Textual Studies in Ancient and Medieval Geometry

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Wilbur Richard Knorr August 29, — March 18, was an American historian of mathematics and a professor in the departments of philosophy and classics at Stanford University.

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He has been called "one of the most profound and certainly the most provocative historian of Greek mathematics" of the 20th century. Knorr was born August 29, , in Richmond Hill, Queens.

Textual Studies in Ancient and Medieval Geometry

Knorr was a talented violinist, and played first violin in the Harvard Orchestra, but he gave up his music when he came to Stanford, as the pressures of the tenure process did not allow him adequate practice time. From Wikipedia, the free encyclopedia.

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It traces the early history of irrational numbers from their first discovery in Thebes between and BC, Knorr speculates , through the work of Theodorus of Cyrene , who showed the irrationality of the square roots of the integers up to 17, and Theodorus' student Theaetetus , who showed that all non-square integers have irrational square roots. Knorr reconstructs an argument based on Pythagorean triples and parity that matches the story in Plato 's Theaetetus of Theodorus' difficulties with the number 17, and shows that switching from parity to a different dichotomy in terms of whether a number is square or not was the key to Theaetetus' success.

Wilbur Knorr

Theaetetus classified the known irrational numbers into three types, based on analogies to the geometric mean , arithmetic mean , and harmonic mean , and this classification was then greatly extended by Eudoxus of Cnidus ; Knorr speculates that this extension stemmed out of Eudoxus' studies of the golden section. Heiberg , are especially significant.

For comprehensiveness and accuracy, his editions are exemplary. In his textual studies, as also in the prolegomena to his editions, he carefully described the extant evidence, organized the manuscripts into stemmata, and drew out the implications for the state of the text.

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In examining textual questions bearing on the Archimedean corpus, he attempted to exploit as much as possible evidence from the ancient commentators, and in some instances from the medieval translations. It is here that opportunities abound for new work, extending, and in some instances superseding, Heiberg's findings. For at his time the availability of the medieval materials was limited.

In recent years Marshall Clagett has completed a mammoth critical edition of the medieval Latin tradition of Archimedes,8 while the bibliographical instruments for the Arabic tradition are in good order thanks to the work of Fuat Sezgin. Medieval Geometry Former Library book.