9u$ backw>d 7z 9 fig4 #ach17 !y %\ld ga!r toge!r ab\t ! axis at a place m remote f ! glass1 ?an ! po9t is1 :5ce !y actually proce$4 ,9 ^! & ! foll[+ figures ,a d5otes ! po9t to :i* ! rays are relat$ be=e refraction1 ,b ! po9t to :i* !y are direct$ aft]w>ds1 & ,c ! c5t] ( ! refract+ surface4 ,"h we may obs]ve1 t x is possible to =m ! glass ( su* a figure1 t all ! rays :i* proce$ f "o po9t %all aft] refraction be r$uc$ aga9 exactly into "o po9t on ! axis ( ! glass4 ,b 9 glasses ( a sph]ical =m ?\gh ?is does n happ52 yet ! rays1 :i* fall )9 a mod]ate di/ance f ! axis1 w unite extremely ne> toge!r4 ,if ! light fall on a concave sph]ical surface1 aft] refraction x %all spread quick] ?an be=e 7z 9 fig4 #aci17 unless ! rays proce$ f a po9t betwe5 ! c5t] & ! surface ( ! glass4 ,if we suppose ! rays ( light1 :i* fall ^u ! glass1 n to proce$ f any po9t1 b to move s z to t5d all to "s po9t 9 ! axis ( ! glass beyond ! surface2 if ! glass h a convex surface1 ! rays %all unite ab\t ! axis soon]1 ?an o!rwise !y w\ld d 7z 9 fig4 #adj17 unless ! po9t to :i* !y t5d$ 0 betwe5 ! surface & ! c5t] ( t surface4 ,b if ! surface be concave1 !y %all n meet s soon3 nay p]haps conv]ge4 7,see fig4 #ada & #adb47 #e4 ,,f>!r1 because ! light 9 pass+ out ( glass into ! air is turn$ by ! refraction f>!r (f f ! l9e drawn ?r\gh ! po9t ( incid5ce p]p5dicul> to ! refract+ surface1 ?an x 0 be=e2 ! light :i* spreads f a po9t %all by p>t+ ?r\gh a convex surface ( glass into ! air be made ei!r to spread less ?an be=e 7z 9 fig4 #adc17 or to ga!r ab\t ! axis beyond ! glass 7z 9 fig4 #add47 ,b if ! rays ( light 7 proce$+ to a po9t 9 ! axis ( ! glass1 !y %\ld by ! refraction be made to unite soon] ab\t t axis 7z 9 fig4 #ade47 ,if ! surface ( ! glass be concave1 rays :i* proce$ f a po9t %all be made to spread fa/] 7z 9 fig #adf17 b rays :i* are t5d+ to a po9t 9 ! axis ( ! glass1 %all be made to ga!r ab\t ! axis f>!r f ! glass 7z 9 fig4 #adg7 or ev5 to div]ge 7z 9 fig4 #adh17 unless ! po9t1 to :i* ! rays are direct$1 lies betwe5 ! surface ( ! glass & its c5t]4 #d4 ,,! rays1 :i* spread !mselves f a po9t1 are call$ div]g+2 & su* z move t[>d a po9t1 are call$ conv]g+ rays4 ,& ! po9t 9 ! axis ( ! glass1 ab\t :i* ! rays ga!r aft] refraction1 is call$ ! focus ( ^? rays4 #e4 ,,if a glass be =m$ ( two convex sph]ical surfaces 7z 9 fig4 #adi17 :]e ! glass ,,ab is =m$ ( ! surfaces ,a ,c ,b & ,a ,d ,b1 ! l9e drawn ?r\gh ! c5t]s ( ! two surfaces1 z ! l9e ,e ,f1 is call$ ! axis ( ! glass2 & rays1 :i* div]ge f any po9t ( ?is axis1 by ! refraction ( ! glass w be caus$ to conv]ge t[>d "s "p ( ! axis1 or at lea/ to div]ge z f a po9t m remote f ! glass1 ?an t f :5ce !y proce$$2 = ! two surfaces bo? conspire to produce ?is effect ^u ! rays4 ,b conv]g+ rays w be caus$ by su* a glass z ?is to conv]ge soon]4 ,if a glass be =m$ ( two concave surfaces1 z ! glass ,a ,b 79 fig4 #aej17 ! l9e ,c ,d drawn ?r\gh ! c5t]s1 to :i* ! two surfaces are =m$1 is call$ ! axis ( ! glass4 ,su* a glass %all cause div]g+ rays1 :i* proce$ f any po9t 9 ! axis ( ! glass1 to div]ge mu* m1 z if !y came f "s place 9 ! axis ( ! glass ne>] to x ?an ! po9t1 :5ce ! rays actually proce$4 ,b conv]g+ rays w be made ei!r to conv]ge less1 or ev5 to div]ge4 ,illu/ration #f4 ,,9 ^! glasses rays1 :i* proce$ f any po9t ne> ! axis1 w be affect$ z x 7 9 ! same mann]1 z if !y proce$$ f ! v axis x self1 & su* z conv]ge t[>d a po9t at a small di/ance f ! axis w suff] mu* ! same effects f ! glass1 z if !y conv]g$ to "s po9t 9 ! v axis4 ,by ?is means any lum9\s body expos$ to a convex glass may h an image =m$ ^u any :ite body held beyond ! glass4 ,?is may be easily tri$ ) a common spectacle-glass4 ,= if su* a glass be held betwe5 a c&le & a piece ( :ite pap]1 if ! di/ances ( ! c&le1 glass1 & pap] be prop]ly adju/$1 ! image ( ! c&le w appe> v di/9ctly ^u ! pap]1 b be se5 inv]t$2 ! reason :]e( is ?is4 ,let ,a ,b 79 fig4 #aea7 be ! glass1 ,c ,d an object plac$ cross ! axis ( ! glass4 ,let ! rays ( light1 :i* issue f ! po9t ,e1 :]e ! axis ( ! glass crosses ! object1 be s refract$ by ! glass1 z to meet aga9 ab\t ! po9t ,f4 ,! rays1 :i* div]ge f ! po9t ,c ( ! object1 %all meet aga9 almo/ at ! same di/ance f ! glass1 b on ! o!r side ( ! axis1 z at ,g2 = ! rays at ! glass cross ! axis4 ,9 l mann] ! rays1 :i* proce$ f ! po9t ,d1 w meet ab\t ,h on ! o!r side ( ! axis4 ,none ( ^! rays1 nei!r ^? :i* proce$ f ! po9t ,e 9 ! axis1 nor ^? :i* issue f ,c or ,d1 w meet aga9 exactly 9 "o po9t2 b yet 9 "o place1 z is "h suppos$ at ,f1 ,g1 & ,h1 !y w be cr\d$ s close toge!r1 z to make a di/9ct image ( ! object ^u any body prop] to reflect x1 :i* %all be held !re4 #g4 ,,if ! object be too ne> ! glass = ! rays to conv]ge aft] ! refraction1 ! rays %all issue out ( ! glass1 z if !y div]g$ f a po9t m di/ant f ! glass1 ?an t f :5ce !y really proce$ 7z 9 fig4 #aeb17 :]e ! rays com+ f ! po9t ,e ( ! object1 :i* lies on ! axis ( ! glass ,a ,b1 issue out ( ! glass1 z if !y came f ! po9t ,f m remote f ! glass ?an ,e2 & ! rays proce$+ f ! po9t ,c issue out ( ! glass1 z if !y proce$$ f ! po9t ,g2 likewise ! rays :i* issue f ! po9t ,d em]ge out ( ! glass1 z if !y came f ! po9t ,h4 ,"h ! po9t ,g is on ! same side ( ! axis1 z ! po9t ,c2 & ! po9t ,h on ! same side1 z ! po9t ,d4 ,9 ?is case to an eye plac$ beyond ! glass ! object %\ld appe>1 z if x 7 9 ! situation ,g ,f ,h4 #h4 ,,if ! glass ,a ,b _h be5 concave 7z 91 fig4 #aec17 to an eye beyond ! glass ! object ,c ,d w\ld appe> 9 ! situation ,g ,h1 ne>] to ! glass ?an really x is4 ,"h also ! object w n be inv]t$2 b ! po9t ,g is on ! same side ! axe ) ! po9t ,c1 & ,h on ! same side z ,d4 #i4 ,,h5ce may be und]/ood1 :y spectacles made ) convex glasses help ! sight 9 old age3 = ! eye 9 t age becomes unfit to see objects di/9ctly1 except su* z are remov'd to a v great di/ance2 :5ce all m51 :5 !y fir/ /& 9 ne$ ( spectacles1 are obs]v$ to read at arm's l5g?1 & to hold ! object at a great] di/ance1 ?an !y us$ to d be=e4 ,b :5 an object is remov$ at too great a di/ance f ! sight1 x _c be se5 cle>ly1 by reason t a less quantity ( light f ! object w ent] ! eye1 & ! :ole object w also appe> small]4 ,n[ by help ( a convex glass an object may be held ne>1 & yet ! rays ( light issu+ f x w ent] ! eye1 z if ! object 7 f>!r remov$4 #aj4 ,,aft] ! same mann] concave glasses assi/ su*1 z are %ort sight$4 ,= ^! require ! object to be br\ght inconv5i5tly ne> to ! eye1 9 ord] to _! see+ x di/9ctly2 b by su* a glass ! object may be remov$ to a prop] di/ance1 & yet ! rays ( light ent] ! eye1 z if !y came f a place mu* ne>]4 #aa4 ,,:5ce ^! defects ( ! sight arise1 t 9 old age objects _c be se5 di/9ct )9 a mod]ate di/ance1 & 9 %ort-sight$ness n )\t be+ br\ght too ne>1 w be easily und]/ood1 :5 ! mann] ( vision 9 g5]al %all be expla9'd2 :i* ,i %all n[ endeav\r to d1 9 ord] to be bett] und]/ood 9 :at foll[s4 ,! eye is =m'd1 z is repres5t$ 9 fig4 #aed4 ,x is ( a globul> figure1 ! =e "p :]e( sc>ce m protub]ant ?an ! re/ is transp>5t4 ,und]nea? ?is transp>5t "p is a small collection ( an hum\r 9 appe>ance l wat]1 & x has also ! same refractive p[] z common wat]2 ?is is call$ ! aque\s hum\r1 & fills ! space ,a ,b ,c ,d 9 ! figure4 ,next beyond lies ! body ,d ,e ,f ,g2 ?is is solid b transp>5t1 x is compos$ ) two convex surfaces1 ! h9d] surface ,e ,f ,g be+ m convex1 ?an ! ant]ior ,e ,d ,g4 ,betwe5 ! out] membrane ,a ,b ,c1 & ?is body ,e ,d ,g ,f is plac$ t membrane1 :i* exhibits ! col\rs1 t are se5 r\nd ! sight ( ! eye2 & ! black spot1 :i* is call$ ! sight or pupil1 is a hole 9 ?is membrane1 ?r\gh :i* ! light ent]s1 :]eby we see4 ,?is membrane is fix$ only by its outw>d circuit1 & has a muscul> p[]1 :]eby x dilates ! pupil 9 a weak light1 & contracts x 9 a /rong "o4 ,! body ,d ,e ,f ,g is call$ ! cry/all9e hum\r1 & has a great] refract+ p[] ?an wat]4 ,beh9d ?is ! bulk ( ! eye is fill$ up ) :at is call$ ! vitre\s humor1 ?is has mu* ! same refractive p[] ) wat]4 ,at ! bottom ( ! eye t[>d ! inn] side next ! nose ! optic glass ent]s1 z at ,h1 & spreads x self all ov] ! inside ( ! eye1 till )9 a small diftance f ,a & ,c4 ,n[ any object1 z ,i ,k1 be+ plac$ be=e ! eye1 ! rays ( light issu+ f ea* po9t ( ?is object are s refract$ by ! convex surface ( ! aque\s hum\r1 z to be caus$ to conv]ge2 aft] ?is be+ receiv$ by ! convex surface ,e ,d ,g ( ! cry/all9e hum\r1 :i* has a great] refractive p[] ?an ! aque\s1 ! rays1 :5 !y are ent]$ into ?is surface1 /ill m conv]ge1 & at go+ out ( ! surface ,e ,f ,g into a hum\r ( a less refractive p[] ?an ! cry/all9e !y are made to conv]ge yet f>!r4 ,by all ^! successive refractions !y are br\ght to conv]ge at ! bottom ( ! eye1 s t a di/9ct image ( ! object z ,l ,m is impress'd on ! n]ve4 ,& by ?is means ! object is se54 #aa4 ,,x has be5 made a difficulty1 t ! image ( ! object impress$ on ! n]ve is inv]t$1 s t ! upp] "p ( ! image is impress$ on ! l[] "p ( ! eye4 ,b ?is difficulty1 ,i ?9k1 c no long] rema91 if we only consid]1 t upp] & l[] are t]ms m]ely relative to ! ord9>y position ( our bodies3 & our bodies1 :5 view'd by ! eye1 h _! image z mu* inv]t$ z o!r objects2 s t ! image ( our own bodies1 & ( o!r objects1 are impress$ on ! eye 9 ! same relation to "o ano!r1 z !y really h4 #ab4 ,,! eye c see objects equally di/9ct at v diff]5t di/ances1 b 9 "o di/ance only at ! same "t4 ,t ! eye may accomodate itself to diff]5t di/ances1 "s *ange 9 its hum\rs is requir'd4 ,x is my op9ion1 t ?is *ange is made 9 ! figure ( ! cry/all9e hum\r1 z ,i h indeav\r$ to prove 9 ano!r place4 #ac4 ,,if any ( ! hum\rs ( ! eye are too flat1 !y w refract ! light too little2 :i* is ! case 9 old age4 ,if !y are too convex1 !y refract too mu*2 z 9 ^? :o are %ort-sight$4 #ad4 ,,! mann] ( direct vision be+ ?us expla9$1 ,i proce$ to give "s acc\nt ( telescopes1 by :i* we view m di/9ctly remote objects2 & also ( microscopes1 :]eby we magnify ! appe>ance ( small objects4 ,9 ! fir/ place1 ! mo/ simple sort ( telescope is compos$ ( two glasses1 ei!r bo? convex1 or "o convex1 & ! o!r concave4 7,! fir/ sort ( ^! is repres5t$ 9 fig4 #aee1 ! latt] 9 fig4 #aef47 #ae4 ,,9 fig4 #aee let ,a ,b repres5t ! convex glass next ! object1 ,c ,d ! o!r glass m convex ne> ! eye4 ,suppose ! object-glass ,a ,b to =m ! image ( ! object at ,e ,f2 s t if a %eet ( :ite pap] 7 to be held 9 ?is place1 ! object w\ld appe>4 ,n[ suppose ! rays1 :i* pass ! glass ,a ,b1 & are unit$ ab\t ,f1 to proce$ to ! eye glass ,c ,d1 & be !re refract$4 ,?ree only ( ^! rays are drawn 9 ! figure1 ^? :i* pass by ! extremities ( ! glass ,a ,b1 & t :i* passes its middle4 ,if ! glass ,c ,d be plac$ at su* a di/ance f ! image ,e ,f1 t ! rays1 :i* pass by ! po9t ,f1 aft] hav+ proce$$ ?r\gh ! glass div]ge s mu*1 z ! rays d t come f an object1 :i* is at su* a di/ance f ! eye z to be se5 di/9ctly1 ^! be+ receiv$ by ! eye w make on ! bottom ( ! eye a di/9ct repres5tation ( ! po9t ,f4 ,9 l mann] ! rays1 :i* pass ?r\gh ! object glass ,a ,b to ! po9t ,e aft] proce$+ ?r\gh ! eye-glass ,c ,d w on ! bottom ( ! eye make a di/9ct repres5tation ( ! po9t ,e4 ,b if ! eye be plac$ :]e ^! rays1 :i* proce$ f ,e1 cross ^?1 :i* proce$ f ,f1 ! eye w receive ! di/9ct impression ( bo? ^! po9ts at ! same "t2 & consequ5tly w also receive a di/9ct impression f all ! int]m$iate p>ts ( ! image ,e ,f1 t is1 ! eye w see ! object1 to :i* ! telescope is direct$1 di/9ctly4 ,! place ( ! eye is ab\t ! po9t ,g1 :]e ! rays ,h ,e1 ,h ,f cross1 :i* pass ?r\gh ! middle ( ! object-glass ,a ,b to ! po9ts ,e & ,f2 or at ! place :]e ! focus w\ld be =m$ by rays com+ f ! po9t ,h1 & refract$ by ! glass ,c ,d4 ,to judge h[ mu* ?is in/rum5t magnifies any object1 we mu/ fir/ obs]ve1 t ! angle "u ,e ,h ,f1 9 :i* ! eye at ! po9t ,h w\ld see ! image ,e ,f1 is