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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 91v, page id 00068194:0182
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Si X -X quodratus positi Xaqu. a, r git a - = quadratus seu c. ab
erit quadratus. Ergo ab- ab quadratus. Ergo denique ab- ab quadratus in integris
et es is ergo componitur ex a, b, a-b, a+ b. in se in vicem ductis.
maximus
jam a et b non sunt primi inter se, roduce ponatur (communis divisor esse
et fit  sit a aaqu. ec, et b aequ. Cd., fiet ec, ed, ec- ed, ec+ ed,
et oc factum ex omnibus erit ecd. ecd, quadratus, qui divisus per et
dabit 
i
Cd- cd quadratum, eantu in quo
exe C et d primi inter se
c. d. c- d.: c+ d primi inter se
cum fiat ex e, d, c-e, C+d, fiet etiam ex
id in C-d ergo qui duo numeri etiam erunt primi inter se
Ergo cum producant quadratum erunt ambo quadrati. Jam. si
cd quadratus, cum c. d. sint primi inter se, erunt ambo quadrati
ergo pro c ponamus f. pro d ponamus gt. habebimusque
duos quadratos. f- _, et f+G  imo habebrinus tres
quadratos f-g f+9. et f +q omnes inter se primo
itaque f4 g2  erit etiam quadratus, item 1g afq
eu +5 - fg + f9 - 4 iteu f + f9 + f9 + g
item f3 - fig fg +97
ilem + f + flg - f 92 - 93
posito f + g esse quadrntum fiet:
s + g aequ. h in integris. Ergo f aequ. ki - g
29 Vc cageeg
item f aequ. g + 
Ergo h+9, et h-g. quadrati
nompe t aqu. h. +g aequ. m  et h. 9 aequ. n.
Ergo haequ. m =g. et et h aequ n 4 g.
Ergo non-ina n quadr ae quam f. 2
item
N n - nt aequ. 29. et faequi in
vadi
hursus quia sg quadruto  aequalis, qui sit 1 fiet.
f2 aequ. g2 + (, et 45 aequ. 49 + 4 a
est autem 4f aequ. amn et 49 aequ. m - 2m n + n
Gets a m assu. m - 2m nl + x + qp
 - 4l quadratus, seu nin - l quadratus.
 M NF, tap. m + 2m N + n + l2 qua
Ergo 6mere  squadratus seu omre-
Heabemus ergo russus duos quadratos:  mr-  et 6mn 4
ergo nn ut quadratus, et mnal quadratus et Y
sive f- l et 6f2- 41, seu 45= 4l. quam auseramus a6f- 9s
a  restabit afr
f+l aequ. p. sou f aequ. p - l ( Erpo ssg
fal aequ q seu f aequ. 9. + l 25pP+
go  qua 6f gl aequ. Y. p 6 pe seu 1252- 81pq 2V fiet:
p +6p4. + 24 - 2 p + 4p g- 29 aequ. r aqu. p + 10p9 + 9