Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ad
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PS,
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adeoque ratio
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PQ
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PS.
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Auferendo hanca data ra
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tione
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PQXPR
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PSXPT,
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dabitur ratio
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PR
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PT,
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addendo datas rationes
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PR,
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PT
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ad
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dabitur
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ratio
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PI
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ad
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PH
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atque adeo
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punctum
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P. Q.E.I.
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DE MOTU
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CORPORUM</
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Corol.
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1. Hinc etiam ad Loci
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punctorum infinitorum
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P
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pun
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ctum quodvis
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D
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tangens duci
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poteſt. </
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<
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>Nam chorda
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PD
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ubi
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puncta
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P
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ac
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D
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conveniunt, hoc
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eſt, ubi
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AH
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ducitur per punctum
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D,
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tangens evadit. </
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<
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>Quo in caſu,
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ultima ratio evaneſcentium
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IP
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&
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PH
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invenietur ut ſupra. </
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<
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>Ipſi
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igitur
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AD
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due parallelam
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CF,
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occurrentem
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BD
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in
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F,
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& in ea ul
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tima ratione ſectam in
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E,
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&
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DE
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tangens erit, propterea quod
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CF
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& evaneſcens
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IH
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parallelæ ſunt, & in
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E
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&
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P
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fimiliter ſectæ. </
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Corol.
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2. Hinc etiam Locus punctorum omnium
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P
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definiri poteſt. </
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Per quodvis punctorum
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A, B, C, D,
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puta
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A,
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duc Loci tangentem
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AE
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& per aliud quodvis punctum
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B
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duc tangenti parallelam
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BF
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occurrentem Loco in
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F.
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Invenie
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tur autem punctum
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F
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per Lem. </
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>XIX. </
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Biſeca
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BF
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in
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G,
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& acta indefinita
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AG
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erit poſitio diametri ad quam
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BG
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&
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FG
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ordinatim applicantur. </
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Hæc
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AG
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occurrat Loco in
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H,
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&
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erit
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AH
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diameter ſive latus tranſ
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verſum, ad quod latus rectum erit
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ut
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<
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BGq.
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ad
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AGH.
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Si
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AG
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nullibi
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occurrit Loco, linea
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AH
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exiſtente
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infinita, Locus erit Parabola & la
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rum rectum ejus ad diametrum
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AG
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pertinens erit (
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BGq./AG
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) Sin ea alicubi occurrit, Locus Hyperbola erit
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ubi puncta
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A
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&
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H
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ſita ſunt ad eaſdem partes ipſius
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G:
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& Ellipſis,
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ubi
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G
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intermedium eſt, niſi forte angulus
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AGB
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rectus ſit & inſuper
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BG quad.
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æquale rectangulo
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AGH,
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quo in caſu Circulus habebitur. </
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>AtQ.E.I.a Problematis Veterum de quatuor lineis ab
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Euclide
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incæp
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ti & ab
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Apollonio
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continuati non calculus, ſed compoſitio Geometri
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ca, qualem Veteres quærebant, in hoc Corollario exhibetur. </
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