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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 32v, page id 00068198:0064
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10 X + AX +14 aequ. quadrato 10x +12,  in 5eX est, aeq. to
 An SoC 10 X +  n =  + et (E(y+ er, : 34y A31yt 32
sit sit X = 4y +42, : 530 yy +3ry + 32 fit : 10. 4iy +10. 2. 4142y + 10. 92 60 ∞ 2I y + 2. 21. 1G+ 22
+ 12. 30 +12. 31 +12. 32
fit 21 110. 41 + n.3o et 22Dh0. 42 + 1. 32 et Z0. 41 + 4, 12. 30. H10. 42+12.32 =(. 10 41 42F 12. 3
et eodem plane modo:  fit
2 (50. 4+ 52. 30. 150.42+52. 31 = 2. 50. 41. +2 +52. 3)
et fit 31 f S10.4C + 1230  Sio. a2m 3 - f. 10.41.42 8, : 12
= X 150. 41 + 52.30 Se0. 424 52.32 - f. 50. 41. 42 p : 52
O = 10. n4230, 10. 42=12.32
D = 50. 41452.30,50. 42452. 3
Ergo fit A, s0  D = EB 1oSL. A A2- 12. 50. 41. 42 (10. 52 - 12. 50 41. 42 seu 2) B41 42
seu Si 0 + 12D - 2. 12. 520D = B. 41. 42. seu 529, 12Dr. 1 42. (252 nO. 5i9 q s O
Majoris brevis quia autem habemus arbitrarias plures, quam opus est, possumus facere 32 =0 et 41 =0
fiet C = 10. 12. 30. 42 et D = 5030 50. 52. 30. 42. sed ita 30. 42, Wanescere RH nec ulla remaneret
incognita; ergo faciamus solum 41 = 0 et retineamus 32 fiet O = 10. 12. 30. 42 +12. 12.30.32
et d = 50. 52. 30. 42+ 59.52. 30. 32. Et ex aeq. 16. fit 520 = 12D, et evanescit 30
adeoque fit 32 = 10. 12. 522. 42 - (8. 50.52. 12 42: 122. 52 - 12.52 sic ergo non habetur
exitus  Retentis ergo 41 et 42. faciamus 32 =0 fit O = 16. 41. 42+ 10. 12. 20. 42 et3 = 50. H. 47 0 s. er
10(2 2. 18.12. 41 (42) + 10. 52.30 (4)
naesi
Errores duo in hoc calculo
idaic longillincet eexicare taita
+ 2, 52, aty 10. 52. 18. 4i (2) + 1052. 10. 1. 30 (12 2. 10. 12. 50. 52, 10. 41 (42) - 2.10. 12. 50. 52. 10. n2. 30 (42412. 50. 10 4 (41 2. 50. 10. 12. 304)
+ 12, 504142 + 2. 50.524 (42450. 52. 30(4)
52
 2, 12. H1. 42, 10. 52. 50. 4i (1 ) 16. 5r. 50. 52. 30(42 -2. 10. 12. 50. 52. 58. 4(72) 2.10. 12. 50. 52. 50. 52. 30 (1 2) 12. 55. 58. 41(42 12. 50. 50. 52. 3. (42)
2,12. 5t, 10 50. 4l(F 10.50.52,30. 41 (417) + 10. 12. 50. 30. 41 (4274 10. 12. 50. 52. 30 (42)
omnia nembra quibus abest eo ubi reperiemus semper extare 41. et ita excerptam.
s
4I, (10. 52 + (15. 58+ (2) 10.52 - 4. 10.12. 50. 523 4 2512. 50. 52) + 2. 10.12. 50. 52 + 2  s- 410n2. 50. 52t 3) 5t 50)
equationem, per 41 posse dividi, et set aequalio sint 30, fiet
18. IR. 50. 52)
30,10. 2. 52 + 1. 30 52
sio in casxonso
+2. 10.12po( .(910 i 1osi
smri
41, 3. 102356 = 4. 10. 12750. 50
s. 
2. 3041, 718. n. Si  - 10.12.5052
250.52. 13
50. 52 10. 12
Quae poterit divelli in duas: 48 3.15. 5d - 4. 18. 12 50. 55 + 2. 10. 12. 50. 5 
259.521
F12 50. 52
quanquam possemus instituere vulsione)
m
39852 4. 10 . 1012
ertao
seu , 41 C
x30, a
+ Bai, 26
+4.30 (13 E. 18. 125.
=10.12.50. 51 =0
50. 52. 10. 12
20
se hihi vener
F50. 52. 12
sed jam video cur nulla sit ultra relicta divellendi livertas, quoniam scilicet ex ipsa aequatione indivulsa
seu per compendium a4 +b30 =0 Verum haec divalsio ideo non placet, quia ita
50. 51. 12
compend faciamus; ab2 + b62 + 3 fetqu 6. breviter ergo pro 30: 4 scribamus 62, et conpendii causa
q
una tantum est incognita 41: 30. Brcviter ergo pro 41. 30 scribamus 62.
62 habet dimensionem virtualem lucus exponens -2) et fiet
e sit  Ef 6r + b. 62 +  +. 64 - b 1 aC et 62 =  b +ac - b
a
a62 + b. 62 + + C =0
4a
4a
b 4ac - b
ex aeque indioulsa facicmus:
X 62+ B61 14a
Eror in calculo, ora evanescur
ea
adeoque fit 30: 41 =
.18. 1259
et
N.30,
1050
104701
10+ G0. 1050. 12