Page:First six books of the elements of Euclid 1847 Byrne.djvu/77

O construƈt a parallelogram equal to a given triangle and having an angle equal to a given rectilinear angle .

Make $=$ (pr. 10.)

Draw .

Make $=$ (pr. 23.)

Draw $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	$\parallel$	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,}$ (pr. 31.)
	$\parallel$

$=$ twice (pr. 41.)

but $=$ ^[1] (pr. 38.)

$\therefore$ $=$ .^[1]

Q. E. D.

1. the area is equal