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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 400v, page id 00068196:0796
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sRestat ut tentemus an ex
sanbx tex, cum ralonali acp
formari possit, quud nondum habentuo sit sarox = y, et fiet
arabx taxx= eegus + reffxyu + fxyy. quaeratur jam X et
fint Xx seu  Xx + 22 y1X f ec gy - a = 0
XX +
2eyy - a b
hy - ac
regy-ab
gy - ac X + 4
gy-ac
gy-ac
tecy +44yy
seu fiet
+4aceegus - ac Z: 4 (2) gy - ac
+4ee - aealyus + abb
sed ibi praecavente natura (vaneseit  t ndeoque quia y haberi it
rationaliter, ex aliqua unte X habetur ratioraliter patet etiam y
eberi haberi ex aliqua unde Y haberi, e ration aliter habetur
quod non facile fari posset, si daretur, sempersieri posset si haberetur
maneret y
Hic est puti renimus modus
de. eventum
praevidem
genemlii aa A + a x de p 
adextqua
aalt abX L 9XX
=3
va a bx t acex
+ aa fXX + 2af9X + gg + = a yy + a bX yy + ac XX yy
 deberet X posse ration aliter per quam et yratu
aec F 2 efX + 2a CGXX
ponaum gea et
calculi facilioris causa sit sta
ut fiet BX + 2aeg XX + a ec: gg = 0
noniter inventur
f20
= a4 gy. 93
Cum X detur elsi Nu rationaliter, tamen rationabilifice per
-q
XX sic dabitur quia datur per y
et X
et (Xyax, sed horjem tum estat
F
Sax
datur ergo sxxay
arbx in fex eX houm disea  213
fatsdxarx
hujus diff est fdx ex dx f
satbx,dX
jin sx txL  (4 s - fix X 42 + = EE
atba
TV EX sax  area
Ergo
at bxix +
cujus diff est dx  atcx
atbx  (ax
(a+bxX = (X Sax ar ex
dx d a +ex
Dix
spem facit. oga Etsi et ipsa admodum sit tennis
atbx)
(ax arex
2
1
2X
= L dx
satbx
2YX
dx sodx atex
Haec via
sane si da ponantur
et x = (eco1o =b) 2acodco 2(a - acoco) cco dei: (Elccoto -b seu 2b acodu - rcacodeo seu
l2 (Cco co - b)
Hinc si Coco = v fieret ax 2 ( )Cv dx Y a +x = a dv (buc) vo. quod
ex.
aTEK
sed video hnc d dare atrusus gntunalem rplic
aD, fiat dx = adv (B. C)
sit X = ev-
sed nit javar
ax
fbX = ad fit a tbx = acoco + Excoco seu  X = a - acoco rX, croro - b
sit sa lade
2a0dco (b-C). Ergo si pro coco ponamus V frit a do (hac) de faro. Caco - b
(D- b
(2s, C2 - b
-av
et te 2
(2 ser -b) mandu
adv (b0c).
(2T (cv - 6)
urgo
d X = 3XX C