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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 5v, page id 00068160:0010
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Y+2Y - 423r-9
r- 2r +g = q- V - p
X44 5, c. 3
eg. 7. 
fi et 6= 10. 15. 7 - 27.
 1+ 10. H1. e ex
aeq. 10 fit .. 6=
12. 131.7. 7, : 12. 13-1
ee pp) - 4qrr = (eCpP) - 2 CpV + v. fiet ep- vvr. ggrr: 2V
seu ep = v: 2 + ggrr: 2D sit Yv par, seu = 2d siet
sit Gr av seu v- gr: 2. seu co qr s+ pe pares
et 2 seu 4co =  4. fiet co=4: 4 sumamus ergo a = 4 fiet
pan
(0 =1. et v = 2 t et fiet ggrr: 2V = 44 , 6rr. 2. 2 = 4r2
et fiet ep sit e =1 et fet p = 1 + Fr ar? Ergo cepp- ggrr
1+8r + 16r - _16Y = - 8r + 16Y cujus radix erta - 1
Opp- rr et respp - ggrr
et see- pp exprimenda in numeris.
et 9q ee
quod fiet si
horum factores sint quadrati  se  aut quadrati ad idem
latus applicati p+r =  42
e+ p = 6. 7. C- p = 6. 7.
ex + qu = 4. 5 ep - qr = 4. G
etq q+e = 89. et q - e = 8f. 9. Ergo 9 = 8.9 +5. 9: 2
si contenti simus aequatioibus
usque ad 10
et ex
f
et C = 8.9 - 829,: () et e = 6.7 +63752) et p = 6.7 = 6. 7,: (39)
et p = 2. 3 + 2239: () et
(1)
n= 2. 3 - 22. 3: (2). Ergo fiet
 ob e fiet 8.9. 9- 8(.2 =
6. 7. 7+6(.2), et ob p fit 6. 5. p b:
2. 3. 7+2(2) e et ep fiet 627 1- 62 (4) 
2
fil 6. 7, 7- 6(. P2
quos duos valores aequando et 9r = 8. 9, 2.3. 9+B. 7- 2, dui paulo ante eunt ex = 45. 57 4. )
connescnt 7, et fit
10, 11  1. 12. 13.-1=
et gr = 4. 5. 5-4: (2) ergo rursus habemus: 627. 7 - 6 (2)4. 5. 514
5
et 8. 9. 2.3. 9+8. 3-2 = (2) 4. 5. 5.4 tantum ergo efficiendo
(6
si jam aequationem sunt aequationes 1, 2, 3,4. proaeq. 1. fit 8 = 10.6, et 9= H,7, fiet
12. 13, - 1. 1. 410.11
divellamus in duas,
10. 72 =1 L0, et
12. 1  = 0. fa
10  V: 11
et 12= ri
pondtur cpu e
ponatur 10 = o et
12-e2. fll
20
Are
20. 11 =  12 13-1 =
= 22. 1-. 1+20. 11
sit 26. 11 +1 = 
19. CB 52.k-
et
ex aeq. 1. 10. 11. 1B11.7 - 10.6 =7+6 rursus ex (2) (it 2 = 12. 6. et 5- 13.)
()
1928. 11 - 1, 127. 13 - 1 =
se
(2s
12
fiet. 12. 13. 13.7 - 12.6 = 7 -6 ob aeq. 3 fit 4 = 14, 62, et 5= 15.2
12
fiet. Ob aeq. 3 sit (es 4( 14 6os. 7 6 et 5 sit 15, 6. 7. 46,
e
et fec en aqa fiet: sit 4 14.6 et 5 = 15.  p. siet
-62 (2). 14. 15. 146+ 15. 72
i
postremo ob 0g. E. fili
14)
10. 6. 11. 7. 12. b. 13.7. 10.6+ 11. 7. 13.7-12.6=(2) 14, 62,. 15. . 15,-146
Superest ergo tantum ut aequationes
13 14 in numeris grantur
sed maxime aeq. 1 (3. ubi fiet _6
1 4157: 1H)14
debet esse v 14. 15= v. 1+ (2)14. 15 sit 14 = 164 2b et 15- 22
siet , 16. 17 16(2) 17. 22 - 16. 22 - 21, 17 = 21 (2)17. 22 - 21 28119
ete
= V + ()  57. 16+(2) 16. (21 1 et + 22. 162+22(2) 16. 21427. 21
2 v+ 2) st 4. 21 posito jam B=
fit e 22  () 24 sed non debet esse v= i difficultas autem
et f fiat, 21. 22
est priori similis, sem aeq. 15. ipsi aequationi 17. sit re eamus ergo
ad aeq pp vel 16  In aeg. 16 faciamus V = 1+ 16. fiet
(1-14. 15 1 1 (1) 16 4 (4) 1B (1 + (2) N. 15 + (2) 16+ 167, 1 + (2) 14. 15
sit si sit 14. ise 17 14(g. 19.1 sit 1+ (4 15 17. 14. K
fieteec cujus aequationis ope hibetur 15. si jam hunc valore
p(2)42 15 = h. 15 Sit  L Sit f1 1bq
sit (2)16 + 16= 17. 15 tollitur tera 16 ex ag. 18. et simul via
assumtum sit
in ea dividi possunt per 15 et fit 14. 15= (2) 14. + + (2) 1 1. 17.
e
quae aequatio dat f15 sed solverta adhaque aeg.  19. id est devet
17. 15 + t aquadi quadralo = (4∞ 14. (2) IY. 18 + 1718,
hec in duas, seu ponatur
et fit 15 = (2). _ 18 + 17. 18 (2) 16 + 16 =d seu 16 = -2. sed hot non ot H 
v
Dividatur aequati
in Numeris
~22. 13 + 1, _ +20. 11