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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 44r, page id 00068217:0089
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ab equ. abx - 3abc
- 3
(4)
aeb aequ. a X - a. ab equ. X - 2ab X = a 2ab aego X - aX - babe
i
= 3
27 = 2,3, 2 = 3 4)2 127 23, 2 -6
16
3a b aqu. N a babe. Auferantur a Sccrricem aequatio 3 ab aqu. 4 fiet: a b aequ  a Xt pabta  babe
118
27 - 3 - 6
-9 + 18 +3 - 6
sed Lm. Sed aequationem 6 etiam obtinuissemus si ab aequ. 1 duplicata
subtraxissemus aquationem 2.
Eodem modo si ab aequ. S auferatur aequatio + restabit a b aequ. aX- a. ut supra
Unde patet Sufficere aequationes 1. 2. 3. 4. 5. cum enim sint quantitates 
na
 a X aX. ab X. a. a. a b tolli poterunt  exempli caut 
duae a b. et ax. ita ut maneas tertia verbi gatia X aequ. a + habX 5 abc
itaque rufficiunt nobis tres aequationes fundamentales: aeb qui
b aqu. ab X - 3 abc. ab aequ aX - a. ab aequ. 33 - 2abX - a
Unde fient: e +a X + habe aequ. a. et _ aqu. 3ab X + 
rantitptes
 equ abx -gbe
Scilicet sex. et cum quatur ex illis restare necesse sit mininum quinque, quia
eriderem
C
inveniri potest X per at. abcd. abc. ab Hinc aequationes utiles
poterunt tantum esse ex. ita ut in ses tollantur ope 5 reliquarum:
ae a. a  ab. a bc
aX aequ. a + a b. abc X aequ. 4 abcd + a bc
aeb aequ. ax- a
(abc aequ. abc X - 4 abcd.
ta X aequ aequ. X - 3ab X aqu. a3
1b
atc
Ergo ab aequ. +a X +3a bcX - at
Cat + a
b a abx 1a + 2 ab 2 qu i a X + 2ab X - 1a- 1 ab - 2ab. 2ab
Ergo
cab. 
O1 a + 2ab)
X a
X - a)... ... . . aequ.
a X aqu. a + ab.
ab equ ax- at.
+ a X  - 12 a
- 12 ab.
+(3) 1 abc.
et
a bx equ. ab + ab + a bc abcX rqu. abc bca
aex- a abex (ubed
ab aequ. a bX - 2abcX = (k b + g ab0d
abc aqu. abcX (2 ibed et abe aequ, a bX - aX + at -() a  seu abeaqu. ab x- ax
abcX + a . 2ab 18)
ser nqu. 4. 5. sit a bX aequ. aX 12abc X - a + )a b  8) abcd
abXcque  aX +, abCX= a b-8’abed ut ante
et per aequ. 6,7. fit.
er anam
a1X aequ. a+ a b  a bX aqu. ab+ ab bc ab X aqu. ab 1ab 
a bcXaequ abc +() abC +t bcd. abcdX aequ a bcd 1Habcde.
si in aequ. 4 pro abcd dX () abode substituas ejus valorem ex aequ. 5. fiet:
 aebc + ae bC aequ aebc X = () abcd X + (15) abcde. Porro a bc bis haberi potest
ex praecedentibus. Ergo fiet: abc + (2) a bc aequ O ae bcx - B) abcd X + (5) abcde
et a b0 . + 2) a VC aequ D a beX = (3) ab cd X + (15) abcde
et pono ex aqu. 3. fit abc aequ. a b X - a b Quem valorem substituendo
in aequ.  Sit a bc aequ  a bcX = (3 abcd X + (5.) abcde ()a b X +bD Ca
10
Porro ex aequ. 2. fit  pro atb substituendo valorem ex aequ. 1. fit ab4+ (bcab a. ab
atque ita habemus at. Ergo per aequ. 10. eti a bc. )a bcX -(5) abcd X + (30) abede - (4) abX
ergo per aequo 9 etiam a bc Ergo per aequ. 6 etam a brg. Veruus quia, 
tum ab tum abcd bis invenire debemus, sac per consequens caeterat
d
quan formas hinc necesse est ut adhibeatur duplex valor opraecedenti
formaru, ut ab, vel abe
=habe X
 12abcd  3a bc
Pab XH() arraN
+b. 96. abc.
a
abed