Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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Corol.
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1. Unde ſi Solidum
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Cylindrus ſit, parallelogrammo
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ADEB
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circa axem
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AB
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revo
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luto deſcriptus, & vires centri
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petæ in ſingula ejus puncta ten
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dentes ſint reciproce ut quadra
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ta diſtantiarum a punctis: erit
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attractio corpuſculi
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P
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in hunc
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Cylindrum ut
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AB-PE+PD.
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Nam ordinatim applicata
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FK
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(per Corol. </
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>1. Prop. </
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>XC) erit ut 1-(
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PF/PR
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). Hujus pars 1 ducta in lon
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gitudinem
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AB,
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deſcribit aream 1X
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AB
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; & pars altera (
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PF/PR
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) ducta
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in longitudinem
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PB,
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deſcribit aream 1 in —(
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PE-AD
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) (id quod
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ex curvæ
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LIK
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quadratura facile oſtendi poteſt:) & ſimiliter pars
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eadem ducta in longitudinem
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PA
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deſcribit aream 1 in —(
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PD-AD
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),
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ductaQ.E.I. ipſarum
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PB, PA
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differentiam
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AB
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deſcribit arearum
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differentiam 1 in —(
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PE-PD
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). De contento primo 1X
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AB
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aufe
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ratur contentum poſtremum 1 in —(
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PE-PD
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), & reſtabit area
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LABI
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æqualis 1 in —(
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AB-PE+PD
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). Ergo vis, huic areæ proportiona
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lis, eſt ut
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AB-PE+PD.
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Corol.
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2. Hinc etiam
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vis innoteſcit qua Sphæ
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rois
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AGBCD
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attrahit
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corpus quodvis
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P,
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exte
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rius in axe ſuo
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AB
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ſi
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tum. </
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<
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NKRM
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Se
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ctio Conica cujus ordi
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natim applicata
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ER,
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ipſi
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PE
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perpendicularis, æ
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quetur ſemper longitu
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dini
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PD,
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quæ ducitur
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ad punctum illud
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D,
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in
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quo applicata iſta Sphæroidem ſecat. </
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<
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A, B
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ad ejus axem
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AB
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erigantur perpendicula
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AK, BM
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ipſis
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AP, BP
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æqualia reſpective, & propterea Sectioni Conicæ occurrentia in
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K
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&
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M
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; & jungatur
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KM
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auferens ab eadem ſegmentum
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KMRK.
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Sit autem Sphæroidis centrum
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S
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& ſemidiameter maxima
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SC:
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& vis </
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