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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 39, page id 1066518432:0067
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DE VTRTDUS ET MIOTTBUS CORPORUM. LIB. I.
39
quaesita, seu summa omnium ida, crit A compolita ex indetermina-
ta a rarie affecta e cum constantibus implicata. Pro inveniendo
vero ralore ipsius A, ex dato elemento idu, loco ipsius y substitui
debet ejus ralor in x ec constantibus, quem requatio currae quadran-
dae praebet. Ouod de quadratura spatiorum scu arearum dictum est,
id etiam de dimentione Colidorum imo, de omnibus summationibus,
Pariter est intelligendum.
89. In hisce Suppoluimus literas A, B, C, D, P ecc. ulque ad
MI denotare seriem magnitudinum decrescentium, sed infiniti etiam
sunt casus, in quibus eadem licera iisdem ac praecedenti articulo
Factis Subscicutionibus indecerminatarum ∞ =dx, ∞ = 2d~ QEC. lOcO
iplius a in magnitudine A, proveniant B, C, D ecc. majores quam
A, adeo ut tota carum series repraelentet progrectionem carundem
crelcentem ita ut differentiae Futurx sint B = A, C = B, D - C.
F = D, XC. quo casu M, quae antea minimam seriei magnitudinem
denotabat, nunc sit maxima, ex quae antea crat maxima A nunc (IL
minima, necesse est. Vrriusque casus exemplum est adducendum.
90. Fxempl. L. Sic Cummanda quantitas mam: V (aa L mm), in
qua m est rariabilis et a data seu constans. Fritque hoc ca-
Cu A = V (aa L mm), adcoque B = V (aa L mm - 2mdm + dm:)
=VCaa +MM), - mam: V (aa LmMm) + ecC. TIINC A - B = V (aa L MM)
=V (aa L mm), + mam: VCaa = mm) = mam: V (aa + mm), unde le.
ries magnicudinum A, B, C, usque ad M est descendens: ec s locO
IDCIUS M In GVanLIEaTC A (5. 89.) DOnatUT O, HetCOCaTU A = a = M;
cum igitur Cumma omnium A - B, B = C ec. vel omnium mam:
V (aa LmM) SIE (87.) A -M, crie Smam: V (aa = mm) = Y (aa + mm)
9r. Faempl. 2. Sin detur elementum summandum aamdm:
au =mm V aa L mm, FUINC eriE A = aa: V aa =mm, aEque adco B = aa:
Vaa tmm -2mam am hoc est extrahendo revera radicem ex deno-
minatore =aa: (Vaa F mm -mam: Vaa +mm) quae fractio ob denomi-
natorem minorem, quam in Fractione A, hac ipla Fractione minor cAt.
atque adeo hoc casu erit B - A = aamdm: ac + mm V aa L mm. TTinc
procressio quantitatum A, B, C, D _C. eA alcendens Icu crelcens;
atque adeo summa omnium (87.) B = A, C = B, _EC. CA MI = A,
verum hoc casu M iterum est a, quoniam Facta m =0 in sequatione
A = VeFet V (P. + mm) = a3 atque aded N = A = a = aa: V aa + mm.