Published on behalf of The Mathematical Association
The locus of the points of contact of tangents from A to the conics of the confocal system with foci B, C is the same curve as the locus of the feet of normals from A to conies of the system. For any tangent AP to one of the conics is a normal AP to the orthogonal conic of the system through P. Hence if the coordinates of A referred to BC and the perpendicular bisector of BG be x0y0 the equation of this locus is the eliminant of λ between
In all the English text-books on Analytical Trigonometry, so far as I know, the power-series for cos x; is obtained as the limit, when n tends towards infinity, of the finite sum for cos x,
where 
and the number of terms is equal to the integer next greater than 
. The power-series for sin x is obtained similarly; the two series and the method of finding them being both due to Euler.