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It is a variation of the basic principle that if you know one angle and one side of an equilateral or right-angled triangle, then you can determine the other angles and sides.

Pythagoras had learned the triangle theorem—that the length of the third side of a right-angled triangle can be deduced mathematically from the length of the other two sides—from Indian or Babylonian geometers.

They fold the crisp sheet to an oblong, and the oblong to a square, and the square to a right-angled triangle.

Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute-angled triangle that which has its three angles acute.

An important application of these theorems is at once made to a right-angled triangle, viz.:—