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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 95r, page id 00068197:0189
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X = YC + SD X erit Xx + ab, XXHac  = O+ 1∞ D + B, 9+ 2OD+ C, = O Ft B(B +bc + 0) 1BD. io (ersia
fin  = 20 + 22 tabi C )is. Ergo siet
4
4t
+20)
+40)
aa ff1O + 6ffOp (b +C) ssB. trabess = f49) + 4aa 0 + 840D. + 44(61) B +  qu bt C)
ut prodeat aequitroidentica sed hebet idem
expheculur faciendo 1d = 10Z rua, et D = 20Z+ 2ia, pt 9 = 30213a  a
a
pottatet extab, Xx tac aequam qu (10d +  16D)
qui fa vel sic potius 09+ DD = 1024 + uaZ + 12 aa
phamiffici, ex solis C et, D, seu ut ( +D
fiat = 402+ 4la, et hoc valore substitule
prodeat identica cum eodem modo se hateant
in aequatione vel sic OO+ DD-73
et 15 = 2032+ 21aZ + 22 aa fiet 00 +D) + 2D = quadrul = 410ZZ +, 11aZ+, 12aa = quadrato
1. 12 + 22V = quadrato adeoque l. 12+ 2.222. 204 , l.H f2. 4
seu ZZ +. L. H 12.21 aZ +
1.10+2.20
110+2. 20
V 1. 10+2.20 4)1. 10+2. 20.)
et fiet: 4. (1. 12+2. 22) (1. 10 +220) = qu (1. 11+2. 21) seu 1. 112 + 4. 2121, 4. 11. 21 = 4. 10. 1 + 8. 1. 22
sed quia etiam D +FDD- 26D debet esse quadratus fiet rursus
16. 20. 22 + 8,1220
113 f4. 21 = 4. H1. 21 = 1410. 12 = 8. 10.22. Et duas aequationes a invicem subtiahendo
fiet
+.16: 20. 22 = 9. 12. 20
8. I1.21 = - 16. 10.22-16,12. 20, seu 11. 21= 2. 10. 22 +2. 12.20
Et invicem addendo fiet 11 + 4. 21 = 4 10 2 + 16 2. 10. 12 + 9. 20. 22
sit 21 = 2 10. 22 + 2, 12.20,: II et 11. H( + 1618.25+ 12. 26 + 32. 10. 12. 20. 2; 11=
2. 10. 2E 2. 12. 20. seu W + (2. 10, 22+2. 12. 20)1 + 10. 22+1220+ 2.1012. 20. 22 =
10. qu (10.22+ 12. 20) 0 (1 - 16 = -8) et siet 11n = 10. 22 + 12. 20, -1 + 2 Y. 2
et 21 . 21 = = 4 (10. 22 +  20): (qu (-1 + 2 f.2)
seu 21 = 2 il (0. 22412. 20). + (- 1 + 2 f- 2) et 11 = 10. 22 +1220, 1 (- 1t 21.2)
n
D= 40Z+ ala, fint
( +7 = 35(3 + 2. 30. 3143 + 3131aa et OD = 30. 407Z + 30. 41 aZ + 31. 41 a
Aliteret medius
 = 30 + 31a.
fiit 44
40 +2 40. 41 + 91. 4
30297 + 2. 30. 31 aZ + 31. 31 aa
aaff) 402
2. 41. 4
2140. 41
+(494) 30.4073 + 30. 41, aZ + 3. Maa
6aaHs
4 d (br9)
=aH(brC)
aaque
n b
+ 31. 400
00. 30 a7
0040 aZ
+. vo. 31a4
+ 00. 41 aa
ia
usb)
+oe
bct
aa
31. 40 2
An sic O+) = 10Z + ua
aff0
 daffsh1onBaf00 + 2.10. 1B. _D + H. 1I. aatsaa
ait siet od
4 59 94
00. 10 OO
saaffV
+4WbFC))
aff(brct
aa qu (br
-bc. f5
+ 00. 11 a0.
20000. a1
+00. 10a0
+00. H1 a a
00 e aa
0000. aa
et  et O - D = 20Z+ u a
seu b-bb+
ita habebimus 9O + 9D + 2OD = 187+210. 1a 2 212
et 9O + DD= 2OD = 20 +220. 2 aZ + 21. 21 aa
1O +D) = 10 27 +2. 10n ay + I1. Haa
20C 42. 20. 21 a 2121
28 = 2. 20.2
= 21.2
sed calculus non fit brevior
sed me sed optime, ut sufficiat
facere D = 100 + ua
=0 hoc est drevissimum
compendio scribatur
20F1
2500
120500.00
30, 10. 10
40 00. 10
140. 00.00
50. 11. 11
40. 00. 11
1C 39. 30. 10.10 4+ 30. ( 00. 10 +20. 30  fint 30. 10 = 00. 5o + )e(53 - 4. 20. 30):2
et eodem 60. H1. = - 00. 80 +00 (8- 4. 40. 60), : 2
ristal 2. 30. 10. 1I +00.50. 11 + 90. 00. 00 + 90.00. 10
10=- (5229a5) 7 (au (518a - 6aaes) - +4u (4a = auss))  2 (+ a aats)
bretstaa ) + S (que brcs 4aa. ) L 4 caa quilo vC) - be ss) (4 c aas)) : 2 (4 - naf))
Saaf
Eb) Q rese
M+H.2
-bVree
sit ((= 1
et cc - 2bb
=∞-1, sit
et 2 etb
fiet C = 1: b
et cC 2bb
=   - 2bb