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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 27
# Folio 10r, page id 00068240:0019
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e
e
(11)
2
219
Numerum invenue Integrum, invenire, qui divisus pert multiplicatus
mlli
per
quateimau
narium; det integium, qui auctus multiplicatus senario, auctus quinario minutus
er iintegrum, qui multiplicatus per biharium
auctus unitate, divisus per denalium
sit in bger
(3)
9  +8  A B. (76B+  pC, et C-
a
D.
9A+8 B. Ergos A,  A,B. siic P B  p sR+A. Uende
1+
YA, et 16 - 1  ( - 33, F,
Unde 2 F + 1 E. Ergo E+, 2F+ 1. Ergo j B A -. Ergo:
B
+ (DF +t + ACD B A
per6
Ergoc) 2 A + 1 14 F + 7
ergo 2A F) 14 F + 6 sive(u) Ap, 7F + 3.
Unde:
(14) 63_ + 27 +8 B sive ) 9 F + 5  B. Qua valore
in aeq. 2
16)
Unis  sive 54F + 30 45 + Y C, sive 54F +31C
+F + 4 3
H C.
unde G e G - 1
1)
(19)
Ergo aF + 4
(21)
26
per 19, trer 4F +4 B 4H. sive F 20H - 4 sive Fp, pH - 1.
ergo 54F, 270H = 54, Unde in aeq. 17. fier: 270H - 54 +34. C sive
170H. = 20 p C, sive 54H -4
28)
5
sive A p 35H - 4
C
CM
52
1 et erit per 1 p 35Y-7 +3
(2
3. f cumqentm sit 2C p, 198H-8, fiet: iodH - - 1 D. unde
3d)836H - G F D. Hinc patet A sumi posse pro arbitro et fur:
tans
38∞+ 41 ponendo  ob  1. qui casus est minimus, fiet. per 20 pecst 31.
700+50
20s
G, fier: 5G - 4 F
(23)
2
 A F. Ergo 1G  H. et G⊓ +H. Ergo
G7l Nam ita: 331 +8 p 41 et 116, +4
246
55l
50
50C2, 41
33
quod si velimus tam primum H qua  A quam ultimum D esse quad ratum,
 ex 18 fiet (33):  A.A.
A +29 _ M. sive A hoc Ap S35H- +, sive 36H ~ qua sumendus est talis
_, H, ut per 25 multiplicatus dec quadratum ali numerum quadrato progimum
fiab 35 H p 35C35 D L2 et erit H 
d
et A, ponendo N (+)
ponendoque 3 M a  35 M. 4 p
M
3
2B - 14 s fer. 1A + 1 + C H B. Ergo 2A + 1 E( X
siae () 7E - 1  A. sive 3E,L
∞) N2 (1
1
35 L +M fier L
70NL (+ 3535 L (353510) + 35 M - 4
sive P+4 M. Tivioulum taec aequatio in duas:
Ap 4 Y, et H 4 V, ter: 45
Not a B35 N  4
X N (4) Zet p 35 M = 4 S. ero Nsp +4 3e 
x
1.
per 4
16
10