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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 321r, page id 00067993:0643
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(1 (13) (1) est autem rB A
Esto non Hyperbolica ABC. cujus, centrum A. Asyngtoti
Ad. Scimehio dimmeter EAF. Semuilatus trans versum AB,
en ommordinata
0 eique aequale semilatus rectum AG. applicata ad axem, diametim
exdiametro ; et  puncto curvae ordinata ad curvem BH. abscssa
mptota HS. positaque HI= HE. erit 1B. tanens
quae proluicatur, dum dccurrat Diumetio conjugatae in L.
et opsi diumetro in M. erit resecda AL. intervallum Tan-
tentis a centro in Asymptota 1E. intervallum ejusdem a
jum ut ad calculum accedamus, constat IH esse = HC. ex
daen natera Hpabitae GA- EA ex Hypothesi, Recrangulum
BHE a AN +d
ex na Hytolai uni
H GA= A+ exhyporesi idcoc ava est
dr 1By5 = AN= a
(1)C I QA = FC
n. Aer H X Ea Io n
()V MEB:. Ylo MAL.
(6) Eopes Su Bebecta AL  r B Nm = ErB    D) sota, Lm - sot N 
t oprisM
(7) Et quia D 3F- oA + AF. dOA = Z AE. L AE = At  XN2AN- rea
(1) ideo erit FD L et posito FA - X. et FB = y. et AO =b
 () ideo erit AD - b = 2 s2 a = 10 a
(10) d +D = y = b+ X, CX = bx + X NSaX  X. 1 y 1- xab .
1(1D posito item EA = W. HB - 7. erit per 
(1) erit per 3. Woq= a et H_Z
et poa HG- M lnc  F Y AEAFE - _ FE, sive Fs = X + 
(15.) et Am  tx + 8 - X = bx + x- x - 
oc M b s (16) Et ded per 15 qualta 6. erit p Resectu AL = sX + X A
sa bx 2b
abX v 
 ductui ib t, vet
laq pive AF-
centr
deahus erit et t sspe icularis ex vertice in Asy mplita s
tise canscur
JH = HE
Ergo Sy b = X)
+b 15+E L = 2X.
FE  quia s A qur ea quae dabet Auzutus apud se hoem.  al. 61. Cartes Geom. p. 245.
AE. 1-
Xex +6X
ponalur
2b + 2X
ismu at s.
et AL = bX + bx
ab + 4x 4 8bx.
e+ AL  -bx 4 X. Esposito b.. f.x
b+ X+bx
M fies, mbest nx + 2mbx = bx + X, fint f b+ x habebimus:
barab  n + m bx L fX et prot f+ X sunto g. habelimus et pro f+x sunto g. fiet
a  seu mb4 amb Mbs mxsatio XC X ponams f. b + X hubebem:
mb + mx + m bx  fx mb + mx + 2 mbx = bX + X b - spro X. ponatur m+. f. hateliuus
mo + nx + xmbx = b im + fn, + XbC xmb + sxb
alesest
inb ans = bf - b pro bf - b ponitur Cf. scibed e. posita ostat
nde sim un  pralis potius b - f = 9. fiet - 8b
fiet ande imb + his. = cf sive mb + nisX = Cf X, vel mb = ef x - mfX
 podendoque fx = g. pe mb  cg mg. sive  denique c. m
potius gro X = f2 2b1d
mx + 2mb= t Xh
s.6 eeraudla s
mpb
s 6
ne ou b  b. eut
ie ergo enor  alculo
sequitur alfdum
hg, et hg = Yd y, ad nunc hiteris Cartesianis enuntiemus, fiet: Xa
9 Alit mehodo tentemus idem, ut fer apparecte veridas: mb A mx. + emb = b + Xb posito in b18
ium mb posito rn. suit m - nb. fietque rike = Hb- nb
.= b imb
ertto l- i - 2m.
bmt
runque hatelimus nbi F mx = lbx. conamus b + x = n. fiet pr= lb X, fet mn = bX + bx.
nx + 2mb. = H + xb.  imb + mf. = ls - b
.
x = f- 26.
fiet imb = nf = b vel b  nsx - b
m = q fiet qn = 2mox
adxia
bdlen l
xxb bn = nr + 2nXb. = b = - b bn = 2 X ln = n7
ed.1
er    X Xb pbo bt un L B, fe) b hbum nX
teser 11 = r∞ 4
Ex +b
tn rex co- sbxt
in l ibsp e cen
alteri us sde
Hs ad dium
2X A ordi
desectae. Ergo
ed uc
x+ H b 1 Xb =
4b2X + 4b3
182 sbx + 2
3 posita 3, fiet:
abjaecta  9
dici. y + b-C
si + - X
sive su
ot
Cx + Xb - 2m bx = Mh =  (+ 14 X
nx+nb-2mbx= mu
n. = 2 m bx = mn seu - mn= 2nlx