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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 61r, page id 00068197:0121
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X + bxX +aCX a quand. quadrato. sit X: = 10ZZ + 11 aZ + 12aa, :, 202037 + 2127 aZ 2
fiet 10333 +3.10. 1071 a Z + 3, 10. 10, 12aa Z XX: an = 18. 102 + 2. 10. 12, +7. 10. 127 aa , : 20. 20L + redt  Dmet
12. 12a 42. 11. 13aZ + 1ast. 11 ZYaa 22yaa
43. 10. I1. H1. a4 24 + 6. 10. 11. 12aZ +3. 10. 12. 12a2
bioi ae +2lso  a Z + 2b. 0. 1220 aa 74 + 1. 11 a3 Z3+ 3. 11. II. 12a Ly 2 + 3 1. 1a Z+ 1 a
1b. HH. 26.-
72s10. 10. 8. 4 +( so. 11. 20. 2
l.C.1928. +. 610. 2822
F b. PB. 18. 22
46C. 102d.
F1. C. 11. 20 +4C. H. 2812
= 1C12. 20
+2b. 11. 1220 423 4II. 11. 20.42
t4b. 18. 12720. 2. a 3 + 4b. 1. 122. . + 2b. 13. 13.2029
+2b. 11. 11.5
42b. 13. I1. 22
+4C, 10. 20. 23
+6c. I1. 20.U
+2b. 10.12)2 + 2b. 1.2. 2E t, L  2 2
1b. H. H
4 lC. 10. 22
+46, 12 20. 22 F6C, 12. 28.29 24C. 12. 10.17
Z
O+301361
+ 4c. 11. 20. 2 +1. b, 11.2
ut destruntur 76
10a + . 10. 20] + B20c =0
seu 10.10aa + 10a. 206 + = 20b6 = =. 20 bb - 26 ac
1.3 3
206241626247+
et fiet 10a- f20 2.2052020, - b + ((1b - 4 ac) seu 10 a = 20. 20f, compendio
tis ut destrmatur 20 B, et 3
similiter (12a = 2d. 24, -b - + (bb - 4ac) seu 12a = 22. 22g compendio
19 12 = 20C, a
18. 12 = 20. 22 dC
2
10+ 12 = 20. 20 c. a
 Ut destmatur 95, fiel 3  3. 20. 1 f+ 2. 20 1bf 4 26. asfb + 9 26 ntc + 113C
Ergo fiit 20. 22 = 3. X. 1155 + 2. 1b f +UC, :, 2. ffb + 4 fe
2. 11. 22 b9+ 1. 1b. 22t,
Ut destruatur Z fiet 3. H. vss + 2. 2f 223. 20b99 + X 11 2 Y 4. 2 1BC = 0
seu 2D. 22 = 3. 11gg + 2. 11 b9 + 11b, :, 299 + 4gC
e 1
14 64 1
15 10105
quos duos valores aquando destruitur u, nec obtinemus quaesitum
nisi in certa lege datorum si sit 2f+ 2b5 +C = 39g + 2b9 +C
2f+ 4fc
299b + 4gc
cujus aequationis solutio una est ut sit g-f,  seagif - 1. sed sunt datur
altuc alius vulor (3 2 gg6) + 265299b + C 2990 =(399556) + 2bg 2fb + c 266
fit
+3f4gc (F 2bf49c) + c498
6
43994 fc (+ 269459+ c 4fc
a
 4ffg BC - bp) + 4599 (bb - 3c) + 2bi (gg - H) + cC (9 - f) = 0
seu (bb - 30) 45g (g- 5) + 2bc (gg- ff)  4cc (g- f) =0
seu
O
(bb - 35) 8f9 + (2bc (9+5) + (4CC _ - 0 et fot g- 4bcf + 2cC
Et quia _ f = - b + Y (bb - ac) et g = - b - + (bb- ac) quaeritur Bcf - gbbs. BC
Crelationis
transsonatione)
an his valoribus subsitutis, qtum aliqua rao obtineri possit haec aequato inter frtge
sed vix puto
 4 1 1.5,18. 15010. 5. 1
6 15 26 15