86 
A Proposep NoTATION FOR THE GEOMETRY OF THE TRIANGLE. 
By Rost. J. ALEY. 
Everyone who has studied geometry very long has felt the need of a uniform 
notation. Much time is wasted in getting acquainted with the notations of dif- 
ferent authors. This is especially true in modern pure geometry, where the 
figures are necessarily complex. The notation here proposed has been success 
fully used in the schoolroom. It is partially used by several well-known writers 
on modern geometry. It is hoped that its simplicity and system will commend it. 
Let the triangle always be lettered ABC and in the usual positive direction of 
mathematics, i. e. counter clock-wise. Designate the sides, opposite the angles, 
a, b, c, and when necessary to refer to them by number, use 1, 2, 3. Particular 
points are made the basis of the notation. An example will make the method 
clear. 
Suppose Z is some particular point. In studying such a point we usually 
need the points of intersection with the sides of the lines from the vertices through 
Z, and also the feet of the perpendiculars from Z to the sides. We designate the 
first set of points as Z/a, Z’», Zc and the second as Za, Zn, Ze. 
For the particular points, the symbol most frequently used has been im 
general selected. 
A 3 C = vertices of the fundamental triangle. 
M = centre of the circumeircle. 
Ma Mp» Mec = mid-points of the sides of the triangle. 
I = centre of the inscribed circle. 
li Ie Is = centres of Ist, 2d, 3d escribed circles. 
TI, I» Ice = points of contact of;sides with inscribed circle. 
VY’. I» Ve = points of intersection of AI, BI, CI with the sides. 
Ihe =i» Sie = points of contact of sides with Ist escribed circle, and so on. 
G = centroid of ABC. 
Ga Gp» Ge = feet of perpendiculars to the sides from G. 
K = symmedian point (Grebe’s). 
Ka Kv Ke = feet of perpendiculars to the sides from K. 
K’, K’» K’e = points of intersection of AK, BK, CK with sides. 
Ki Ke Ks = Ist, 2d and 3d ex-symmedian points. 
Kia Ki» Kic = feet of perpendiculars to the sides from K, and so on. 
K’1a Ks» K“ic = points of intersection of AKi, BKi, CKi with sides, and so on.. 
H = ortho centre. 
