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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28
# Folio 1r, page id 00068241:0001
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(4
D2)
10+2 uX +ux A d
(22
Maii ibceq schem
20 +21∞ + 22 X aequ. N . Unde multiplicando seconda
per cuucem secundum coefficientes terminorum altiorum, fiet: +10. 22 + 11. 22 X ae qu. N
-12. 20 - 12. 21.
Unde velut ex A et 1 fit 6 ita ex 4 et 23. firt (24)  si in 6 loco 20  scribatur
10 22 12. 20. et loco 21 scribatur 11. 22 - 12. 22. et prodibit  Ruasus multipli.
1C Nl1 10. 11. 11. 22. 22 do sursus multiplicando per ciucems
)E  22. 22 secundum coefficientes terminorum inferiorum
24
firt: Cb + 11. 20+ 12. 20X aequ. N. Ex quibus duabus aequationibus
- 10. 21 - 10. 22.
23 et 24 multiplicando per crucemo secundum terminos altiores facile
(25)
2,  3 + risegro
3F1 2. 20 (- 12. 21) 21922
F- 10. 11.21. 22 +10.10. 22. 22 ((25)
=IL. 225 fall. 26 + quade  1. 20 aequ N. seu distincte scibendo +
F 11. 1B. 20. 2L = 10, 12. 20. 22)
= 11. 12. 20.2) + 12. 12. 20.20
10+HX + 12 X + 13 X aequ. N 20+ 2IX + 22 X aqu. N. Unde multiplcando
per crucem secundum terminos summos fit: +10. 22 +11. 22X + 12. 22X aequ N.
1320 13 24 X ( Z dXX
at secundum terminos infimos fit + 11. 20 e
10. 21 -F, 10
= 13. 20X =13, 2IXX,
(29)
ex aequ. 26. et 27. per crucem secundum en fis: et. 12. 20. 12 + 12. 21 22X aequ. N
sumnos
- 13, 20. 21, = 13, 21. 21.
secundum infinos sit:  10.21. 22= 10. 22. 22X, (34 - 10. 2_ - 11. 2222
1D. 20. 22 - 12. 20, 22.
13, 20.26 + 13, 20.21.
qu. aN.
+13. 20. 22.
nullibi opindr
Ex aequ. 26 et 28. secundum terminos summis fit rusus, equ. (30) at secundum nenta
terminos infimos fit:
+ 11. 20. 21 = II. 20. 22X aequ. N.
- 10. 21. 21 = 10. 21. 22.
- 12, 20. 20 = 13, 20. 20.
+ 10. 20. 22
Sed opus est ut aequationem inveniamus in qua omnino absit X. idque
exaego Nempe ut ex aequ. (4) et (2Y. fiebat aqu.  25. ita ex aequ. (26) et 27)
faciemus novam si in aequ. (25t pro 10, 11, 12, scribamus 12c2, +122 f 12. 22
a
c -1 2. 21. 22
3 F13, 21. 21
f - 13, 20. 20
g - 10. 21. 22
=12. 20. 22 i
+ 13. 20. 21 K
G
=13.20) - 13. 21
(32)
) aequ. N
ubi nota cum aab a c +d tellentur in et fty, non posse aliquid driri compendium,
quia tilli posse af esse af ad be ae itam fieri h eq X df +k aequ. N.
et hinc sublatis arminis in quibus abest 22 fit ut omnia dividi possint per 22
hi et b Eri bg aequ hi. et denique cf + 6 ik aequ. N
unde scribendo distincte fiet:
+ 13. 1. 20.20.20 + 13 13 28 29, 8] + (3). c0. 13(2D. 21. 22
= 10. 13. 21. 21. 21
+10. 10, 22. 22. 2
+13. 13, 20. 20.20
= 10. 13. 21, 21. 21
+ 10. 10. 22. 21. 22
is
20. 20. 22
202
+8: 13) 22. 21 22
+H 21. 22. 22
D. 12. 13, 20,20. 21
- 10. 11. 22. 22. 21
+ 11. 13. 20, 21. 21
+ 10. 12. 22. 21. 21
+ 12. 12720, 20. 22
(2) I1. 13 S
+ 11. 11. 2 20, 22.22
(2)10. 125
11. 12.5
Calculus est probus nam praecedente pagina, alia via, eundem
reseri.
2151. 20 - =2 511. 20X
-10. 27
+20. 1220 +20. 13. 20
iop
O+ DX - ~ D, 62 = N fiet - 06+ 2D =0
= 11. 127
b)10. 13S
s. et.
in aequ. (29)
22 assurgit ad quadra
tum, non 20. in aequ.
(31) 20 non 22. in
aequ 130) utraque, sed
(32)