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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 45v, page id 00068124:0090
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bxIE e (sit G=b. , fint Cx1 = c bbc 262 1Z C, et X- b- 262123- 1,: b
 sil fn Cy- - et (+ = b-el
biiem a _ZC1C. bX V
in intrgn st  bX +H = gy, posito = 1.  sorilatur 1 + H- 27. 2t, fiet 21 = 22- l
vaeritur
seu rb +bl = 2 e 2. et  scribatur  yminor b
Faciamus 1b + ( = 21. 21 fiat 21 = b - l et prosibit 1b +l = bb - 2bl + Il et 11 = b -2l
Aliter 21 = b - 22 fiet 11b + Il = bb - 2622 +22. 22 et 1 = b2. 22 + (22. 22 -Il, : b)
Ergo quaeritur 22. 22- l, ib = integro 12 et fiet 2222 = 1gb + Il, quod solvendo
ut ante fipt 22 = b - l et A = b- 2l et 2 cb bet 4n- b etgl 2
et 21 =, b - b + l = L et 1 = b- 2b + 2l f, b-2 = 0. itaque sequens solutes non prodestprerri
3 +d = 5. 5 8. H + - 2. 2) sit 21- 8 fiet
T
8. I1 + l= 8. 8 - 2.8l + Il fiet X = 8 -2l L6 fiet 8.6 +ll
Aliter _ N + l = 21. 21 fiat 21 = 8 22, et 8. 11 + HI= 88 2. 822 +21.22
et 11Z 8- 2. 22 + 22722- quaensur 22. 22 -l-AZ seu 22._ =8. p + 1
fiat 22 =7 et 12 = 6 fiet 11 = 8 - 14 +  = 6 undo 11 =0
Znnor b
172- 1, :b = v. sit Z+1 divisebile per  b fint Z=  b-
et V = b = + et Z1 - V et b et Z-1 = V = b -2 fiet
enim bb = 2b + 1  - 1 = bb - 2b = b v
2
LIX
et
r
bfg Z1 - f 7+1 = g0
F ZH1, Z-1 = f9V posito Z-1 = f Z+ 1 =gu
Aliter .
Z= f + 1
14
14
yl
f12 = 9
l
quot Tot modis fieri potest solutio, quot modiis effici potest, ut nom ut factor
dati b, vrlut f, anctus unitate dicidi possit per confactorom
a sit Z+I = f fint Z = f- 1 et Z- 1 = gV et f - 2. Ergo rursus tot modis potest
bnario
haberi solutio, quot modis unus factor binario diminutus potest dividi per confacto
1
2+1 =f5 et Z= f5- 1 et Z-1 = gt = f5 - 2=9l
et ot + 23: f = 5. Opus ergo est ut alter factor factor per numerum aliquem
Z+1, 2 1 = fgst si.
rem. Aliter
multiplicatus, et bnarium minuti dividi possit per confactorem
est 3.1 +2 divisibilisper 5, fit F-1 et f = 1, sod ita Z=V
moducta per.
et
Aliter
4 et Z = H 11 et v = 24
e fiet = 12. 10 = 120 = 15. 24 Rursus 3. 11 +2 = 35 = 7.5 fit T=H et 5-7
3.6+2 =20 fit t= et s=
f=3
e
sit b, = 15
3. 4F
et ∞ =77 et Z = 20, sedua sit Z major quam b
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