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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 40, page id 1066518432:0068
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216. 29.
40 DE V EREBDS F Y NIOTTBOS CORDORDM. LIB. I.
92. Pxempl. 3. Pari ratione infinitx hyperbolae intra alymptotas pol-
Cunt quadrari. Sit earum aequatio generalis vey=, in qua a abscistas
a centro in alterutra alimptotarum, ex y ordinatas significant; ele.
mentum arex abscirx adjacentis crit rda =Xdae. Invenictur ve-
rO A = F: (a -= 1). ∞  3 e B = F: ∞ 1. (X -= d ~) = = = I: (a- +). a -
ac + 20 = 1). ~2 da + eC. hinc B major cs quam A ob denomina-
torem minorem quam in A, atque adeo invenietur B = A = dX:
X =x d =7da, unde cum A, B, C, D Sit Series alcendens, fent
Omnes B = A, C = B, D - C ecc. id eAt omnia ydX, =MI = A, AF
vero substituendo in aequatione A = T: 4 - F. a vel = (T: ∞) a-1.
a - 1, loCO X, O ACt MI = (s: 0) : a - 2, aE VerO T: 0 eAt magnitu-
do infinita, quam designabimus per ∞, CrGO M = ∞ = : a - 1, at-
que adco MI = A seu arca srperbolarum abscisx adjacens, crit
= ∞ : a  1, = L: _ = L∞ , vel quia F: ∞ = ~y, CFIE M - A =
∞ = =∞y): a - T. F X quo apparet ejusmodi areas juxta direrlos
oradus infinite magnas ese, siguidem a sit quilibet numerus positi-
vus ex unitate major. Scd de his (ufticit.
PROPOSITTOZTT. PHEOREMA.
93. Tenacitas fili ZBABX ad Rcuram manentem redacti a potentiis
BHI, BFI _C. ipsi applicatis, aequatur in quolibet sili elemento Bb, te-
nacitari fili in vertice A auctae omnibus CHI, quae ex sinculis potentiis
BII, BII_C. curva AB applicatis derivantur, resolutione illarum
BII in aequipollentes potentias laterales BC e OI sinculis curvae AB
elementis BB perpendiculares ex parallelas. Ioc est exponendo tenacita-
tem sili in A; erit Y = A + (6tI.
Sit demissa ex elementi curvae Bb termino b perpendiculo b8 ad tan-
sentem B8 curvae in B, Sumatur in hac tanzente, Bh aequalis elemen-
t0 curva BB, e aeantur m parallela ordinatae DC, BF vero aequi-
distans axi curva AC, ex per curvae punctum B, indefinita BMF. ei-
dem AC etiam parallela, in quam MF cadat perpendicularis TIF ex
termino II lincae BII potentie curvae puncto B applicatae repraesentatri-
cis: ac denique junantur lineola bh, atque hisce factis habebitur in
anculo contactus bB8 fgura bFhs similis, et similiter posita cum fieu-
ra majore BFTTO, si elementum BB fuerit ad elementum BB ut illius
tenacitas T ad hujus tenacitatem E; atque adeo erit quaelibet lineola in
sieu