■ H i
- — ^ . —
ON THE RECIPROCAL OF A CERTAIN EQUATION OF A CONIC.
523
541]
or, as it may be written,
i 2 66'c"c'" + 2 6"6'"cc'
{X (6c' - b'c) ± /x (b"c'" - 6"'c")} 2 + 2\/i - (bc'+ b'c) (6V" + 6 /,, c")
(+ (be'— b'c) (b"c'" — b'"c")
Taking the upper signs, this is
{X (6c' - b'c) + fx (6"c- 6"'c")} 2 + 4X/a / 66'c"c"' + 6"6'"cc'
V- 6c'6V" - 6'c6 / "c"
viz. the term in \/x is
+ 4Xya(6c"'-6'"c) (6'c"-6"c').
Taking the lower signs, it is
{X (6c' - b'c) - /a (6"c'" - 6"'c")} 2 + 4X^
viz. the term in X/a is
66'c"c'" + 6"6'"cc'\
6c'6'"c"-6'c6"c"7
+ 4X/a (6c" - 6"c) (6'c'" - 6"'c').
And it is thence easy to infer the forms of the other coefficients, and to arrive at
the foregoing result.
66—2