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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 7
# Folio 15v, page id 00068220:0030
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s
()
sit aequatio _ data X + pX + Gd + tae + sx +t aeq 0.
quasdam, non tamen om
duae aliae, quarum quaelibet unam habeat radices communem cum
( 3)
Xs IX blX n aq. 0. et  a X _ AX + JX + h aequo
10
Itae duae ducantur in se invicem fiet a + sX + AS l’X + bsXs
reto
N 4 X + f X +gx + he aequ. 0 Durantur in se invicem aequationes 2 et 3.
fiet. X +
fx
Ux + bl X + m X
sex
afstsmX
grb +gVX 1b9 (X +g m X
+ h X +fi lX C ex 1+bhI(EX + tm
Acquatio data ducatur in aliam eti arbitrarium formulam
tertius gradus lx ex dX +e aq. o fiet nempe 4o dxt eaequo
X ApX+qxr + Se +ta
CX +CpX rcqX terX+ Csx + etx
+ d. + dp. 4d9. +d72 +d15 + d. t X
+8. + ex. +eq. +er. + es
comparandae jam aequationes 4 et 6.
+
caequ. s= P dequd +sp pp +q equ. 98+ l. Ergo dd aequ 99+H sprpp - 4
ea 3gP +up = Sp p3 4p + f9. pq aequ st a h
Aequatio b comparetur cum generali
X +1 X +2X +DX +4X + 5X+ 6X + 7X + 8 aeq.c
fiet: caequ 1 - p. dt d + 1p = pP _ + q aequ. 2 seu dd 5g. 2 - 1p + pp - 49
e + 2p = 1pp + pd - 44P + 19. p9 a. + r aequ. 3
1
(60)
seu
deniq ob aluus terminos mectios. sa1c p A
dq ip qq a ppqq=  + ap: Hi aequ.
aequ 3 - 2p + 1p - p + p9 - 1 9 - p3, E1 tE4 st a psa L. 9 fach. L + 7r. P + Bp. 15  1. 5
2
aequ. 8. t dd aequ. - 854. f + 7: t
es(H)
ad C aequ 6 t+ s  Grs2. Fe+ Zr. V + 84. t aequ. 6
seu caequ b ct  - 85 D: t + 75: l + 81: + aequ. 6
seu caequ 858: +5 - 7s: f - 8r: t + b: t
jungendoB et 15 fit 1 aqu 858: + - 7s to - 8Y: t + 6; 1 + p
s
 aqo pSpS f: L = 7p S: F - 8pr: t  + 6p: (= pp +99- 85 + 4 7
axex. 9 et 12 fiet
et 3 aeq. 8p s: F - 7 p s2 +-8pP: t  + 6p t - p 1 9ip - 5(H: t 1 2p: +
8p58: ( + 7p5. f + sp P. to - 6p. + ( pd + pd L p 9
Tn + 84 sd. f3 - 754: f = 8913. f + 64: F +pq + r + 8:
exo
5
Comparemus jam aequationem a cum eadem generali 7. fier
faequ 1. ll + gg aequ 2. H + h aequ 5 seu gg aequ. 2 - Il
21)
et R aequ. 3 = 1 11
(22)
et b1 + H 14 aequ 4
incipiehido a H aequa 8 M
eate
 (23
1
seu gg aequ G. M = b1 8:
Et à fine
et gu ine+ b ( 8: m aqu.7 seu gngagrn
10
uo
aliod erf aqu. 6.M  b
et
da
deniqe  bl + 2H- 1+ aequ 4.  ec em +, b P D L l. = i agi
sangendo aequationes 19 et 24 fit 1 aequ. 6: m - 7b 17 _: m + b l 8: M
20 et 23 sit 2 aequd I + 7: m - b 17 8: m
9
13
i 1
Sitem aegq. 13. 14 cum aequ. 25. 26.
ujus in
25. 26 pro. 12.2. sub
superest ut jungamque aequationes 16. 17 18. cum sgqu. 27. 28.29, et prpun   4 est 7. 1
c. 60)
21 et 22. fit
3 aequi l + 8: m
 gin . 7. 16+6ers 8 1t4 h. 1b
frt BM 8 sem E 52 V Z satSN BP(M GLME+ pt m aequ.
14 et 25 scribumus per copendina.
6+ M YbV (  +e HIE erex ioentu is et 26 fit unde exargent aeqq. 5
quarumope invenienda literae b.7. 8. b.m.
verum praevideo
Assumantur
ata