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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 237, page id 1041163592:0271
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PRIMCIPTA MATHEMATICA.
2 3 09
recta illa b, FC a. F d C, CFY e e CD o; rectangulum a F O LIBEI
I c = a = 0 TCu aC = aa = 2a0 +c0 = 00 aequale CA rectanSWIO SECVRDOS.
b in DF, adeoque DF aequale aC = a a, c = 2a
bendus eset hujus seriei secundus terminus
es
Ob
Jam Ccri-
O PEO OO3 ter-
eius icem terminus = PrO R0O. Cum vero plureS nOn HnE teF-
minis debebic quarti coefticiens S cranelcere, et propterca quan-
titas
RVF +90
cui Medii densitas proxortionalis est, nihil
erit. Nulla igicur Medii densicate morebitur Projectile in Para-
bola, uti olim demonstrarit Calileus. 9. F. I.
Faempl. 3. Sic linea ACK FIyperbola, AErmpeocon habens
NX plano horizontali AR perpendicularem; et guaratur Medii
densitas quae Faciat ue Projectile moreatur in hac linca.
Sic M X ACymptotos altoras ordinatim applicatae DG productx
occurrens in V, ex ex natura IIyperbolae, rectangulum XV in VC
dabitur. Datur aurem ratio D N ad V X, et propterea datur criam
rectangulum D N in VC. Sit illud bb; e completo parallelogrammo
D NXZ, dicatur BN an BD on NX c, de ratio data V L ad Z X
vel D N ponatur eNe =. Et erit D NV aequalis a = o, V C aequalis
=  Y Z aequalis = a = 0, e GD Peu NX -VZ, -VC x-
qualis c - a + m 0 - bb
Resolvatur terminus- in seriem
convergentem = + 0 + 00 + - 0 ec. de Hiet CD aequa-
M
lisc-
bb
a
a
aa
m
bb
2
bb
n aa a
bb
nus secundus mo -
aa
0 -
40 c. Flujus seriei cermi-
usurpandus est pro 90, tertius cum signo
MuEatO == O PrORO, ee quartus cum sixnO etiam MuEatO , 0
ProSo, corumque coeficientes - bb bb, bb
e
n aa a
at
Scribendxe TunE
in Regula superiore, pro, R et S. Duo Facto prodit medii densitas
uC