Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ſi in vacuo cecidiſſet de loco
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T.
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Exponatur igitur hæc velocitas
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per chordam arcus
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TA.
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Nam velocitatem Penduli in puncto in
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fimo eſſe ut chordam arcus quem cadendo deſcripſit, Propoſitio eſt
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eſt Geometris notiſſima. </
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<
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>Poſt reflexionem perveniat corpus
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A
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ad
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locum
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s,
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& corpus
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B
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ad locum
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k.
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Tollatur corpus
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B
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& invenia
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tur locus
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v
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; a quo ſi corpus
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A
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demittatur & poſt unam oſcillatio
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nem redeat ad locum
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r,
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ſit
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st
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pars quarta ipſius
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rv
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ſita in medio,
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ita videlicet ut
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rs
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&
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tu
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æquentur; & per chordam arcus
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tA
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ex
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ponatur velocitas quam corpus
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A
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proxime poſt reflexionem habuit
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in loco
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A.
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Nam
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t
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erit locus ille verus & correctus, ad quem cor
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pus
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A,
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ſublata aeris reſiſtentia, aſcendere debuiſſet: Simili me
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thodo corrigendus erit locus
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k,
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ad quem corpus
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B
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aſcendit, & in
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veniendus locus
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l,
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ad quem corpus illud aſcendere debuiſſet in va
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cuo. </
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<
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>Hoc pacto experiri licet omnia perinde ac ſi in vacuo con
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ſtituti eſſemus. </
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<
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>Tandem ducendum erit corpus
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A
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in chordam ar
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cus
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TA
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(quæ velocitatem ejus exhibet) ut habeatur motus ejus in
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loco
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A
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proxime ante reflexionem; deinde in chordam arcus
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tA,
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ut
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habeatur motus ejus in loco
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A
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proxime poſt reflexionem. </
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<
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>Et ſic
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corpus
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B
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ducendum erit in chordam arcus
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Bb,
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ut habeatur motus
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ejus proxime poſt reflexionem. </
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<
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>Et ſimili methodo, ubi corpora duo
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ſimul demittuntur de locis diverſis, inveniendi ſunt motus
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tam ante, quam poſt reflexionem; & tum demum conferendi ſunt
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motus inter ſe & colligendi effectus reflexionis. </
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<
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>Hoc modo in
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Pendulis pedum decem rem tentando, idQ.E.I. corporibus tam
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inæqualibus quam æqualibus, & faciendo ut corpora de intervallis
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ampliſſimis, puta pedum octo vel duodecim vel ſexdecim, concurre
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rent; reperi ſemper ſine errore trium digitorum in menſuris, ubi
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corpora ſibi mutuo directe occurrebant, quod æquales erant muta
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tiones motuum corporibus in partes contrarias illatæ, atque adeo
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quod actio & reactio ſemper
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erant æquales. </
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<
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>Ut ſi corpus
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A
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incidebat in corpus
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B
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cum
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novem partibus motus, & a
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miſſis ſeptem partibus perge
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bat poſt reflexionem cum du
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abus; corpus
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B
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reſiliebat cum
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partibus iſtis ſeptem. </
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<
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>Si cor
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pora obviam ibant
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A
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cum
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duodecim partibus &
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B
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cum ſex, & redibat
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A
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cum duabus; redi
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bat
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B
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cum octo, facta detractione partium quatuordecim utrin
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que. </
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<
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>De motu ipſius
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A
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ſubducantur partes duodecim, & reſtabit </
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