of the Hyperbola. 
141 
f • . A 
1 a x : l + 
' 1 aa 
-3 B i _5 C _ -7 D _ ; .,9 E & 
a* ^ a 6 a 8 * a 10 ’ <XU 
r/ = < -}- a x : — 
aa 
. » y 1 ® 6 o 
+ ~ — — -r ~ ’ &c ” 
j Sr 7^ 1 9 £ 
+ + — > &c * 
+ d/x : — £- ' - sr ' 91 
8 aa a 
2 A , 3 . 4 B 5 . 6 C , 7 . 8 D 
8 o! ’ “^ 7 ” T 
d = dtf < 
• x. o 
"a 
+ 
a 3 
_£ 
6j9 
9.I0E 
a 11 
1 Os 
, &C. 
4. !L 4, & c 
^ a 7 flS a 3 * » 0601 
a J 
— 2 a 
a 
_ -iL + 
a 5 “ 
+ /:x^-“ + 2# 
57 
a 7 
4. 
fl 7 ‘ 
zi . 
9 T 
9 £ 
a 
7.8* 
a 11 
9.10s 
" «“ 
-, &C. 
, &C. 
The last two equations, more concisely expressed, are 
r 
j . 1 
a = a <( 
1 
i -K x : 
A- a 
aa 
a 
aa 
3^— £ I 5 C ~ 7 
n* I' 
2 E.-L 4. 9 E -i & 
1“ /y I3 J OCC « 
3« 
_s_ ___ - V° 4 _ 
T fl 6 a 3 -t- 
7^ 
a 
9 £ 
&C. 
H 
1 
<c 
3 . 4 B — 76 
5 ‘ 6 C — 11 y 
! 
7 . 8 D— 15 ^ 
9 . 10 E --19 e 
a 3 8 
a s 
a 7 
nr 
a ' 9 
a " » 
oCC* 
— 2 a j, 
3-4 e 
5.67 
+ 
7 . 8 ^ 
9 . 10 s 
O r /> 
a* T 
a* 
a 7 
a 9 
a" 7 
OtC. 
L 
r 
y • • I “ 
d = a a ■( 
[+/x: 
These values of d, d, and d, being written for them in the 
equation add -f- (-^ a) ad — [aa -j- 1 ) d = o, and the al- 
gebraic and logarithmic terms severally collected together in 
two parcels, and the whole divided by da, we have 0 == 
a — - — ■+• - — — — — -j — — — , &c„ 
■ a 
+ 
+ 
+ 
B 
C 
J 
D 
a 3 
a* 
a 7 
J 
3 b-s 
v-a 
0 
1 
7D— 
4 
-f- 
« 3 
i 
a 7 
4 ” 
A — a 
3 B-g 
4 - 
5 C- 
7 
3 
a 5 
a 7 
3.4B— 76 
/>3 
4 ° 
5.6C— Ily 
7.8D— 
,j 7 
15^ 
ao 
' 9 e- 
+ 
2 A — 3* 
a 9 ’ 
a 9 
7 D_4 
a 9 
+ 
3 . 4 B — -jQ . 5 . 6 C— ily 7 . 8 D— 15 ^ 
* ' a 7 1 j 9 
at 
&C. 
& c. 
-, &c, 
, &c. 
a 
