By W. W. Rouse Ball
This article continues to be one of many clearest, so much authoritative and so much exact works within the box. the traditional historical past treats hundreds and hundreds of figures and colleges instrumental within the improvement of arithmetic, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.
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Extra info for A short account of the history of mathematics
Xii, 7 and 10). It is believed that he proved that the volumes of two spheres were to one another as the cubes of their radii; some writers attribute the proposition Euc. xii, 2 to him, and not to Hippocrates. Eudoxus also considered certain curves other than the circle. There is no authority for the statement made in some old books that these were conic sections, and recent investigations have shewn that the assertion (which I repeated in the earlier editions of this book) that they were plane sections of the anchor-ring is also improbable.
The Sophists. The sophists can hardly be considered as belonging to the Athenian school, any more than Anaxagoras can; but like him they immediately preceded and prepared the way for it, so that it is desirable to devote a few words to them. One condition for success in public life at Athens was the power of speaking well, and as the wealth and power of the city increased a considerable number of “sophists” settled there who undertook amongst other things to teach the art of oratory. Many of them also directed the general education of their pupils, of which geometry usually formed a part.
These propositions were subsequently put by Euclid as the first five propositions of his thirteenth book, but they might have been equally well placed towards the end of the second book. All of them are obvious algebraically, since l = a + b and a2 = bl. ” This proposition was placed by Euclid as the first proposition of the tenth book of his Elements, but in most modern school editions it is printed at the beginning of the twelfth book. By the aid of this theorem the ancient geometers were able to avoid the use of infinitesimals: the method is rigorous, but awkward of application.
A short account of the history of mathematics by W. W. Rouse Ball