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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 167r, page id 00068199:0333
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si formula 10 10NX + 1X + 12 posset aequari quadrato  y ponendu
X: a7 = 20X X + 21 X + 22, : 30X X + 31X +3. et y: a = 40XX + g1X+ 42,:, 30+31  +3
modo sit 31 = 62 130. 32, poterit A: a deinde aequard quadratot atque adeo etiam
10X3 + uxX + 12X poterit aequari quadrato
+10 XX = + 10m 20. 20 74 2. 20. 21 23 + 2. 2022 24
+ 2b
+ 11. X = + ua 20. 30.. + 1. 203
1. 21. 30.
+ 12 = + 12, 30.30.. 42. 30.31..
ocyy = B00aa, - 40. 40. 42. 40. 41.
= 
+1. 21. 21 2 + 2, 21. 22Z8X22. 22
+ 1. 2B, 3L..
1. 21. 31.
+ 1. 21. 32 2
1. 22. 30.  1. 22. 31 . +22. 32
+ 2.30. 32..
4 1. 31. 31..
+ 2. 31. 321 + 32. 32
= 1. 41. 41., - 2. 41. 92.- - 92. 42 
2.90. 42.
Tentemus destructitias veriticare in numeris, 00 40 1∞ 20 + n. 2030+ 12. 30 sit
 ngi
ob terminum Z idestruendum sit 00, 40 = 10. 20 +, 114 20. 30 + 12 30, sit 10 idem quod 1 etfiut = 10 20 + 2. Si0
= 102420 +2. 10. 20. 00. 50+00. 50+ a fiet 20 - 00 5i 10 13. 309, 10. 1. 30- 2. 601b. 51 et fiet
42 (00. 10) 20 = 10 10 + 4. 10 20 +00. 51 seu 40 100o -, 08.  15. 12. 30 +00. 51, 10.1. 30-6051. 0,. 5
fiet 20 = 00. 58. 10. 12. 30: 10 10. 14. 30 - 2. 00. 10.50 et 160. 10) 40 = 10. 20 +00. 50
et fiet 1600. 10) 40 = (90. 10. 5P - 10, 12. 30 + 00, 10. 11.30. 4 - 1. 90. (5) (2)00. 10. 59 :, 10. 1130 -2,09. 15
seu Y(00.40) 40 = 107 12. 30 + 00. 10. 50 = 00. 1. 11. 30.509:, 2.00.. 51, 11. 30a
Et pari jure ex ob termi
et 20 = 10. 12. 30 -00. 51 :, 2, B0. 10.59- 10. 11. 30a.
num ultimum, fiat 1(00. 10) 42 = 10. 12. 32 408.522- 00. 11. 32. 54):, 2. 00.52a 11. 32
ergo ex Termino 2d0 fit (2.10. 21. + 1431) (10. 12. 30 - 00. 507 + (11. 21 + 2. 12 35)30 (2. 00. 10. 50aa - 10, 11. 30a)=
et 22 = 10, 12. 32 - 00.527:9 2.00. 10.52 - 10. 11. 32
Et ex termino penul timo fil (2. 10. 21 aa = 1a 31) (10. 1. 32 - 06. 5 a) H (ua. 21. 4 2. 12. 31)32 (2. 00 10. sraa - 1011.73a)=
ita habemus duos valores ipsius 41, nempe
= 2. 00aa [: 180.10) 41 (10. 12. 30. +00, 10.504a)
ex priore fit 41 = (2. 10. 21 aa +HI. 31a) (10. 13. 3 5 - 00. 50 4) +I. 2a + 2.M. 31) 30 (200. 50ac. - 10. 11. 30a)
= 2ouaa (: 160. 10) 41 (102, 12. 32+00. 10. 52aa)
20 aa (: 100. 10) (18. 12. 302+00, 10.50 aa)
per quas duos valores
ipsius 41, habebitur 21. Hinc tandem inventos valores ipsorum 20, 22, 40, 42, 41, ( ZI, substi
Et eodem modo 41 adhuc semel pro 30, 32, 50, 52, ponendo 32, 30, 5, 50.
tuendo in  Termino merio destruendo, fit tm aequatio in qua supererunt arbitraria
50, 52, 30 et 32. Suspico Unde puto licere ponere, 32 =0, adeoe et 31 =0
compendio sit 29 = 150 + 202,:, 50a +301 et 4ca = 150aa + 402, :, 50a +301 ( ut post patebit)
et (iet 20 quidem et 40 ut posuimus sed 42 =  10. 22: 100. 10
Unde ex termino 2do fib 2. 10ac (50aa + 202)21 + 11a (0a + 301) 21. 30 =7 00 aa (50 a a + 402) 41 = 2. voca  daa + 42) et 10
et Ex Termino ultimo 42 = += 22 Y10: 00 ex et renultimo. a0 Et ex penultimo fit
2. 10, 2122a = 2. G1. 42a seu X. 10. 21. = f, 41 10:00 seu 41 o100) = 41 = 21 110:00
Hes valores inventos ip 20, 40, 42, 41 substituamus in Termino medio destruendo, fit
21020. 22Baa (+ 10. 21. 21 aa) + 11. 22. 30a -200. 40. 92 a a L(10100) = 10. 21. 21 aa = 0 et pro 0, et 4o somendo 
fit 2. 10. Z2 (5oaa + 202)  + 10. antaa LH 22. 30 a - 2. 22 Yp0 10) (30 aa + 402) + (1v. 2. 2, + 1. 22. 30) (0 a +301)
2I. Ct a H 1))
et fiet1  =  (0 1 1)) (10 -  (00. 10)) E. E (50a + 301). 
