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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 124v, page id 00068200:0250
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(1) Numt. al.
Tres invenire Numeros, quorum binorum
differentiasque vatrati; et differentiae binorum quadrabuum
ab ipsis etiam Quadrati.
).... 1I al.X Ergo diffeentia Numeri 2im a H ~ erit quadratus X
(3). .n. HI al X. 7.
erit endipter Xe
Ergo ... . . ... . . . . . .. IIdi aItio..-
(4) Differentia (ner Ihi X + Z7
c 4 2cZ +
per B∞aXVAoVar:
(6) intelgata X p ne fiet Z A  2 C sie 
D Summa u YPd
2al - X  d2. Ergo al p D + X
(8) Ego al d, n Nuncarmus, RReessumtio)
(9) Num II.
Reassumtio.
(8) Num L. Erg al p d + X satis factum ita est
(9) ..... 11. Y d= +
2 conditionibus quatuor
ut differentiae binorum
(10)...... 11I  d - x = 272 Quorumlibet, et summa
primi et secundis int
(11) summa  IIri 42- q2, 1 M. pro Z2. substituatur ejus
valor inventus  (5). (6), fiet d- sCm
(11) intelligatu, D B = F 5. c +5 fiet d p s.
quo valore in aeq. (11) substituto
Cs(tD2sCt +(
E()2 SCf ef
MI = fl sive ponndo lmp, f9 tet cp 84- f
C+D25f sive Cp  e f
() summa H) et V d - Z - X ( sive pro d 92
substituendo ejus valorem m erit
smma Idii et tertii m -X. aequanda
trtm
Ye Z nn sum terell
quadrato, faciamus ergo. ( X, m)ADemp +p
1 fq sven p + 3 292- 24l+ 
P +X. sive lp + napis
Habens ergo Aequationes ergo problematis
prpositi omnes reddidinmi rationales, Jam etium differentia quad rntorum secundi et tertus
quod suffici Obfinnimus ergo tot aequetur quadrato
d2- X B facit d cd X + X4.
Aequationes ad parglolum, quot ponere et  d= X, 23 fuit d 4 1dX ad.f x 4 2y∞
coacti sumus Aequationes, quod erit differentia. Advy- Z 4X g  4)
sufficit solution. Superest
determinatio, ut evitentur
Numeri nihilo minores
dH X f72. Nam tunc tertius
numerus est nihilo major, si  majus quam
X + 2Z. Ergo et secundus nam si d est
majus quam x+-72 eri etiam
majus quam x. Numers autem
primus manifeste est affirmatious. deter-
minationum ergo conditio non nisi unica
est  
-n
 aequanda quaduto a 2+) Z p suoefi  Z P+ Z
erit aequatio d - x (a 2Zp + p
sβf(B 25(fl + C 1 uca
2531+ p2
Ponamus  sive Cpax Ao)cos: 21 fv f
pro fnserendo ejus valorem ex priore fier:
tl5
Faciamus ita: potuus si m - aequanda quadrat
ergo etiam em-ex aequanda quadrato.
c m (2+) remp
Summa secundi et terti (. Z +
(A +) d2dco + Co. Ergo d  - c . ZC + X et ponendo co ri 4C.
per cucem: (3f)co CZ + (34) c 1Z
a-1702
Z 1 = co- g
d - Z  quadnato, er Zat- x2
 quadrato Z
(3F co sive multiplicando
Aquadrato, et d +Z d. Z (Y quadrato (X) nc, Ergo quaerendum quadratus
m Y mp ) m VrV
quod sit   quadinti F Xresive
sur n  i
d + Z B d + 2dZ
ld. q p Cd2 + 2d  + c7. tioisis omnibus per
d+ Z, fier P d - 1
sive l 1dC
L. loco es pone q f C (12) vato simplex
9 (+) 29l +I, et habetimus:
)-g d , (5+) egld (Vd)p
Z191Z + 21Z
9 (+) 2gl + 21