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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 4
# Folio 21v, page id 00068001:0040
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seu explicando:
anurr raantimm. + aaIl rr, mull
2UImm + aa IIrr + aammunvanner L-8a lmni =0
12U InM + 2aa lrY + 2aammnn- 3a nurY
1
16a mar
c
Nulla quae duae exunteris cequationes sunt solvendae, nulla loteraram
pon polest aequalis derhuo.
Si ponatur aa urr = 8 a lmur seu  Ir = dmn
e
sit: 3 Umm + aa inmnn = 3a nurr = 0 seu - 3. 64mn aammurr - 3 a (nnr-
et 60- c2Uum + raammun - 3a nntr = 0
sed ita coanesante  hacebitur 
inquacble
tar tatius est sinc ulla Hypothesi facere solvere duas aequationes
et
raaller Faammuna lmur = Cumm+ba nurr = 12Umm + 3a narr
Ergo seu siet: 3a nn rr 6Uum seu a nurr = Zunm
seu anr - im s2 seuar = (m 52 : n
sed ergo fiet aatr na 2aalm + a m nt -8Sal m n = 3ummn + b allnn
2
d et divisis omibus per m, fit: l+ an = 3+6a + 8Aa ln
1
4
e
seu l + a n + 2a l’n = 3+ (~ +  8(2+2a Unn
seu Utann =  In 10 et 1+ 2Ba + ann = (8+ 2 a ln
et l + 11 In + LO un = = D = a nI
seu l +  On = n Y L O- a
Se. l+ L On = n Y3+ saa +8T2F1a
ergo problema foret solutum
falerum ergo
et quia d y
E  d = O+ d0
(7
talem formam du f
M Cn
a + βV
V+ dY
fiet dy = (mrV + IY ( mrD+ mn
m v + C
rv + n
= a ∞ LB  A
r2v +2pnV + un
Ergo curra Hype holae (idem est de Ellipsi) invenietur  per summum
1
1
ta
a 4 (3V
7+ 1D 51D - B+O: m
enavae figurae cujus monata est d Talis formae
+ dv. nn∞ = + 2nX V.
per, ca quadratirem
It de sequitur posse inveniri Curvam Hyperbolae
Hyuibol seu per rogarithmos. Eadem Methodus etiam
ac Ellipsia et Hyperbolam quamlibet appercari potest.
bis tam ex una quam adsera
aqualre unde pt prodire