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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 2r, page id 00068195:0003
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nadrat
Duo numeru aequales
quatrato numero datr Dato in numeris AC vel AD, radio circuli DC. contro
A descripti, vig. 15. invenire in numeris ipsas
AB et BC
Manifestum est si in numeris irveniantur DB et BC
etiam haberi AB et BC quia DB auferendo a radio
in numeris dato, restat AB.
jam appellemus DB, X
fier aequatu 2a X - X B y.
pro y sub stituamus X7
fiet aequatio reformata.
B2
et BC, y. et AD, a.
eptolt
ponendo bp, 1.
2aX = X s X
et divisis omnibus per X, fiet 2a - X p XZ2
l
2
sive 2ab   ,, bX + X. sive 2ab
et erit AB,, a - X, +
et BC 
Z ay
b +7
posita AC  a.
ab + ay - 2 ab b2+ 72 H
e
2+Z2 1 sive B
X
itaque in rumeris, ponendo a  15
x
e
2
D
ay2 ab2
b2 + Za
et sumta Z. pro arbitrio
b
1
1. -
2
fier b + Z2 15. adeoque a dividi poterit per b +7. ac proinde
L
etiam in numeris integris habebuntur, et fiet: X p 6. et AB, +9.
et BC AV ⊓ 24. Nempe 24 - 9 e 15.
Ratio cum pr summa quodratorum exierit differentia, haec est, quod
det debet fieri X minor quam a.
Erit ergo a  24b
et
9 + 24 1
seu  b+
62+ Z2
152
a
P 2b
sed si quastio nec sit dato in numeris quadrato radii, non ipso
operatio ese. Nec semper exitus habet
radio, inveniie AB, BC, in numeris, alia difficiliorque quaestio est
videamus. Estr AC, 1ab. ponendo a B 1.
ponendo AB e C, et BC,y. fiet: co + y r ab.
et ponendo M DB, X fiet: 2 fab X - X H V. et X, sab = co
erit
earde
Cd1 tab = X. et ponendo X Y + sab
2)b (= 2 sab co)  et b + 2 sab 1) = Co ny
L
sit aequatio yx Y + v + er + dv + ac 0.
Unic ordinando auterantur ut auferatur ter minus ex, ponet pro Y, s- =C, fiet:
n S C, 1 (F
+ +2 - = c2
a c
C)
et ex e (Cs)- () c. item DH T- Ld, et fier:
v. pone +C+
+ab ne
L4 25, 12, 2
B p. 10
BC
ax
100
aX
a + X