﻿( 445 ) 



xvir. 



Demonstration of the I2th Axiom of the 

 first hook of Euclid. 



BY THE. REV. PAUL LIMRICK. 



Prop. 1, Fig. I, ^'. 



Fio: 



7tl 11 



Fig. 



Oy7\h . S 



\/.U 



If two right lines, 

 m a and o c, be equal 

 and perpendicular to the 

 same right hne a c, and 

 a right line m o be 

 drawn joining their 

 terms; a perpendicular 

 nb, let fall, from any 

 point n, in the line m o, 

 upon the line a c, is 

 equal to ma^z.co. 



Proof, 

 than it. 



h cannot be o-reater that m a, nor less 



Produce a c, till c e=rt c; erect a perpendicular 

 e ^=:« m, draw the right line os, take c d—a I? ; erect 

 a perpendicular dk. Now, if the figure maco be ap- 

 plied to oc cs so that the point a may fall upon c, 

 and the line ac ow c e, the point b will fall upon d^ 

 aad c upon c; and since the angles at a, b^ c, d, and 



e are 



