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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 47, page id 1041163592:0081
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s
PRINOIDTA MATEIEMLATICA.
dxe arcus P Q erit aequale rectangulo VP V; adeoque Circulus qui LIVe
cansit Sectionem Conicam in P ec transit per punctum g. crantibie
etiam per punctum V. Cocane puncta F ec Q et hic circulus
ejusdem erie curraturx cum sectione conica in P, ee P Vaequalis erie
2DC
PC. Proinde ris qua corpus P in EIlipsi revolritur, erit reci
Proce ut
OCQ in PFg (Ber COrOI. 3 PFOp. YL.) hoc ett (ob
datum 2 D Cg in F F9) directe uE F C. G. F. T.
Corol. 2. F. IF igitur vis ue distantia corporis a centro Ellipseos: _
vicissim, si vis sic uc distancia, morebitur corpus in FIlipsi centrum
habence in cenero virium, aue forte in Circulo, in quem utique
Ellipas migrare pocest.
Corol. 2. EF aequalia erunt revolutionum in EllipsibusunirerHs cir-
cum centrum idem factarum periodica tempora. Lam tempora
illa in Eslipsbus similibus aequalia sunt per Corol. 3 ec 8, PFOP. IV:
in Ellipsibus aucem communem habentibus azem majorem, sunt ad
invicem ut Ellipseon arcae torae directe ec arearum particulae simul
delcripea inverie; id eAt, uc azes minores directe ex corporum ve-
locitates in verticibus principalibus inverse; hoc est, uc axes illi mi-
nores directe e ordinatim applicatae ad axes alteros inverse; eE prOD-
cerea (ob aequalicatem rationum directarum ec inverlarum) in ra-
tione aequalitatis.
Scholium:
Si Ellipsis, centro in infinicum abcunce vertatur in Parabolam;
corpus movebitur in hac Parabola; ex vis ad centrum infinite di-
sans jam cendens cradet aequabilis. HJoc es Theorema Calilaei.
FF Si coni sectio Parabolicas inclinatione plani ad conum sectum
mutata, vertatur in HIyperbolam, morebitur corpus in hujus pe-
rimetro, vi cencripeta in centritusam versa. Et quemadmo-
dum in Circulo vel FIlips, Si rires rendune ad centrum EBurx
in AbCcissa pontum, hx rires augendo rel diminuendo Ordinatas in
ratione quacunque data, vel etiam mutando angulum inclinationis
Ordinatarum ad Abscissam, semper augentur vel diminuuntur in
ratione distantiarum a centro, si modo tempora periodica maneane
aequalia: sic etiam in Aruris universIs, si Ordinatae augeantur vel di-
minuantur in ratione quacunque daca, vel angulus ordinationis ut-
cunque mutetur, manente tempore periodico; rires ad centrum
Quodcunque in Abscista policum cendentes augencur vel diminuun-
ur in ratione distantiarum a Centro.
SF. C
PRI MVS.