Download Algebraic Geometry - Bowdoin 1985, Part 1 by Bloch S. (ed.) PDF

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Extra info for Algebraic Geometry - Bowdoin 1985, Part 1

Example text

His project was in the agrimensorial tradition, but its execution much in debt to the theoretical tradition, as this was recovered by the Latin mathematicians and humanists. Prior to a description, in Book VII, of his work on the circle quadrature problem, Clavius reviewed efforts by Campanus of Novara ( 1296), Nicholas of Cusa ( 1464), Orontius Finaeus ( 1555), and the contemporary Joseph Scaliger (1540-1609). Scaliger's Cyclometrica elementa (1594), Clavius showed, had adopted in clumsy fashion Arabic interpretations of Archimedes and even misunderstood Archimedes' fundamental circle measurement theorem.

Page 9 Another text, Podismus, is diverse and didactic (Lachmann, 1848, pp. 295-302). Here Nipsus distinguished three measures: linear, planar, and solid. All this became common to the early medieval tradition, but Hugh was the first to specify altimetry, planimetry, and cosmimetry as basic parts of the genre of practical geometry. The standard angle is the right angle; the acute is less than it; the obtuse, greater. Nipsus set the volume of a box as the product of length, width, and height. The volume of a cylindrical cask was height times area of base, as in Heron.

Medieval university statutes on the teaching of mathematics are few and not very detailed. But noting how Hugh of St. Victor and Dominicus Gundissalinus, a twelfth century Spanish philosopher and translator who took directly from Arabic sources, distinguished between the theory and the practice of an art, Shelby identified three forms of geometry in the High Middle Ages. Theoretical, or mathematical geometry, came to the West from the twelfth century onwards with translations of Euclid and Archimedes from the Arabic.

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