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Apollonii Pergaei De Sectione Rationis - APOLLONIUS, of Perga - 1706. 
Opera & studio Edmundi Halleyâ€¦ Numerous woodcuts in the text. Much Greek printing. 5 p.l., liii, 168 pp. 8vo, cont. panelled calf, remains of label on spine. Oxford: Sheldonian Theatre, 1706. First edition of Halley's translation of Apollonius's "cutting off a ratio" from an Arabic manuscript. This text of Apollonius, like Books V-VII of the Conics, survives only in Arabic, and in this case the Arabic remains unpublished. "Much of Halley's scholarship was exercised upon the works of Apollonius of Perga, one of the greatest mathematicians of antiquity, and indeed of all time, who flourished in the latter part of the third century B.C. One of his minor works, Sectio rationis (Cutting-off of a ratio), an exercise in geometrical algebra, was thought to be lost until an Arabic translation of it was found among the Selden manuscripts in the Bodleian and identified by Edward Bernard, the Savillian Professor of Astronomy. Bernard set about translating it into Latin; but the manuscript was very defective and he soon laid the task aside. His successor, David Gregory, made a fair copy of the original for the use of Henry Aldrich, Dean of Christ Church, at whose invitation Halley, upon succeeding Wallis in the Savillian Chair of Geometry, undertook to complete the translation. He had never previously studied Arabic; but, using as a key the few passages translated by Bernard, he eventually made out the meaning of the text. He proceeded to restore the lost companion tract, Sectio spatii, following hints from Pappus. He gave his reasons for regrading the works as genuine; and he included in his edition the earliest printed Greek text of Pappus's preface to the seventh book of his Synagoge (Collection)."-Angus Armitage, Edmond Halley, p. 160. Five hundred copies of this book were printed and, by 1713, 122 copies were remaindered. From the library of Jacob Bronowski (1908-74), the mathematician, biologist, historian of science, poet, and inventor.
[Bookseller: Jonathan A. Hill, Bookseller, Inc.]
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