Euclid's Fourteenth Book
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|Ivars Peterson (MathLand)|
|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|
|Math Topics:||Non-Euclidean Geometry, History and Biography|
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