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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 246, page id 1066518432:0274
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246 D E V ERTBDS F Y NIOTIBVS GORPORDM. LIB. HI
diagonalis AF promoti in Auido, praecedente quadrati vertice F, ad
relistentiam lateris BF. Auidi, imprestionem ad angulos rectos exci-
Pieneis, est uEBF ad BA, Seu uElatus BH ad diagonalem BR, adco-
que invertendo, resistentia lateris BF super AF perpendiculariter in
Auido delati, ad relittentiam quadrati juxta diasonalem incedentis,
est ut diameter ad latus.
GOR OL E A R L U M TT.
440. Resistentia coni recti BER juxta directionem axis AF in
Auido delati, praecedente tamen ejus rertice P, erit ad relistentiam
ejuSdem, pEXCuNEO ejuS BaSI BR SIECrUM NE AI ad AP, PCu UE BF ad
BF. Nam (5. 435.) relistentia primi calus est ad alteram, ut cylin-
AruS ex rectanguIO AEI CirCa AP ad Cplindrum Cx GUadEaLO ANI
circa eandem AP, Led prior cslindrus eM ad alterum ut AI ad AP,
cum utriusque cxlindri basis sic cadem. Argo ec.
PROPOSTTIOZLVI. PRODLEMA
E1s. 2r0: 44. I. Assienare resistentias Sectionum Conicarum juxta directionem
axis in puido motarum.
Si ABC AE ellipsis vel Byperbelat CUjUS CeNErUm SIE in MI; dican-
turque TemilatuS FranSVerTUM AM, b; Parameter c; absciAX AN,
X; lemiordinatxe NB, y; aequatio ellipleos e hyperbola erit byy =
2bcx + caex, in differentiata aequatione brdy =bedae F caeda, loco dif-
Ferentialium du, dae carum proportionales a e m Tubstituantur, quae
Funit nomina lincarum R A e AS, Aetque aby = bem L CMX, atque
adeo m = aby: bc L C∞, _ mm = aabbyy: bbcc F 2bCC~ + CCa∞ (vel sub.
SIFutO ex aequatione Currae ralore ipSIUS = 2bCCX F CCXN, in y) =
aabbry: bbcC = b0); hinc aa + Mm = (aabyy 4 aabCc F aaCYy): bCc = Cy);
hinc, quia (5. 437.) t = a: aa + mm, exit t = abcC  acyy: bcC + byy F Cyy
(Icu Ponendo e pro b =C) = abcc F acyy: bCC - + eyy, eE HXC FOTCE Xqua-
tio Ccalae resistentiarum CIY; ponatut insuper bec = eff, et xquatio
CUEVROIP eritE = aess F acyy: efs + eyy = + ac: e; + aff + aeff: ess +
ery (8 Tubstituendo in numeratore poltremae Fraecionis, loco + C + C
Cuum ralorem B) = F ac: e; + abff: eff. + ey7.
Tgitur elemenEm aPCX MTTIV, seu rec lum IITB = = acdy: e; +
abffdy: efs + eyy =  acdy: e;  abda: e; nominando arcum circularem
Cujustansens elty ec radius f; quandoquidem (8. 166.) hujus ar-
C