248 ELEMENTARY. DEMONSTRATION, &c. 
3. Let BAD be an angle in- 
commensurable with a right +. 
angle. The proposition is true 
in relation to BAC, the multiple 
of (a) next less than BAD, and 
of BAE, the multiple of (a) next ™ 
higher, the difference between 
which (= a) may be less than any «= 
assigned angle. But the equivalent of AB and BD must, in 
respect of direction, be always intermediate between the equi- 
valent of AB, BC, and that of AB, BE. It must, therefore, 
pass through D; and this is evidently true in the case of any 
similar rectangle ; that is, so long as the angle BAD remains 
the same. Hence it must be represented by AD, also in quan- 
tity (vid. Lemma). 
From what is said above in § 2. it is manifest that celia has 
now been proved universally of the rectangle, may be extend- 
ed to the oblique-angled parallelogram. 
XIII. 
