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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 14v, page id 00068229:0028
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9 uit tres quadrati
2X 12XZ 1 2 y
pone C B S Habernus valorem
Ent enim b sf. 2. ∞2 + 3X2- .
est autem b pX. L. H.2
Rrectius factrer
uit
X X-
L.   quadvando: fiet:
X2Z + X Z sive 
Pace ergo, hin quadrata: X
ponendo 2 Ry. et C A
5 22, fet egoh
seu ctp fr - XZf. + quga
fa - 2 XZ f + q2 4
1) f+
X + af. (4d)
, ad ed quod (+)
15. Riet E qualio destnctis destmendis
Het 5 9h. l e pa E 29ht 1
et habelimus quu Eg 1C 41
seu a2h
nes 7C2 + 4
pone X. 1 f 1I
3gh ponc r 91
+ 4 a 3
d
a +b p X. Cago a X - b.
a -d B y Ergo a. p X + b. = y.
Ergo X + X H. Yb
Erit X4 b a etiam quadratus
nempe X. Y + 2y 
re a 2Xy +1
-X+  axb - b2
fet . = 3 a + 2X y  + y -Xb - b2
quadratum estu imB L A p 2. b13
deorema.
a +6130 =, 9 B  - 
est quadratus verum ergo
Enficissimmia futurum
ad destrnctiones. Imo execunda 6
fiet 2 seu quod 2 et  2xr9 2Y
a n a -. 5.
Ego a p,. +x- git
est quidem, sed imitile ad destructiones
hodem modo:
15 3 + 816, 10 - o 25
pet + d2+ ad   4 2d (4) 32 seu f 73 (4) or
it aea
(4) 2+ 1. seu 45 + 2 (4) X f 1 0. Emo (4) X 1 Y + 2. ponc sM 4
P. 
pone neis det. +  H +, e
ta t
2 5 45 + 2f vel (1 e. 253 + 2f ponendig  2s fit 4X et (4) et esse, fier 5f 31 45
et 
et s euit e
ponendo f p 2. f’ erit 8 er 2f erit 4 fiet 4f3 + 2f5 36. ergo porendo () esset
erit g76. et X73. Ergo 4f + 2
Ergo in aequatione seu restat tantum seme bis ipsa d
semel ingrediens in quoddam quadratum semet pura destruendum part est quadratum alteius:
ex prout ergo vel g vel d, vis esse, dtum, alterius quadratum destines, explicando ad quod
est dalum;
pone quadratium este datum, culi aequari debet laberum summa; explrabis, et fretogo
 A 9. unde gr he + 2X d. + x d destnctis igitur utrobique  pure
 d + X
Possumus ergo problema solvere hoc modo: tres numeros ivenore
di suuma sia quadratus datus, et quadratorum surmma sit quadrato quadratus
alqaatitur vator ipsius.
pato idem sic solvi posse ut  quadrato quadiatus, quam quadratus sint dati. Ponatur  esse datus
ego sumatur quadratur so
minus quod ab ex differa numero
C, et fie pro cot porremus l+ on
SH + m pone m B4r + m fiet:
morm () pr+  ft + (2) erit me e 14 1. Latera jum erunt.
+ p +q
p 1q0 + r(7t
sa e la. +
 adug
+p 14q Bs. ant fit. fr + p + qu + (4) l +  9
quiia numtur pn esse muntius quadratus seu aeguaut F lonatur 5 n + v+ t.
jen ponantur +r + p2  lam poriatur et L (++)
fiet aequatie pr  +
() c p2 qe l + m + r- Ern (+ n) . Ergo n e
sed jam video hoc non procedere si
coa sumponitur datus,  quia n rependet ex Y et m. F. nisi ponatur vig; (+r a
et fiet aequatio: 2r A P  0 sed an forte rectius, in p n. ponetur
u
unde fet p2 + q H
Erunt tuta latera: m. p. 4.  pp g2 sumtis M et
ut et g habetur +
Exgrat esto quadrato quadratus 16., seu 2Y9.
fiet (9) + pr a a  7 (. 9) Ergo P n 7 - q. seu PB 7 - qu
 proartitir habetur
ladera. 3. S7-9 9 B g, sive 17 - 91 5 - 9 - 3.
sive 7 - 4 t g -g q - bg4. + 9 +69+9.
pone g1 1. fiet q H 7 + G - 1 - 9. seu erit 4 73. Absurdio.
1+ n fit l⊓ p +4 vel pr 4 l - q
Resumerus quod supra C XA fa  2 Xf Z +d + B (0. pone Z A 5 + f. fei 2 X5 Z n 2Xf5 - 2X f  pone XA Z
n + p2 + qu p
et fier X + d 1
2Xf5. et fiet XSr L+ d. Jan latera erunt 52 + +  + 2d+
explicata jum
8 ut sit pth, 4d, tar q +h 4
3u 3t
1o re 
+ 2d +82
 ponc 5pd. tit Ad2)  etc 19n B t +4to  4d) sumta ergo
d hores
  suit d 1
et b p ng atro quod verissuum
Jam tria latera erunt
3s 10d