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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 389r, page id 00068196:0773
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quformulam quadrato aequandam indefinitam
unius litere semper salva indeterminatione simplici augmento vel diminu-
tione raticis eo possumus redigere ut careat termino ultimo
sit ergo XX + bx aequanda quadrato, X  yy xtb =
x = gytrpGEPB X+b = (99, + 29y +99 = (2) (2p tpp +b (y9+ 2py + 
hoc non procedit, nam fieiet. q- p. unde foret b = 0 quod absurdum
An sic = X = gyt ipy+pp, :, ytq X+b = yyt Ery+I, :, y+9, et fiei
b sed ita recidimus in eandem etfret ny + 2ty +AP ∞ yy tEryerr, adeoque
+by +bg
2Y = 2p + b et q- rr + seu r= p + b ergo q= (p)+t bP + L bb ( pP): b = pF L b
et sint X = yy +EpyEPP, :, y+ p+ + b
x+ b = yy + 2pus +pp + by +bp t = bb
su X +b = gy + 2py + pP3: y+ p b quod succedit
9 + bp
+4bb
XFbXXFEx sit x - yy + ipy App, 35yYq radices X 4 Y x et X+ m, xrn
X sit X = yy + 2py + pp B ipsius XX + bX + ce radices sunto X+ m, et X + N
3F Gy+ 299199
sit X+m = gytarytrr et XAn = gy + 25y+rr. sed 
biscluendo
sed ita subistituem
7+9
G +2prry+r , ayyt 49y1
Xt m = yy + 259+55, y+ t, : 49 +
fit y +2py + errgy +
eP yy R prry + p
amyus +zamgy tamqque
D.
_t n = 7y + 2VG + WW, yrt, : 19 a1
yt + 25 y3 +55 yy +55ty + 53tq 8B
+a est.
559 
4 ;, 259.. 25tg..
ubi extunt 114 et tg
idem pro in Eadem identificatio repetenda est pro m et 5, ponendo n et 
l+q= 2p- 25 19 Tr npptat 
tg = 2rr+pp + am  35_-45p + 455
255PC 153) + arus (+ 25pp) + 2sam. (  p + B 2 - 2 pertrama
p = 5 + L + +  esinejari B.
1tZ9
stam5 t +Sq- am = l LF + L9 = Wt +WV9 - an
squtus
sed video tres pro id mali video quod sit sunt s aequationes _, et arbitrariaae
sunt tantum sex. imd tit sul quod absund
An sic x - yyairya pe, ytt, yt 4
4+5, ytW, 9r9
Xtm = syt 2ByteB, yet xn- ytasvidR yt 4
3t5, 9+3 ytg2
y1W. g
ita prodeunt etiam B ubitrarie 98
licebit habere plures, si pro osricumus y+ t, ytq scribamus Byt B dyat, aa ytq
imo licebit adhuc ubique dividere ner + A,ag Et fient 9 mibitrariae
An sic e vel sic ut ubi idem arbitrariarum rumerus
nyne ytet
3td
P7py+N
byys tstg +sst
1 + 259y455y
y 42y 43gy + s1ty
Cy 2stgy
9y +29599 45sgy +sst0
xinea
Equu +utus)
Ly9t43
1s. L yy p+
(1y +5, ustlu, 3d
xde-
 et
X+m =
9+B2, yt h
yt g pyrt.
rin
uaajytn
9rg A.yAt
X+m.
to