"Ptolemy's method of calculating chords seems to be his own. The measures of the sides of regular polygons, as chords of certain arcs, were known in terms of the diameter. He next proves the proposition, now appended to Euclid VI. (D), that "the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides", and then... how from the chords of two arcs that of their sum and difference [may be found] and how from the chord of any arc that of its half may be found."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Ref: , Aperçu Historique sur l'origine et le Développement des Méthodes en Géométrie (1837, 1875) p. 27, note I. says that Carnot in his Géométrie de Position shewed that all rectilineal trigonometry could be deduced from this theorem in quotes above. Note: Ptolemy's proofs follow on pp. 294-296 of Gow.
https://en.wikiquote.org/wiki/History_of_trigonometry
Revision History
No revisions have been submitted for this quote.
Categories
History of trigonometry
begins with the early study of triangles, traced to the , in () and . Trigonometry was also prevalent in Kushite mathematics.
130 quotes on TrueQuotesView all quotes by History of trigonometry →
Related Quotes
"Similarly to the spread of the Indian place-value system, Indian trigonometry came to Europe via the Arab world, for …"
"[I]n 1575 Western Europe had recovered most of the major mathematical works of antiquity now extant. Arabic algebra h…"
"At its higher levels the golden age of Muslim civilization was both an immense scientific success and a exceptional r…"
"As in the rest of mathematical sciences, so in trigonometry, were the Arabs pupils of the Hindus…"
"Chapter X., which follows, is on the obliquity of the ecliptic... The next, XI., XII. contain spherical geometry and …"
"Euler wrote... Introductio in Analysin infinitorum, 1748, which was intended to serve as an introduction to pure anal…"
"The development of Indian trigonometry, based on sine as against chord of the Greeks was another of 's achievements w…"
"The second part of the book... contains an exposition of the first principles of the theory of complex quantities; hi…"
"The idea of the logarithm probably had its source in the use of... trigonometric formulas that transformed multiplica…"
"Isaac Newton... went to school at Grantham and in 1661 came up as a subsizar to Trinity. ...He had not read any mathe…"