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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 89v, page id 00068049:0180
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Aequati resolvenda pro dimensione curvae conia centrum habentia est.
ec bdco = X do sV: +cevo
V.4a - v0
eifint v ex + Bb
2X+ 2b
posito esse b axe rectum, seu latus tansversum
primarium, e distandiam focorum. + est pro Hyp et = pro Eli
itaque reterto quod invenimus esse Bat + ter bat= +Brr
Video igitur non posse suunt nrumeratorem a nominatorem fieri extrahibiles
forte ulilius uit farere Nominatorem si Numerator solus sit extunhibilis siet Numerater Gxtrast
 ece Xar + cceib, seu
 S ut numerata sintextrahibilis video fuisse erratum
bB X nempe pBE2 scublum est brY, ce sic ergo:
18r)+b eat +br e+C βat= (6 f 26 reeat(t e 5a f)
d
tq
sit at + FB - 2 at BY = 0 seu at = D BY
et Numerator extractus erit b + ee B. X +Y. Sed jam rursus video si at = BY
idem Quodsi Nominatorem velimus redder
extraribiem, si prodibit idem gempe Br= at quod ut dixi non licet
fieri V constantem = β: 2..
quoniam ergo extahibilitatem hac via obtenere nor liet
pesc srctum simul terminorum destrnctionem, quia tunc tertius itidem
destinitur, superest, ut videamus anliceat obtinere ut numerator Xt nominator
habearit communem divisorem sit X+ h in lx + m fit lXX + hlX + hm
et similiter ∞ = h in px+n = PXX L heX + hn, harum formularum prio
aequetur numeratori, posterior nominatori f l = b + e0 βB M = 264 2ee pat - hb qhes
a Caf
et hm = 7 bh + reeBath - h b 4 he
c
B2C
similiter p = bb - BC n = 2bbr - 2B at - bbh + Bβh
et hn = 2brh - 2Bath = bbth + (Bhh = b r - ae F
aeq. D multiplicetur per bb, fit 2b rh - hhb- Vr = 4 2Cea t + h eβ + eat = 2Bb ath
Ergo oportet facere vel 4 ec = bb e quod non fit nisi in casu ciiculi,
vel fit  a t + B h = 2 at Bh = o seu at = Bh, sed
ita fit quoque YY+hh - 2th = 0 seu h = Y ergo at = Y redit, quod
tamen evitare volebamus. Itaque etiam obtinere non licet communem
divisorem.
e
ba