Triangles with Sides and Medians Commensurable

Extract

It is economical in the use of symbols to express the sides of a triangle fractionally, by dividing the expressions for a, b, c given in my previous Note (Gazette, XXIII, October, 1939, Note 1398, p. 380) by qy. Thus writing h for x/y and K for p/q, we have

a = hk + h − k + 1,

b = hk − h + k + 1,

c = 2(h + k),

and n = hk − 1,

where l, m, n are the medians bisecting a, b, c.