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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 29v, page id 00068217:0060
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Bravissima illa denique madie riu qua suffiit nos uti ipsis v. 3. co.
Mt. Duae ex. g. sunt aequationes  per y. Z. rempe X - 4)X + 4ZX + 2y2 - 4
et  X - 8Y X + 9ZX + 20y X 32 yZX = 16y X + 12Z X  24 yt ZX+ 20
ope pioris tollatur y in secunda et habebitur quod quaritur. Auxilii causa adhiber 
opeharum tium aequationum tollatur y. quam commo
19 - + x y +  X  +ZX = a dissime  , gX L YX + Saequio
X a - 4y X + 4ZX + 2y - a+
X + byX + cZX + dy + e a
X - ayX + 4ZX5 + 2y X - a t X
+ by x
+ cZX
- 4b9
+9 X +rSX +)
1ay..  4Z -25 +a
tabZ VX + 2by X - ba yX
= 4 cZyX
aequ.0
+ac Z X + 2cZ) x
tadz YX 42dy
tacat.
ea X - 2 equ. 0
2a
protest aequatio: - a bF y-5xZ t3 - ab + yt 4XZY +4)2y + 2_ g. aequo 65536F omnia ordine nullo negotio inveniemus. Etiam regulas generales pro omnibus
40qu
+ dy x
tayX
-4eayX
gX - 8g)X +8g2X +roqY X - 32gYZX - 169 pX
+15ZX - 4fZYX
EngEX mage
+4)(8
sunt tollendae 9. arbitrariae vero 6. tolli poterunt pleraque, sed et postea egne
reliqua, sed exaltatione, usque ad aequ. 12.
optimum esset si leularemus invenire, y per a.  ab. X
Video adhibitionem ipsius aequationis datae XY + qu + YX + S. aqu. 0 ess e
inutilem, quia si auget nunerum aibitariarum auget etiam numerum tollen
Dorum tunc enim accedunt tollendi termini inferiores ad C cum tam en
seu fieret. XV. 8. y X .. ZX5 a yt 14 etc.
y X5
. Z 44
. 25
.y
onsideandum: sunt a. a. ab a. abt. ab Unigiuinque separatim inveniri
potest valor per X. y. Z. Hinc si non volumus ascenderea ultra X. seu ultra a. ab. a
tunc Habenius tres aequationes, quatum ope tollenda est litera y. Sufficerent duae ad tollendum, sed tertia
acedea videtur ad bene tollendim. He ergo Et quidem non possumus errare, quia si plures
inveniamus aequationes diversas, quaerendus earum maximus divisor communis. Haec videstur
via maxigae compendiosa et maxime determinata: Cexcepta altera illa per numeros.
Adrem hanc compendiose perficiendam prius opus at esset, Tald inveniri
Forte etiam ex sola numerorum
2 regulas de a um incognitis tollendis
ab consideratione treoremat condit possent, quibus ea res facilius inveniretur, et progressio
b3
aet
determinaretur
X. ad
X. abX. a. 
ab 
abc X a
bX abe 
 at a a
t. X
euique ita rem commodissimi exequi posse videor: v. g. pro aequatione XEaqX +rX+s aequ.o
ab X abc
solvende adhilebimus Xta ayx + 42X + 2 L(. aequio. et X - 8yX + 8ZX +20 y X- 32 yX N. 1673 ∞ tras
+11Z2.
trgtt 87Z - ab aequio
et denique Xet etc. - d aequ. 0. uttollendo X ale. =a) aequ. o  et
x et-a aequ o. ad X. et in prducta o trillu les aequationum composito tollendo omnes terminos qui
sendunt ad  e snt quadrato quadrati. aequalro autem in quil reperitur valor ipsia
A finstra adhibebuntur, quia. ab2 + in 3d. fit ex ductu a in valor ipsius b2 + ab. fit ex
multiplicato valore ipsits aF. iis autem rator multiplicatus jam tum adhibetur, et praeterea
m     Eodem modbo 468. valor imuliliter ad hibetur
quonium ergo inveni rem