In teaching Analytical Geometry very little attention is often given to the interpretation of the form of an equation, although this may often convey a good deal of information; by grouping the terms of an equation in different ways, a variety of useful and interesting results may be obtained with very little labour.

Some suggestions as to the possibilities of this method may be afforded by the cases given below. A considerable number of results are obtained, purely by simple manipulation of the general equation of the conic section in point and line co-ordinates. Except in one instance, no reference has been made to infinite elements; if we include the notions of infinite points and lines, and of the circular points, the power of the method increases very greatly. The only knowledge that has been assumed is that which is quite fundamental in point and line co-ordinates, and the meanings of certain simple typical forms.