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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 349r, page id 00068196:0693
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jam ope aequ 12, 5, tollantur 2X et 2X
in Ellipsi  vel Hyperbola sit L centrum fietus LG AGAG ad G
ge 2rx + pXX = yy sit XA  Z  X +4 seu X- (. 9 fet 21 Z 19+ 7  (2 4r 
Hinc
seu yy = xZZ- Y9 seu AG. AG = r (LG. 1G) - r
Ce= sint LG, LI, LN, LP, LZ, Et GA, 1B, NC, pd, 
W X 3 Z
(V), (1) (X), (3)  (0(v) 00- r
ee = qut B = vv + W01 - 2∞WV + Y vD + ruI 29 - 2 ((rVV - (, 19, Y 0u -r9)
qu. BC = qu AB= WW + XX = 2WWX + Z WWW+YXX -2r9 - 2 +(rWI -193 Z XX- 19)
LGe. D tG + LIqu en  G. La) C . 2. 15) - (15 - 1A) (2E1 4 7 + C)
ff = qu AC = vo + XX - 2 Vx gF 00 + Z XP - 2rq = 2 +(Z vV - r9, Y Xx r4)
ope harum trium aequationum tob debent W. et x
Ex aequ fiet Cel  c v irq  at vrrrvo- 2
ee = (1) v0 + Wo - 2VV + (V(V) + (1) (10) - 2 f 11)
ee = (2) WWW +XX = 2WX + (o po) + () () - 2 () (X)
ff = ( VD+XK = 2VX + (v (V) + (X) (X) - 2 (V) (X)
Oste rarum trium aequationuu posunt tolli W0 et x; sed
remanente v. sed video jam praestare omitti tertiam aequationem
solis adhibitis prima et 2da ita ut maneant v et X, sublata
H
vn F W0 -2u +(V(V) ((10) 20) = 2(∞(10) = (Wou XX BrWOX ((o (Co  ( (a) - 2 ) (X)
1) + (V) = B
 et 2 C  ) -1
vocemus am
sum solum media W. Erita
int n 2p () e et q posito
 
seu un-rxho+ (V ()- 2(∞120
compendii causa vo B() () + XX + (X) (X
Wo esse radicem, fint aamm- Jamno + annioro = ap uto). F
V) - 2(X)
in Hyperbola est (1) (10) = Wco = rq et fiet aamm -4amnuo + annioco = apporo
3C
o) (u)
e5lX=
=4 pprq compendi causa aa seu Ce W0W + tamn W = aamm + IPX YI
op. 4n pV
pp - nn =(X) + (vYV) - 2(X (V)  - XX -vn + 2XV
seu (XX - r9 (t  vD -rg = 2(4) (V) (XX vV) + 2xV
App ann arb
in =IL 2rg - 2XV)
et am = - vv C∞ - v) v) + Xx + () () = vv + 2XX (= r9 Frq
am = X+V, X- v et =amn =  ~ + v)nu X+Asi
sit fiet: itaque positis X+V, l; Et X V, n; set (X) -(V), p. et = am = 1a
seu am = 2 (v0 -XX)
Inn
2rg - 2Xv + 2() (1)
fiet oi 
W
+) Una + rg que ) rare
 814 _ 8, r9 - X~ + () (1)
lavenietur e per alterntiam
1 vel 2. ita datis punctis extremis et et C, habetur medrum B
inte invento ergo valore ipsius. W, per a g. 4
sit jam tertius valor ipsiis ee aequatione sta
adeoque et AB et CB aequales.
nempe
ope harum trium aequationum 1, 2, 5 tolli debent literae W et X. jungantur aequationis
ee -5) Xx + gy
=Eyx +  () + (5) e3) - 26 (s)
2 et 5, fiet 18 1d + XX ad instar aequrtionus 3, Wov - 21oX H(o ) (1) - 2 (0 YX) C y - 2 Xy ~ 1) 17)- 
d = jungatur aequ. l et 5 fiat eeraroro - Wto 4 (r) C~) H ) 10) 2(1) (o) = XX 49y - 27X + 1Y) (Y) es) () 2B
unde Wno + (1) (1) = = VV + 2vW- 1) L 2(V) (1) + XX +yy. 2yX 2(1) CX) + (y) Cy) txH)
 + 210X 4 2(10) (X) + gy - 27. 9 + (1) () (Y) (7) q 3
Ex 6 est (20) = (X)+ (9y- 2Xy +(XX + (7) (7) = 2 (4) (7) = 1010 + 210X)
qui valor conjungatur cum sore aeq0 (((3)
Aequandoque duos valores fit:
hinc quaratuo
valor ipsius ro
V 2v0 + (n) (n) - Xx = 2op C (X) (∞B - 2(X 1V) +(3( 6) L (yy - 2p7. etc)
Pro V, 10, X, 9, Z scribamus 12, 12, 13, 14, 15 etc L. v + X = 113 X B = 13) -
2, 23, 24, 25 et 5- (∞) (X) - 213 (∞ (∞) = 231 -
Ex apo Ex arq. (3) fit nB-2MId,: Ep = (ut seu substitulis numenis
21
2(∞) - 2 (X)
(1), (20), (X), (1), 2)
Ex 1et 2 e L    113. 131 Y 213. 231
Et ex 2 et 5
similiter
mus
12t. 192 +224. 242 - 2. 132 1
135, 1534235, 253 - 2 153,14
 = 2. 131. 12 - 2. 231. 22 -0
2.292. 27
2. 262
146. 164+ 246. 264- 2. 164. 15 - 2. 264. 25
Co
qury qy 1
349