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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 227, page id 1041163592:0261
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PRINOTDTA MATHEMATICA.
 t 
cibus (Data Squatione quotcunque Flventes quantitates involven. L. LDen
le Fluxiones invenires es vice versa) eandem celarem: rescrip(IE SEConnOS.
Vir Claristimus se quoque in ejusmodi methodum incidisse, ec mc.
thodum tuam communicarie a mea vix abludentem praeterquam in
verborum ex nocarum Formulis, ec Idea generationis quancitatum.
Veriusque Fundamentum continetur in hoc Lemmate.
PROPOSITIO VIII. TIEOREMA VI.
Si corpus in Medio uniformi, Gravitate uniformiter agente, recta
ascendat vel descendat, e spatium torum descriptum distingua-
tur in partes equales, inque principiis sincularum partium
Caddendo resistentiam Medii ad vim gravitaris, quando cor
pus ascendit, vel subducendo ipsam quando corpus descendit
collicantur vires absolutae; dico quod vires illae absolutae sunt
in progressione Geometrica.
Exponatur enim vis gravitatis per datam lineam AC; resisten-
cia per lincam indetinitam AN; vis absoluta in descensu corporis
per differentiam KCC; relocitas corporis per lineam AF (qua SIE
media proportionalis inter R et AC, ideoque in subduplicata
ratione resistentia;) incrementum relistentix data temporis particu-
la Factum per lincolam R L, ex concemporancum velocitatis incre-
mentum per lincolam PQ; ex centro C Alympeoris rectangulis
C A. C HL delcribatur FIyperbola quaeris B NS, crectis perpendi-
culis AB, R NV, L. O, F R, QS occurrens in B, N, O, R, 5. Ouo-
niam AR CA ut APg. erit hujus momentum KL ut illius mo-
mentum 2A P 9. id cA, ut AP in KC. Nam velocitatis incre-
mentum F Q. (per motus L.Cg. II.) proporcionale est vi gencranti KC.
Componatur ratio ipsius R I. cum racionc ipsius R N, ec het rect-
anGUIUM RL XR N UE AF XKC. Z K N; hoc est, ob datum rect-
ANGULUm RCZRN, uE AF. Requi arcae IIyperbOliCA RNOY
ad rectangulum AL L Z R N ratio ultima, ubi cocunt puncta H d L,
elt aequalitaris. Ergo area illa Ilyperbolica eranescens est ut AF.
Componitur isitur area tora IIyperbolica ABO L. ex particulis
KNVOL velocitaci AF semper proportionalibus, et propterca
spacio relocitare icta descripeo proxorrionalis cst. Diridatur jam
area illa in parres aequales AB M L, LMNK, XNO L, dec. de vi-
8
red
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