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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 123, page id 1041163592:0157
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PRTNCIDTA MAEEEMAETCA.
ut angulus VCp ad angulum VC P. Pgitur eodem tempore quo
COrpuS P motu suo utroque perrenit ad punctum R, COrDUIS P X. PRLHOS.
quali in centrum motu aequaliter morebitur a p rertus C, adeoque
completo illo cempore reperietur alicubi in linea m k r, qua Per
punctum k in lincam pC perpendicularis est; et motu transverso
acquiret distantiam a linea pC, quae sic ad distantiam quam cor
pus alcerum F acquirie a linea PC3 UE CA MOEUS EPANSVCTTUS COF-
Poris p ad motum transvertum corporis alterius P. Ouarc cum
er aequalis sic distantix quam corpus P acquiric a linea F C, siEquC
mr ad er ut angulus V C p ad ansulum VC P, hOc CA, UE MOTS
erantrersus corporis p ad inotum transversum corporis F, manite.
Cum est quod corpus p completo illo tempore reperietur in loco
m. Haec ita se habebune ubi corpora p ee F aequalicer secundum
lineas pC sc F C morentur, adeoque equalibus Viribus secundum
lineas illas urgentur. Capiatur aurem angulum pen ad angulum
DCk uE es angulus V C p ad angulus VCP, Sicque nC sequalis
C, e corpus p completo illo tempore revera reperierur in n; ad
eoque Vi majore ursetur quam corpus P, si modo angulus mep
angulo kC p major cA, id cst ( Orbis W p R vel moretur in con-
sequentia, vel movetur in ancecedentia majore celeritate quam
sIE dupla ejus qua linea C F in consequentia Fertur; ec Vi mino
re s Orbis cardius movetur in antecedentia. FAque Virium dit-
ferentia ut locorum interrallum mn, per quod corpus illud 
iplius actione, dato illo temporis spatio, transterri debet. CCntro
C interrallo Cn vel C e describi incelligatur Circulus sccans
lineas mr, mn productas in sect, ec erit rectansulum mnxmt x-
quale rectangulo mkeZms, adcoque mn aequale mk X m 5
Mt
Cum
aurem criangula pCk, pen deneur magnicudine, sune ter ec mr,
carumque differentia m R ec lumma ins reciproce ut alticudo pC.
adeoque rectangulum mk Zms est reciproce uc quadracum alcicudi-
nis pC. E.A ee mt directe ut Z mt, id est, ut alticudo pC. IIX
sunc primae rationes linearum nascentium; et hinc fit m RX m5
EF
ict
est lineola nascens mn, eique proportionalis Virium difterentia reci
proce ue cubus alticudinis pC. Q. F.. D.
Corol. T. Flinc differentia virium in locis F sc p vel K ex k, eA
adrim qua corpus motu Circulari revolvi postit ab R ad K eodem
cempore quo corpus P in Orbe immobili describic arcum PK, uE
mecta nasceno mn ad sinum vertum arcus nascentis _ s, id cud
U