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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)
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L IB. V. DE RESISTENZIA CORPORVM.
Scorum, Cunt ad C, re exerema hu- duplum resistentia: siE DO, duplaris q
ius ad D; sed ancequam vicerius DE; sieque re DE, ad DR, ita DK, Fab. 2.
pergamus in prismatis, nonnulla ad DC; dico momentum cplindri
de cylindris demonstranda LunE.
PROD. ZL I.
Cylindri ejusdem basis, es diversae
longitudinis, habent momenta, quae
sunt, in duplicata loncitudinum. prae-
scindendo ab appenso pondere: Ouia
momencas rarione ponderum; CunE
re cplindei; ec his re longitudines;
icemque carione rectis, re longi-
cudines; isitur in Patione compo-
lica, Peu duplicata longicudinum.
dixi, praescindendo ab appenso pon-
dere; quia s hoc eancum pondus
consideres, momenta (unE, ve lon-
sicudines; li vero verumque Cimul,
procede, re Cupra, vide prop. 32.
ROP. ZLLI
Flinc si momentum brenioris cy-
linari sit tantum subdupium resisten-
eiae, qua scilivet resistit, ne francatur
a proprio pondere; si assumatur du-
pla loncirudo: momentum erit du-
plum praedicta resistemia; cum enim
momentum dupli, sic quadruplum
alterius; certe si hoc eA Cubdu-
DK, esse tale, re rehistentiam adae-
quec; quod demonsero; IMOMeHEa
DE SE DK, Cunc in duplicata ea-
tione longicudinum, PeF PIOP. 4Y.
igieur vE quadtatA DE DR; Ced qua-
deatum DK, est duplum quadrati
DE, ve constat ex geomerria;igitur
MOIENCUM DK, est duplum ino-
MCnEI DE; ISIEUI MOIENELIN DR,
adaequat relitentiam, quod erat
dem. pari modo (ic momentum da-
ei exlindri, ad relistentiam, vr 3. ad
4. lic ve lacus guadeati 3. ad lacus
quadraci 4. ita longirudo cylindri
daci, ad aliam; haec est longicudo
GUX(IEA; CII CHIIM IOIENTA LINE
ve quadeata longieudinu, Cerre (I
quadrarum lonsicudinis daca, AIF
ad quadeacum longicudinis inuen-
Ex, rc 3. 2d 4. est eadem pFOFOF
rio OMenEI vE 4. 2d OMenEuM
vE 3. quae est relistencia, ad idem
momentum ve 3. led quae ad idem
habent eamdem proportionem, lune
aequalia; igituE moentuM VEq.
adaequac relistentiam; idem dico
de omni alia proportione; quomo-
plum relistentix, duplum huius, est do vero invenianeur latera quadra-
aequale resistentiae; igitur quadeu-
plum illius, est duplum resictentia;
hinc crelcune momenta, in dupli-
corum quorumlibet, Facile geome-
eria docer; nos eriam docuius
primo cractatu: Cacerum (I mo-
cata exlindiorum; quia hi sunc mencum cylindri dari luperet resi
re lonsicudines, supposira aequali senciam, eodem modo proceden-
balI.
PROP. ZL TTY
Trinc data qualibet proporiione,
momenii, ad resistentiam, in dato ex-
lyndro, porest determinari longitudo
alterius cxlindri, cuius momentum
adaequet resistentiam: V. 8. Ec cylin-
deus DE cuius momeneum sic Tub.
dum est; SIC CHII LOIeNEuM Cy-
lindri ad relistenciam ba(IS, vE 5. ad
4. AIE ve latus quadrari s. ad lacus
quadrari 4. ica longicudo dari cy-
lindri, ad aliam, Ccilicer minorem;
hic est cylindrus quaesirus, cuius
momencum balim adaequac.
PRC
A A. 2 a