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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 35v, page id 00068201:0070
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a +b4c. a + XCF) aequ
Xagu. 4 Xapa + ab. Naequ a 13 abX + babe. X ae quorq ab X - 8abCX +
b
oc
Ergo si qt aequ. abtact bc. et abc aequ + 3. fiet:
ac
bc
- 2a
q aqu. ac fier t aqu ab + X X agego ab. A1GX 16r6. Et 9 aqu. rC
bc
aetue
M
ac
b
in se ducta dabit:
res
at4
et
2462
At
4tt
+
bit (trroX=gr aqu. q- 2rq x(
nC
Unde idem poditt quod ante nihil ergo sic novi
X= 29
apx (47 qu
si bis reperiri posset vator ipsius a b4 per X Z. X. 9. p.
Sequeretur posse resteriri Xper 9. et r3. seu possibte t reperiri a + b+c per
ab + ac+ Bc et abc. quod non videtur possibile. nam sit
ab + ac + bc aequ. qr. et abc aequ r. fiei ab aqu. qac-bc aequ Y
Ergo a aequ. 4 c 5 aqu a aqu g bc. fir  et a aqu 
+
a aequ q - bc aequ . Ergo 9bc - b aequ Y3 b + rC. patet itaque
produabus bn b. c. inveniendis unam tantum esse aequationem
C
Ergo repertis a. b, tertiam c. sumi posse pro arbitrio, nec proinde ex
d + b +c esse determinatam ex abjac+ bc, et ex abc Hinc etiam
patet non posse inveniri valorem ipsius a+ 64 persola y. Z. Sine X. quia
 C9
alioqui bis eliam haberetur aliquando ha4 per X aliquando sine x per y et y
et ita haberetur rursus X per y et Z. Quod Et aliunde impossibile, quia possunt
y. etZ haberi per cognitas. Itaque absolute impossibite, ut posito
radicem aequationis esse  aequa +b + c. habeantur tres
aequation smi
a B cognito.
b7 4
4
4 (44
 aequ. cognito a b caequ cognito
4c4
quia 762c aequ.... cognito. et ab aequ. cognito, et ab  aequ. cognito
quia haetres
ac
bl ab + ac + bc aequ. cognito non potest
haberi ab + a 4=64 4 aequ. cogito, quia alioqui duo haberentur
jam habentur, si autem haebetur
valores ab ab + a cY
4
includit ipsam  X satis depressam, ergo ita haberetur ipsa X.
quod est abs per aequationem inferiorem suo gradio quod est
absurdum
au exitum
reperire licet, unica
sit X aequ. X  gX + YX 5. et rursus X aequ.  a + 4 ab + 646 + 12 abc
aequatio d
Et rursus vel X aequ. X q’ a +9ab +a +s+ Ergo fier: a + 4 ab +bae b H1rabe _ ∞ qu. gub. Fa- s  0
addatum
fiatque a+ b+ C + aquo. restabit: 4a b +6a b + 12a bc - 4a - 9 ab - r a- s4 aequ. v.
6
-+
fequatio T. muttiptiretur per forutam cajus itamt aobitiariam: imo melius ea ratione quae explica
bitur pagira sequenti.