C 347 ] 
23. Draw fp, /p, from the focii /, to any point p of the curve; and draw 
the conjugate diameters P p, Q ^q. 
Put pf = z; P /=s®} PC = Tj.Q_c = c; ; ^= y . Then 
pf i —vv=.yy-\-xx-\-2xf-{-ff=.tt+.2fx + ££- w = tt + ff + 2 />. 
PF ? zrzzrryy-J-A-x— 2xf tt — 2fx-\-££-xx— r X'X-\-ff - J -2 fx. 
I xx. 
r- f tc 77 \*tcr>ff 
For yy — ( — xtt cnxx — ) LL. xtt <Jj. 
\it tt 
24. pf=v=z (\/tt+2fx + -^-xx = ) t -{.fix — t -\-fpx — 
pf — z — (\! tt — 2 f x -\-if~xx — ) t— £-x ~t—<px — 
25. pf + p/= 2: + z> =r 2 / rr a <7. 
26. py^-j-pp 1 — w 4- zz — 2jyy + 2*# -f- iff — lit + Ifpxx — 2 TT-f 2y^ 
27. p/ — pf zw — zz rr 4/* =: 1/ + z xv — z 2= 2/ + z. 
28 . FPf~zv=zzX 2 t=^z = 2tz =i=zz =: tt go (pp.xw ~ tt cn xx X —xx 
J tt 
ff tt . CC 2 . 2 
— CC tt IX- yy — — y y-| XX Z C£ 4- £ Q 
cc ce JJ tt . 
rr cc — t x p. 
29 . Let m — t-z — v — t — if- —<$>x— 
— — ~^ X " ■— — — ^tt^zcc — ftt ^zv 
*J cc +ff t 
— s/tt q= cc = f ff ■i- cc’—zv. 
30. Hence k — —v = <px = — — 
t px 
/• 
Andrus — -x —$x~ —x ~ — — v. 
t px J 
Vol. LXIII, 
Zz 
31 . AC 
