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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 108r, page id 00068196:0213
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Applicatio ad curo conicam
sel 10 ipso dum Ya + b est revocabilis ad rationalem, etiam va- s1. est
1118 - 1b = 3
-S liflis -a
2- i
AC3- 2Cy
revocabilis ad rationalem, ex natura ambiguorum. Hinc
165+22810. 20 et faciamus 
n
11. 50. 2. 2. s.
q
ex + yt extrahendo fiet y = a + xF = b - X
et CcX = b - CX
est
1- sia XF b cx
1btro
(3
bant X +CCXX
SatesEc Xx ∞ b - cx.
berbea
 x cxx
bc
A) + 2b cX + ex
et  
F2bC
+ Sa + eX + CCXX - b - CX quae quantlus revocari pt
+26c)
 -a + ex +CCXA - b - Cx
+ 2bCX
fractionis per
ad rationales, explicando X
ex aequ. 1.
Et multiplicando, utrumque terminumnumeratorem,
+ 13X + cCXX - b - cx
fiet y4 arbe.
Y a: BX(= CCXF
(4 (-2bCX
+6) +2bcx) (+ cexx)
sit (5) ( (i + ex + Cex
.se  Ego v - C fb2 +1b cx
a - C3X
+
revicari potest ad rationates.
Quia ergo Zixrevocari potest ad quadraturam rationalem, 
pro X substituendo valorem ex 19. 1 et B+ ex de revocari itidem
potest ad quadra
V. a ex tuiam rationate
it gsrat
Ergo utique et Vdx ad quadraturam rationalem revocari pt, ad qua
e sed vax ei similis est ad quam curvam Conicam reduximus
Y =  s + 2by - a, :, 8- 2c9 Ergo d. ex- (agt 2cay-8y. beyta)
videtur subesse in calculo error. Resumamus
a a + ex = 2b y + y fit, )a + CX
1
e3. 2cy
 = b- ex
+ B + 2b cx + ex
jam exaeq. 1. fit X = = a + 269 +,:, e- 2c quem valorem ipsius X in aeg. 3, si substitu-
3
2CX y
arius in aq. 2, prodit identica y =g. quod et signum calculi probi.
ipsam agamus: C3X =  a  + 2be y + e’ y
Sed rem
126CX - 26 a + 41Cy + 2bcH
x compendo O: D fiat +a5 + e OD +C6  opartet numeratorem esse extrahibllem
+ C2X
.  Fibca
tCxX
. 22b
si aetaeacec
eb eCabceyabc
At
(a9 + 26 85  eb y
P. a+ (
_d= e- _cey + 4cCy
tracehi bcey -2cey OD. etabe
-2bco  u 2bce
bc Meu (. qVc
etabids Cide y tabeystcy
Aqy
Oc
OD = - at + 2b 3y + e ist
y- (. - l- 8_ G . Th. b. 3. 10
+2acy2 - 4bcy - 2Cy
412
=a 4ab y- 249
+462y + 4by +y
unde sob e e +cy
+dc Xy
 1. We (+2bc
0 = +ac ( 1y)  cy
subest enir in calculo, sed nil matans
nai summam.
Ad hibeantur numeri veri, p quod
hic ficu pt; ut eror evitetue in calculo
- b
1- b
+
aa +bb
(a + e PX+CX