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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 30
# Folio 11v, page id 00068243:0022
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(17
invenise tres numeros ita ut duorum quorum libet
summa sit quadrajus.
a + b  X.
4
fiet: c aqu. - X + y +2
a - b aequ. 12.
(2)
a+ c r yt.
btC s 
b aequ. +X- 9 + 22
a tqu. 1x +y 
a - C aequ. m.  b - c aequ. n
(12)
(15)
a aequ 1 + b a aequ. m +C. Ergo. b aequ - 12 + m +C rursus b aequ. a C.
(10)
invenire tres duo numeros ita ut duorum quorumtibet
differentia sit quadratus
(1)
4
fiet n l’ aequ’m- n manonte C arbitraria
(11)
12
(4)
 aequ. m - n
invenire tres numeros ita ut duorum quorumlibet summa
et differentia quadratus.
xnssniua
per 6. 11. fiet: 2m +5 aequ. X . per 4 erit 2m -X ( y  Z aequ. X (  et
(15)
seu fiet: m aqu. x - Z2.
(17)
per 5. 13. fiet: 2n + 2C aqu X- 7 + Z2. per 4 erit 2n- X +y Z equ. X. es( 2d
(18)
seu fiet n’ aequ. X yt
Omnia ergo reducta sunt ad has tres aequationes,
12 (14)
aequ. m - n2
quas ita absolvemus.
(+
(16)
m aequ. X. Z n aequ. x= y. seu
(19.)
sit aeqo  fn fn
 m 42 ms + n aequ mn seu f
(24) 
seu im aequ A
f2+1
fiet
C2
in +n aequ m +n. et m aequ. 
+n
16)
sit Z equ XPp. a fiet ex   hitm n aqu (X - ∞ D p + 2xp
(2)
seu
It + 1
ns
et X aqui n 1)  +P seu x aeqo 2 1))
t
(14)
ecece
aequ m- n
(19)
m+n aequ P9
(24)
X +Z aequ
X+y aequ Up
(34)
Lu 65t
(20)
(18
(1)
(12)
f+sn
(13)
m- n aequ pat. fiet l aequ. pg. m aequ P 4+ PY. Mago Yq. p
25
X- Z aequ r52
X. y aqu tr.
fiet irsaequ p4, psq per 22 et 26
2tV aequ. p4, pg per 23 et 31
36
rs, r+s Eequ tv, + +V per 27. 32.
en
2
(2
(16)
fiet maequrs X aequ r(+rsi xeg. rS. rs1
32
fiet: n aequ. tr xago tv+ t. frgo tx. tr
v
(31)
(37)
aequ
25
etq prs- qus aequ txpt tvu
p - 9
v
dolrs+ tr 
rs- +
es -tn, . typ (t)
AvH ras (fiet rsi 1
 irs+ sin aqu pus pr 14 + 15 cuit gaego sastr
a
rs+ +p f2)
rs - +v
(29)
Ergo 1 +0 aequ rs+ e p- tto osilv - es+ t
(40)
Ers- YtV ago 7p92 erit 14 aequ rs- +
aequ L. Ergo P aequs
seu fiet: rs
r
rs+ tv- rs+ Av
Is aeqo  + +v. +D aego r+s
4u is+ to H
25+ +V
9. et per 37. fiet: 1) aeqe is to
5. 1v
P s+ +
+v
+q
rsntn q
ra de grreit
A
suit