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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRIMCIPTA HATETEMATICA.
Corol. P. F.x cribus norissimis Proxolitionibus consequens est, quod
li corpus quodris P, secundum lineam quamris rectam P K, Qua- PRINOS.
cunque cum relocitace exeat de loco P, de vi centripeca qua sEre-
ciproce proporcionalis quadrato distantix locorum a cenero, simul
asitetur; morebitur hoc corpus in aliqua sectionum Conicarum
umbilicum habente in centro virium; ec contra. Nam datis umbi-
lico ec puncto contactus e politione tansentis, describi porest sectio
Conica quae curraturam dacam ad punctum illud habebit. Datur
autem curvatura ex data vi centripeta: ec Orbes duo se muTUOFAN-
sences, eadem vi centripera describi non portunt.
Corol. 2. Si velocitas, quacum corpus exit de loco (uo P, Ca
IE, qua lineola P R in minima aliqua cemporis particula describi
Posic, ex vis centripeta poris sit eodem tempore corpus idem mo-
vere per spacium  R: morebitur hoc corpus in Conica aliqua (c-
ctione, cujus latus rectum principale est quantiras illa 4. quxe
A
ultimo Ac ubi lineolae P R, O R in inAinitum diminuuneur. Circu-
lum in his Corollariis refero ad Elliplin, e calum excipio ubi cor-
Dus recta descendic ad centrum.
PROPOSITIO XIV. TTEOREMA VI.
Si corpora plura re volvantur circa centrum commune, e vis centri-
peta sit reciproce in duplicata ratione distantiae locorum a centro;
dico quod Orbium Latera recta principalia sunt in duplicat a ratio-
one arearum quas corpora, radiis ad centrum ductis, eodem tempore
describunt.
Nam, per Corol. 2. PrOp. XIII. Lacusrectum L xequale eAt quan-
citati EFg
0F Quxe ultimo sic ubi cocunt puncta P ee G. Sed linea
minima R, dato tempore, oAt uc vis cencripeta generans, hoc
eAt (per FIypochesin) rCCIpROCE UE SP g. ErgO
N CA ut
QTg. XSP g. hoc est, lacus rectum L. in duplicata ratione arex
TXST
Q. E. D.
Corot.
E I BER