Page:First six books of the elements of Euclid 1847 Byrne.djvu/14

angled triangle, and express some of its properties both by colours and the method generally employed.

Some of the properties of the right angled triangle ABC, expressed by the method generally employed.

1. The angle BAC, together with the angles BCA and ABC are equal to two right angles, or twice the angle ABC.
2. The angle CAB added to the angle ACB will be equal to the angle ABC.
3. The angle ABC is greater than either of the angles BAC or BCA.
4. The angle BCA or the angle CAB is less than the angle ABC.
5. If from the angle ABC, there be taken the angle BAC, the remainder will be equal to the angle ACB.
6. The square of AC is equal to the sum of the squares of AB and BC.

The same properties expressed by colouring the different parts.

Byrne's Euclid page x image 1

That is, the red angle added to the yellow angle added to the blue angle, equal twice the yellow angle, equal two right angles.

Byrne's Euclid page x image 2

Or in words, the red angle added to the blue angle, equal the yellow angle.

Byrne's Euclid page x image 3

The yellow angle is greater than either the red or blue angle.