Newton, Isaac - Philosophia naturalis principia mathematica

Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1

DE MOTU
CORPORUM

Producantur AB ad K,& BDad L,ut ſit BKad AB ut
HI ad GH; & DLad BDut GIad FG; & jungatur KL
occurrens rectæ CE in i.Producatur iLad M,ut ſit LMad iL
ut GHad HI,& agatur tum MQipſi LBparallela rectæque
AD occurrens in g,tum giſecans AB, BDin f, h.Dico
factum.

Secet enim Mgrectam AB in Q,& AD rectam KLin S,&
agatur APquæ ſit ipſi BDparallela & occurrat iLin P,&
erunt gMad Lh (giad hi, Mi ad Li, GIad HI, AKad
BK) & APad BLin eadem ratione. Secetur DLin R ut ſit

69[Figure 69]
DLad RLin eadem illa ratione, & ob proportionales gSad
gM, AS ad AP,& DSad DL; erit, ex æquo, ut gSad Lhita
AS ad BL& DSad RL; & mixtim, BL-RLad Lh-BL
ut AS-DSad gS-AS.Id eſt BRad Bhut AD ad Agad
eoque ut BDad gqueEt viciſſim BRad BDut Bhad gQ,ſeu
fhad fg.Sed ex conſtructione linea RLeadem ratione ſecta fuit
in D& R atque linea FI in G& H:ideoque eſt BRad BD
ut FHad FG.Ergo fheſt ad fgut FHad FG.Cum igitur
ſit etiam giad hi ut Mi ad Li,id eſt, ut GIad HI,patet li
neas FI, fi in g& h, G& H ſimiliter ſectas eſſe. q.E.F.

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