By Thomas L. Heath
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Extra resources for The Works of Archimedes: Edited in Modern Notation with Introductory Chapters
Example text
RELATION OF ARCHIMEDES TO HIS PREDECESSORS. xli Pythagoreans. , referred to any diameter and the tangent at its extremity as axes; and the latter equation was compared with the results obtained in the 27th, 28th and 29th Props, of Euclid's Book vi, which are equivalent to the solution, by geometrical means, of the quadratic equations ax + - a? = D. ~c It was also shown that Archimedes does not, as a rule, connect his description of the central conies with the method of application of areas, as Apollonius does, but that Archimedes generally expresses the fundamental property in the form of a proportion and, in the case of the ellipse, where x, xl are the abscissae measured from the ends of the diameter of reference.
Of the 15th a), which is still extant and contains the same books of Archimedes and Eutocius with the same fragment of Heron as F has, and in the same order. If the above conclusion that F dates from 1491 or thereabouts is correct, then, as V belonged to Cardinal Bessarione who died in 1472, it cannot have been copied from F, and the simplest way of accounting for its similarity to F is to suppose that it too was derived from Valla's MS. * Tiraboschi, Storia della Letteratura Italiana, Vol. vi.
From a letter written at Venice in 1491 by Angelus Politianus (Angelo Poliziano) to Laurentius Mediceus (Lorenzo de' Medici), it appears that the former had found a MS. at Venice containing works by Archimedes and Heron and proposed to have it copied. As G. Valla then lived at Venice, the MS. can hardly have been any other but his, and no doubt F was actually copied from it in 1491 or soon after. , while they all savour of an ancient archetype, agree marvellously with the description which the note to B above referred to gives of the abbreviations used in Valla's MS.