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# Title: [Physica, Id Est, Scientia Rerum Corporearum, In Decem Tractatus Distributa] Physica, Id Est, Scientia Rervm Corporearvm, In Decem Tractatvs Distribvta (shelfmarks Leibn. Marg. 7:1-2; ZEN Leibn. Marg. 7:1-2)
# Folio 110, page id 779782283:0196
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P E YSTOA LR ACFAFVS Y.
PROD. CLZVI
Sitendatur planum circulare, V. 8.
menibrana rympani; potest determi-
nari sparium aquinalens decursum:
Sic enim membrana cympani, cen-
EtO A, diamCErO TN; priusquam
cendatur; vbi vero censa est, sIE
diamerer IL, dupla prioris THI; sc
radius AFI, qui sC resticuic in AZ;
igicur spacium decursum à puncto
HL, eAt HY, vel iph aequalis HC;
igitur duCatEx AC, Si Spacium de-
curlum a puncto HI, est HO, de-
curtum a punctoY, cxir YD; d a
puncto Z, ZF, ecc. igieur si altu-
inacur longicudo radii non censi
AY, ec T7, aequalis excestui YFI,
vel HIO, ducacurque A), habe-
bitur in criangulo AX2 Eparium
aguivalens decurlum ab AY cen(a
i AII per proP. 83. ve aucem ha-
beacur spacium a quiualens à plano
circulari le Sc reducente decurlum,
a plano inquam cuius censi radius
SIE AFI, non censi vero, AY; cri-
satus planum crians ilate A Y 7,
voluatuIEqUC CIFCA aXEI AZ, donec
incubet perpendicularites praedicto
plano circulari; in quo deinde ica
A, decurcar, relinquit Tolidum cy-
rensis praedicta spacia aegninalenria.
lindricum excauatum, quod est ad
cylindrum eiuldem balS, _ alci-
cudinis rE 2. ad 3. nempe illa caui-
c2s, 2 cono ciuldem balis, ex alti-
eslet torius cylindri igitur quod
Cuperest, 3. Orlindri concinet; igi-
cur inventum est spatium aequiua-
do, quo prius, habebicur Colidum
In membranis inaequalibus, aeque-
sunt vi cylindri, quorum bases sint
crectum per incegrum orbem circa
cudinis, impleretur, sed hiCCOnUS
ACF, quod Si voluatur eodem mo
CxCaIaLHI, XC.
PROD. CLZVII.
lens, ac. pari modo sic circulus
cujus Cubduplus sIc radius AF;
piiu(quam cendatur membrana. vbi
et membranae es alcicudines ut ex-
cessus: v.Z. (E membrana maior,
cuius ren (a radius sIE AFZ , HON Fig. 28.
cenLa AY; sic inor, cuius cenlae
Fadius (IE AZ. nON EenLa AF; (p2-
rium aequiualens decurtum à ina-
iore Le reducemle continet =, cy-
lindei, cuius balis sic ipla membra-
vero Tenta est AZ; SIC FCs aequalis
na e alcicudo, exceltus censionis
YFI, vel ipsi aequalis Z7; decur-
Cum vero a minore continet,, cy-
lindei caius Ba(IS AE ipCa IeM-
beana minor. _ alcicudo excessus
centionis FZ, vel ipli aequalis FC;
isicue sparium primum est ad le
cundum, ve.=. primi cylindri, a1
=Secundi; Led ica se hab et cylin-
deus ad cylindrum, ve =. rnius, ad
 alterius, igieur (pacia (UNEVE
prediai cylindri, quod exac de-
monstrandum.
PROP. CLXVL1
Tlinc praedicta sparia sant in rario-
ne triplicata diametrorum membra-
narum: Nempe Cune re praedicti
cylindri, per prop. 167. Scd hi Cune
in ratione criplicaca diamecrorum
vel radiorum balis; quando enim
alticudo, est ad alcirudineim, VE Pa-
dius, ad radimm, NE AE in ROC Ca-
TU; SI HaDCaEUE EanEUIM FatiO alEi-
cudinis, cylindri lune re alcicudines,
vel ve radii; si cantum ratio balIs,
Cune re bales; he rero in duplica-
ta radiorum; si vero veriusque, lunc
excellui FX, haberur rriangulum in ratione compolita ex rarione
radiorum.
21C