HYPOTENUSE

, or Hypothenuse, in a rightangled triangle, is the side which subtends, or is opposite to the right angle, and is always the longest of the three sides; as the side AC, opposite to the right angle B.

It is a celebrated theorem in Plane Geometry, being the 47th prop. of the 1st book of Euclid, that in every right-angled triangle ABC, the square formed upon the Hypothenuse AC, is equal to both the two squares formed upon the other two sides AB and BC; or that . This is particularly called the Pythagorean theorem, from its reputed inventor Pythagoras, who it is said sacrificed a whole hecatomb to the muses, in gratitude for the discovery. But the same thing is true of circles or any other similar figures, viz, that any figure described on the Hypotenuse, is equal to the sum of the two similar figures described on both the other two sides.

HYPOTHENUSE. See Hypotenuse.