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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 266, page id 1041163592:0300
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III
266
PEITLOSODTITA NATURALIS
DF MOEDEateM BF ut summa omnium AFP + BY + CK + DL, in intini.
onronontum, ad summam omnium BY F CR f DL, _C. EE BI den-
sicaS secundae B, CR ad C R densitatem tertix C, ut summa om-
nium BT + CX + D L, Scc. ad summam omnium CH F DL, _C.
Sunc isitur summe illae differentiis suis ATI, BT, CK, _EC. PrO-
portionales, aeque adeo continue proportionales, per hujus Lem. 1.
proindeque disterentia ATI, BI, CK, _c. Cummis proxortionales,
Cunc etiam continue proxortionales. Ouare cum densicates in locis A,
B, C, _EC. (INEUE A YH, BI, CK, eC. Crunt etiam hX COntInUC DFOPOr.
cionales. PergaTUE per TaIEUM, _ (ex Xquo) in dictanciis S A, SC,
SF continue proportionalibus, crune densitates ATI, CK, P. M
continue proportionales. Ec eodem argumento, in distantiis qui-
bulris continue proporcionalibus SA, SD, 50, densitates AII, D L
GO erunc continue proportionales. Coeant jam puncta A, B, C,
D, L, ecc. eo ut progressio graritatum speciticarum a Fundo A ad
cummitacem Eluidi continua reddatur, ec in distantiis quibusvis con-
tinue proportionalibus S , SD, SCi densitates AFI D L GO)
semper existentes continue proportionales, manebunt ctiamnum
continue proportionales. . B. D.
Corol. Elinc si decur densitas Fluidi in duobus locis. puta  ec
En collisi potest ejus densitas
in alio quoris loco 9. Centro
S, ACrmpeotis rectangulis S9:
SX, describatur FIrperbola sc
eans perpendicula ALY, F. M.
T in as e, q uc e perpendicu
Ia FLX, MT, F Z ad ASmp
eoton SX demista, in B, m EF +.
Fiacarea Z YmF Z ad aream da-
eam Zm B X UE area daFA F eg C
ad aream datam P ea A; dc li-
nea Z+ producta abscindet li-
neam T denscati provortio.
nalem. Namque Si linexe SA, SF,  Cunt concinue proxortiona
ICS, CFUNE arEK F eg Q F ea  aequales, et inde arexe his prOPOr.
tionales rm+ Z, Xhm L etiam equales, et lincae SX, SY, 5Z, id est
ATL, F MI, QF continue provortionales, UE OPOTECF. EF Si linex
SA, SE SQ obtinene alium quemris ordinem in serie continue
proportionalium, linex AFI, F M, QT, ob proportionales arcas
typerbolicas, obcinebunc eundem ordinem in alia serie quantita-
cum continue proportionalium.
C
PKO.