of the conic Sections . 473 
Now, if 10 be written for y in Theorem IVth, we shall have 
A = 
B = 
C = 
H. L. 
- 1 
VO’y+O 
zyy 
-v / (rv + 0 
Ay* 
2 
_3B_ = 
4 
— o 0938,341, 
— 0-0003,323, 
— 0-0000,020; 
of which terms, two only are wanted to obtain a result true to 
seven places of figures. And then, ee being = aa + 1 = 50, 
we have 
+ — ' 
^ 07 +U =71-0633.520, + _L A = 0-0070,593, 
0-0000,001, —d=6- 7989,144, (Art. 21,) 
2.4^ 
B 
sum 
of the posit, terms J 1-0633,521 ; the sum — 6-8059, 737 ; 
neg. term, and correct. — 6 * 8 059 * 737 ’ 
the difference is -j- 64-2573,748 = %. 
Example v. 
27. Let a be given = and y = 10, to find z. 
This example may be computed by Theorem Hid, IVth, 
Vth, Vlth, VUIth, and IXth ; of which the IVth, Vth, and 
IXth, are more eligible than the other three. I make choice of 
the fourth, on account of the facility of the computation by it, 
with the present value of y. 
Now, by writing 10 for y in Theorem IV, we shall have (as 
in the preceding example,) 
A = H. L. — — ■■ === — 0-0998,341, 
B 
C 
— VCy.y+O a 
zyy 2 
—• Vby-A 1 ) 3 e 
Ay* 4 
— 0*0003,32 3, 
— 0-0000,020 ; 
and then, ee being = aa -f- 1 s= we haver 
