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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 17, page id 1066518432:0045
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DE VIRTEVS ET MOTLBOS CORPORDM LIB. T. 17
cC, dD, _ OpPOsIEX Pa, Pb CX Una _ PC aC Pd ex altera plani
PS parte; atqui ex conspirantibus resultat Colicitatio ipsis omnibus
(5. 38.) aequalis id est Colicitatio aA + bB + CC + dD F _C. (R. TL.)
=N. eF (R. T.) = PS, et ex omnibus contrariis (5. 38.) nalcitur (0-
licitatioxqualis excessui quo fortiores excedunt debiliores, id est
iDA PC + Pd + REC. - Pa - Pb = _C. (HUM. TT.) =NV. PC (NUM. T.)
=SR, ergo omnibus obliquis PA, PB ScC. Xequipollent dux late
rales PS e SR, e (5. 39.) hisce unica PR: haec ergo denotat me-
diam directionem Colicitationum PA, PB, PC, PD ecc. e Colicita-
tionem ex ipsis nalcentem, rel quod idem est, ipsis aequipollentem.
Ouod crat demonstrandum.
Elegans hoc theorema IIlustri Leibnitio acceptum est ferendum,
utpote quod in aliqua ejus epistola, jam pridem ad W allisium da-
ta, sine demonstratione exhibetur. Vid. Tom. III. Oper. Wallisi
Fol. 687.
O OR OLL A RTUN T.
50. Hlinc punctum P, cui quatuor solicitationes PA, PB, PC, PT FiB. B.
ad aequilibrium quidem compolitxe; sed non in eodem plano existen-
TeS, Impressa TunC, erit in centro graritatis prramidis TAC, in cu-
jus angulis Colicitationum repraesentatrices linexe terminantur. Sit
E centrum praritatis punctorum A, B, C _ jUInGAtUE PF, quae me-
dia directio erit solicitationum PA, PB e PC, ac hisce aequipolle
bit solicitatio 3. PF; hinc quia omnes in aequilibrio sunt, crit
PT = Z. PF; atque adeo est PT: PR = 3: T = A + B + C: Y conS-
derando haec puncta tanquam ponduscula aequalia, ac proinde P
est in centro graritatis punctorum quatuor angularium preamidis
A, B, C, T. Scd idem est centrum graritatis preamidis, quod pun-
ctorum ejus angularium. Ergo liquet assertio.
HIoc est alterum cheorema, quod Roberrallius Torricellio olim
propoluerat in loco supra (5. 4 3.) jam indicato.
. OE OE E A R F U M TY
51. Cee ectat, I MobIle L ad lingula luporticiei currae ABC F18. 9.
puncta urseatur Colicitationibus exprestis punctorum Cuperticiei di-
stantiis a mobilis centro; media omnium solicitationum directio
erit recta PE, jungens centra graritatis mobilis P ec superticiei cur-
vae ABC, ac solicitatio ex omnibus nalcens iplisque aquipollens
CAt,