ne>ly ! same z ! angle1 "u :i* ! object appe>s by direct vision2 b :5 ! eye is 9 ,g1 & views ! object ?r\gh ! telescope1 x sees ! same "u a great] angle2 = ! rays1 :i* com+ f ,e & ,f cross 9 ,g1 make a great] angle ?an ! rays1 :i* proce$ f ! po9t ,h to ^! po9ts ,e & ,f4 ,! angle at ,g is great] ?an t at ,h 9 ! proportion1 z ! di/ance betwe5 ! glasses ,a ,b & ,c ,d is great] ?an ! di/ance ( ! po9t ,g f ! glass ,c ,d4 #af4 ,,?is telescope inv]ts ! object2 = ! rays1 :i* came f ! "r-h& side ( ! object1 g to ! po9t ,e ! left side ( ! image2 & ! rays1 :i* come f ! left side ( ! object1 g to ,f ! "r side ( ! image4 ,^! rays cross aga9 9 ,g1 s t ! rays1 :i* come f ! "r side ( ! object1 g to ! "r side ( ! eye2 & ! rays f ! left side ( ! object g to ! left side ( ! eye4 ,!re=e 9 ?is telescope ! image 9 ! eye has ! same situation z ! object2 & see+ t 9 direct vision ! image 9 ! eye has an inv]t$ situation1 "h1 :]e ! situation is n inv]t$1 ! object mu/ appe> s4 ,?is is no inconv5i5ce to a/ronom]s 9 cele/ial obs]vations2 b = objects "h on ! e>? x is usual to add two o!r convex glasses1 :i* may turn ! object aga9 7z is repres5t$ 9 fig4 #aeg17 or else to use ! o!r k9d ( telescope ) a concave eye-glass4 #ag4 ,,9 ?is o!r k9d ( telescope ! effect is f\nd$ on ! same pr9ciples1 z 9 ! =m]4 ,! di/9ctness ( ! appe>ance is procur$ 9 ! same mann]4 ,b "h ! eye-glass ,c ,d 79 fig4 #aef7 is plac$ betwe5 ! image ,e ,f1 & ! object glass ,a ,b4 ,by ?is means ! rays1 :i* come f ! "r-h& side ( ! object1 & proce$ t[>d ,e ! left side ( ! image1 be+ int]cept$ by ! eye-glass are c>ri$ to ! left side ( ! eye2 & ! rays1 :i* come f ! left side ( ! object1 g to ! "r side ( ! eye2 s t ! impression 9 ! eye be+ inv]t$ ! object appe>s 9 ! same situation1 z :5 view'd by ! nak$ eye4 ,! eye mu/ "h be plac$ close to ! glass4 ,! degree ( magnify+ 9 ?is in/rum5t is ?us to be f\nd4 ,let ! rays1 :i* pass ?r\gh ! glass ,a ,b at ,h1 aft] ! refraction ( ! eye-glass ,c ,d div]ge1 z if !y came f ! po9t ,g2 !n ! rays1 :i* come f ! extremities ( ! object1 ent] ! eye "u ! angle at ,g2 s t "h also ! object w be magnifi$ 9 ! proportion ( ! di/ance betwe5 ! glasses1 to ! di/ance ( ,g f ! eye-glass4 #ah4 ,,! space1 t c be tak5 9 at "o view 9 ?is telescope1 dep5ds on ! bread? ( ! pupil ( ! eye2 = z ! rays1 :i* g to ! po9ts ,e1 ,f ( ! image1 are some?+ di/ant f ea* o!r1 :5 !y come out ( ! glass ,c ,d1 if !y are wid] asund] ?an ! pupil1 x is evid5t1 t !y _c bo? ent] ! eye at once4 ,9 ! o!r telescope ! eye is plac$ 9 ! po9t ,g1 :]e ! rays t come f ! po9ts ,e or ,f cross ea* o!r1 & !re=e mu/ ent] ! eye toge!r4 ,on ?is acc\nt ! telescope ) convex glasses takes 9 a l>g] view1 ?an ^? ) concave4 ,b 9 ^! also ! ext5t ( ! view is limit$1 because ! eye-glass does n by ! refraction t[>ds its edges =m s di/9ct a repres5tation ( ! object1 z ne> ! middle4 #ah4 ,,microscopes are ( two sorts4 ,"o k9d is only a v convex glass1 by ! means ( :i* ! object may be br\ght v ne> ! eye1 & yet be se5 di/9ctly4 ,?is microscope magnifies 9 proportion1 z ! object by be+ br\ght ne> ! eye w =m a broad] impression on ! optic n]ve4 ,! o!r k9d made ) convex glasses produces its effects 9 ! same mann] z ! telescope4 ,let ! object ,a ,b 79 fig4 #aeh7 be plac$ "u ! glass ,c ,d1 & by ?is glass let an image be =m$ ( ?is object4 ,above ?is image let ! glass ,g ,h be plac$4 ,by ?is glass let ! rays1 :i* proce$ f ! po9ts ,a & ,b1 be refract$1 z is express$ 9 ! figure4 ,9 p>ticul>1 let ! rays1 :i* f ea* ( ^! po9ts pass ?r\gh ! middle ( ! glass ,c ,d1 cross 9 ,i1 & !re let ! eye be plac$4 ,"h ! object w appe> l>g]1 :5 se5 ?r\gh ! microscope1 ?an if t in/rum5t 7 remov$1 9 proportion z ! angle1 9 :i* ^! rays cross 9 ,i1 is great] ?an ! angle1 :i* ! l9es w\ld make1 t %\ld be drawn f ,i to ,a & ,b2 t is1 9 ! proportion made up ( ! proportion ( ! di/ance ( ! object ,a ,b f ,i1 to ! di/ance ( ,i f ! glass ,g ,h2 & ( ! proportion ( ! di/ance betwe5 ! glasses1 to ! di/ance ( ! object ,a ,b f ! glass ,c ,d4 #ai4 ,i ,,%all n[ proce$ to expla9 ! imp]fection 9 ^! in/rum5ts1 occasion$ by ! diff]5t refrangibility ( ! light :i* comes f e object4 ,?is prev5ts ! image ( ! object f be+ =m$ 9 ! focus ( ! object glass ) p]fect di/9ctness2 s t if ! eye-glass magnify ! image ov]mu*1 ! imp]fections ( x mu/ be visible1 & make ! :ole appe> confus$4 ,our au?or m fully to satisfy himself1 t ! diff]5t refrangibility ( ! sev]al sorts ( rays is suffici5t to produce ?is irregul>ity1 und]w5t ! lab\r ( a v nice & difficult exp]im5t1 ^: process he has at l>ge set d[n1 to prove1 t ! rays ( light are refract$ z diff]5tly 9 ! small refraction ( telescope glasses z 9 ! l>g] ( ! prism2 s exce$+ c>eful has he be5 9 se>*+ out ! true cause ( ?is effect4 ,& he us$1 ,i suppose1 ! great] caution1 because ano!r reason _h be=e be5 g5]ally assign$ = x4 ,x 0 ! op9ion ( all ma!maticians1 t ?is defect 9 telescopes arose f ! figure1 9 :i* ! glasses 7 =m$2 a sph]ical refract+ surface n collect+ into an exact po9t all ! rays :i* come f any "o po9t ( an object1 z has be=e be5 said#ccj4 ,b aft] our au?or has prov$1 t 9 ^! small refractions1 z well z 9 great]1 ! s9e ( incid5ce into air out ( glass1 to ! s9e ( refraction 9 ! r$-mak+ rays1 is z #ej to #gg1 & 9 ! blue-mak+ rays #ej to #gh2 he proce$s to comp>e ! inequalities ( refraction aris+ f ?is diff]5t refrangibility ( ! rays1 ) ! inequalities1 :i* w\ld foll[ f ! figure ( ! glass1 7 light uni=mly refract$4 ,= ?is purpose he obs]ves1 t if rays issu+ f a po9t s remote f ! object glass ( a telescope1 z to be e/eem$ p>allel1 :i* is ! case ( ! rays1 :i* come f ! heav5ly bodies2 !n ! di/ance f ! glass ( ! po9t1 9 :i* ! lea/ refrangible rays are unit$1 w be to ! di/ance1 at :i* ! mo/ refrangible rays unite1 z #bh to #bg2 & !re=e t ! lea/ space1 into :i* all ! rays c be collect$1 w n be less ?an ! #ee? "p ( ! bread? ( ! glass4 ,= if ,a ,b 79 fig4 #aei7 be ! glass1 ,c ,d its axis1 ,e ,a1 ,f ,b two rays ( ! light p>allel to t axis entr+ ! glass ne> its edges2 aft] refraction let ! lea/ refrangible "p ( ^! rays meet 9 ,g1 ! mo/ refrangible 9 ,h2 !n1 z has be5 said1 ,g ,i w be to ,i ,h1 z #bh to #bg2 t is1 ,g ,h w be ! #bh? "p ( ,g ,i1 & ! #bg? "p ( ,h ,i2 :5ce if ,k ,l be drawn ?r\gh ,g1 & ,m ,n ?r\gh ,h1 p]p5dicul> to ,c ,d1 ,m ,n w be ! a #bh? "p ( ,a ,b1 ! bread? ( ! glass1 & ,k ,l ! #bg? "p ( ! same2 s t ,o ,p ! lea/ space1 into :i* ! rays are ga!r$1 w be ab\t half ! mean betwe5 ^! two1 t is ! #ee? "p ( ,a ,b4 #bj4 ,,?is is ! error aris+ f ! diff]5t refrangibility ( ! rays ( light1 :i* our au?or f9ds va/ly to exce$ ! o!r1 consequ5t ^u ! figure ( ! glass4 ,9 p>ticul>1 if ! telescope glass be flat on "o side1 & convex on ! o!r2 :5 ! flat side is turn$ t[>ds ! object1 by a !orem1 :i* he has laid d[n1 ! error f ! figure comes out above #ejjj times less ?an ! o!r4 ,?is o!r inequality is s great1 t telescopes c\ld n p]=m s well z !y d1 7 x n t ! light does n equally fill all ! space ,o ,p1 ov] :i* x is scatt]$1 b is mu* m d5se t[>d ! middle ( t space ?an at ! extremities4 ,& besides1 all ! k9ds ( rays affect n ! s5se equally /rong1 ! yell[ & orange be+ ! /ronge/1 ! r$ & gre5 next to !m1 ! blue indigo & violet be+ mu* d>k] & fa9t] col\rs2 & x is %ewn t all ! yell[ & orange1 & ?ree fif?s ( ! bright] half ( ! r$ next ! orange1 & z great a %>e ( ! bright] half ( ! gre5 next ! yell[1 w be collect$ into a space ^: bread? is n above ! #bej? "p ( ! bread? ( ! glass4 ,illu/ration ,& ! rema9+ col\rs1 :i* fall )\t ?is space1 z !y are mu* m dull & obscure ?an ^!1 s w !y be likewise mu* m diffus$2 & !re=e call h>dly affect ! s5se 9 comp>ison ( ! o!r4 ,& agreeable to ?is is ! obs]vation ( a/ronom]s1 t telescopes betwe5 tw5ty & sixty feet 9 l5g? repres5t ! fix$ />s1 z be+ ab\t #e or #f1 at mo/ ab\t #h or #aj seconds 9 diamet]4 ,:]eas o!r argum5ts %ew u1 t !y d n really appe> to u ( any s5sible magnitude any o!rwise ?an z _! light is dilat$ by refraction4 ,"o pro( t ! fix$ />s d n appe> to u "u any s5sible angle is1 t :5 ! moon passes ov] any ( !m1 _! light does n1 l ! planets on ! same occasion1 disappe> by degrees1 b vani%es at once4 #ba4 ,,our au?or be+ ?us conv9c$1 t telescopes 7 n capable ( be+ br\ght to mu* great] p]fection ?an at pres5t by refractions1 contriv$ "o by reflection1 9 :i* !re is no sep>ation made ( ! diff]5t col\r$ light2 = 9 e k9d ( light ! rays aft] reflection h ! same degree ( incl9ation to ! surface1 f :5ce !y are reflect$1 z !y h at _! incid5ce1 s t ^? rays :i* come to ! surface 9 "o l9e1 w g (f also 9 "o l9e )\t any p>t+ f "o ano!r4 ,accord+ly 9 ! attempt he succe$$ s well1 t a %ort "o1 n mu* exce$+ six in*es 9 l5g?1 equall$ an ord9>y telescope ^: l5g? 0 f\r feet4 ,in/rum5ts ( ?is k9d to great] l5g?s1 h ( late be5 made1 :i* fully answ] expectation#cca4 ,,*ap4 ,v4 ,( ! ,,ra9b[4 ,i ,,%all n[ expla9 ! ra9b[4 ,! mann] ( its production 0 und]/ood1 9 ! g5]al1 be=e ,sir ,,isaac ,,newton _h discov]$ 8 !ory ( col\rs2 b :at caus$ ! div]sity ( col\rs 9 x c\ld n !n be kn[n1 :i* obliges him to expla9 ?is appe>ance p>ticul>ly2 :om we %all imitate z foll[s4 ,! fir/ p]son1 :o expressly %ew$ ! ra9b[ to be =m$ by ! reflection ( ! sun-beams f drops ( fall+ ra91 0 ,,antonio ,,de ,,dom9is4 ,b ?is 0 aft]w>ds m fully & di/9ctly expla9$ by ,,desc>tes4 #b4 ,,!re appe>s mo/ frequ5tly two ra9b[s2 bo? ( :i* are caus$ by ! =esaid reflection ( ! sun-beams f ! drops ( fall+ ra91 b are n produc$ by all ! light :i* falls ^u & are reflect$ f ! drops4 ,! inn] b[ is produc$ by ^? rays only :i* ent] ! drop1 & at _! entrance are s refract$ z to unite into a po9t1 z x 71 ^u ! f>!r surface ( ! drop1 z is repres5t$ 9 fig4 #afj2 :]e ! contigu\s rays a b1 c d1 e f1 com+ f ! sun1 & !re=e to s5se p>allel1 ^u _! entrance into ! drop 9 ! po9ts b1 d1 f1 are s refract$ z to meet toge!r 9 ! po9t g1 ^u ! f>!r surface ( ! drop4 ,n[ ^! rays be+ reflect$ ne>ly f ! same po9t ( ! surface1 ! angle ( incid5ce ( ea* ray ^u ! po9t g be+ equal to ! angle ( reflection1 ! rays w return 9 ! l9es g h1 g k1 g l1 9 ! same mann] incl9$ to ea* o!r1 z !y 7 be=e _! incid5ce ^u ! po9t g1 & w make ! same angles ) ! surface ( ! drop at ! po9ts b1 k1 l1 z at ! po9ts b1 d1 f1 aft] _! entrance2 & !re=e aft] _! em]g5ce out ( ! drop ea* ray w be incl9$ to ! surface 9 ! same angle1 z :5 x fir/ ent]$ x2 :5ce ! l9es b m1 k n1 l o1 9 :i* ! rays em]ge1 mu/ be p>allel to ea* o!r1 z well z ! l9es a b1 c d1 e f1 9 :i* !y 7 incid5t4 ,b ^! em]g+ rays be+ p>allel w n spread nor div]ge f ea* o!r 9 _! passage f ! drop1 & !re=e w ent] ! eye conv5i5tly situat$ 9 suffici5t pl5ty to cause a s5sation4 ,:]eas all ! o!r rays1 :e!r ^? ne>] ! c5t] ( ! drop1 z p q1 r s1 or ^? f>!r (f1 z t u1 w x1 w be reflect$ f o!r po9ts 9 ! h9d] surface ( ! drop2 namely1 ! ray p q f ! po9t y1 r s f z1 t v f 1 & w x f 4 ,& = ?is reason by _! reflection & succe$+ refraction !y w be scatt]$ aft] _! em]g5ce f ! =em5tion$ rays & f ea* o!r1 & !re=e _c ent] ! eye plac$ to receive !m copi\s en\gh to excite any di/9ct s5sation4 #c4 ,,! ext]nal ra9b[ is =m$ by two reflections made betwe5 ! incid5ce & em]g5ce ( ! rays2 = x is to be not$1 t ! rays g h1 g k1 g l1 at ! po9ts h1 k1 l1 d n :olly pass out ( ! drop1 b are 9 "p reflect$ back2 ?