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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 202v, page id 00068196:0400
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flia Methodus tollendi incegnita literam quae duabus aequationibus gunetur hac esse potest Esto aequalio 1 10 L IX + MXX =0 et 20 + 21X + 22XX + 23X3 = 0
aportet ut hae duoe aegrationes habeant vul unam, vel duas radices communes.  quod si duus communes habent, habent et unam communem. Habat prior aequatio radioes bimet
sei et radices Fg secunta andices flia, crgo si illa multipiretmrper (m, horper 9, fiet utrebique fum. Assumaur ergo pr. 9, 40 +4 X; et pro lm, 30)1X + G2XX, et suotibit
Hocge + 2r 30 X + tu 30 XX 10, 30 t  + 1l. 3
fiet EE = 20 3 = 7 31.
~ 20.40 + 2,. 40X + 22. 40XX + 23.40X
+ 10. 32 +11. 32 +12. 32X
+20. 41 +21. 41 +20. 41 +23. 41X
1 +1X + 2 X∞ +BXLAE te 1 X: 4 1C=E N 2 + 123 Xe +1 C.4 X 2 + etc = 0
20+ 21X + 22 XX + 23X3 f. 244  etc + 2f. X  + 25 - 1 25:1 + 2f.2 4S: + 2f. - 3 XS. 3 + 2f - 4 X55 4 + ete = 0
ultiplicetur.., 30+3IX+grXX + 33 X +gax t ete H. 3 G~L Xs a  + 35- F AS: 2 +. 3. fu3 F. 35 - 4 X F: 4 + 3F-5 YS -5 + et = 0
pucamst per .. 4ot a(xt arx X + 43  + 3qX terc + 4 -1 XC. +q C. 2 XC. +4 C. 3 x 3+ eaa xC- + + 4 6 - 5 X C. + etc = 8
i
A ab cde  annopus
productum prius, et productum poperius eosdem habebunt terminos, B. coincidentientur inter se
st
 mnopuse tectum
rectum bcd
abedemnoxus abcde mnopu
arbitimiae 4 + 5=, 9 aequationes 10
cuonen solum invendentur novem
abbitrariae, sed et tandem prodibu
solae restibunt, 10, 16, eti; 20, 2 etE
aequatio. in qua suolacis arbitrariis