Alexandria, the Golden City, Vol. I - The City of the Ptolemies by Davis Harold T

Author:Davis, Harold T. [Davis, Harold T.]
Language: eng
Format: azw3
Publisher: Hauraki Publishing
Published: 2016-11-11T05:00:00+00:00

11. The Spiral of Archimedes.

Perhaps the most amazing result of all these astonishing achievements of Archimedes, however, was his investigation of the properties of spirals, which he later published in a treatise entitled On Spirals. In the introduction to this work, which he dedicated to Dositheus, Archimedes makes the following interesting statement:

“Of most of the theorems which I sent to Conon, and of which you ask me from time to time to send you the proofs, the demonstrations are already before you in the books brought to you by Heracleides; and some more are also contained in that which I now send you. Do not be surprised at my taking a considerable time before publishing these proofs. This has been owing to my desire to communicate them first to persons engaged in mathematical studies and anxious to investigate them. In fact, how many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

“Now Conon died before he had sufficient time to investigate the theorems referred to; otherwise he would have discovered and made manifest all these things, and would have enriched geometry by many other discoveries besides. For I know well that it was no common ability that he brought to bear on mathematics, and that his industry was extraordinary.”

The curve which has come to be called the spiral of Archimedes is described by its inventor as follows:

“If a straight line drawn in a plane revolve at a uniform rate about one extremity which remains fixed and return to the position from which it started, and if, at the same time as the line revolves, a point move at a uniform rate along the straight line beginning from the extremity which remains fixed, the point will describe a spiral in the plane.”

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