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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 13r, page id 00068229:0025
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7+XB X + 4γX +6yX+ + VX + X
res N raperire, quorum summa quadratus et summa quadratorum, quadrato quadratu
 i numeri ab. ac
X - ab - ac.
 etac 2tabC 
Cab + 2aC pone C p bd
X -valde - 2ac X + art rcabeta
summa quadratorum 2aeb + ra 5 + abe (+ X) - 2 ab X - 2aC N H A ae qualis quadrato quadrato. (yt) et a.   ettor abh
aba
un quadrati: a
perr 2b + a hc  2a tX  y
Siet 2a + X+ - 2ab X B0
vel po B ponc 2a b 12 ab X  2a
fiet 2a bc + X - rac X  yt. pone hoc amplius  b ⊓C
Ergo b e ax et d1 = V X
av+qu 1 1
Ergo b B dEX Xb + 2db x
2ab 1b 4.E
ploge sios
et a e V- X + 2dbX , et d1d. X
2 d ba + 2 2d f itaec inutlia:
pone ce hb + g. fiet  2a c  2tb + 4 hbga g et rabe r abt + xbg.
pone 2abc n y
Unde cha B  2he b + rtbga +290 + 2a bh + 2a bg. + X  - 2 ab X - 2p hbX - 2agX yt
None 9  + lb p 0 fiet C F, lb . 9 4 g. pon 1 - d, po liccemuus BY est o dac
faebt aph b2 afabth X - fAhB ende
e)t i
a b + ho b + abh - hX  0. ponamus
jam b h ri  s b fer: a  + s bt + abtt - sCX
Repetam: fali fate  fdba (A ∞2) - 1 4b. X pdC X 1 (t
CX + cX  sumamus ergo b esse L. c esse 2.
b+c + bc
fietque a ei
jam  - 1X abc  - . bX cx
B  aliquid
hogu. -. b + 2be r C erit minor quam b  AbC + e, quod est alsuntum Res ergi sit non
procedit.
ponamus sic:
a b  dech, u e Xbe
~
qus
b2 + c4 bc
dech. quorum summa aequalis quadrato.
Video toram artem in eo consistere,  quam tultas licet arbitrarias nancisamur. Quas postea
Efc
pro arbitao explicemus: earum enim explicitio ita enim in nostra erit potestate aequationem
inventam in tot alias resolvere, donec exx tot arbitrariis vel unius varoem mancsamur
quo facto artitrarias omnes superfluas, quantum liet faciemus aequales unitati: et solutio habetitur
sic satis simplex. Ea arterredo etiam illud efficiemus, ud aequatur quadm et quadrato
quadrato ab eodem latere vato..
Interest etiam a quat aequatione inipias;
Dominus osannam credit non posse dari, aut saltent faletur non posselei se vari quidrato. quadcatum
duobus quadrato quadnatis aequalem. Ego id suri posse non dubito, et facile quidem
Sunto tria quadrata:
 4 2WF, 7a5
+b + +3 n y
 ue c 5 3 - ila 5.  ac fiet. CH
jam 1b  ab +y ea + da p, A.
tins videmo effici posse, ad tam quadrator quadratisi quam quadratus sint dati, et duo  numens.
quaesitis etiam dati. Suuto enim quaes duo numeri dati, b e 1.) 4 12.1I VB
fier C. X 1 42 + 16 = g G, C. seu 10 higua Ct c ,  A 14 14 s b
sunte Ecce ergo tres numeri.
Eorum quadrati
l (+ 5)rea Y ae
21F l4 3uf
vouasatera. b. p
Torum summum
s  vir in scalcula resumendu
s
undea W H Z
eie
 eni
ri itif i 
1a 6. 25 aC   5 13   1
gerea
quia veW. 3 nea) + a, ideo vu  Y- pea
2. d. n  et W B V 5Z. ea Z   t dem fW e V + 12  rd a - 2cay rac, ciritus H F 5Z   
 estis
Poumus jam H  Eesi  rac
afict. Vd 125154
Ponamus. Su eay  A . Pro b sultituatur 
 ca Y 11+quu aegrationis ope Invenitur vator a ipsus e
rea H f17 +a  p + 2
Fiar aequutm 2t  11 + s L + erZ sive 2.  1
2ax + 2a