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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 39r, page id 00068195:0077
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ruae sunt aequationes 2ak + aX -
C apax  + d (t +) y, = y, (+ ()) (+ +)X quarum
interset locus prioiis est sectio conica, locus posterioris
quaritur, ut ais pe solvi possit problema horum duorum
locorum intersectione. a quatio posterior digesta dabit:
(+ =) VX (1+) fV + 2 X - daque = 0)
+(+ +). (+ +)aq
Convertatur aequatio in proportionem, utroque ejus, ut initio
expressa est membro, tum per y, tum per a F X,
diviso, fiet:
d(+ +) v.1
f+ f) f (+ +) X
a + ZX
Ut rem numeris probemus, ponamus. a- 1..
fier 1(3  (t )4 (. n
= f. = 2 - 12
es- - f E 2 - 19 2
104e3 -51-6152
 - 14
34 36.
2 X =  - Z -a
a- 9t Say osae s -  (1  et
in (irulo po Z = 2, fiet: a - X - 47-
(11) fot1F) XV cplicetur 
X u circulo = g- ta y
fet  - 4+ 5a s = cy - ad r 4d
Ergo add = cs = 2 cy ad 4 2Cyqd
Ergo ad-  cy, seu a d = cy +39
seu adr
Sa( 4(1) 4 ras, +a
=2 19 16
B - - 12 - - 3.
(1X) 1 (+ +) +
d =  =
(+4) f. (3. +) =4 .. .. (+ +) 
M
a
murim
+DFC + Fa d
2 A m- vd
. et
et 7= cy su es posite V de p 
 d+ βy
erit Z et y = d fict Z= cY - cd ad 
+ (++) s. C
d +23
vel + Eg + 9+ X - =  a
sit Hypertola cuus rectingulu
ACE= F cdq
abscissa FA = EC  sit Cd- 3+ - y
Applicata FE = s AC sit AB- + c4 +4, + BCX
Sectio lonica GC, cujus abscissa X = GD,  = BC
applicata DC- y est DC, erir
t quaesita, puncto intersectioniss
Hyperbolae, et sectionis Conicae hatae
de terminata,
+ (es (+ f da (+ f) 15) syA rayi  (t +) olt +)da Substibunu p (3
e
= cdga
+Y- -1 + 4 si +(1 +) cg +91 X -  q 
(+ +) da X y
(+Fda + y
X =+C d.
(Guadutum de +4 + X, est -
+1 44) Sa 13Y ad a ( ) adays t
mnliplicetur utaque aequa troni pars per L( +) da +yV, D +9+X
fiet = c0
d- 2day) + da
aqu +ya f - aq +74 23 a (+ +) 2da) +7)
3a (++) adayY + y)
2t Ctda
=, D + A (+ X) + s a
(1) cqda = cqty + cqda
et Cq C etc = aqu F v  etc = S (20). (+ +) das 9 = r9V 4) da
eu altogda da i
 er pra tlpsir e
144 - 95 = 49)
122 243
 yx (( () foda
dit
++) 1=
fiat a + x
.. . . . . .
4K4
. X = 3. 1 =4
+fi + (+)t
- 3524 - 35 2
Edle 20
 v = 5 - 12. = - 7.
Y = = 7 - 5 - - b - 4 1 = 5
B5 a2 12 +5-
70 + 120 3 + 41=7
324 = 24
 (s)- 5 - 2
35-60
+ 2= 3
85 156
(+)(+ +) 4 4
et habebimus: X.
----.-
B....... -- r - ∞
(+ +) a ( +) +
ABLIEEHEE
BV
12  5-2+
5412 7
1+2 - 7
3535  9 - 5b + 120 + 95 = 14 5, 24 - 16,  2   49
62q
25 235 - 1225, -
c 49 diffi - et 1
6549 24
35(X4357 134 136
+5- 3C2, +92 ~4 4533, + 933
f 18 + 30
st
a