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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 113, page id 1041163592:0147
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PRTNOTPLA MATTIEMAETCA.
corpus cadendo describit lineolam D F, ut lineola illa directe et L IDEK
velocitas V inverse, eAque vis ur relocitatis incrementum l’directe vuimvs.
ec tempus inverse, adeoque s primx nascentium rationes luman.
cuC ut= . hOc Chuc loneicudo DF. E,8O Visips D F vel F. C.
proportionalis Facit ut corpus ea cum Velocitare descendat quae sit
ut arcae ABG F. latus quadratum. 9. F. D.
Porro cum tempus, quo quaelibet lonsitudinis datae lineola D L
describatur, siE ut velociras inverse adeoque uc arcae B FD laFUS
quadratum inverse; SIEgue D L, aEque adCO ArCA MALCCnS D L NIF,
ut idem lacus quadratum inverse: CriE COMPUS UE aECa D P NIF, e
summa omnium temporum ut summa omnium arcarum, hoc est
(per COrOI. Lem. YV) Tempus torum quo linca AF describieur aE
area tora AMF. 9. L. D.
Corol. Z. Si F sE locus de quo corpus cadere debet, uE, urgen.
te aliqua unitormi vi centripeta noca (qualis vulso supponitur
Gravitas) velocitatem acquirat in loco D aequalem velocitati
quam corpus aliud ri quacunque cadens acquisirit codem loco 
ex in perpendiculari D F CapiatUE D R, gua sIC ad D S uc vis illa
unitormis ad vim alteram in loco D, e compleatur rectanoulum
PD RQ. eique aequalis abscindatur arca ABF D; erit A lOcuS
de quo corpus alterum cecidit. Namque completo rectangulo
DRSE, cum SE area ABF D ad aream D EG F UE V V 2d
2 V I, adeoque ut ZV ad I, id eAt, ut semissis velocitatis torius
ad incrementum relocitatis corporis vi inaequabili cadentis; et I-
militer area P QR D ad aream D RS F. uE semissis velocitatis to-
eius ad incrementum velocitatis corporis unitormi vi cadenEis;
sintque incrementa illa (ob aequalicarem temporum nascentium)
ut vires generatrices, id est, ut ordinatim applicatae D F, D R,
adCOque UE ArEA NASCenTCS D FG F, D RS L; crunE (CX XquO)
ATCR EOEX ABF D, P Q R D ad invicem ut semisses totarum re-
locitatum, et proprerea (ob aequaliearem velocitatum) aequantur.
Corol. 2. Vnde si corpus quodlibet de loco quocunque D data
cum relocitate vel sursum vel deorlum projiciatur, et detur lex vis
centripetae, invenietur velocitas ejus in alio quoris loco es crigen-
do ordinatam es, ec capiendo relociratem illam ad velocitarem in
loco D uc cA latus quadratum rectansuli P  R D area curvili-
nea D F∞C vel auctis si locus e est loco D inferior, vel diminutis
Ei is superior eA, ad latus quadratum rectanguli solius P Q R D, id
et, uc V P QRD + vel- D F Se ad s P QRD.
COrelu