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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 26r, page id 00068229:0051
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exemplum sumamus. in venire tres numeros, quila da ut
ductum quoramlibet summa et differentia sit quadintus Numeri Xg1
X 10 + nC 1 nC +9e 19C41  eu
C1
y= 2012 Cs n 5 +23 C 124 e +25 e Mt
7 = 50 +31C f32C+53C +3+  +35 cM
(2)
(4)
X + y quad  quadrato v X + y= M, x - y = n X + Z = p x+ q x- Z = 4
7)
X y+ q(2) r y-
9)
2
6)
= 55
Ex et 2, Z2X = mm + un Ex let 2 = mm- nn Ex e 2X; = pp - qq
Set6 
(11)
12
rr + 5S Ex5.t 62Z = rr - ss
(
(o
Ex 7 et 80 fit nin + una = pp + 4q. fiat m p+  foi a ex 3, p+pt1F +n- paq
5)
(13
116
1ex ay. 14))
seu p seu mn - pp = 49 - nn sit M+ p = t q+n fiet m- p = . 44 q n: t
8
4)
rursue ex g et 12, sit pp - rr = 49-55 sit p+r = v g+S et, ex aeq. 17
fiet P- r = q 5: v. Ergo ex aeg. 16 et 19 fit m == g-n: t + p. 
19)
et p qu s: D + Y. Ergo ex 20 sit m = q - n: t + 9- 5: v + r.
Jam ex aequs. d et 11. superest aequ. nm= nntrrtss ubi tantum opus,
13
est explicari m, fit. 99: t - 2gn: l + n: t + g. v - 295. v + 5: v.
F 2gY: t - 2nr: t + 2gr: v = 2sr: v (+ WI) Teuarr si
G 44: tv - nq: Lv, - 95: tv + e ng: tr
= nn(rDiss
porro ex 15 et 16 fil 2m = + gin + q-h: t.
pursus ex
(27)
25 et 22 fit Y q- n: t + p 2t qin + : 4n: t. Ergo g- 5. v + r 4 4 9. n: t = it gin
g. 5. vir
(28)
partus ex +8 et iu rursus ex 18 es 21 fit  v. qis r = 9 5: v +r seu
fit (r = sit 2Y C29 b. 9+ - 45: v
30
In polius post 19, fiei  ex 15 et cb, 2m = t qtn + q n: t
yr
et 2p. = t qin = q- n: t et ex 1g, 19 2p = a v. 9+5 + 9-5: v
+
et 2r 23lv. 9+5 - q- 5: v et ex 31 fit + gin - q. n: t = v. gus + q. 5: v
Unde habetur g. nam fit tg + tn = g: t + n: t = v9 + v5 + q. v - s: v uunde fit
(25
Q tn +n: t = v5 + S: v (. v + 1: v, - + + 1:t 
q
Coe
(90)
jam compendii causa t + I: F sit (3, v + 1: V sit D _ t - 1: t Fit at v - 1: V sit e
3
7)
39
et ex q. et β+ A = t, et B+ n = v fit et ex 36. fiit en - nBC:, b - 5 = q
(41)
(+2)
rursus per compend β: D. X sit r et n: B- A sit o et ex ag. 47 sit Hn - v  = q
+
45)
qui valor ipsius g substituatur, in aeq. 30 et 33. jam ex 30, 37, 39 tit 2M = β9 + An
et ex 33, 38, 40, sit 2Y (2 n9 + 85. Ergo in 47. et 48 pro q substituentae vulorem
0
ex aq. 46. fiet 2m = BNN - β~ S+d et 1 EY = (n Nn - n 15 + 65
jam in aeq 23, qum nn trrass pro m et r substituantur valgres, fiet
)
  vel copendio e B1+ At _ sit  et  +  sit ip
54
Ergo 2m Gn = βa5 et 2Y = v5 + (nN n
Ergo denique
in aeq. 23, qnim = 4 un + 4rr + +ss substituendo hos duos valores q m, Y ex 46, 53, 14
fiet gn + β~5 - 283V n5 = 4nn + 455 + W5 + eAn + 2Ip ni nS
(5,
ponamus BN 4 F  et habetur solata aey. 35. pervalorem ravalem ipsius 5. jum 56 ita solvetur: sit
rC explicemus 1 = - nov +b  = n: B- A. Ergo  =-(n n: 6- X + B, ergo ex 56 si B n: 6- 1 = 4+ (. B. d
a6-a n A: B= X sen β5 = 4B- 2 + ei + d8. X. 2D et B. 
iquae revoranda ad t et i verte