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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 21r, page id 00068229:0041
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2. Numerus 1. F. al.
(2).... 2.  al - X
3. L. al - X-
(differentia Nunen  X2,
in et 2di
(5) 2d1 et 3tii au X
(6) xin et 3tii.
(7). Ergo
(9) per 7. 8.
i quoi
(10) Summa L et I
LH + 26
Tres Numeros invenire, ita ut duorum
2al - X2 , d2
(1) Ergo NumF. alpi d + X2
(12) Num. IL.
13) Num UI.
(11) Summ. H et IIt.
(15) Ponatur
quorum libet differentiae summaeque sint
X +Z H c +2CZ
er  er
X7 FC.
X7
Ia 12
d2- x2
d- X-
Quadrati
 (22) p20. Et explicata M, fiet:
Tac
C  hg.. Exaequatione 14 fiet:
A
sive: dH- ft  qu 
fasistet
(17) sonn. X er AlL (d = Z sive) 3 pdg rg2, tsh 9
o(t o p Ingh +
42t M
B d (+) 2d m +m 2 1C
ersit rg
t t
Nacti ergo tandem sumus duo quadrata contrariis
signis affecta, quorum alterum literam habet
non extantem nisi in quadrato nempest
et - n’g et p
(23.) Ponamus ft A+ Ap n9, sive hp + lp + +19.
fiet fek e lpH)alpng + Ng2.
(24) Unde ex Acg. D2 fiet: L(  127 Ing + CpB . lxng
(25.) Et erit pg V B(s () - It p= 12 - ng.
1a u2 apo pt  dg t9
s
es
nt + D) alpr.  ( 
Haec operatio pro modulo esse potest,
multis aliis difficilis exitus, soplicandis.
Habemus ergo, solutionem Problematis
indefinitam, id est possumus infinities
exhibere tres numeros, quales postulantur
sumant sumi ess enim possunt pro
arbitrio f. p. n. Tantum opera
danda est ut d fint majus quam _X,
et 4X majus quam st
Ex( 1.
(26) d- f5 -
side destructo utrolique d, t et explianta (27) sive d
12 -1 2
((+39 per sM A (5 ju
s
a
apuso 1 V
hadet
 atic
f4 - 25 1 14 co quadrus
= 4(4
destuentur et et sp et fiet: (Ponamus de 54 1 .. Et quadratum cui aqualia
FACS. ) Gra 1. m2
sive explicara dursus d, fiet:
F ponantur ponamus a latere:
(29) f2 +
9. et fiet:
+21V 1
La( 1) 9HY. Sng - )3 = mg v (30) e - et B q, et ponendo quets
+DCF
(0) sonatur Sed quia hunc aequationem charaitere
quadratico exuere difficiler o explicata potius
1. d9, sed q explicata dm, fiet: ex
d(s)
ex aequatione 17 (F) m fiet:
qu+ fkeg- m2
Din (F) 29
fiet (32) (- C7 (+ 25e + 5
Ergo e  23, 52 + et 533)
jam ut d Z aequetur quadrato, fier:
(34) 5a + 25( + 17 5425C, 2 - f 2+25 = (2
45 + 41+
mi 9+S.9+  Cunus aequandus quadrato. Quod statim sine ullo
itaque valoris ipsius d num. 1d. numer ator
nov eatculo eveniet, easii panamus
exacte dividi potest per suum nominatorem, (1)sC
et paradigma ita stabit:
sigu igus quus n fgrsitg ro
pr5. kgr mng, - Angs - 5 t nus minus, 
29 - 2m 
Ergo ut divisio exacte procedat, necesse est
Angs  m esse  glg +   u + m no 
sive m esse  9 + 9 - 28. quod
e
falcta num. 19.
didisio ergo exacte procedit.
3
apr + mng 1 qui valor
t
onferatur cum valore numeri 16. fiet:
 +8C8) tLn 1 s mn
sive H (5- 12) h
il e
LH 35 34, 16
C sive 5+c E
25 F
 Ergo perca  e C, quod est abtir
dum ex aequ. 30n fieret enim 4p0.
Alito ergo instituenda suppositio est
Ponamus (S2s+ 2C 15= 25V212
(35)
A3. ) al
dant.-54 + 2 flv. H 142
ponamus 154425te
si+ ac
15
45
BC
C. Ergo
sivi 547 3 SC
unde su+  sc +de
9 + e Ergo 5 + 3C515C
Quaeuud qumieus
semper faciat quadratam. Ab-1
quad
b2t (2 e quad
(10) Ponatur: F
(5) Touutur
(21) Quare