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Lectures on Fundamental Concepts of Algebra and Geometry (Paperback) Loot Price: R349
Discovery Miles 3 490

# Lectures on Fundamental Concepts of Algebra and Geometry (Paperback)

## John Wesley Young

Loot Price R349 Discovery Miles 3 490

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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: LECTURE in ON THE HISTORY OF THE PARALLEL POSTULATE Euclid's Attitude toward his Fifth Postulate. ? Before attempting to answer the question proposed at the close of the last lecture, it seems desirable to consider briefly the history of the parallel postulate. Euclid's fifth postulate states that if two lines in a plane are cut by a transversal in such a way as to make the sum of the interior angles on the same side of the transversal less than two right angles, then the two straight lines meet on that side of the transversal. There is internal evidence to show that, for some reason, Euclid himself did not regard this postulate as being quite so fundamental, or quite so self-evident (if we may use that expression) as his other postulates. For, although he states it with the other postulates, he avoids using it until Theorem 29 of Book I. This theorem says that, if the given lines are parallel, the sum of the interior angles is two right angles. He divides his discussion of the exterior angles of a triangle into two parts, as he probably would not have done had he not wished to avoid using the fifth postulate. He first shows, in Theorem 16, that in any triangle, anexterior angle is greater than either of the non-adjacent interior angles. By means of Theorem 16 he proves Theorem 28, that, if two lines are cut by a transversal so as to make the sum of the interior angles equal to two right angles, the lines are parallel. For this theorem he did not need to use the fifth postulate. It is the converse of this, namely, Theorem 29, mentioned above, in which he found difficulty and was forced to use the postulate. In Theorem 32 he continues his discussion of the interior angles of a triangle, and shows that their sum is precisely two right angles. This division of the treatment of...

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 Imprint: General Books LLC Country of origin: United States Release date: 2012 First published: 2012 Authors: John Wesley Young Dimensions: 246 x 189 x 3mm (L x W x T) Format: Paperback - Trade Pages: 104 ISBN-13: 978-0-217-49977-4 Categories: Books > Humanities > History > General Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Geometry > General Books > History > General LSN: 0-217-49977-5 Barcode: 9780217499774

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