\gh ! second reflection ( ^! p>ticul> rays does n =m ! out] b[4 ,= ?is b[ is made by ^? rays1 :i* aft] _! entrance into ! drop are by ! refraction ( x unit$1 be=e !y arrive at ! f>!r surface1 at su* a di/ance f x1 t :5 !y fall ^u t surface1 !y may be reflect$ 9 p>allel l9es1 z is repres5t$ 9 fig4 #afa2 :]e ! rays a b1 c d1 e f1 are collect$ by ! refraction ( ! drop into ! po9t g1 & pass+ on f !nce /rike ^u ! surface ( ! drop 9 ! po9ts h1 k1 l1 & are !nce reflect$ to m1 n1 o1 pass+ f h to m1 f k to n1 & f l to o 9 p>allel l9es4 ,= ^! rays aft] reflection at m1 n1 o1 w meet aga9 9 ! po9t p1 at ! same di/ance f ^! po9ts ( reflection m1 n1 o1 z ! po9t g is f ! =m] po9ts ( reflection h1 k1 l4 ,!re=e ^! rays 9 pass+ f p to ! surface ( ! drop w fall ^u t surface 9 ! po9ts q1 r1 s 9 ! same angles1 z ^! rays made ) ! surface 9 b1 d1 f1 aft] refraction4 ,consequ5tly1 :5 ^! rays em]ge out ( ! drop into ! air1 ea* ray w make ) ! surface ( ! drop ! same angle1 z x made at its fir/ incid5ce2 s t ! l9es q t1 r v1 s w1 9 :i* !y come f ! drop1 w be p>allel to ea* o!r1 z well z ! l9es a b1 c d1 e f1 9 :i* !y came to ! drop4 ,by ?is means ^! rays to a spectator commodi\sly situat$ w become visible4 ,b all ! o!r rays1 z well ^? ne>] ! c5t] ( ! drop x y1 z 1 z ^? m remote f x 1 1 w be reflect$ 9 l9es n p>allel to ! l9es h m1 k n1 l o2 namely1 ! ray x y1 9 ! l9e 1 ! ray 9 ! l9e 1 ! ray 9 ! l9e 1 & ! ray 9 ! l9e 4 ,:5ce ^! rays aft] _! next reflection & subsequ5t refraction w be scatt]$ f ! =em5tion$ rays1 & f "o ano!r1 & by t means become invisible4 #d4 ,,x is f>!r to be rem>k$1 t if 9 ! fir/ case ! incid5t rays a b1 c d1 e f1 & _! correspond5t em]g5t rays h m1 k n1 l o1 are produc$ till !y meet1 !y w make ) ea* o!r a great] angle1 ?an any o!r incid5t ray w make ) its correspond+ em]g5t ray4 ,& 9 ! latt] case1 on ! contr>y1 ! em]g5t rays q t1 r v1 s w make ) ! incid5t rays an acut] angle1 ?an is made by any o!r ( ! em]g5t rays4 #e4 ,,our au?or deliv]s a me?od ( f9d+ ea* ( ^! extream angles f ! degree ( refraction be+ giv52 by :i* me?od x appe>s1 t ! fir/ ( ^! angles is ! less1 & ! latt] ! great]1 by h[ mu* ! refractive p[] ( ! drop1 or ! refrangibility ( ! rays is great]4 ,& ?is la/ consid]ation fully compleats ! doctr9e ( ! ra9b[1 & %ews1 :y ! col\rs ( ea* b[ are rang$ 9 ! ord] :]e9 !y are se54 #f4 ,,suppose ,a 79 fig4 #afb47 to be ! eye1 ,b1 ,c1 ,d1 ,e1 ,f1 drops ( ra91 ,m n1 ,o p1 ,q r1 ,s t1 ,v w p>cels ( rays ( ! sun1 :i* entr+ ! drops ,b1 ,c1 ,d1 ,e1 ,f aft] "o reflection pass out to ! eye 9 ,a4 ,n[ let ,m n be produc$ to till x meets ) ! em]g5t ray likewise produc$1 let ,o p produc$ meet its em]g5t ray produc$ 9 1 let ,q r meet its em]g5t ray 9 1 let ,s t meet its em]g5t ray 9 1 & let ,v w meet its em]g5t ray produc$ 9 4 ,if ! angle "u ,m ,a be t1 :i* is d]iv$ f ! refraction ( ! violet-mak+ rays by ! me?od we h "h spok5 (1 x foll[s t ! violet light w only ent] ! eye f ! drop ,b1 all ! o!r col\r$ rays pass+ bel[ x1 t is1 all ^? rays :i* are n scatt]$1 b g out p>allel s z to cause a s5sation4 ,= ! angle1 :i* ^! p>allel em]g5t rays makes ) ! incid5t 9 ! mo/ refrangible or violet-mak+ rays1 be+ less ?an ?is angle 9 any o!r sort ( rays1 none ( ! rays :i* em]ge p>allel1 except ! violet-mak+1 w ent] ! eye "u ! angle ,m ,a1 b ! re/ mak+ ) ! incid5t ray ,m a great] angle ?an ?is w pass bel[ ! eye4 ,9 l mann] if ! angle "u ,o ,a agrees to ! blue-mak+ rays1 ! blue rays only %all ent] ! eye f ! drop ,c1 & all ! o!r col\r$ rays w pass by ! eye1 ! violet-col\r$ rays pass+ above1 ! o!r col\rs bel[4 ,f>!r1 ! angle ,q ,a correspond+ to ! gre5-mak+ rays1 ^? only %all ent] ! eye f ! drop ,d1 ! violet & blue-mak+ rays pass+ above1 & ! o!r col\rs1 t is ! yell[ & r$1 bel[4 ,& if ! angle ,s ,a answ]s to ! refraction ( ! yell[-mak+ rays1 !y only %all come to ! eye f ! drop ,e4 ,& 9 ! la/ place1 if ! angle ,v ,a belongs to ! r$-mak+ & lea/ refrangible rays1 !y only %all ent] ! eye f ! drop ,f1 all ! o!r col\r$ rays pass+ above4 #g4 ,,b n[ x is evid5t1 t all ! drops ( wat] f\nd 9 any ( ! l9es ,a 1 ,a 1 ,a 1 ,a 1 :e!r f>!r f ! eye1 or ne>] ?an ! drops ,b1 ,c1 ,d1 ,e1 ,f1 w give ! same col\rs z ^! d1 all ! drops ^u ea* l9e giv+ ! same col\r2 s t ! light reflect$ f a numb] ( ^! drops w become copi\s en\gh to be visible2 :]eas ! reflection f "o m9ute drop alone c\ld n be p]ceiv$4 ,b besides1 x is f>!r manife/1 t if ! l9e ,a be drawn f ! sun ?r\gh ! eye1 t is1 p>allel to ! l9es ,m n1 ,o p1 ,q r1 ,s t1 ,v w1 & if drops ( wat] are plac$ all r\nd ?is l9e1 ! same col\r w be exhibit$ by all ! drops at ! same di/ance f ?is l9e4 ,h5ce x foll[s1 t :5 ! sun is mod]ately elevat$ above ! horizon1 if x ra9s opposite to x1 & ! sun %9es ^u ! drops z !y fall1 a spectator ) 8 back turn$ to ! sun mu/ obs]ve a col\r$ circul> ar* rea*+ to ! horizon1 be+ r$ )\t1 next to t yell[1 !n gre51 blue1 & on ! inn] edge violet2 only ?is la/ col\r appe>s fa9t by be+ dilut$ ) ! :ite light ( ! cl\ds1 & f ano!r cause to be m5tion$ h]eaft]#ccb4 #h4 ,,?us is caus$ ! int]ior or prim>y b[4 ,! drops ( ra9 at "s di/ance )\t ?is b[ w cause ! ext]ior or second>y b[ by two reflections ( ! sun's light4 ,let ^! drops be ,g1 ,h1 ,i1 ,k1 ,l2 ,x y1 ,z 1 1 1 d5ot+ p>cels ( rays :i* ent] ea* drop4 ,n[ x has be5 rem>k$1 t ^! rays make ) ! visible refract$ rays ! greate/ angle 9 ^? rays1 :i* are mo/ refrangible4 ,suppose !re=e ! visible refract$ rays1 :i* pass out f ea* drop aft] two reflections1 & ent] ! eye 9 ,a1 to int]sect ! incid5t rays 9 1 1 1 1 respectively4 ,x is manife/1 t ! angle "u ,a is ! greate/ ( all1 next to t ! angle "u ,a1 ! next 9 bigness w be ! angle "u ,a1 ! next to ?is ! angle "u ,z ,a1 & ! lea/ ( all ! angle "u ,x ,a4 ,f ! drop ,l !re=e w come to ! eye ! violet-mak+1 or mo/ refrangible rays1 f ,k ! blue1 f ,i ! gre51 f ,h ! yell[1 & f ,g ! r$-mak+ rays2 & ! l w happ5 to all ! drops 9 ! l9es ,a 1 ,a 1 ,a 1 ,a 1 & also to all ! drops at ! same di/ances f ! l9e ,a all r\nd t l9e4 ,:5ce appe>s ! reason ( ! second>y b[1 :i* is se5 )\t ! o!r1 hav+ its col\rs 9 a contr>y ord]1 violet )\t & r$ )92 ?\gh ! col\rs are fa9t] ?an 9 ! o!r b[1 z be+ made by two reflections1 & two refractions2 :]eas ! o!r b[ is made by two refractions1 & "o reflection only4 #i4 ,,!re is a f>!r appe>ance 9 ! ra9b[ p>ticul>ly describ$ ab\t five ye>s ago#ccc1 :i* is1 t "u ! upp] "p or ! inn] b[ !re appe>s (t5 two or ?ree ord]s ( v fa9t col\rs1 mak+ alt]nate ar*es ( gre51 & a r$di% purple4 ,at ! "t ?is appe>ance 0 tak5 notice (1 ,i gave my ?