85 



Hammond and other lloui'isliuig- cities in the northwest part of the 

 State would experience the most direct benefits by the increase of business 

 and manufacturing facilities and consequent increase in population. 



The proposition is worth at least a passing thought and is commendwl 

 to the State and general governnionts for further consideration. 



Some Peopekties of the Sym.aiedian Point. 



By Robert J. Aley. 



Monsieur Emile Lemoine, at the Lyons meeting of the French Associ- 

 ation for the advancement of the Sciences in 1873, called attention to 

 a particular point within the triangle, which he called the center of ajiti- 

 parallel medians. Since that time a number of mathematicians have 

 studied the point and have discovered many of its properties. The point 

 is such an interesting one that a brief collection of its more striking 

 properties may be of some value. No claim is made to completeness. 



DEFINITIONS OF THE POINT. 



1. The point of concurrency of the bisectors of all lines antiparallel 

 to the sides of the triangle. 



2. The point of concurrency of the lines isogonal conjugate to the 

 medians of the triangle; that is, the point of concurrency of the sym- 

 medians of the triangle. 



3. The point within the triangle, the sum of the squares of whose 

 distances from the three sides is the least possible. 



4. The point within the triangle, whose distances from the sides is 

 directly proportional to the sides. 



NAMES OF THE POINT. 



1. Center of antiparallel medians, proposed hy Monsieur Emile Le- 

 moine. 



2. Symmedian point (sym§diane, from sym6trique de la mediane), 

 proposed by Monsieur Maurice d'Ocagne. The Engish form "symmedian" 

 was suggested by Mr. R. Tucker in 1884. 



