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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 105r, page id 00068194:0209
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assumitur ad gtadum nonum, pater e rerum terniones
e 8 biniones esse 36. Quarum tiens est (a 12. verum
quia multiplicad est per arbitrarias, ide an ideo fortasse id
g corrigitur. Ut vero dicam haec Meditatio
nondum satis perfecta est, vitetur tamen aliquid pulchium
in ea latere plamu exemplis brevibus; satis adtur aqua haeret
E inspiciamus exemplofacila
+ bx +c
C
(1
X + bx + C =0
20X + 21 20X +2. 20. 21 X + 212
Cum sint 2 rerum Uniones 2 debet
aequatio ex comparnioe orta
asingere ad secundum gradum, sed
2a
 10X + 11  10X + 2 0 aIX, 1
+ 20X + 20bX + 20.C.
(=10X= 1 bX = 10C = 10X 12010.1+
+ 10 X + ∞. 10. 1X + 11
20 X + 2. 20. 21 X + 21
 11 = 2 20. 21 - 20 b + 10b, : 2.10
tautum ive freret enim et H = 4 2 X 11 = 21 - 20b. 2. 10 +a
videamus an ad unum tantum
sed viden non
posse ad unum
absurdum
ut 10 =2 et 204 fiet seu daretur
11 = 21 =  b + b - 2p - 36
et  n= v 21 -6. 21b + 9b
quem valorem ∞8 substituendo
in aequ. ex termino altrmo, utrobque
evanescit 21
et (b, = 4 + (217=6. e1 b + 9b = (2Y). ergo 21= e 3b - 45. 2b
c
X + bX HG
+_X AbX +IC
= 4 X + 4bX + 4C
+ e X  4. 11X + 11
16X + 8. 21X +
ED X  sunt 21 termini
restage solu debent X, X3. X
2X + 11
Ax + 4_11 X + 11
4X + 21
1bX + 8.21. X +21
solutio aequationis quadraticae
per communem. ideo methodus
haec non precedit
45. X id est 5. Ergo tolluntur termini  b
sed arbitrariae sunt plummodo 15. iaque prius praeparanda esset aequatio
1260
 24
 sunt tenmini 31. si jum restere debent X.
id est Termin 8. ergo tollendi termini 25, cum tum sint arbitrariae solum 24
Y
non succedit nnisi in casu particulari
dato. sic