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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 41v, page id 00068198:0082
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+40. s2VV +41. 52 aWV(+2. 52aa2
=5. 42 4 4 = 31. 42 a 15. 4 aa
sed si velingreunquer d seu 20 et 21, serimamus compendio 4o2B Y + 41 a V + 4raa
et 0= 50 1 + 51 a V +52 aa, Et componendo duas aequatirenes fiet
4+40. 50 21() + 40. 51 a W + 40. 52 aa = v fint 40. 51 = 41. 50 et 4052 =4)
- 40. 50
= 41. 50
compendio (1: 2) nabb=aec vocetur af
= +7. 50
quod applicando aequationibus duabus
mo vierroumer quae ssunt initio paginae praecedentis, fiet
3, 10. 20. 30.. 2. 10. 11 aequ. 2. 10.20. 317 (10. 10
20.2
30.3)
10. 30, 21 (310. 20
20.30. 11. 430.30
O 3. 10203011. 1 4 1t bia +f. a=
et 3. 10.20. 30, 11. 11 + 1yb: a + f: a aequ. 11. 21. 30 75 10. 10
11. X. 20 5
21.31. 10 ) 30.30
ubi neglectis 10, 20, 30,
quiqe altius assurgunt quaeramus
solum 11 et 31
ID si compendii gratia 10,20, 30, essent 1. haberentur pro non ascriptis
31. 31
et fieret ex priore aequatione 6. (11 +21 + 31) = 6 (31 + 21 + 11) quod est divinasse
Exposseriore 3. 11. 11 + 117 +
29. 21
31. 31
8II. 21
7II. 31
(21. 31
et fiet tandem 11+ 2 + 3t = - f: b
unda jam quaeramus 21
fietque ordinando
= 1I. 31 - (11 +31) Za
+ (b B -  (11 + 31)) 2
si essent 11 +31 = 0 fieret 21. 21 + b 21 + bb = 4. gaa - 3. 11. 11 = ha
21. 21
qua  sit mipor quam
4. 9aa
sed si non sit major, alia opus est hypothesi, et fe possumus facere
se = 11 + 31 seu 31 = b -11
et fiet 21.21 = H.  11 6 - 11. 11 = bb - 11. 11 - 11. 11 - b +
praestabit videri an omnia liceat
fiat
( H absolutus terminus en
I aequalis nihilo, V
secundum 31, fiet 31. 31 + b 31
za
+ bb = +-
4. gaa
= 2. b 1 = a. b. 11
+ 11. 11
2b. 11 = a
quod etiam non semper inrealibus
revocare ad
rationalitatem, ideo
succedet.
11. 11 + b _(1 = 11. 31 +d
31.31
4. 3a
2o et ordinando
P
a
= a6aa - 6. 1b - 3. 1111 - 5a
4.3. a c = bb - 18. 1 ab 2711. 11 12 fa
+ 11. 11
l 3) et Il ita explicemus
javicem, at in 11. II + 31. 31 - 11. 31 evanescat quadralum, sit 31 =  _11 g: a,
unde
fiet 11. 11 F 11. 11. 99: aa = 11. 11. g: a =0 seu aa + g9 - ag =0
Ergo faciamus
+aa - aa, quod non licet.
21 = 1t g + a,  _ nh 1 = 514 et 31 = 61h. et fiet
et fiet
aa gg - ag + =aa =
C 1 = S19 +Y1 h vet 31 = 61g +814,
+51. 5199 + 2. 51. 71gk + 71. 71hk quod debet esse = 0
+61. 61 98 + 2. 61. 81 gh + 81 81 hhr
516149 - 1. 51. 81 gh, 4 71. 71 hh
d - 1. 61. 71 gh
faciamus 11. H + 31. 31 = 2. H3 + 2. 11. 31
faciamus 2._. 3HII. 1 + 31. 31 B  (G: a) (11+31) = 0 et
+ 29. (11 431) + 11. 31 X f = 0
b+ 39g + Q11- 11. (5 +
3a la
fiet 11+ 31 = g: a et 31 = (9: a) - 11 et fict
seu 11. 11 - 4 11 + 88 = 39 + bg +94 + F=
2a
qua 3aa.
99 + bg + f
raa 3aa 3a
quod aequandum quadrato ab 9 Aequatio 1 divellatur in duas
1. 11 + 31. 31 + 2. 11. 31 ∞ = 4 (11+31) =0 et b (11431) + Q (11131)  = Z. 11. 31 - 11. 31 +a
11+ 31 = g: a seu 21-9.a
seu
seu b+ 29 (1+31) = 3. 11. 31. + F: 3a. Ex priore fit
quem valorem substituendo in posteriore fit b+74 9 - 3118 + 3. 11. 11 + 3
= b+ 39 g = F = raa gua ga
qqu
gua d
3
4
Aliter redeundo ad aequ. A  fiRt. 11. 11 + 31. 31 -2. 71. 31 (+ 2. 11.31 = 11.31 Y B (11131)+
= de
gaa
I1. 1) = da 11 +Deaqe
=11. 31= Za= a aequanda quadrato seu copendio - H. 31 -  m: 3a = quadratio.
sit 31 = -11 + 41 et firt er. 1 - 1. 41 m. 3a = quadcuto H H - 2. H E + 51. 5I
Erjo
a
vidamus an 11. 11. + 31. 31 - 11. 31 + se 31f. 1M + in F possint reddi divisibiles
adeoque A Auadrabo H. H. - 1. 4Y + Z 41. 4+ 4 2, 1, 51 - 2. 45I + 51. 51
per f aq + 31F hocdu r+ 31L + p divid sit 1tHgq L9 n eq +31. 31 Th +(Gh + CG, + p. 119+ P31)
eit eq = 1 et lA = 1 et gh + et = - 1 sit p = 0 et m = 0 et n -
a die t eihs 1su te
ert 4- 1. e t= 1.  quod hon licet