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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 20
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prop. VI)
1
Invenire ticequadratos progressionis
L
e eernee in uite linostenditur
ese
simul eorum differentiant non posse essequadratum
a
G
Arithmet
erit 2y aequ. X
sint illi X. V.
sete  eaeq fiat, xaequ y 43 Et Q aequ ∞+3.
v
fiet: y+is aequ y 2y7 +Z + y + 27Z+3
urqi
seu y aequ. 5- . fiat 2- Z aequ n erit
2, 7-3
3 aequ. M + Z.
+ 2ZM+ 2V 59
Ergo y aequ. C
(10). 2β
3
a a d. seu y aequ (2+Z +3
e
2 n
e
Loco, ( scribe l4. et loco _ 3 scrite Ai, seu 2s β
fiet: y aequ (+ 2AB + 2 A B
v
X p per aequ. 2. 6. fit X aego β + 2AB+cAB, 2B- A P
1.)
B seu X aequ2AB - B it  Et per aequ. 3. 11 fres
13
e Z aequ B+ 2dB + 2Nβ + 2Aβ.
Ergo Z aequ β + 4 AB + 2A B
aequ (2β 8A β7 81
ss
d
a
se
V
aequ B( 8 A B A a AB
al
2
Hinc ergo
sa
ays + 16 3
a
aequ. sa e A β A AB
22
a
et
+8
16A  416 Vβ + (45
ss
d
Unde patet. X + Z esse aequ. 2y qut desiderabatur
si ponatitur β et A. esse T. fet. Laq.
fiet X aequ. 1. et y aequ. 5 et Z aequ. 7.
nam 1. 25. 49. sunt tria quadrata
progressionis arithmeticae omnium possibilium
extrima
simplicissima.
Defferentia inter Z et X, est: eAB + d4 A β + 165
cinus dimidium +AB Y 124 B. + 53B? est differentia 4.
u hujus arithimetic 
dunce dividengoi
ests quadratus, ut alionde puctt, ergu  +
foret quadratus. Sed hoc impossibile esse patet, quia hujus
Naculo gisinis.