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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 37r, page id 00068217:0075
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25 Maji 1678
X aequ. a.
X aequ. a + 3ab.
X’aequ. a + 3a b + 6 abc.
X aequ. a + 22b + 6aV + 12 a bc + 24 abcd.
ab aequ. y. abc aequ. Z.
c120abcde
Xrqu. a + 5 ab + 20 ab + 20abc +30a b + soabed
abcd aequ.  xaqu. arbabtab3 3b+0ab 160 a b7 120a bedrgoab
00abid.
60 a bcd e+720 abedes
Neducendae omnes fornae ad has tantum: X. V. Z c0. earumve potestates
aut rectangula.
a aequ. X - 2y.
ab cogu. ab q aequ 3X - . a aqu. X - 3yX +9
ab aequ. ab   fier: _ X = abe- 1 ab- ab0 2co
49
+2Cd
X aequ. ax + 2abX aequi a +5aeb +6Z
N aequ. a X + 2 ab X aqu.
ab + abc (aequ. y a) aequ. yX - 25.
C
 2ab  + a aequ. a, 4 aequ. X- 4 yX+ 4y
Denique   + 4ab +6ab + 12abc aequ. X = 24 c0.
a aequ. (3- 3yX + 37X aqu. ( OyX +4y - 2a 
ab
a +ab (aegu. Xa) aequ. X - 3yX +3ZX.
ab + 24b + 2a bc (aequ. X Ab) a qu. yX - 37X
ab aequ. 3ZX (+ yX - (4y + 2ab lequ. (y X(2y - a bc aequ. yX - 3ZX- 2a0- ab2
(10
a Ergo (9X - 2y = a b0 aequ. (y∞ - 3ZX - 2a b - 3) a bc
Ergo expriori 2a b aequ. 2y - abc - 37X  post equ 2y
musus (3ZX (+ yX) - 4y + 2a b aequ. (yX  3 Z∞ - 2 a V - 24 bc
Ergo Hae b aequ. 2y - a bc - 3ZX
anserantur valores reperti in aequ. 5. fief: ex qu 8 agu. 13
at 7  aqu. X2 (= 4yX (+ (Dy) = 2y ( a b d + 3ZX)
+a b H
6ab 1
12abcr
aequ.
XP. 24c0
4yxy
(14)
(= abc)
6
vi
1
set
=Gabd (9X
Vor
1 aebc
aequ. X+= 24c
Ergo 6a bc aequ. X3- 24c0 +3y +6ZX
5)
s
29
per aequ. 8. 13
per aequ. 10
Ergoita b aequtGy = X + 24c0 (-3y - (62X (= 18Z X)
Debet esse error in calculo, nam hinc alioqui sequeretur alioqui
omne X dividi posse per 3. Quod labsurdum estt.
(16)
Rectius ab aequ. Y - 2XZ. quae substituendo in aequ. 3. fiet at aequ. X  4yX (9529, 4x7
quod et verum esse scio. Ergo per aequ. 2. fiet a b a qu ( 3 7X (1Z∞ (x  yX - 2y- ( Z
Ergo a b aequ. yX -2y = XZ. Ergo per aequ. 1. fiet: a bc aequ. yX ( 29, (y X 2y + xZ
quod verum esse est, si sint tantum tres literae, a. b. c. sed quando dantur plures tunc
ipsius co. non debermus oblivisci. Ergo abc, erit abc a - abcd seu XZ- +co
Ergo abc aegu. XZ- 4c0. et ab equ  abe ab
a b aequ.
15
2
+3k
per aequ. 13
elatur