Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1
DE MOTU
CORPORUM
SECTIO III.
De motu Corporum in Conicis Sectionibus excentricis.
PROPOSITIO XI. PROBLEMA VI.
Revolvatur corpus in Ellipſi: requiritur Lex vis centripetæ tenden­
tis ad umbilicum Ellipſeos.
Eſto Ellipſeos umbilicus S.Agatur SPſecans Ellipſeos
tum diametrum DKin E,tum ordinatim applicatam Qvin
x,& compleatur parallelogrammum QxPR.Patet EPæqua­
lem eſſe ſemiaxi ma­
21[Figure 21]
jori AC,eo quod
acta ab altero Ellip­
ſeos umbilico Hli­
nea HIipſi ECpa­
rallela, (ob æquales
CS, CH) æquentur
ES, EI,adeo ut EP
ſemiſumma ſit ipſa­
rum PS, PI,id eſt
(ob parallelas HI,
PR& angulos æqua­
les IPR, HPZ)
ipſarum PS, PH,
quæ conjunctim axem
totum 2ACadæ­
quant. Ad SPde­
mittatur perpendicularis QT,& Ellipſeos latere recto principali
(ſeu (2BC quad./AC)) dicto L,erit LXQRad LXPvut QRad
Pv,id eſt ut PEſeu ACad PC; & LXPvad GvPut Lad
Gv; & GvPad Qv quad.ut PC quad.ad CD quad; & (per Corol.
2 Lem. VII.) Qv quad.ad Qx quad,punctis Q& Pcoeuntibus,
eſt ratio æqualitatis; & Qx quad.ſeu Qv quad.eſt ad QT quad.
ut EP quad.ad PF quad,id eſt ut CA quad.ad PF quad.ſive (per
Lem XII.) ut CD quad.ad CB quad.Et conjunctis his omnibus ratio­
nibus, LXQRfit ad QT quad.ut ACXLXPCq.XCDqueſeu 2CBque
XPCq.XCDquead PCXGvXCDq.XCBqueſive ut 2PCad Gv.

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