Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/76

52 But because the angle DAC is a right angle, [Construction.

the square on DC is equal to the squares on DA, AC. [I. 47.

And, by hypothesis, the square on BC is equal to the squares on BA, AC.

Therefore the square on DC is equal to the square on BC. [Ax 1.

Therefore also the side DC is equal to the side BC.

And because the side DA is equal to the side AB; [Constr.

and the side AC is common to the two triangles DAC, BAC;

the two sides DA, AC are equal to the two sides BA, AC, each to each;

and the base DC has been shewn to be equal to the base BC;

therefore the angle DAC is equal to the angle BAC. [I. 8.

But DAC is a right angle; [Construction.

therefore also BAC is a right angle. [Axiom 1.

Wherefore, if the square &c.

 

1. Every right-angled parallelogram, or rectangle, is said to be contained by any two of the straight lines which contain one of the right angles.

2. In every parallelogram, any of the parallelograms about a diameter, together with the two complements, is called a Gnomon.