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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 175r, page id 00068194:0349
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Invenire
Hujus problemalis osanna non nisi unum exa
porut vid. Dian
690. 
anver
3 jil 1t14 A
eactem
Ut Triangulum Rectangulum in numeris, ut summa aboruta id lalentus
sit cubus. Tiranguta Latera Trianguli Rectanguli sunt
2ab, 4a - bb aa + bb. Horum cub 32 a Cubi collecti dant
2
14) 162 (17
3ab + a =3 at bb f3a a b b + a (3 a b0+ 3aa b + b = c
(3
2
seu 8ab +2a + 2b = C3. sit a= cd et b2 ce et fet
sit c aa + bb + d et fiet 8ab u + (2b (a) + 3 ab + 3a  b+
+ 3 a bd+6a bd + 3abD+ 3aa dd, +  le dd + d3
sit c = 2ab + d fiet (8a b) + 2a + 2b = (8a b3+ 12 a bd +6 abdd + d
jam aggregatum duorum caborum semper est divisibile sit X3 +13 dividi potest
per, XX - xy + yy. Ergo et  a + b dividi potest per a- aabb + b+
sed  nescro an sic rucremur prastat aequavem reducere
(2)
problema ad simplius, e nempe sitr a = d et b = e, fiet
eab + a 8 de + 2dd + 2 ee , C faciamus eru d
 c= fd et e  c= fe, et d = ge et ReY
8gec +299eC+ 2eC L f3C3 et divisis omnibus per ce,
fiet e= 2+ 8g + 2998,: f3
63
110)
63. Ergo tantum
dpus est 2 +89+ 24g aequare cubo (5b3 seu) h
seu 99 + 4g. = 13. 2- in seu 99 + 49 + 4 = b: 2 + 3
V(II
 unu uende 9 +2 = Sih + 12. 2
seu fiet 2+
(10)
itaque opus est 2+8G + 299 aequare cubo, (f3b seu)
et fit99 + 49 +4,
∞2)
(1) Dxh - 1 + 4 seu g + 2 = S2t + DE : 2
ergo seu a: B3  4Y t3+ E2 B. 16, :8 Ergo re
(74.
huc redit ut V4 St+i = 16 sit numerus. Ante omnia
ergonh3+ 12 aequetur quadrator in definite seu nm videamus quomodo
formemus 12 ex A. H + un + na + n U + tm + mn = 12
I + m 3. m sit latus quadrati a et fret
h1) amm (F 12) + ginim seu mmh = 4m + 9
 fiat aef. n -2 et m pt2 Ergo ex aequ. N. fie b
n_ - 6n + 121 = 8 + 12 = pp p + 4 Unde sit
l1ct)
+94s
Ergo se sed ita oporteret = 12 +89 + 1299.+q aequare quadrato
Et ita nihito facilius hoc est pri aeque Isi
prastato rec
uideamus quid fiat, si redeundo ad aeq. I1 pro g Rbnamus
pro9 seu a:6, faciamus r3. et siet.
2 + 8Y3 + 276 = h quia autem
habemus unum exemplum 3, 4, 5, fiet tunc a = 2, b = 1, 2 + C = 6 d = 8 C = 1 f =
V
6
 = 8.
AY3 + 4
Error fuit in calculo reassermam