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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 122r, page id 00068198:0243
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Xta = H LMX Xtb = A LMp. Er uta in net
aL A
Xta = H LM X+ t = Y, N et X ta, , A rB = F +L M N
2
Xta- _L Mri xib = HLMA
e
Xtc
X+ a = H LN D X+b = HLN et x+a, in, x+ b = H LM N 2
sed video literam H esse superfluam, nam pro HM sufficit M, ut
et pro HN sufficit N, et fiet
X+a = LM et X+ b = LN et Xta, in x+b = LM N
Haec pro duabus quantitatibus ita assumendis, ut productum
aequetur quadrato. Sint jam assumendae tres:
ael et XtC = LMNR
ta = LMNP X+b = LM NL
et x+a, in X+b, in X+C, =L M NF 2
d
XL L MNP - a = LN NZ - b = LmNRC
Ex 7 fit = b - c,: m 2 - MN
02
LN = a - b, : LM p - M Z
E
Hic quoque posset
pro P poni
caeteris
et sit: LF_ LP b =c - Mq b -C = HL M 2 a - b = NR a- b
LPb = LVC = Mg B +M EC = M Q a (= Ma b) - NRa + NRb
fit L = ME a = NRa + NRb - M 9 C
92
- PC
M GLN - MNF
fiat P = 8MA
et sit
16
qui duo vatores si aequentur, e aequatio dividi poterit in
b - PC = M
N = MN
et Mga - NNa + NR b - MQC
b - C set
e
sit P = SMN fiet S MN b = SMNC = M9= NR
addantur in unum aequ l et a coq. 2 mulsiplicatu per h, fiet
+au
a aNR
  t h+b, smh  +
C
c
A
a b
1 =NI
ex aeq. 1 ordinando fit +2a M + Rb N ∞ b X0 sA
dc
re
4
et +5 b MN - qM + R N +0
C
Ra
opendio fo M+ 20N=
3o ANt
p exaeq neq 3. fit compendio ex 3, fit aGoM +20N +1 =0 eg. fi
et
ita exhacus
ex aeg. 4 fit 20 MN + 31 N 41N = 0 ECfi N = - 11: 20 = 10 M : 2
vic cenerali calculo sagus Quo substitulo in aeq. 6 fit
rursus, = b - c.
duas
e
a
seu 88 10. 30 M f+20. 31 M = 11. 41 =6
erunnata erv. sign. C
=11. 30
10. 41
am + bM + C. fit aaM + abM+ac
et aumM + b. aM + Zbb = Zbb-ac
et am + Zb =1bb= ac L
, et et ita in
st MN bc= +qM Z
Asra
seu
m= 1b- ac - b
2a