| dc.description |
1. The invariants and covariants of a system of two conics have been much studied<sup>2</sup> but little has been said about those of three conies. Three conics have a symmetrical invariant Ω<sub>123</sub>, or in symbolical notation (a b c)<sup>2</sup>. According to Ciamberlini<sup>3</sup> the vanishing of this invariant signifies that the Φ conic of any two of f<sub>1</sub>, f<sub>2</sub>, f<sub>3</sub> is inpolar with respect to the third; and in a previous paper<sup>4</sup> I have derived by symbolical methods a more symmetrical result, viz., if Ω<sub>123</sub> vanishes, then u being any line in the plane, u<sub>1</sub>, u<sub>2</sub>, u<sub>3</sub> are concurrent, where u<sub>i</sub> is the polar with respect to f<sub>i</sub> of the pole of u with respect to Φ<sub>jk</sub>. |