\ghts conc]n+ ! cause ( x#ccd1 :i* ,i %all "h repeat4 ,sir ,,isaac ,,newton has obs]v$1 t 9 glass1 :i* is poli%$ & quick-silv]$1 !re is an irregul> refraction made1 :]eby "s small quantity ( light is scatt]$ f ! pr9cipal reflect$ beam#cce4 ,if we all[ ! same ?+ to happ5 9 ! reflection :]eby ! ra9b[ is caus$1 x seems suffici5t to produce ! appe>ance n[ m5tion$4 #aj4 ,,let ,a ,b 79 fig4 #afb47 repres5t a globule ( wat]1 ,b ! po9t f :5ce ! rays ( any det]m9ate species be+ reflect$ to ,c1 & aft]w>ds em]g+ 9 ! l9e ,c ,d1 w\ld proce$ to ! eye1 & cause ! appe>ance ( t col\r 9 ! ra9b[1 :i* app]ta9s to ?is species4 ,"h suppose1 t besides :at is reflect$ regul>ly1 "s small "p ( ! light is irregul>ly scatt]$ e way2 s t f ! po9t ,b1 besides ! rays t are regul>ly reflect$ f ,b to ,c1 "s scatt]$ rays w return 9 o!r l9es1 z 9 ,b ,e1 ,b ,f1 ,b ,g1 ,b ,h1 on ea* side ! l9e ,b ,c4 ,n[ x has be5 obs]v$ above#ccf1 t ! rays ( light 9 _! passage f "o sup]ficies ( a refract+ body to ! o!r und]go alt]nate fits ( easy transmission & reflection1 succe$+ ea* o!r at equal int]vals2 insomu* t if !y rea* ! f>!r sup]ficies 9 "o sort ( ^? fits1 !y %all be transmitt$2 if 9 ! o!r k9d ( !m1 !y %all r be reflect$ back4 ,:5ce ! rays t proce$ f ,b to ,c1 & em]ge 9 ! l9e ,c ,d1 be+ 9 a fit ( easy transmission1 ! scatt]$ rays1 t fall at a small di/ance )\t ^! on ei!r side 7suppose ! rays t pass 9 ! l9es ,b ,e1 ,b ,g7 %all fall on ! surface 9 a fit ( easy reflection1 & %all n em]ge2 b ! scatt]$ rays1 t pass at "s di/ance )\t ^! la/1 %all arrive at ! surface ( ! globule 9 a fit ( easy transmission1 & break ?r\gh t surface4 ,suppose ^! rays to pass 9 ! l9es ,b ,f1 ,b ,h2 ! =m] ( :i* rays %all h _h "o fit m ( easy transmission1 & ! latt] "o fit less1 ?an ! rays t pass f ,b to ,c4 ,n[ bo? ^! rays1 :5 !y g out ( ! globule1 w proce$ by ! refraction ( ! wat] ,9 ! l9es ,f ,i1 ,h ,k1 t w be incl9$ almo/ equally to ! rays incid5t on ! globule1 :i* come f ! sun2 b ! angles ( _! incl9ation w be less ?an ! angle1 9 :i* ! rays em]g+ 9 ! l9e ,c ,d are incl9$ to ^? incid5t rays4 ,& aft] ! same mann] rays scatt]$ f ! po9t ,b at a c]ta9 di/ance )\t ^! w em]ge out ( ! globule1 :ile ! int]m$iate rays are int]cept$2 & ^! em]g5t rays w be incl9$ to ! rays incid5t on ! globule 9 angles /ill less ?an ! angles1 9 :i* ! rays ,f ,i & ,h ,k are incl9$ to !m2 & )\t ^! rays w em]ge o!r rays1 t %all be incl9$ to ! incid5t rays 9 angles yet less4 ,illu/ration ,n[ by ?is means may be =m$ ( e k9d ( rays1 besides ! pr9cipal ar*1 :i* goes to ! =mation ( ! ra9b[1 o!r ar*es )9 e "o ( ! pr9cipal ( ! same col\r1 ?\gh mu* m fa9t2 & ?is = div]s successions1 z long z ^! weak lights1 :i* 9 e ar* gr[ m & m obscure1 %all cont9ue visible4 ,n[ z ! ar*es produc$ by ea* col\r w be v>i\sly mix$ toge!r1 ! div]sity ( col\rs obs]v'd 9 ^! second>y ar*es may v possibly arise f !m4 #aa4 ,,9 ! d>k] col\rs ^! ar*es may rea* bel[ ! b[1 & be se5 di/9ct4 ,9 ! bright] col\rs ^! ar*es are lo/ 9 ! inf]ior "p ( ! pr9cipal light ( ! ra9b[2 b 9 all probability !y contribute to ! r$ t9cture1 :i* ! purple ( ! ra9b[ usually has1 & is mo/ rem>kable :5 ^! second>y col\rs appe> /ronge/4 ,h[ev] ^! second>y ar*es 9 ! brighte/ col\rs may possibly ext5d ) a v fa9t light bel[ ! b[1 & t+e ! purple ( ^! second>y ar*es ) a r$di% hue4 #ab4 ,,! precise di/ances betwe5 ! pr9cipal ar* & ^! fa9t] ar*es dep5d on ! magnitude ( ! drops1 :]e9 !y are =m$4 ,to make !m any degree sep>ate x is necess>y ! drop be exce$+ small4 ,x is mo/ likely1 t !y are =m$ 9 ! vap\r ( ! cl\d1 :i* ! air be+ put 9 motion by ! fall ( ! ra9 may c>ry d[n along ) ! l>g] drops2 & ?is may be ! reason1 :y ^! col\rs appe> "u ! upp] "p ( ! b[ only1 ?is vap\r n desc5d+ v l[4 ,z a f>!r confirmation ( ?is1 ^! col\rs are se5 /ronge/1 :5 ! ra9 falls f v black cl\ds1 :i* cause ! fi]ce/ ra9s1 by ! fall :]e( ! air w be mo/ agitat$4 #ac4 ,,to ! l alt]nate return ( ! fits ( easy transmission & reflection 9 ! passage ( light ?r\gh ! globules ( wat]1 :i* compose ! cl\ds1 ,sir ,,isaac ,,newton ascribes "s ( ^? col\r$ circles1 :i* at times appe> ab\t ! sun & moon#ccg4 ,illu/ration ,illu/ration ,,conclusion4 ,,sir ,,isaac ,,newton hav+ conclud$ ea* ( 8 philosophical treatises ) "s g5]al reflections1 ,i %all n[ take leave ( my read]s ) a %ort acc\nt ( :at he has !re deliv]$4 ,at ! end ( 8 ma!matical pr9ciples ( natural philosophy he has giv5 u 8 ?\ghts conc]n+ ! ,deity4 ,:]e9 he fir/ obs]ves1 t ! similitude f\nd 9 all p>ts ( ! univ]se makes x und\bt$1 t ! :ole is gov]n$ by "o supreme be+1 to :om ! orig9al is ow+ ( ! frame ( nature1 :i* evid5tly is ! effect ( *oice & design4 ,he !n proce$s briefly to /ate ! be/ metaphysical notions conc]n+ ,god4 ,9 %ort1 we _c conceive ei!r ( space or "t o!rwise ?an z necess>ily exi/+2 ?is ,be+ !re=e1 on :om all o!rs dep5d1 mu/ c]ta9ly exi/ by ! same necessity ( nature4 ,consequ5tly :]ev] space & "t is f\nd1 !re ,god mu/ also be4 ,& z x appe>s impossible to u1 t space %\ld be limit$1 or t "t %\ld h _h a beg9n+1 ! ,deity mu/ be bo? imm5se & et]nal4 #b4 ,,at ! end ( 8 treatise ( optics he has propos$ "s ?\ghts conc]n+ o!r p>ts ( nature1 :i* he _h n di/9ctly se>*$ into4 ,he beg9s ) "s f>!r reflections conc]n+ light1 :i* he _h n fully exam9$4 ,9 p>ticul> he decl>es 8 s5tim5ts at l>ge conc]n+ ! p[]1 :]eby bodies & light act on ea* o!r4 ,9 "s p>ts ( 8 book he _h giv5 %ort h9ts at 8 op9ion conc]n+ ?is#cch1 b "h he expressly decl>es 8 conjecture1 :i* we h already m5tion$#cci1 t ?is p[] is lodg$ 9 a v subtle _s ( a great ela/ic =ce diffus$ ?ro' ! univ]se1 produc+ n only ?is1 b _m o!r natural op]ations4 ,he ?9ks x n impossible1 t ! p[] ( gravity itself %\ld be ow+ to x4 ,on ?is occasion he enum]ates _m natural appe>ances1 ! *ief ( :i* are produc$ by *ymical exp]im5ts4 ,f num]\s obs]vations ( ?is k9d he makes no d\bt1 t ! smalle/ p>ts ( matt]1 :5 ne> contact1 act /rongly on ea* o!r1 sometimes be+ mutually attract$1 at o!r times repell$4 #c4 ,,! attractive p[] is m manife/ ?an ! o!r1 = ! p>ts ( all bodies adh]e by ?is pr9ciple4 ,& ! "n ( attraction1 :i* our au?or has giv5 to x1 has be5 v freely made use ( by _m writ]s1 & z mu* object$ to by o!rs4 ,he has (t5 compla9$ to me ( hav+ be5 misund]/ood 9 ?is matt]4 ,:at he lays ^u ?is head 0 n int5d$ by him z a philosophical explanation ( any appe>ances1 b only to po9t out a p[] 9 nature n hi!rto di/9ctly obs]v$1 ! cause ( :i*1 & ! mann] ( its act+1 he ?