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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 245v, page id 00068201:0490
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Quod ut fiat, seu ut solvatur altius aliquod, prius jam solutum supponens
problema:
Fres Numeros Quadratos reperue 
tales ut duorum quorum libet differentia 
sit Numerus quadratus.
determinandus est valor ipsius a. et d.
utriasque aut alterurrius. ut C-B sit = ee  praotatum p mm tono su
4a2 8a + gadd 4a + 4a + 1, PDdd.
L∞F CCF
Ep. . +.. +. see s +.. +. 1+ =
seu 4a  + 8a3 = 4a - 1 = ee
ad
Jam ostensum est alibi, si solvendum.
sit hoc Problema: invenire duos
numeros quadratos, quorum differentia
ee
dd
sit quadratus Numerus datus, ut hoc loco isdatus
supponatur esse ee. Radicem minoris, ut hocloco, +add f dd. seu
esse  2a+ 1 = 4e seu 8a + 4 = e
quod obiter ne quid non comprobatum assumatur,
et si alibi demonstratum sit, hoc loco exemploostendam
Esto quadratum datum el36. Erit C = 6
Multiplicetur e= 6 per 4 erit 24 (8 = Radici
minoris quadrati, ergo minus quadratum est
64= e. addatur ad 36+ Erit 64 + 36 = 100DC
His ita positis in nostra ratiocinatione peresemusi
ostensum est 4a + 8a - 4a - 1 dd esse = ex. Eripsm 
et ipsum e est = 8a + 4 Ergo eP est 64a.  640 + 
36 + 361d
Ergo 4a + 8a2- 4a - 1 dd = 64a f. 64 a. f. . t6. Ergo
16
36
36  v + 9
4add + sa dd - 4ddd- dd - 16at+ 164 + 10 Reiihiaiti a ubrue seu + dc
= . . - - - -
-
(t
1
+dd
0
aga dividant naperia4a
dda add + 2 a 2 =) dda at= dd a + 2=
ga a+2 + 4-
ti
ita tamen pt post Dividantur omnia per a +2. fiet:
F
ada + dd=dd = 4a + 4 = 4a 7 + dossterum pro dd
1 aut2
a +2
dd 9
29 at2, 39 at2
4a
Et ita hoc saltem assecutisumus, ut in priore termino aequalium a in posteriore
a2 quae erant in uno quoque altissimae potestates, eas destruxerimus.
reprimetur 4a
a
geat
ga
3, a+2
ta
a seu + 2a. Hseratur a jam a quodr rdo fiet.
ra, 24 r 2qigq 1d c 2o 10 ia 4a 144
4t 2 d3 
a
10
s
aa n2ata 2-  2 00
rice seu per = horum numero-
rum A. B. C. dent differen-
etias quadratas:
Radicem de B