Oct., 1887.] ELLIOTT SOCIETY, 183 



The numerical value of the ssides being given the area t may be obtained from 

 equation 1, then the five radii from the equations marked 2, and the three per- 

 pendiculars from equations 3. From equations 1 and 2 may easily be derived, 

 algebraically, the following equation 4 : 



p,—rr'r"r"' (4) 



This shows that these four radii can form three pairs of rectangles, between 

 the members of each of which pairs, the area of the triangle is a mean propor- 

 tional. 



15. To render more complete the present view of our subject, we venture to 

 add the following equations, in order to find any one of the perpendiculars as p, 

 when a, 6, and c are given without first finding the area. 



The perpendicular p falls on the side a and divides it into two segments, 

 whose sum constitutes the side a, and whose difference we will call d. As p 

 divides the triangle into two right angled triangles, we can, by the use of the 

 well known theorem applicable to such triangles, easily show that 



d-=: (5), supposing h greater than c ; 



a 



Find d by equation 5 and then p by each of equations 6 ; the agreement of the 

 resulting numbers will be a check or test of their accuracy. 



16. Lastly, if we now find t by first of equations 3, we may then find the 

 radii, r, r' , r", v"\ by equations 2, which will complete our view of this subject. 



OCTOBEE 27th, 1887. 

 The President in the Chair. 



Books Received. 



Koninklijke Akademle van Wetenschappen, Amsterdam : Vers- 

 lagen en Mededeelingen, Af d. Naturkunde, III Keeks, Deel 1 ; Afd. 

 Letterkunde, III Keeks, Deel 3. 



Koninklijke Akademie Disciplinarum Neerlandica : Judas Mach- 

 abaeus, &c. 



Koyal Society, London : Proceedings, No. 257. 



New York State Library -. Keport, 1 886. 



