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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 601, page id 779782283:0687
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PIB. V. DE RESISTENTIA CORPORNM.
cum criangulo AGB; iGICUF LK, metrorum; Sed AC est ad AB, VE
rel ipsi aequalis, TII, eAt ad LC, quadracum AO, ad quadtatum AP;
ve AG, 2d AB; quod auCeM LKC, igitur ve circulus (uD AC, ad cir-
ec AGB. Sinc aequiangula, patet;
quia omnes linea parallela AB,
plani AEBD, cadune in parallelaS
erectas, in plano AMOO; igituE
Faciune angulos aequales: Pratercd
eor postune duci linea parallela
AB, in plano elliprico, AEBD, quoF
duci polsunt parallelae, AC in pla-
no circulari, AOOM; nempC MO,
_ F.D. Cunc aequales; Led toc pol-
Cune duei in priori plano, quor Pune
puncta in FD; e tor in secundo,
quoc lune puncta in MO; igiEUE
cocidem in veroque; de cum quae-
libet plani circularis, sic ad aliam,
Sibi respondentem, plani ellipricis
VE AC, ad AB; quod eodem mo-
do demonstraeur, de lingulis, re
demonstratum est, de FIL, cuires-
pondet LC; denique cum sIc ca-
dem rario collecti ancecedentium,
ad collectum consequentium, qua
est viius anrecedencis, ad Cuum
consequens, per prop. 12. lib. 5.
Fucl. Cerre lequitur omnes lincas.
Cimul CuriptaS; parallelas AO, quX
duci portune in circulo AOCM,
id elt eorum ipsum planum circula.
TC, ROOM, etle ad omnes simul
Cumpeas, parallelas AB, quae duci
Pollune in ellipsi AEBD, id ett ad
eorum planum AEBD, ve est ipla
AG e ad AL; id est VE IINIOF
dIaMCFer ED, ad maiorem AB,
quod exat demonst.
TTinc colligo, S sc media pro-
portionalis, inter AB, FD, v. 9. AP;
circulum sub diamerro AP, etse
aequalem ellipI AEBD; quia cie-
cutus (ub AC, est ad circulum (ub
culum Tub AP; ioicur circulus (uB
AC, est ad circulum CuB AP, ve
AO, ad AB; icemque ad ellipsim
AEBD; ve AG, 2d AB; sed cius.
dem, eadem est caneum rario, ad
idem, vel aquale; igieur elliplis
AEBD, es aequalis circulo (ub AP;
isicur circulus Tub media PrOpOE
cionali, incer maiorem, de mino-
rem diameerum ellipseos, ipsi ellips
aequalis est quod erac demonstr. Pig. 50.
Jam vero, sint dux bales affixa, de Fab. 2.
quibus supea, alcera, circulus LHIBE,
alcera ellipsIS, IDAE; _ veraque
AP, in ratione duplicata, AC, AP;
CirCA tangentem punCtUM CONEA-
CEUS P, voluI CeNTeaEUE, InEra cun-
dem angulum, v. 8, ATM; CCFEC
Spacium, a circulo decurtum, cst
ad decurlum, ab ellipsi, re subdu-
plum cylindri IN, ad subduptum
Colidi cxlindroellipeici IM cuius
Scilicet bases parallelae Cunc elliples,
vel quod idem est re tocus cylin-
deus INI ad eorum Colidum IM; sed
cylindeus INI, es ad TM, in ratione
compolica, ex rarione balis, Peu cix-
culiTEBEL, ad balim, vel elliplim,
IDAE, e ex ratione longicudinis
BI ad AM; Sed circulus pexdi-
ctus est ad ellipuum, ve TB ad TA;
id est reminor diamerer, ad maio-
rem, re supra demonstracum est,
icemque BN, eA ad AM, veIB, 2d
EA, CunE enim IBH, IAM pFOPOE-
tionalia; ergo ratio compolica ba-
Cium e lonsicudinum, est cadem,
cum compolica longitudinum, bis
sumpearum; vel quod idem est, cum
duplicaca lonsicudinum, vel dig-
mecrorum, vel alcicudinum IB, IA;
igicur sparia decursa, a pradictis
Tunc enim circuli, re quadrara dia- balibus, Cune in duplicaca LB, LA:
3C
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ialruE
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