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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 19
# Folio 6v, page id 00068268:0012
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dsannam in problemalibus quae reperi ad recta Traxtatuide lineis
Invenire sres lumeros, ita et summa et differentia duorum
ecuns
segem
quorum cunque sit quadratus. Numeri indefiniti salisfacientes sunt
t
20
1t8
12
e
4(16
a + 21ab - ba0 - 6ab + la b + 1
18
1(10
1416
812
614
6(14
10ab-24a6 460 a b 24a b+10a b
10110
41b
t
6114
6ab+24ab-ge a b +24a8 +6ab
10
item
4
12,2
a + 21a b-4a b - 4ab
a (14
(14
10510
12
12
4116
+ 21ab +
2
10a b-24ab 164a0- 24 a b + 10a
q2 ab - 240b - 240b - 6a8b - 6a (18
6
pesio
4
10
20
 in his a et b se
habent eodem modo
sunt tres numeri, quorum
quadratorum quorumbis
differentiae sunt quadrati
invenire quatuor numeros ita ut summma aequetur
numen dato
difelentia duorunt quorumcunque sit quadratus. si numeri sint
ex + cy + 1Z+ l co = 1c et  Ex ly -lx = pp 1Z- lX = 99 lcoa lX= Y
c
et
itaque numeri 4 erunt lx, CxEpP, lxigq, lxer, restant jam
ad huc diffecentius tres, nempe et summa 4lX + Pp + 9q+ YY = lC seu (x Xl (ppIqr
al
restant disperenliae 1Z. tus to- ty l- tz, ubi susstrtmendo valores invento
sil tlu= gle (p+ qer e Cpp et fit ly = lC - = (pp 199+HV) +pp ( P
ppaqq+hr
seu ly = glc + , et lZ= Zlc+ t et lc = Hlc + ll
pp - 9qWV
-pp + 394- rY
quorum et tres differentiae ultimae lq - lys, lco- ly, l. l2, erunt
pp - 49, pp= rr, 4q- rr; aequandi quadrato. Hoc ergo problema
probelma igitur quatuctam numerum prxo quaesitoruem, reducitur ad
tret suppa dictos problema trinm numerorum sapradictum
ilterntrum
pp - 94 pp -rr, et qu - rr possunt
Ex ax et by fiat trimnque rectanus. 2abXy, aaxx-bbgu, aa + bbyas
Modus quo Ecce modum quo
et viceversa de bx et de ay hiang. rectangulum: 246X9, aagy - bbxx, aagy + bb ∞x, sitque
commaltitudo communis pro latere r, et duae hypotenusae aa XX +bbyque, aagus + bbxx
pro lateribus p et g ita dua ultimae differentiae pp. rr, et 99. er erunt quadratae ex
44 19444 44a
natura frianguli rectanguli, et prima differentia pp -94 dabit ax toyas bex
nc uon sit adtum pone X = 24 ay: b cet prodibil differentia pp-4q aequanda
quadrato (6. 4  42b y2 +6d b9y2
20
(a5Y
6
44e6 ombe
44 _ pro cujus latere sumendu
+ 4db 1. 33 +ab17
gab
M
-(16)2 8Jyy mabys  + a bb 3. 3 aa t 2
 -64