\ght 0 wor?y ( a dilig5t enquiry4 ,to acquiesce 9 ! explanation ( any appe>ance by ass]t+ x to be a g5]al p[] ( attraction1 is n to improve our k 9 philosophy1 b r to put a /op to our f>!r se>*4 ,,f9is4 ,illu/ration ,,footnotes3 #a ,philosoph4 ,nat4 pr9c4 ma?4 ,l4 iii4 introduct4 #b ,nov4 ,org4 ,sci5t4 ,l4 i4 ,aphorism4 #i4 #c ,nov4 ,org4 ,l4 i4 ,aph4 #ai4 #d ,ibid4 ,aph4 #be4 #e ,aph4 #cj4 ,errores radicales 9 prima dige/ione m5tis ab excell5tia functionum rem$iorum sequ5tium non curantur4 #f ,aph4 #ch4 #g ,ibid4 #h ,aph4 #ci4 #i ,aph4 #da4 #aj ,aph4 #aj1 #bd4 #aa ,aph4 #de4 #ab ,de ,c>tes ,pr9c4 ,phil4 ,"p4 #c4 4 #eb4 #ac ,f]mat1 9 ,op]4 pag4 #aef1 c4 #ad ,nov4 ,org4 ,aph4 #df4 #ae ,aph4 #ej4 #af ,ibid4 #ag ,aph #ec4 #ah ,aph4 #ed4 #ai ,aph4 #ef4 #bj ,aph4 #ee4 #ba ,locke1 ,on human und]/&+1 ,b4 iii4 #bb ,nov4 ,org4 ,aph4 #ei4 #bc ,9 ! conclusion4 #bd ,nov4 ,org4 ,l4 i4 ,aph4 #ei4 #be ,ibid4 ,aph4 #fj4 #bf ,ibid4 ,aph4 #fb4 #bg ,aph4 #fc4 #bh ,aph4 #fd4 #bi ,aph4 #fe4 #cj ,see above1 #d1 #e4 #ca ,nov4 ,org4 ,l4 i4 ,aph4 #fi4 #cb ,ibid4 #cc ,ibid4 ,aph4 #aji4 #cd ,book ,,iii4 ,*ap4 iv4 #ce ,book ,i4 ,*ap4 #b4 #ad4 #cf ,ibid4 #he1 c4 #cg ,see ,book ,,ii4 ,*4 #c4 #c1 #d4 ( ?is treatise4 #ch ,see ,book ,,ii4 ,*4 #c4 ( ?is treatise4 #ci ,see ,*ap4 #d4 #dj ,at ! end ( 8 ,optics4 9 ,qu4 #ba4 #da ,see ! same treatise1 9 ,adv]tisem5t #b4 #db ,nov4 ,org4 ,lib4 i4 ,ax4 #aje4 #dc ,pr9cip4 philos4 pag4 #ac1 #ad4 #dd ,pr9c4 ,philos4 ,l4 ,,ii4 prop4 #bd4 corol4 #g4 ,see also ,b4 ,,ii4 ,*4 #e4 #c4 ( ?is treatise4 #de ,h[ ?is degree ( ela/icity is to be f\nd by exp]im5t1 w be %ewn bel[ 9 #gd4 #df ,9 op]4 po/hum de ,motu corpor4 ex p]cussion4 prop4 #i4 #dg ,9 ! above-cit$ place4 #dh ,9 ! place above-cit$4 #di ,^! exp]im5ts are describ$ 9 #gc4 #ej ,book ,,ii4 ,*ap4 #e4 #ea ,*ap4 #a4 #be1 #bf1 #bg1 comp>$ ) #ae1 c4 #eb ,book ,,ii4 ,*ap4 #e4 #c4 #ec ,see ,euclid's ,elem5ts1 ,book ,,xii4 prop4 #ac4 #ed ,ar*im$4 de quipond4 prop4 #aa4 #ee ,ibid4 prop4 #ab4 #ef ,lucas ,val]ius ,de c5tr4 gravit4 solid4 ,l4 ,i4 prop4 #b4 #eg ,idem ,l4 ,,ii4 prop4 #b4 #eh #be4 #ei #bg4 #fj ,pag4 #fe1 #fh4 #fa #bc4 #fb #bj #fc #ag4 #fd #bg4 #fe ,hug54 ,horolog4 oscillat4 pag4 #ada1 #adb4 #ff ,see ,hug54 ,horolog4 ,oscillat4 p4 #adb4 #fg ,pr9cip4 ,philos4 pag4 #bb4 #fh ,*ap4 #a4 #bi4 #fi ,pr9cip4 ,philos4 pag4 #be4 #gj #ga4 #ga ,see ,me?od4 ,increm5t4 prop4 #be4 #gb ,lib4 ,,xi4 ,def4 #gc ,*ap4 #b4 #ag4 #gd ,see above ,*4 #b4 #ag4 #ge ,f ,b ,,ii4 ,*4 #c4 #gf ,pr94 ,philos4 pag4 #g1 c4 #gg ,see ,newton1 pr9cip4 philos4 pag4 #i4 l94 #cj4 #gh ,pr9cip4 ,philos4 pag4 #aj4 #gi ,r5at4 ,des ,c>t4 ,pr9c4 ,philos4 ,"p4 ,,ii4 #be4 #hj ,ibid4 #cj4 #ha #he1 c4 #hb ,pr9cip4 ,philos4 ,lib4 ,i4 prop4 #i4 #hc #ib4 #hd ,*4 ,,ii4 #bb4 #he ,viz4 ,l4 ,i4 prop4 #cj1 #bi1 #bf4 #hf ,*4 ,,ii4 #ba1 #bb4 #hg viz4 ,8 doctr9e ( prime & ultimate ratios4 #hh #eg #hi #c4 #ij ,*4 #b4 #bb4 #ia #ab4 #ib ,*4 #a4 sect4 #ba1 #bb4 #ic ,elem4 ,book ,i4 p4 #cg4 #id #ab4 #ie ,* #a #bd4 #if ,* #b select4 #ag4 #ig ,newt4 ,pr9c4 ,l4 ,,ii4 prop4 #b2 #e1 #f1 #g2 #aa1 #ab4 #ih ,prop4 #c2 #h1 #i2 #ac1 #ad4 #ii ,prop4 #d4 #ajj ,prlect4 ,geometr4 pag4 #abc4 #aja ,newton4 ,pr9c4 ,lib4 ,,ii4 prop4 #aj4 #ajb ,newton4 ,pr9c4 ,lib ,,ii4 prop #aj4 9 s*ol4 #ajc ,torricelli de motu gravium4 #ajd ,*4 #b #he1 c4 #aje ,newt4 ,pr9c ,l4 ,,ii4 sect #f4 #ajf ,l4 ,,ii4 sect4 #d4 #ajg ,see ,b4 ,,ii4 ,* #f4 #g4 ( ?is treatise4 #ajh ,lib4 ,i4 sect4 #aj4 #aji ,de la ,pesanteur1 pag4 #afi1 & ! foll[+4 #aaj ,newton4 ,pr9c4 ,l4 ,,ii4 prop #d4 s*ol4 #aaa ,see 8 ,tract on ! admirable r>ifaction ( ! air4 #aab ,book ,,ii4 ,*4 #f4 #aac ,pr9c4 philos4 ,lib4 ,,ii4 prop4 #bc4 #aad ,book ,i4 ,*4 #b4 #cj4 #aae ,pr9c4 philos4 ,lib4 ,,ii4 prop4 #bc1 9 s*ol4 #aaf ,pr9c4 philos4 ,lib4 ,,ii4 prop4 #cc4 coroll4 #aag ,lib4 ,,ii4 ,*4 #e4 #aah ,ibid4 ,prop4 #ce4 coroll4 #b4 #aai ,ibid4 coroll4 #c4 #abj ,vid4 ibid4 coroll4 #f4 #aba ,9 #b4 #abb ,pr9c4 philos4 ,lib4 ,,ii4 ,prop4 #ce4 #abc ,ibid4 #abd ,id4 #abe h4 #a4 #bi4 #abf ,pr9c4 philos4 ,lib4 ,,ii4 ,prop4 #ch1 comp>$ ) coroll4 #a ( prop4 #ce4 #abg ,l4 ,,ii4 ,lem4 #g4 s*ol4 pag4 #cda4 #abh ,lib4 ,,ii4 ,prop4 #cd4 #abi ,lib4 ,,ii4 ,lem4 #g4 p4 #cda4 #acj ,s*ol4 to ,lem4 #g4 #aca ,prop4 #cd4 s*ol4 #acb ,ibid4 #acc ,ibid4 #acd ,book ,,ii4 ,*4 ,i4 #f4 #ace ,vid4 ,newt4 pr9c4 9 s*ol4 to ,lem4 #g1 ( ,lib4 ,,ii4 pag4 #cda4 #acf ,sect4 #ag4 ( ?is *apt]4 #acg ,see ,pr9c4 philos4 ,lib4 ,,ii4 prop4 #cd4 #ach ,vid4 ,pr9c4 philos4 ,lib4 ,,ii4 ,lem4 #e4 p4 #cad4 #aci ,lemm4 #f4 #adj ,ibid4 #g4 #ada ,newt4 ,pr9c4 ,lib4 ,,ii4 prop4 #dj1 9 s*ol4 #adb ,lib4 ,,ii4 9 s*ol4 po/ prop4 #ca4 #adc ,book ,i4 *4 #b #hb4 #add ,book ,i4 ,*4 #c #bi4 #ade ,*4 #c4 ( ?is pres5t book4 #adf ,*4 #d4 #adg ,9 ,pr9c4 philos4 "p4 #c4 #adh ,philos4 pr9c4 ma!m4 ,lib4 ,,ii4 prop4 #b4 s*ol4 #adi ,ibid4 prop #ec4 #aej ,philos4 pr9c4 prop4 #eb4 coroll4 #d4 #aea ,ibid4 #aeb ,coroll4 #aa4 #aec ,see ibid4 s*ol4 po/ prop4 #ec4 #aed ,pr9c4 philos4 pag4 #caf1 #cag4 #aee ,*4 ,i4 #g4 #aef ,book ,i4 ,*4 #c4 #aeg ,book ,i4 ,*4 #c4 #bi4 #aeh ,ibid4 ,*4 #b4 #cj1 #ag4 #aei ,book ,i4 ,*4 #c4 #afj ,*4 #a4 #g4 #afa ,*ap4 #e4 #h4 #afb ,pr9c4 pag4 #fj4 #afc ,/reet1 9 ,a/ron4 ,c>ol94 #afd ,see ,*ap4 #e4 #i1 c4 #afe ,9 ! =ego+ page4 #aff ,see ,newton4 ,pr9c4 ,lib4 ,,iii4 prop4 #ac4 #afg ,*ap4 #e4 #aj4 #afh ,pr9c4 ,lib4 ,i4 prop4 #fj4 #afi ,book ,i1 ,*ap4 #b4 #hj4 #agj ,pr9c4 philos4 ,lib4 ,i4 prop4 #eh4 coroll4 #c4 #aga ,newt4 ,optics4 pag4 #cgh4 #agb ,newton4 ,pr9c4 ,lib4 ,,iii4 prop4 #a4 #agc ,newton1 ,pr9c4 ,lib4 ,,iii4 pag4 #cij1cia4 comp>$ ) pag4 #cic4 #agd ,book ,i4 ,*4 #c4 #bi4 #age ,pr9c4 philos4 ,lib4 ,i4 prop4 #d4 #agf ,ibid4 coroll4 #agg ,newt4 ,pr9c4 philos4 ,lib4 ,,iii4 pag4 #cij4 #agh ,newt4 ,pr9c4 philos4 ,lib4 ,,iii4 pag4 #cia1 #cib4 #agi ,book ,,iii4 ,*4 #d4 #ahj ,newt4 ,pr9c4 philos4 ,lib4 ,,iii4 pag4 #cia4 #aha ,ibid4 pag4 #cib4 #ahb ,see ,book ,i4 ,*4 #b4 #fj1 #fd4 #ahc ,book ,i4 ,*4 #b4 #ag4 #ahd ,see ,*4 ,,ii4 #f4 #ahe ,! second ( ! laws ( motion laid d[n 9 ,book ,i4 ,*4 #a4 #ahf ,newton4 ,pr9c4 philos4 ,lib4 ,,iii4 prop4 #f4 pag4 #dja4 #ahg ,newton's ,pr9c4 philos4 ,lib4 ,,iii4 prop4 #bb1 #bc4 #ahh ,newton4 ,pr9c4 ,lib4 ,i4 prop4 #ff4 coroll4 #g4 #ahi ,m5elai ,spha]ic4 ,lib4 ,i4 prop4 #aj4 #aij ,vid4 ,newt4 ,pr9c4 ,lib4 ,i4 prop4 #ff4 coroll4 #aj4 #aia ,vid4 ,newt4 ,pr9c4 ,lib4 ,,iii prop4 #cj4 p4 #ddj4 #aib ,ibid4 ,lib4 ,i4 prop4 #ff4 coroll4 #aj4 #aic ,:at ?is proportion is1 may be kn[n f ,coroll4 #b prop4 #dd4 ,lib4 ,i4 ,pr9c4 philos4 ,newton4 #aid ,pr9c4 ,phil4 ,newt4 ,lib4 ,i4 prop4 #de4 ,coroll4 #a4 #aie ,pr4 ,phil4 ,newt4 ,lib4 ,i4 prop4 #ff4 ,coroll4 #g4 #aif ,see #ai ( ?is *apt]4 #aig ,phil4 ,nat4 ,pr4 ,ma? ,lib4 ,i4 prop4 #ff4 cor4 #h4 #aih ,ibid4 ,coroll4 #h4 #aii ,ibid4 #bjj ,ibid4 #bja ,newt4 ,pr9c4 ,lib4 ,,iii4 prop4 #bi4 #bjb ,ibid4 prop4 #bh4 #bjc ,ibid4 prop4 #ca4 #bjd ,newt4 ,pr9c4 pag4 #dei4 #bje ,9 ,pr9c4 philos4 "p4 #c4 #da4 #bjf ,*ap4 #a4 #aa4 #bjg ,newton4 ,pr9c4 philos4 ,lib4 ,,iii4 ,lemm4 #d4 pag4 #dgh4 #bjh ,pr9c4 philos4 ,lib4 ,,iii4 prop4 #dj4 #bji ,book ,i4 *ap4 #b4 #hb4 #baj ,pr9c4 philos4 ,lib4 ,,iii4 pag4 #dii1 #ejj4 #baa ,ibid4 pag4 #ejj1 & #ebj1 c4 #bab ,pr9c4 ,philos4 ,lib4 ,,iii4 prop4 #dj4 #bac ,ibid4 prop4 #da4 #bad ,ibid4 pag4 #ebb4 #bae ,ibid4 prop4 #db4 #baf ,newt4 ,pr9c4 philos4 edit4 #b4 p4 #dfd1 #dfe4 #bag ,ibid4 edit4 #c4 p #eja1 #ejb4 #bah ,ibid4 pag4 #eai4 #bai ,ibid4 pag4 #ebd4 #bbj ,newt4 ,pr9c4 philos4 p4 #ebe4 #bba ,ibid4 #bbb ,ibid4 pag4 #ejh4 #bbc ,ibid4 #bbd ,ibid4 pag4 #dhd4 #bbe ,ibid4 pag4 #dhb1 #dhc4 #bbf ,ibid4 pag4 #dha4 #bbg ,ibid4 pag4 #eji4 #bbh ,see ! =e-cit$ place4 #bbi ,ibid4 & ,c>tes4 ,pr9c4 ,phil4 "p4 #c4 #acd1 c4 #bcj ,vid4 ,phil4 ,nat4 pr9c4 ,ma?4 p4 #eaa4 #bca ,book ,i4 ,*4 #d4 #aa4 #bcb ,*4 #e4 #bcc ,all ^! argum5ts are laid d[n 9 ,philos4 ,nat4 ,pr9c4 ,lib4 ,,iii4 f p4 #eji1 to #eag4 #bcd ,philos4 ,nat4 ,pr9c4 ,lib4 ,,iii4 p4 #eae4 #bce ,*4 #e4 #bcf ,see ,*4 #a4 #aa4 #bcg ,newt4 ,pr9c4 ,philos4 pag4 #ebe1 #ebf4 ,an acc\nt ( all ! />s ( bo? ^! k9ds1 :i* h appe>$ )9 ! la/ #aej ye>s may be se5 9 ! ,philosophical transactions1 vol4 #bi4 numb4 #cdf4 #bch ,newt4 ,pr9c4 ,philos4 ,nat4 ,lib4 ,,iii4 prop4 #f4 #bci ,*4 #c4 #f4 #bdj ,book ,i4 ,*4 #b4 #bd4 #bda ,newt4 ,pr9c4 ,lib4 ,,iii4 prop4 #f4 #bdb ,*4 #c4 #f4 #bdc ,newt4 ,pr9c4 philos4 ,lib4 ,,iii4 prop4 #g4 cor4 #a4 #bdd ,see ,book ,i4 ,*4 #a4 #ae4 #bde ,ibid4 #e1 #f4 #bdf ,*ap4 #b4 #h4 #bdg ,newt4 ,pr9c4 ,lib4 ,i4 prop4 #fc4 #bdh #h4 #bdi ,see ,introd4 #bc4 #bej #d1 #e4 #bea ,newt4 ,pr9c4 philos4 ,lib4 ,i4 prop4 #gd4 #beb ,ibid4 coroll4 #c4 #bec ,lib4 ,i4 ,prop4 #ge4 & ,lib4 ,,iii4 prop4 #h4 #bed ,lib4 ,i4 ,prop4 #gf4 #bee ,ibid4 cor4 #e4 #bef ,vid4 ,lib4 ,,iii4 ,prop4 #g4 coroll4 #a #beg ,newt4 ,pr9c4 ,lib4 ,,iii4 prop4 #h4 coroll4 #a4 #beh ,ibid4 coroll4 #b4 #bei ,book ,i4 ,*4 #d4 #b4 #bfj ,newt4 ,pr9c4 ,lib4 ,,iii4 prop4 #h4 coroll4 #c4 #bfa ,ibid4 coroll4 #d4 #bfb ,book ,i4 ,*4 #d4 #bfc ,lib4 ,,ii4 prop4 #bj4 cor4 #b4 #bfd ,*ap4 #d4 #ag4 #bfe ,ibid4 #bff ,vid4 ,newt4 ,pr9c4 ,lib4 ,,ii4 prop4 #df4 #bfg ,pr9c4 philos4 ,lib4 ,,ii4 prop4 #di4 #bfh ,*ap4 #c4 #ah4 #bfi ,newt4 ,pr9c4 philos4 ,lib4 ,i4 prop4 #ff4 coroll4 #ah4 #bgj #h4 #bga ,*4 #c4 #e4 #bgb ,*4 #c #ag4 #bgc ,ibid4 #bgd ,see bel[ #dd4 #bge ,newton ,pr9c4 ,lib4 ,,iii4 prop4 #ai4 #bgf ,lib4 ,,iii4 prop4 #ai4 #bgg ,lib4 ,i4 prop4 #gc4 #bgh ,lib4 ,,iii4 prop4 #bj4 #bgi ,ibid4 #bhj ,opt4 ,b4 ,i4 "p4 #b4 prop4 #a4 #bha ,newt4 ,opt4 ,b4 #a4 "p #a4 exp]im4 #e4 #bhb ,ibid4 prop4 #d4 #bhc ,newt4 ,opt4 ,b4 #a4 "p #b4 exp]4 #e4 #bhd ,ibid exp]4 #f4 #bhe ,newton ,opt4 ,b4 ,i4 prop4 #aj4 #bhf ,ibid exp4 #i4 #bhg ,newt4 ,opt4 ,b4 ,i4 "p #a4 exp #ae4 #bhh ,philos4 ,transact4 ,n4 #hh1 p4 #ejii4 #bhi ,opt ,b4 ,i4 p>4 #b4 exp4 #ad4 #bij ,ibid4 exp4 #aj4 #bia ,opt4 pag4 #abb4 #bib ,opt4 ,b4 ,i4 "p #b4 exp4 #aa4 #bic ,ibid prop4 #d1 #f4 #bid ,opt4 pag4 #ea4 #bie ,opt4 ,book ,,ii4 prop4 #h4 #bif ,opt4 ,book ,,ii4 p>4 #c4 prop4 #b4 #big #ag4 #bih ,opt4 ,book ,,ii4 p>4 #c4 prop4 #d4 #bii ,opt4 ,book ,,ii4 pag4 #bda4 #cjj ,ibid4 pag4 #bbd4 #cja ,ibid4 ,obs4 #ag4 c4 #cjb ,ibid4 ,obs4 #aj4 #cjc ,ibid4 pag4 #bjf4 #cjd ,obs]4 #ba4 #cje ,obs]v4 #e4 comp>$ ) ,obs]v4 #aj #cjf ,ibid4 prop4 #e4 #cjg ,obs]v4 #g4 #cjh ,obs]v4 #i4 #cji ,ibid prop4 #g4 #caj ,opt4 pag4 #bdc4 #caa ,newt4 ,opt4 ,b4 ,i4 "p4 #a4 prop4 ,i4 #cab ,opt4 ,b4 ,i4 "p4 #a4 prop4 #b4 #cac ,opt4 ,b4 ,i4 "p #a4 ,expec4 #f4 #cad ,opt4 pag4 #fg1 #fh1 c4 #cae ,ibid4 ,b4 #a4 p>4 #b4 prop4 #c4 #caf ,opt4 ,b4 ,,ii4 p>4 #c4 prop4 #aj4 #cag ,opt4 ,b4 ,,ii4 p>4 #c4 prop4 #ae4 #cah ,ibid4 p>4 #a4 obs]v4 #g4 #cai ,ibid4 ,obs]v4 #ai4 #cbj ,opt4 ,b4 ,,ii4 p>4 #b4 pag4 #aii4 c4 #cba ,ibid4 p>4 #d #cbb ,ibid4 "p4 #c4 prop4 #ac4 #cbc ,ibid4 prop4 #ag4 #cbd ,ibid4 prop4 #ac4 #cbe ,opt4 ,qu4 #ah1 c4 #cbf ,see ,concl4 ,s4 #b4 #cbg ,b4 ,,ii4 ,*4 #a4 #cbh ,opt4 ,b4 ,,iii4 ,obs4 #a4 #cbi ,ibid4 ,obs4 #b4 #ccj #b4 #cca ,philos4 ,trans4 ,no4 #cgh4 #ccb #aa4 #ccc ,philos4 ,transact ,no4 #cge4 #ccd ,ibid4 #cce ,opt4 ,b4 ,,ii4 "p #d4 #ccf ,*4 #c4 #ad4 #ccg ,opt4 ,b4 ,,ii4 "p #d4 obs4 #ac4 #cch ,opt4 pag4 #bee4 #cci ,*4 #c4 #ah4