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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 365, page id 1066518432:0393
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DE VEREDUS ET MOTIBUS CORBORUM. L 1B. II. 365
PROPOSITIOLXXXI. PRODLEMA
635. Deducere constructionem curvae PDE. praecedente propositione
exhibitam ex principio aequilibrii canalium; seu columnarum Auidi DC.
PC secundum explicationem propositione T. XXIX. traditam.
Polica constructione propolicionis praecedentis, quia FF ad FC
vel AB eAt ut P ad N, Peu ut graritas ad conatum centritugum in
E, conatus vero centrifugus in R ad conatum centritugum in D,
SICUE FC ad DL, Teu BP ad TP, id eAt, siCUE AB ad FTI; CxIE CX X-
quo graricas ad conatum centrifusum in D, Sicut B F ad HII, adeo
ut III semper significet conatum centrifugum particule D in canali
DE vel DC, adeoque omnes ordinatxe LII, quae in triansulo FTIP
continentur, seu hoc iptum triansulum, exponet conatum centritu-
sum torius canalis DL vel DC. Atqui excessus ponderis columnx
DC supra pondus columnae PC sequiralet conatui centrifuso co-
lUIMNa DC. VeI DL (BaEI enIM dUarUM COnAtUS centrifugi in FIN-
sulis punctis ab axc PC aequaliter distantibus aequales, atque adeo
iplarum columnarum DC e VIL conatus centrifugi aequabuntur),
ergorec- lum RV XK aequale cAtriansulo HITP, quandoquidem tti
vel RL exponit scaritatis solicitationem, de Facta CV =CP recta
RV, disterentiam, qua columna DC excedic alteram PC ec (5. 3F.)
volumen RV in Graritatem EF (CU KR ductum, exponit ejus POn-
dus, id esc, excessum ponderum DC e PC. Propterea erit etiam
tocum criansulum P AB aequale rec. l0 VL, ac per consequens abla-
tis ex hisce spatiis aequalibus PFI et V X, remanebit crapezium
AIIIB = reC. IO EKRE, ut in propolitione antecedenti reperieba-
EUT.
COR OE L A R Y u H I.
636. Duoniam ergO TrIaNS. PBA = Z _RH, eFIE EF: ;AB (= P:
) = L. DI  D. DE =CP, CFIE CONVerTeNdO CF: CP = P.
OECLC a kCaM 110
637. Si dicantur CB, a; PC, b; CL, X 3. L37a B Ca
ap. M Eam rocabimus cum Llugenio f, ec quia (5. 5. 63 4y e635.)
AB = L. Y. F. F, het analytice af. =f (dX + 7y) = iaa = :yy 3 9uX