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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 177r, page id 00068194:0353
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y, 1. X, 2  (,3
riangulum Rectangulum in numeris invenire
cujus cuborum a lateribus summa sit cabus.
471
4
2. 1. 2
 e
Latera quaecunque Trianguli rectanguli possunt sic designari, Xy, Exy, Xty
Htorum cubi erunt X - 3X + 3Xy - 8Xy, X+ 3Xy+3Xyt
summa cuborum 3xb +6Xy + 8Xy e aequanda cubo xe Adeoque 
2.8
2.(9. + 6. 4. 1. +8. 8. 1
8. 27
(
(2)
2X +6y +DXy = xC
32 16 + 16 = 2. 27 -5G
Explicemus omnia per y, et sit X = et troy 01+ 10y et e= 20+10y, et fiet
2X+ = 72. O1 + 2. 401. 10y + 2. 6. 01. 105y +2. 4. 01. 1037 +2. 10 y (e = 20 +3, 20. 100yr 3. 20. 100 y11107
6 =
...  - -   ---
.--
+16 2
+ 0 1 + 109
. . . - - - - - +8. 01. 1 + 8.10. 25) +,o y 4 3 1oddicoy 19 , 0 3. t 10100 G
+8xy =
Xe = fO1. 2= 10203y - 3. 1a 20. 1001 4 3 1020 ve P  1o 1 s y (F 1 20 + 3o1 1 . ) 3. 31 b 15 + 01 10
16(7
=3. 91. 20.100y 4-3. 01. 20 1004,2+ 01. 1007 y
Si fiat 10 =2 et 100 =3 evanescit At.
aqu. 0. unde ut evarescat ist, fir  2 - 5. 848-27,:54 01
seu 20:01= (45: 54 =) 5:6. Restant termini Y y, y.
t qui explicati dabunt: +2. 6: 52. 26 +1b 6: 5 26 y +48.6: 5 26 y
(10
- 6:5 20 = 82. 2037 - 18. 28
= 96: 5. 28 y - 27. 6.520 y2
sit jamaequatio  m + mq y + ng y
in + ny in p+97
nBy
=0 ubi dividi possunt
omnia per
ubi fi (20 = mq + np, :, 16. 6.53 - 2.  - 9. 6.5 seu qqundio 20 = ingerpi c
fit mp + mgy +nqyus
+n p
2c
ob ysit (12)
et 29 = 48. 6.5 - 18 - 27. 6:5 seu per qend n9= f
sesit (14
65)
Et ob y fit mq + 2mugp + n p, per (2. 6: 5 - 6. 5 seu per) 9 = cemm
et tollendo n per aey. 13 ex aeg. 16. siet W F  Mq + 2M fp + s= cemm: 9
sit mgq p + f  D seu m qp A e sit p ArH et ex
19
aequ et ex aeq. 17 sit in qeamsans coterimqu cm . 9
(20
quae equatio diveltatu in duas mtamsq ce m q. g, lus qsm 
E
ot
seu m= 25 g c 9  et r 2h. Erpo p2. h pr 13 et 9
et aseramsrs
b
sit p= 1 + Y et 1: g = 1+ b quae est cognita ut g.
8
(20)
fiet xg. 17. n g+ Emfgtamfar+mfgr+ - Cmq +em ab
quae aequatio divellatur in duas, ambas deprimibiles  nemper
e1
mq +2mgf+ 54= eniqu et amfrtmr = mb
unde fit m g + f = +C m 9
fit m= f: fq - 49
et 4fr + 2fr = eb m
et m= +frt2FY,: cb
(
et sit cb= 4cqr + 2c9fr- 44gr- 29q r, ubi fuciendo qr = Xc
fiet ctf  4 ac 1 rc fiet cbf - 4cco + 2C frco- 4gco- 2fco
quae divelli potest in duns: cbf∞ t fr et - 4.
cbf  t Cgr + 2C9 frY et  49yr 299 fer=0 simo non licet utiq
aeg. 2a nam ficiet
a
(29)
et fiet q Obsgi aY+2fr et (Y = - a. -(0)
quae divelli potest in duas: +2c9fr2 - 299 fr = 0 et ebf = + 4cqr- 499r
unde ex 28 fit g = fc et ex 29 fit Y = bsg:  4c - 4c quod absur
est
s
16
48