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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
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EAS DE VEREBDS ET MLOTTBVS CORBORDM. LIB. HI.
PROPOSTETO Z. THEOREMA GFOMETRLCUM.
282. Solidi cujusvis CBAD, cujus sectiones cbd bast CBD parallelae
sint, ficurae similes ex similiter positae, momentum respectu plani C AD
basi CBD recti, aequabitur facto ex trilineo quodam AFFFA in re-
etanculum sub FF, quam ipsi BP. rectae CD normali aequalem poni-
mus, e data recta D ejus maenitudinis; ut par allelepipedum sub qua-
drato rectae BP vel PF ex hac data D, aequale fiat solido ex bilineo
CBD in XE, existente hac XF. distantia centri cravitatis X bilinei
CBD ab ejus basi CD, ipsum vero trilineum ea lese descriptum sit,
ut ejus ordinata EF, et sint in triplicata proportione ordinatarum ipsis
in directum positarum BF, bc, in fisura ABBF, quae plano C AD re-
Eta est, e per aem AF. feurae C AD transit.
Sit ae centrum gravitatis figurxe cbd, eritque ve distantia hujus
centri a basi cd bilinei cbd in plano figurae ABBE, quandoquidem
Egurae CBD, cbd. (sccundum hypothelin) similes ec similiter Dosi-
Ex Cunt, eritque adeo CBDC. XF: cbdc. ZC = BB3: be id est constr.
=FF: eF = D. EFE: D. PF. eF; atqui (ConSEr.) CAD. P. F vel D. BF.
requale solido ex CBDC in XE, ergO etiam D. FF. ef aequabitur
Solido ex cbdc in ae, seu momento bilinei cbd axi cd appensi. Jam
quia momentum solidi totius CBAD respectu plani C AD equatur
momentis omnium bilincorum cbdc, quae in hoc Colido COnFinenEuI,
id est, omnibus cbdo in ve, idem Colidi momentum etiam aequale
erit omnibus D. F F. ef, quorum singula Cingulis cbdc. ve aequalia Cunts
atqui omnia D. PF. ef = D. EF. Omn. ef = D. FF. arCam R AFF. FI.
80 momentum Tolidi CBAD aequatur Facto ex arca F AfF in re.
ctangulum D. EF. Ouod erat demonstrandum.
COR OL L A R F U M I.
283. Adeoque momentum complementi Colidi CB AD respectu
ejusdem plani CAD, seu solidi relidui post detractionem ipsius
CBAD a prismate recto _ aquealto CDBO, aequabitur Facto ex
txilinco AFHI in rec. lum D. FF. Nam momentum prismatis CDBC
CA Factum ex rec- lO FFI in rec- lum D. PF, _ Tolidi CBAD mo-
mentum aequatur Facto AF FFA. D. FF, adeoque momentum com-
plementi hujus solidi CBAD aequatur omnino Facto ex rec- lO RFI,
demto trilinco P AF, in rectangulum D. PF, hoc est FaCtO CX AFHI
ia D. EF.
F15. 27
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