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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 400r, page id 00068196:0795
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sed ad simplicius redeamus
(at Exx
y = a v
a+bXX
datur ralionalite
syydx. Ergo et datur (xydus quaeratur X per y et fiet
ayy + bxX yy =  a + aa Cxx seu fit X = Y a L a 1Y. Ergo dabitur
. Sydy 1a- a gy
byy -aac
byy - aac.
ita revolvimur ad priora
sed praestat sic generalius y= a sae + alX+ m
a3 + a nX + p XX
datur ry rulco
datur (yyax. Ergo et (xgdy. Ergo quaeratur X per y, fret
 agy +angyx + pgyxx = a + a lx faamxx, seu fiet
XX +8) + anyy -a l X + a yy = a = 0
pyy-aam
seu
XX +
sen 5
pyus-aam
angys 
an gy- a + 4  pyy -aam
pgy-aam
eanny - 2anaLyy + aell
4) 2a y tapa yy
aaine
+ s)...
+ taamayy aam a
Pegus - a
PgG-aam
1: (2) puu- aam
ubi non licel destruere nec et, nec y aliuqui numerator vel nominas
in valore ipsius yfieret extrahibilis. vdeanus an liceat
farere totum extrahabile
et 2X A.
staannyt - 2atu gy + a
in gy- al + Y -4 pa
pyusnam
sumngari potest
 dy
pyy-aam
4a
+4a m
pyu aam
qam
Stagno st - 2a yy + 46t
V-ap  44a.
um
a
saarx fiet yy =  aXX
sit AB, X BC, y et y = a d aa = Xx
aa = XX
in est momentum ipsius ABCH ex AB, syydx, habetur rationali
quadratura. Ergo habetur et Exydus. seu momentum
ipsius HFCH ex AB eritque sxydus = -syu dx 4 moment.
psius FB ex AB, quod est FB, y
et
erit Caxex ilaa
Cyy-aa
=asydy taa
jam si (ydy se
gy +ac
e ryy. ergo
x + aax
aa - XX
a taaxX dx =
aa = XX
per x
rat
ny-aa habebitur valore nal
ejus differentia sagdus yntaa
altem hansendente rationli sed yndu semper habebur valore rationali, si
Ergo sequetetur etiam Y∞y-aq
gy +aa
haben valore rationalis licet transcendente, per X, imo ut jam patet est ria
ju sit ratunalis
tantum ergo opus esset haberi dus valore to rationali per x
et yg, et gdys
-a
nsat
ex Ygy-aB et gy, et codu  utcunque formatam, sine interventu
ystga
Et video jam omnem formulam in qua
alicuius radicum extractionis ratinaliter, per x haberi posse
rationaliter perx habeantur
y+aque
et qy, et ydy
tinde patet eliam admitti posse yt, et yddus et tales, quae ex jus, et ydas rursus
gys taa)
quia syu dx datur rationaliler, et adeo datur et sxydus ideo haec per X ex
faa - XX ex Ax +. 2X dx   aa x
1 (an - XX
ornantur sed non licel transire ad dy, y
yedq et
a+x et dy-
y= a l aaux
 gydus st dy
sed nec hicquicqua litramur, aeque enim podeunt nisi ax, ndx, et nata
naxp
agAX
quae oia possunt
exressu exprimatur
haber alimaliter per y
Ergo rationaliter raberi pt 
-Xxyy + aa yy- a tadr
XX= aayy -a
X a +
+aa