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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 178v, page id 00068195:0356
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sit eadem sectio conica, in eodem plano aliter popta, nempe
LY, priorem AY secans in Y. sit novers vertex  Axis LZ.
priorem secans in M ex L in AX agatur normalis LN. et fiant
AM, LM, MN, NL, +LZ, a Z Vagus N AX XY. AB BC
5
m
n,
Etprius
secet  ZY, ipsam AX in Q., erunt triangula , MA L, MZ Q, YXq simitia.
Est autem Z M = l - Z ZQ = v - QY et qY = yl:m p. ZQ = v - yl: m
QM = Z M, l: n fit q M = l. Z l: m YY =  X Q = yn: m
_ZM: ZQ = m: n Ergo l- Z:, v- ytm= m: n.. Rursus
AX + XQ + ZM = AM, fiet X + yn:m + (L. Z)lim = B, Ex his duabus
aequationibus habemus l - Z = vm:n - gl:n = pm: L = Xm: L - gn: l.
seu v = pn: l = Xn: l + y (l- ua, :Ah) n: m, -) m: l seu B2 (p. X) u tym, : l
Et ex aequ. 2 fit z- Xm: l + gn: l +l - pm: l  p = m -9, et
l - pm: l eit l = mn + gm, : l = nn + gm,: l, sed relioquendo p, fit
Z= _ l. + gn: l - (p- X) m: l
est generalis pro quacunque curva;
Et dic quidem Calculus
jam habuimus 2YX + LXX = Gy et (bersu +(14Y) xy = rC + = CX
Et ob novum Conicaesitum, habemus 2rZ + 7 22 = vn. pro quo valore
in qua aequatione pro Z et v, substituamus valores inventos, aeq. G et 4
fint 2nl F Ergn: l - 2r(p. X) m: I + ell fr yynnill f Y (ep 2pX + XX) mm: V) 2Xay (2 7 (p. X) M fer y a m . )
aequ. ponn.l - 2px nnill + Xxnn: I + gymm: I + Epyn L + Epy n. l - 2X7 nm: I
seu
Aequationes 6
XX - 2 panu -rpua X rm By + px ru. 1
mip. s. 99 p naxy
e
=20a X Agll. 9 - 2il
H2r mapX
non X  aG + EU
tirumpus Fuptum
+umupus
Aequationes 6 et 7 quae libet multiplicata prius per constantem arvitrariam ett
addantur in unum; et aequatio inde resultans identificetur
aequationig.  ita invenetur situs novus Conicaedatae
Termidentilicandi sunt sex, nempe XX, yy, xy, X, y,  1
AYbitravia sunt, l, m, p, Y, E
itaque verlor ut res succedat
llites
Sed ita una arbitraria deficit
+p+G( +  +B = 0 = aequatio ad est Conicam datam +r, sum najiat
+ Z mm. un ZZ 1 + 2 mA7 sB cirx a1, 12r p  F 2it  - 0
+r un nom ur Hix mui
Zflo - 2+ p2+5
qu
t
aa
+22 m trrnt
TEl. 1
+Z1 l e fy  =
s  t- e y f, X0 + X3
roo + +d +9n + ah =0
Zt x t _ vo + gv + 79g - gg - . f- ah
23= 1711
fit 2EErpEes
pZ
= a.  v - - 29 +3 (1  52 = a1)
AN, H