The advantage of Areal “over Cartesian coordinates is in the greater symmetry of the analytical forms, and in the more convenient treatment of the line infinity, and of points at infinity.”—Cayley, Art. “Geometry,” Encyc. Britt., 9th Edn.

So many questions either directly on Areals, or easily and elegantly treated by means of that system of coordinates, have appeared in recent years in the various Entrance Scholarship Examinations that no apology is necessary for introducing such questions into the following paper, which contains solutions of all those set at Cambridge from 1894-1900.