...(Grelle, t. xxviii. p. 97.) In fact, let £7, = 0, Í72 = 0, U3 = 0 be the equations of three conies, the locus of a point such that its polars with respect to each of these conies, or indeed with respect to any conic having for its equation \Ul + ¡iUí-\-vU3...

...obtained thus : Take any arbitrary line ax + by + cz, and equate to zero the determinant V = a, &, c This equation represents the locus of a point, such...in which a point common to U and F can lie also on v 5 v'z- either the assumed line passes through an intersection of U, F, or at that point the two curves...

...otherwise obtained thus : Take any arbitrary line ax 4 ly + cz, and equate to zero the determinant V = This equation represents the locus of a point,...plainly only two cases in which a point common to U and V can lie also on v ; viz. either the assumed line passes through an intersection of U, F, or at that...

...the Third Class, Crelle, tt. xxviu. xxxvi. and xxxvni. [1844, 1848, 1849], has shown as follows : (a) The locus of a point such that its polars with respect to the three conies X = 0, Y = 0, Z = 0 (or more generally its polars with respect to all the conies of...

...Crelle, t. xxvin. (1844), p. 97). In fact, let £7, = 0, Ut = 0, U, = 0 be the equations of three conies, the locus of a point such that its polars with respect to each of these conies, or indeed with respect to any conic having for its equation X[/1 + ^[75+ vU}...

...first circle which goes through P. Hence, (by considering the orthogonal circle of three circles as the locus of a point such that its polars with respect to the circles meet in a point) prove that the orthogonal circle of three circles, given by the general...