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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 85ar, page id 00068049:0171
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venit in mentem ut a quemque quadratis, non obstantibus
maginariis, ut rru+arrus gri+ 4u aequanda quadrato.
ut Xrul + V. Aiquanda quadmto faciamus vv L coeo + rm, fiet
reul + rrmm + 2Yma  + v. et faciendo U+mm- 0. fiet
rH+  V = 2Ym ergo tantum opus est quadrato aequari
11
2YM + c0co. Quanquam alio difficuitates subdascantur
rell +4rrys = gry +4.y aequandus quadrato ab lr + 2y + yco fiet
uul +4rryg-gru +4y = Urr +qy + yycoco + 4lry + 2ly Co + 47Cd
seu Arry -grus = y coco + 4lry + 2IrW +4 cdy
 sbet sbsc: 0
X sct dependent a SX yAx pendent a (xX. dy nam d. x y = XX dy + 2Xyax
ergo
C
 foca 4 fx sex dy+ ao X dx = Xy
ergo y su ald reducitur ad
S
xra dy
seu Y g. redicitur seu (Vy
0
qs
e
Sdy (xy du + 2(yex de =
Ergo
nd
y y. + a dy + 2es
X y.
sie
V: + a 1. dy =
y
+ a1
atque ita irrationalis esta revocata ad illam rationalem
erg
Xdx = 1 2
+1
 sit X = fy. fiet Si vy dy: sy  seu =
LVyet Cseu (syedu = 2 Vye
e
sitaes
YXtaE ax =
eu dy + SE ex = 1
scur
2 Yxt
d Xy = X dy +2Xy dx.  et dxy = x dy + y dx
V
.2
d=
X dy: 2 sy + sy dx: 2Ux = ddxy seu 2TXy = - X: y dy +
1) dy =
42
Vy: X ax
sit y = sZ fet. SX: y dy = = YX dZ. ergo X aZ + YZ: x ax = 2X ( Z