92 
PROFESSOR CAYLEY ON THE CURVES 
(l,l,l)(l) = (l,l,l) m (l) TO , 
A= 1 
B= S(n— 4)m, +^(^--2), 2 
-+-mm 1 (n—2)(m— 3), 
C= r(m—4)m 1 -l-nn 1 .%(m—2)(m—3), 4 
D= i(m—3)m 1 , 3 
A'= «„ 
B' = r(m— 2), 
2)(w— 3), 
C'= cS(w— 4)^! +mm 1 .-|(w- 2)(w— 3), 
D'= fc(n—3)n r 
( 1 , 1 , 1 , 1 ), =( 1 , 1 , 1 , 1 ).. 
A=-p(S— -1), 
B= &(«-4)(ro-4), 
C = r.^(m— 4){m— 5), 
I)= ;.i(m-3)(m-4). 
1 A'=ir(r-1), 
2 B'= r(ra— 4)(w— 4), 
3 C'= 4)(w-5), 
4 D'= -A.\{n— 3){n— 4). 
43. Secondly, we have the point-pairs : — 
E, tangent to curve from intersection of two curves or of a curve with itself (node), 
and terminated at the point of contact and the last-mentioned point. 
F, tangent to a curve at intersection with another curve or with itself, and terminated 
there and at a curve. 
G, common tangent of two curves or double tangent of a curve, terminated at one of 
the points of contact and at a curve. 
I), ut supra. 
H, line joining cusp of a curve with intersection of two curves or of a curve with 
itself, and terminated at these points. 
I, line from cusp of a curve touching a curve, and terminated at the cusp and at a 
curve. 
J, Inflexion tangent of a curve, terminated there and at a curve : 
and the corresponding line-pairs, viz. 
E', point on a curve in common tangent of two curves or double tangent of a curve, 
and terminated by this tangent and by tangent to a curve. 
F', point on a curve in common tangent of this and another curve or in double tangent 
of this curve, and terminated by this tangent and by tangent to a curve. 
D f , ut supra. 
H', intersection of inflexion tangent of a curve with common tangent of two curves 
or double tangent of a curve, and terminated by these lines. 
I', intersection of inflexion tangent of a curve with a curve, and terminated by this 
tangent and by tangent of a curve : 
and this being so, 
