A History of the Teaching of Elementary Geometry
by Alva Walker Stamper (9780217311458)

A History of the Teaching of Elementary Geometry
Alva Walker Stamper
Release Date: 10 December 0140
Format: Paperback
Pages: 64
Category: Geometry
ISBN: 9780217311458
ISBN-10: 0217311458

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: CHAPTER III THE TEACHING OF GEOMETRY FROM EUCLID TO THE RISE OF THE CHRISTIAN SCHOOLS AT ALEXANDRIA The " Elements" of Euclid marked the culmination of the development of elementary geometry. From a logical standpoint, the system was now complete, so no new developments could be expected in this direction, but there was a wide field for the applications of geometry. Solid geometry was not yet fully developed, and in the field of deductive mathematics there was yet the development of the geometry of the conic sections. To these other fields the later Alexandrian mathematicians turned their attention. In treating that which is contribution to subject- matter, we shall discover some facts as to method that have a particular bearing on our subject. The first geometer after Euclid was Archimedes of Syracuse (b. 287 B.C.). Although he probably did not live at Alexandria, his writings show a thorough acquaintance with the mathematical knowledge of the earlier Alexandrian school. Archimedes was famous for his applications of geometry to science. The nature of his contributions is best seen from the titles of some of his works.1 "Equiponderance of Planes," "The Quadrature of the Parabola," "On the Sphere and the Cylinder," "On The Measurement of the Circle," "On Spirals," "On Conoids and Spheroids," "On Floating Bodies." He also wrote a treatise on the half-regular polyhedra and his addition to the geometry of the three round bodies was considerable. Two of his propositions, at least, are well known. He proved that the' area of a spherical surface equals four times the area of a great circle, and secondly, that the volume and surface of a sphere equal twothirds the volume and total surface of the cylinder in which it is inscribed.1 The value of It obtained by Archimedes is so c...

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