Etymology of the Word Hypotenuse

Date: 01/26/2003 at 13:18:39
From: David Goldberg
Subject: Hypotenuse

Why is the hypotenuse called "hypotenuse"?

"hypo" means "under," "tenuse" I think comes from "tenein," "to 
stretch."  Then "hypotenuse" came from "stretch under."  Does it refer 
to roof supports in ancient Greek buildings?  That is just a guess.

Date: 01/26/2003 at 15:21:08
From: Doctor Sarah
Subject: Re: Hypotenuse

Hi David - thanks for writing to Dr. Math.

From Steven Schwartzman's _The Words of Mathematics, An Etymological 
Dictionary of Mathematical Terms used in English_ (Mathematical 
Association of America):

hypotenuse

from Greek-derived hypo- "under" and teinein "to stretch." The Latin 
cognates, which may be more familiar, are sub for "under" and tendere, 
"to stretch," as combined in subtend. The Indo-European root 
underlying Greek teinein is ten- "to stretch." A Native English 
cognate is the adjective thin, which describes an object that has been 
stretched. When a right angle is inscribed in a circle, the diameter 
of the circle subtends that right angle. The diameter automatically 
becomes the hypotenuse of the right triangle thus formed. Even when a 
right triangle is not inscribed in a circle, the hypotenuse is the 
side that "stretches" from one leg to the other.

- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 01/26/2003 at 20:22:56
From: David Goldberg
Subject: Thank you (Hypotenuse)

Thanks much Dr. Sarah, for finding the etymology of "Hypotenuse" - it 
has been bugging me for a few years - I sometimes suggest to my 
(community college) students the task of researching this, but no one 
ever did. In a similar vein, they are amused to discover why 
"quadratic," Latin base meaning "four," means a polynomial of degree 
(only) two.  It makes a nice tie between geometry and algebra.

Thanks again!
David Goldberg