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### 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
```
Associated Topics:
High School Definitions
High School Triangles and Other Polygons
Middle School Definitions
Middle School Triangles and Other Polygons

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