560 
ON THE TANGENTIAL OF A CUBIC. 
[157 
10 = 
b 2 c - 1 
be/ — 3 
bci 4 3 
be 2 + 1 
bfi 4 3 
bi 2 + 6 
cp - 6 
efi - 3 
P ~ 2 
f 2 i - 3 
fi 2 +3 
i 3 +2 
\y, z) 3 
and substituting these values, the right-hand side of the equation divides by sc 2 , and 
throwing out this factor we have the value of £; and the values of 77, £ may be 
thence deduced by a mere interchange, of letters. The value for f is 
X 4 
X 
V 
x s z 
y 
X 2 
l z 
X 2 l 
.2 
a5?/ 3 
xy 2 z 
bj 3 
+ 
1 
bjH 
+ 
6 
bp 2 
+ 
6 
abek 
+ 
3 
abgi 
— 
6 
abeg 
— 
3 
ab 2 c 
4~ 
1 
abcf 
+ 
3 
ch 3 
— 
1 
ch 2 k 
— 
6 
ch 2 l 
— 
6 
abil 
— 
6 
cic/k 
+ 
6 
ac/l 
4 
6 
cib/i 
- 
3 
abi 2 
- 
6 
.fhf 
- 
3 
Pul 
- 
12 
fghi 
- 
12 
a/H 
+ 
6 
a Pff 
+ 
6 
a/gi 
4 
3 
a/ 3 
4 
2 
a/H 
+ 
3 
+ 
3 
ZP 
— 
6 
№ 
- 
6 
afik 
— 
3 
ai 2 k 
- 
6 
aiH 
- 
6 
bchk 
— 
3 
behl 
- 
12 
h 2 il 
+ 
6 
ghh 
“h 
6 
bell 2 
- 
3 
bgjl 
+ 
24 
bej 2 
4 
3 
bhil 
- 
6 
bejk 
9 
hijk 
+ 
12 
hijl 
+ 
12 
bhij 
+ 
6 
bij 2 
+ 
6 
Pii 
-t" 
12 
bijk 
4 
12 
bghi 
- 
6 
bjl 2 
+ 
12 
cA 2 
— 
6 
Phi 
— 
6 
bl 3 
4 
8 
bgl 2 
4 
24 
chk 2 
— 
12 
chkl 
— 
24 
ZP 
- 
24 
c/d 
— 
8 
bijl 
4 
18 
Phi 
- 
6 
Pf 
- 
6 
/fh 
- 
12 
Phi 
4 
6 
c/hk 
— 
6 
flih 
- 
3 
Zghi 
- 
24 
PP 
- 
24 
PP 
- 
12 
ck 2 l 
- 
24 
/hi 2 
— 
12 
/g.i k 
- 
24 
/if 
- 
3 
/hik 
4 
3 
Pa h 
4 
6 
№ 
— 
24 
ZP 
— 
24 
ghil 
4 
24 
/«* 
- 
24 
Pil 
— 
18 
hi kl 
+ 
24 
ghik 
+ 
24 
hi 2 j 
4 
6 
ik 2 l 
4 
24 
/ghl 
- 
48 
ijk 2 
4 
12 
h 2 i 2 
+ 
6 
ijl 2 
4 
12 
/hil 
4 
12 
hil 2 
4 
24 
PP 
- 
9 
ijkl 
4 
24 
P 3 
- 
24 
gik 2 
+ 
24 
h 2 k 
+ 
6 
ikl 2 
4 48 
xyz 2 
y z 
yz* 
cibci 
— 
3 
abc 2 
— 
1 
b 2 ij 
4 
3 
b-cj 
4 
3 
bep 
4 
9 
bc 2 li 
3 
beg 2 
+ 
3 
acp 
4 
6 
acp 
4 
3 
bek 2 
- 
3 
bc/li 
— 
3 
bchi 
- 
9 
bcgl 
4- 
6 
c 2 /h 
- 
3 
afi 2 
- 
3 
ai 3 
- 
2 
b.P.i 
- 
3 
bckl 
- 
3 
bgil 
4 
18 
beij 
+ 
3 
pgi 
- 
6 
begh 
- 
9 
begj 
4- 
3 
b/hi 
- 
3 
b/ij 
4 
3 
c/kl 
— 
18 
bg'H 
+ 
6 
Pi 
4- 
3 
bcjl 
12 
bg 3 
+ 
8 
bikl 
-1- 
6 
bgik 
+ 
3 
pgi 
- 
18 
c P.i 
4 
6 
chid 
+ 
3 
bg 2 l 
4 
24 
c/gh 
- 
12 
ph 
4 
3 
bln 2 
— 
6 
/Hj 
- 
9 
c/gk 
- 
6 
fgH 
- 
3 
bgij 
+ 
6 
c/jl 
+ 
3 
PJd 
— 
6 
bil 2 
4 
12 
/hi 2 
4- 
9 
c/lii 
- 
3 
gi 2 l 
4 
6 
c/hl 
- 
18 
cl 3 
- 
8 
Pk 2 
4 
3 
cfk 2 
- 
6 
m 
4- 
18 
c/l 2 
- 
12 
i 3 j 
- 
3 
c/jk 
+ 
6 
/P 
— 
24 
Pi 
— 
6 
PP 
- 
6 
ckl? 
- 
24 
P/V 
- 
3 
Pgk 
— 
6 
.fgti 
— 
6 
Pgi 
- 
6 
gin 1 
+ 
12 
pin 
“h 
9 
/fi 
- 
9 
Pfk 
- 
24 
gil 2 
4 
24 
PI 2 
- 
12 
gi 2 k 
4- 
6 
/gin 
+ 
9 
i 2 jl 
- 
6 
/ikl 
+ 
6 
hi 3 
+ 
6 
/¥ 2 
- 
48 
i 2 k 2 
4- 
6 
i 2 l 2 
4 
12 
Pil 
- 
12 
gikl. 
4 48 
m 
4 
18 
i 2 jk 
— 
6 
il 3 
4 
24 
and it is not necessary to write down the corresponding values for 77,