2.10 (50 aa + 202) C) S) F 1. 30 (504 + 301)
(10 - )) (1. 00. 10. 50a - 1d. 11, 304)
Sed paulo ante 210450
de, 2. 10aA50 aa + 11. 30a 50 a + 2. 1030
2=
4 1. 11. 30. 301a
Hoid) aa s0a
= 2 1(00.10)902a
= 2. 00 a
42= S2 +00. 253.
1501 300)4.30, i2
+20d
ita cum bis habearans 50: 30
60. Q evane s et
nulla superent ex incognita
s0 1900
itaque oportet rebruere  et 31 et 32,
2= -52 q eguo:, 52+3d
Et ex temino perultiauo sis A = 2.  Se 400. B)  + 1 (52+ 30Z) . 32, :, 20u ( 1 
0 = 150+ 0. 118 , 30c
Ergo ex temrino 2do fit 41 = 2. s
+100,: 50+200
p  no Se + 320
fiat 20=
et 10 Fial 20= 50+ 00 100g: 50 1500b0 40 - + (0100,27i 50+300400 2
habuimus 
50 100100) +
pa et i
undeaequando hosvalores habe
+ set
40 = +00. 50+00.200:, 400 50+ 60000
tur
no. 52+ 6O2. o
p= 10052+ 0204
 on ra
auat luli5e 600.s4 o ut
e reo
2260 40. 10b700aa - 17. 3231 (320 52 400 ∞)
hoeu i st notun compandi Has a el ante (2 1 vaale 15000sr1 na (. od 10 1o g t 1V. 24400 00 2 5
uli 5o 1002 10 12 3000 seuove il 35
 Unde Z Emino 1do fil 210. 2laa - 00. 50 20B. 100) + 212 30. 31 (300 50 + 00 500):
habetur t S X 1. II.31a. 00. 100, 00. 52 + 2. 12. 30. 1. 30d. 50. 00. 57 + 2. 12.30. 3100. 500. 00. 52
E. tona 00. 2. 52 (00)so rrugil  +2. 10. 2laa (-901000. 204 + 88. 31 a (- 00 30. 80. 27 +2. 10. 21aa 00. 10060. 204 + 153 a 1. 100. 03. 104
F 2. 12. 30131200, 50, 05. 204 + 2, 12. E. 31. 90.500.08.209
quasidu calors aa
aqu. (2. 10. 2 a (- 00) 59. 00. 50 4 11. 31 a (= 00) 52. 00. 50 + 2. 10. 2) aa 00. 104. 00. 50 + 11. 31a od. 10+. 00. 507 21
32. 31. 310.52. 00. 50. + 2. 12. 32. 31. 00. 502. 00.50
3. 10. 2ua (=00) (5. 88. 2 + V. 31 a (00) 52. pd. 200 + 2 10. 21 ac. 00. 10 7. 8d. 200 + 11. 31 a 90. 104 00. 200 R 12. 32. 31. 320. 52. 00.20
L. 31
et B1. C
500, 31
 1100 100. a +, 3: 12. 3
2. 10. 2150 da-
2. 10. 21. 524a 
1. 71. 50. 00sa
sik- 2. 10. 2. 50 00. 52 a
=2. 10. 21.50. 18. 209 a4 - 11. 00. 31. 58.95. 204a
ap C2. 18. 21.31. 00. 50 aa = 11. 00. 31 31. 00. 0 aa
unde
8  2. 12. 30. H. 300. 31. 50 + 2. 10. 00.100. 2 + 702.31,:32 (00. 504 00. 200) = 41 E rursus
2031
100.04a + 2. 12. 32.00. 502,
320. 31. 52 42, 10. 00. 104. 2 + 722 317:) 2 (00.57 +06.204
+2. 1. 30. 300. 31. 90. N. 52 aa +2. 10, 00.100. 21. 00,52 70d 31. v0. s2 aequ.
+2. 12. 30. 300. 31. 50. 0. 204 aa +2 10. 08. 100. 21. 00. 204 + od. 702. 31. N. 204
42. 12. 32. 320.
tr. M.3231. 1. 502. e. 20