Page:First six books of the elements of Euclid 1847 Byrne.djvu/67

F any side () of a triangle be produced, the external angle () is equal to the sum of the two internal and opposite angles ( and ), and the three internal angles of every triangle taken together are equal to two right angles.

Through the point draw

|| (pr. 31.).

Then $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$	=	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,}$ (pr. 29.),
	=

∴ + = (ax. 2.),

and therefore

+ + = = (pr. 13.).

Q. E. D.