James Gow (scholar) citations

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James Gow (scholar)

Date de naissance: 1854
Date de décès: 1923

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James Gow was an English scholar, educator, historian, and author, widely recognized for A Short History of Greek Mathematics. The history drew highly upon the work of Moritz Cantor, as well as upon pioneering works of Carl Anton Bretschneider, Hermann Hankel, and George Johnston Allman, but included material, e.g., gematria, not discussed by contemporary historians of mathematics.

Citations James Gow (scholar)

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„It was Pythagoras who discovered that the 5th and the octave of a note could be produced on the same string by stopping at 2⁄3 and ½ of its length respectively. Harmony therefore depends on a numerical proportion. It was this discovery, according to Hankel, which led Pythagoras to his philosophy of number. It is probable at least that the name harmonical proportion was due to it, since1:½ :: (1-½):(2⁄3-½).Iamblichus says that this proportion was called ύπ eναντία originally and that Archytas and Hippasus first called it harmonic.“

—  James Gow (scholar)
A Short History of Greek Mathematics (1884), Nicomachus gives another reason for the name, viz. that a cube being of 3 equal dimensions, was the pattern &#940;&rho;&mu;&omicron;&nu;&#943;&alpha;: and having 12 edges, 8 corners, 6 faces, it gave its name to harmonic proportion, since:<center>12:6 :: 12-8:8-6</center> Footnote, citing Vide Cantor, Vorles [Vorlesüngen über Geschichte der Mathematik ?] p 152. Nesselmann p. 214 n. Hankel. p. 105 sqq.

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