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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 15v, page id 00068229:0030
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Aequationem huo enturus:
Erv - qut + (alr + ertl- 2lt + 2t rel
. Ponamus V h + t. fiet:
Erh + arht + art - 4hl + atl + B =r (1 2r+) 2 l+2- 6rhl +6rt 2 .
ocuo jam Yp l. fier: Eli  alhit (1- 1F ( +L C) a H. 1B. 2Ut et 2
et fier +
(3 1h, 10h2
1I + 4Ih +10 F 21
Erg. S p l = 12- 21k + 10h p
FAlh 4 1ol + 2t
ex et X f. e. 
    eF
h+
10 h l G1otr
et  Y pch= 1 + eth +Johl
6h1 46t12)
Esto pp1. et 9n 10, et +-
et ++ fi -. et 1+ p
fiet V poi 2- 20- 100 1ini
F4 =2- 40+61 732
et +. 2he 4 Johleseu aquationes deter minatriaes se
44 h + 10l + 22 possint ad impleri, ac prima quidem impleta est.
qura +g 12t semper veru est si p. 1. et  +
s. sed poste papterim tertia semper fere vera modo  D si +
quantitas major binario; se cunda ergo ut ver succedai necesse
duplam D esse majorem quam 9. quod ut videamus an
4 6+2 2+q
sive 24  1e4 1292 49
Ergo  + 124 Y 2gr, ut si 4 sit 4., itique 38 prrce: Nililo minus V p bi ario, erit enim vp 1B  2
attollanus e V ad quadratum ut eppanea est xa ud calulo inseratur charader affrmations,
pl
Et hac methodre semper reperiri potest nmmerus quidratus, e - L + =  + pass,
qui addito
ipo 3
1412
Eto manet
quadcatus, item qui sb potest reperiri semper numers quadratus, qui oblato, numero dato manet
reperdi quadrati; quorum dfeentia est data ut manust
quadra tus, seu duo possum eem u suppletorium duorum quaratorum
Eit datum. v.g. vis eit mangatum
allud suppletorium sit- pr = 12, quaerendae qu sunt du aequanditates quae in se ducta faciant
fingatur ergo quadra
N4, quales si nullae aliae saltem sunt ha: 1 et P + 12
4 In XL +  Y p + 1 fiet quadatum tale:
ld.
t p + (d+ l, erit:
pa + 2p ( + 14. unde radix (a+)  (+)  , Ergo fiet:
V+ B  H (1) (t Y L (1) (1) P Es et mulliplicatus omnibus per. t, fier:
 + P + 1 +
cet (7 (t) ponendo +
2γ+ ,. βt. P.  (+) (4+) t (+  +) pe + 12 noc pro V. et P. substitando numcros quantilates
affi mationis chareecterem  ferentes ut pohytponendo 2g () 2 BC) + =l.   pro B, piontu
Eoplicationem ipso (. et pro + ponemus 5 + l. fiet. 2D2 (95 + 2071) 42l5 ( 21)  2 2
p. C (+) A F+ (o) Si u + L 4 p + t + 57 + 2st ( (2) + p (+ 12) sed
nihill inde, rectius ita. ponamus +p. (54) (p ( +) e
(5 +) pc (5+3 et
fier. pr, 12 (5) p +
(N - 2lD+ 12  2l. Ergo differentia inter V et T. ( S2.
++ fq = +B et  ++ 9 - 1 +7..
1f12 1
iepe
+F1+I iic 149. 1 +4 e +C
11 +. A
1+9- 1+7+
(Ergo _  (+9) + + 9 1+ L (D p (+ q +9 + + t (D Et mulialicando per cucem:
49) + +1 () (1 8, 14 9C9(+ f∞) (B,) (+9 + + 1() (1+3)
1C1)7)
et fiet q pula f 2l, siue 4 ∞, + 1. Est ergo 9 vel = 1. vel +1.
51 2. Ergo 2 149+ 497 - 49- 69 + 41 4 ab B es a ex
v 3+ β- YF. 7 (+) l Sp + 5 + 2. Ergo V + 2YB - )F - 2l4-
HI d p + ld + (12)
Numen  quadintus, qui addita unitate manet quadratus.
1l
 7ath + 10l +P xe videamque au tres conditions
est
lender et illud patet minimam falisfacientium ipsius  explicationum esse per 3.
sive loco ) ponamus 5 fer BF
Nanisum facile effici potest ut +
tum a radice hujgmodi:
tC∞ - F = l
+NaeC
e