Drexel dragonThe Math ForumDonate to the Math Forum

The Math Forum Internet Mathematics Library

Euclid's Fourteenth Book

_____________________________________
Library Home || Full Table of Contents || Suggest a Link || Library Help
_____________________________________

Visit this site: http://www.maa.org/mathland/mathland_4_1.html

Author:Ivars Peterson (MathLand)
Description: Officials of the Foundation for Old Occidental Languages announced today that, after a year devoted to authentication and analysis, they are prepared to release the text of a manuscript that appears to be a Latin translation of research notes jotted down by Euclid in preparation for writing a fourteenth volume of Elements. Euclid's newly discovered notes propose an alternative way of expressing this notion: Through any given point can be drawn exactly one straight line parallel to a given straight line. He goes on to consider two other cases: One in which no parallel line can be drawn through the point and another in which more than one parallel can be drawn. In these two situations, he says, the sum of the interior angles of a triangle is no longer exactly equal to two right angles. On the surface of a sphere, for example, a triangle's angle sum is greater than two right angles, Euclid notes. Such a geometry has no parallel lines, yet it obeys his first four postulates.

Levels: High School (9-12), College
Languages: English
Resource Types: Articles
Math Topics: Non-Euclidean Geometry, History and Biography

[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help
_____________________________________

© 1994-2014 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies.The Math Forum is a research and educational enterprise of the Drexel University School of Education.