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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 83r, page id 00068049:0165
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Ad Act. lips. januar. 1691. pag. 15
Ver  + arryu - 8ry + 4u dy quaeritur ut habantur
longitudo curvae quae fit si axis parabolae convolvatur in
pariboa
perpheriam circuli, et ordinalae sumantur in comvergendubus ad
radis a circulo ad centrum gust)
xrk +4rryy -8ry + 4y = veu + 2rl co  2y. Pr y + coco. 4yy. Fy
seu 2y. r-y = + 2rlco + coc0. 29. r- y et seu - 2yy + 2ry = f2r100 (-2059y + ory
seu gy +2Y - 2e0coY y = + 2rla seu yy - ryH +rr = rcoco- rr + 4rico
Fcoc - 2
quae quantitas
2CdCd  2
ercoco -er qarlcd
4c0c0 - 4
401-4
aequanda quadrato. Sed hoc panto
a
22
diffieilius
rC sit 29. ruy = re fiet Al + +AeC =Z. quaeritur szdy vel fy dzue
est autem ( 2yr - 2yy = re Ergo 2dy -2ydy = rde et dy = rde : 2r- y
vy =yY +: r = rr- 2re. seu C88C =r - y = , Vrr. 2re. seu y = r - Vrr- 2re,: 2
et dy = Yde et 2Y - 29 = 2Y - Y + (rr - 2YV = Y+ Srr- Ere
ergo fit Zdy = r Su+ ee de : r+ Srr-2re, seu = rriutee- r Utee. Trrrre
tantum ergo opus foret facere Su+ ee. rr-2re a qualem qua
+ 2rC
faciendo rr = 2re = vD. fiet C = _ rr - vV,: 2Y. et jam ll+ F - vV + V
2
equantus quadralo faciamus WV: 2Y = W fiet LY = W = C, et ee = Lrr - rW + Wio
et U + : rr - rW + Wveo = quadrato U+ er + W V sU+= rr + WW (1
seu =r + W = 2 b M+ Zir + W (VIP
seu W = 21 M+ = 1r +Y,: B
quae quantitas rorsus aequanda quadrato et a m_ + n9,:, 1+V
fiet  sit 2. a + Lir =h, fitt. hI +Y = ns v + 2mn V8+ nn88
el si m = 0 fiet  L + hr +he Frib
I2 +n  +X +h
d14 1p
1+ V
ungg  nnv 00. seu
 V = = un L hr sed ita extractione
centando reditur ad priora, et radio extrahenta ex quantitate
in qua est D et 
ut supra ex alia ubi ovet vi
praestat ergo solum radicem quaerere ex Urr -Ellre +Carree- 2re
Urr + 2res L ecEE
fit - Ellr + rre = 27CC, = 2lr e∞ + exr
sit Ur + ille ra + 3 (C3
ubi redit difficultas
9+ 3599 +c
nisi in casiba specialobuss sict
Sed nec sic progredi lice
u ut spleciales tamen casus namto
pro nmmris rationatibus refecriri possunt, ut in ag.(t Faciendo nne = hr, seu
n Thr (uam irrationales in ipsis cognitis non curo) fet h + h4 fr = 4 nn
et datur  casu speciali