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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 34r, page id 00068196:0067
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Ad lineam Conieam
Ad lineam conicam AY(Y) 
ec ducenda est ex puncto dato B
minima BY. sit vertex conicae A,
axis AX et ex puncto Y ordinala ad
Axem YX. Ad eundem ic ex puncto
dato B, perpendicularis BC. quae data est ut
et AC. Vocentur  latus rectum Y, latus
transversum t, abscissa AX x Ordinata AY, y. BC, b
et AC, c. Ex natura conicae fiet rat x -
2rX + ZXX = 1 = gy. Ex Y agatur normalis iB YN in BC.
Eritque  YN, X -C; et BN, b - y. et ex natur a per pendicularis ad conicam, erit
X - C, :, b -y = dy. x Z = dy: dx. Ex aequ. 1. disferentiando fiet rdx + = Xdx = ydy
seu dy: dx = 3 = r + FX,: y. Ergo ex 2 et 3 fiet X- C b -y = r+ ZX, : y
sive
br + bF X - ry = YXY Y = 4 = 0 sumatur, alius Axis secundarius per verticem
vel compendio br +b X pG F y
48 et in eum ex h agatur
3e nocito p ransient, et 
WI. Ex Pagatur notmales L in AX, et hop
na EM in YX. et Angulus autem X A sit talis ut AC: L8: A seu YM: M P: YCG
normalis Y P, et vocentur A
sit = e: f: 9. et ee t  = 5= gg. Et fiet AX seu X = (6) GG (An A_) + FW (seu QM)
et X Y seu y = 7 = fW (seu YM) = f (eu 8L). Is ipsarum y et X et valor
substituatur in aequ. 1. fiet
2YX =
 Z XX =
yy =
9 et qu + XeC 99 + F f W010 7 = 8 -0
2re  + 2rfW
+2 efg gW - sF q- ee WdW
ab mb m su
bx =
y
moses ampro tunga
obse
fiat compendio c-r =9=  et
9= 10 Y. l et ex aequ. 4
fiet
nggio
fint compendio c- r = g = p et 4- 10 = =  3d+ et ex oqu4 fiet
+gexy
aequ. 4. fiet br + brX +py +9 Xy = 1 = 0. Hac multiplicata
per m: e et  explicatis  X et y per 6 et 7  addita ad aeg. 8 dabitcio
mbr = m br
x +bmreq + bmytu
2
n py=
me. r9 =
et 9.
mPF e + mp W
XD
+mg ex gro m
-ma ff qW
e
ss Wol
88 et 101o aequales et coeffi
ciens ipsius gio debet esse 0. ob prius rff - tee + mGS. At m tec r5s, : 9s
eo
b debent esse coefficientes ipsarum Edu
tarsis = rec bsf14 = ree - tff - mg F seu M = trCr(ec Ss) 1l (eC 55): 2f
seu M = r t (e r+t, ee- H, :, 4t, et per 10 fit m = c 15 = ff- ee, : f. Rursys
quia pu debet destini siet 2reef + 2teCF + mgee - mq ff 16-0 et fiet,
quia =g = r+t, ideo divisa aequ. per r+t, fiet E0Cf - m(e0 - f7) =
seu fiet
m = 2eef,: ee- f5 seu  et aequando valores fiet 2e(f= - (2) (e C- sf) quae
aequatio ions est impossibilis. Non ergo licet aequationem3 adaptare ad circulum
iaq sentemus an liceat aequationem secundum  itaque non licet efficere ut circulus
quaesitus et onica data se secent in puncto quaesito. Rem ergo revocem us
ad aequationem unius incognila ex aeq. 11 est - y = 18 = bYt F brX,: tp + qX
seu yy = bbrr EF + 2bbrr Ex + bbrrXX,: tpp + 2t GpX + 49Xx quem
valorem substituendo in aequ. 1. fiet bbere abbert X + bbrYXX Mlaquatu
J19
=0
Aequatia ad Conicam
circulus inven
bbr+ tt + 2bbrF +X + bbrYXX
tur consituens hanc aequationem
cum Conica data,
+ NIBBXX + 2Y qpX3 + Z99XV, intersectiones non debet C
CTItDB X F LYHC X
2Y H X + iFgpXI + 2t 49X
sn 
3
aliae quonenda sunt sufficit qu retineriX.
Hai ta g. db 47. ob aequo est W0 - Xx~ gua v. sit aequatio conia
XX+ DV+ (XL XVI XX + compendio fias et WK 34 +33X +32XX + 31)
3+30=0 et conicam
bee C i ∞ 100+ 10Z + 101V += 14-vv0 quae multiplicetur per
et pet rocirg
2107+ 201V(23 +Vn =0
o t 27 n  1. 10 + L H. o, X BV 4 1F 3. 1uVZ
aequa podit quaeante Jog ne v
10. 106 + 100 + 110 Z+ 0. v   (X + 1)Z2. A =0 etfinta
oa q aatsiconide eec reds. toccror
-1
e ase
muttiplicata pet
 fiet o
Cpp + fint com
dacamaequad data sit
10
sit aequatro ad circul
multipli pute per 24 ej 7 1202
ideo
datam m