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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 178v, page id 00068194:0356
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Latera hianguli rectamguli  b, a x, ex- b sypoteus. pnum acuvoiie  ratem bes esse eusins
E cegb. ob Tiang. rectanus. est aa . 2ap (b6) + a - rax +Xp = ccXX - 2bCX(+ 66 ) 
ob cubum, fit (b) + a3- 3aa X + 3 aX -X + Cx - 3ccbX + 3 Cbb X (=b) cubo aequat
abtem cubo a, et praeteren facit c = aa et d = bb, ut habeat aeq. in qua solum
sit X. simpler. aquemus et nos cabo a, sed faciamus c - d tunc utvaque
aequatio rercta erit ad X. nams ex aeq. 2. fiit - Baa + fax- bX + 2b1 =0
et ex aeq. 1 fit a - 2ax t 2bX 0 fiet X = bb = aa : a- b seu X = b - a
sd  la sit bipra cotia intentum et X = a a B, 2a - 2b  et set
(a) =  (2) a - 4 ab + 2bb. sed haec ratione solutio non procedit. nam
fiet + a h a - 2 ab = b 12. ergo sic potius
ponendo ut ute cxd faciamus (a_-3aa X +3aX. a exth aext ex
3cbb  - 3b, X-
sit =d, et sit et  lb. aa,: 4.
Sd 76
et ex aeg. 1. fiat X= a, : 2a -2b Et ex aeg. 3 siet -  a- 3b- aC: e
verum sic sub fineo nihil amplius super est
et sict X = 3a - 3bec: dd = 3a C, : e C: d + 1 = 3a - 3bceids. 2 cb t ad bcttaid a
arbitrarium. contenti ergo simus hoc ut fiat e= cbb -aa,: a
seu  et fit X=
ex aequ. 1. faciamus XX + 2bc: d - 2a + () bci d - a = () bcid - a - aa. 1 - c. dd
dd
16)
1- cc: d
d 13) 1qbc. d - a - ca - cc d dc   c.d. a 
fiet X E cendo
1d ccidd
ergo extahenda est radix ex.
1- cc: dd
x( 3n y + 3XyL y) = Enyre (  yrB
+ (8Y
+ Xo( 3X y) + 3Xy 4 9
x ysteyee (t n yoxyy
+ 8X313
fit 6X  Xy = 2y
3X + 4Xy = yt
seu X
15
a
+x q axsesi
qt
(8Xyst S. Ixjerue ayere
H
=2X + 6X y
T Y y q. A  suu 6xi ros rq
An sic 2X + 6x + 8X1 = H C YGCX
sit Xy= F fiet 2X+ y+ 9f= e
fiet N +Sy +qXy 4 eX
Zry ut Ge X = 1of+ ny et C = 2ot uy
 t X frei   14, I y. 10 +6. 11. 5. 10 4 4. 11.y. 10410t =0
3 yt +4.105) =411. 219 -4, 11. 20y -10. 20
410. 2 y 4  3 et ut ev
XFK
ubi faciendo 611. 10 - 4. 11. 21 = 8 se. 3. 11. 10= 2 21 20 +4. 15 sit 11= -1, coanascent
et 20=103  sea tunc non licet destuere yt.
p
una fit 20 = 10
= 4. 10. 213:, 3. 10 + 2. 21