Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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SECTIO III.
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De motu Corporum in Conicis Sectionibus excentricis.
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PROPOSITIO XI. PROBLEMA VI.
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Revolvatur corpus in Ellipſi: requiritur Lex vis centripetæ tenden
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tis ad umbilicum Ellipſeos.
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<
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>Eſto Ellipſeos umbilicus
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S.
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Agatur
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SP
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ſecans Ellipſeos
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tum diametrum
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DK
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in
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E,
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tum ordinatim applicatam
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Qv
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in
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x,
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& compleatur parallelogrammum
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QxPR.
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Patet
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EP
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æqua
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lem eſſe ſemiaxi ma
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jori
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AC,
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eo quod
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acta ab altero Ellip
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ſeos umbilico
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H
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li
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nea
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HI
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ipſi
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EC
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pa
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rallela, (ob æquales
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CS, CH
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) æquentur
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ES, EI,
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adeo ut
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EP
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ſemiſumma ſit ipſa
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rum
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PS, PI,
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id eſt
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(ob parallelas
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HI,
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PR
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& angulos æqua
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les
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IPR, HPZ
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)
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ipſarum
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PS, PH,
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quæ
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cõjunctim
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axem
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totum 2
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AC
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adæ
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quant. </
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<
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SP
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de
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mittatur perpendicularis
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QT,
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& Ellipſeos latere recto principali
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(ſeu (2
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BC quad./AC
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)) dicto
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L,
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erit
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LXQR
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ad
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LXPv
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ut
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QR
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ad
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Pv,
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id eſt ut
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PE
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ſeu
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AC
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ad
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PC
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; &
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LXPv
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ad
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GvP
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ut
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L
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ad
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Gv
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; &
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GvP
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ad
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Qv quad.
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ut
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PC quad.
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ad
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CD quad
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; & (per Corol. </
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2 Lem. </
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<
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>VII.)
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Qv quad.
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ad
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Qx quad,
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punctis
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Q
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&
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P
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coeuntibus,
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eſt ratio æqualitatis; &
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Qx quad.
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ſeu
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Qv quad.
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eſt ad
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QT quad.
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ut
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EP quad.
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ad
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PF quad,
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id eſt ut
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CA quad.
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ad
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PF quad.
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ſive (per
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Lem XII.) ut
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CD quad.
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ad
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CB quad.
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Et conjunctis his omnibus ratio
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nibus,
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LXQR
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fit ad
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QT quad.
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ut
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<
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ACXLXPCq.XCDq.
">ACXLXPCq.XCDque</
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ſeu 2
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<
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CBq.
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<
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XPCq.XCDq.
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expan
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ad
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<
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PCXGvXCDq.XCBq.
">PCXGvXCDq.XCBque</
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ſive ut 2
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PC
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ad
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Gv.
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