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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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d
CI.
In.
II
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2.
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d
DE VTREBOS ET MIOTIBOS CORPORUM. L AB. II. 16L
finem Facillimum omnium eligemus proxositione lequenti excutien-
dum.
PROPOSITTOXV. PROBLEMA.
302. Data ratione specisicae gravitatis prismatis triancularis ABCF Fi8. 65:
ad gravitatem alicujus liguoris ZBT, determinare situm prismatis, in
quo praecedente vertice D trianculi ABC, id liquori immissum cum
eo in aeguilibrio maneat.
Sit MBN pars liquori immerta et punctum D ejus centrum gra-
ritatis, C vero centrum graritatis trianguli totius ABC, adeoque
(5. 294.) lineam DC, junsentem centra graritatis totius de partis
immerla triangulorum, oportet eNe liquoris superticiei XY. Perpen
dicularem in casu aequilibrii. Jam ex centrobaricis constat, centra
graritatis C, D triangulorum ABC e MBN reperiri in lineis
BP_ BO, bases AC _ MN triangulorum bitariam diridentibus in
punctis P e 1, lincasque vel interralla PC, OD trientes eNe to-
tarum PB ec GB; hinc ductis PC, PM ec PN, ip(X PO e CD
requidictantes CruNE, cum PC et OD sint Partes similes iplarum
PB ec OB. Jam cum oporteat iplam CD perpendicularem esse rc.
etx XZ, necesse eA ut etiam P eidem ZZ vel MN normalissit,
unde, quia jam M ec O aequales ottenlae lunt, iplaS PM et QN
Pariter aequari oportet.
Porro, quia in casu requilibrii mallae liguoris MBN pondus (S. 293.)
reguale et ponderi abloluro prismatis ABC, Per S. 33. Cxit GraVITaS
specitica liguoris ad graritarem prismatis ut triangulum ABC ad
triansulum MBHI; atque adeohac triangulorum ratio data, quando-
quidem ratio graritatis specifiexe liquoris ad prisma ABC (secundum
hypothesin) data est. Propterea problema eo reducitur, ut deseriba-
tUF CeNtrO O ee interrallo quodam PM vel PN circuluS MON, qui
ex lateribus AB ee GB abscindat segmenCA MB et NB talia, ut du-
cta linca NN, triangulum ABC sic ad triangulum MBN, vel re-
ctangulum ABC ad rec. lum MBNI in ratione data specifiex gravi-
tatis liquoris ad graritatem prismatis ABC, quam dicemus a: f.
Idcirco demissis ex P perpendicularibus PR ad BA, PS ad BC ac
denique BV ad AC, si dicantur AB, a; BC, b; BR, l et BS,
m; incognita vero BM, X; ex comparatione triansulorum rectan-
sulOrum PRM et PSNY, in quibus juxta superius ostensa hypothe.
nuIa PM et PN aequantur, elicietur aequatio, qua reducta extribe-
bi