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The term "trigonometry" was derived from Greek τρίγωνον trigōnon, "triangle" and μέτρον metron, "measure". [3]The modern words "sine" and "cosine" are derived from the Latin word sinus via mistranslation from Arabic (see Sine and cosine § Etymology).
The text's 12th-century Latin translator used the Latin equivalent for "bosom", sinus. [6] When jyā became sinus, it has been suggested that by analogy kojyā became co-sinus. However, in early medieval texts, the cosine is called the complementi sinus "sine of the complement", suggesting the similarity to kojyā is coincidental. [7]
At the same time, another translation of the Almagest from Greek into Latin was completed by the Cretan George of Trebizond. [26] Trigonometry was still so little known in 16th-century northern Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium to explain its basic concepts.
It consists of five books on plane and spherical trigonometry. A standalone edition called Trigonometriæ sive de dimensione triangulorum libri quinque (Five books on trigonometry or the dimensions of triangles) was published in 1608 which included trigonometric tables with another, improved, edition being published in 1612. [2]
The state of trigonometry advanced during the Song dynasty (960–1279), where Chinese mathematicians began to express greater emphasis for the need of spherical trigonometry in calendrical science and astronomical calculations. [33] Shen Kuo used trigonometric functions to solve mathematical problems of chords and arcs. [33]
The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, [1] a treatise on mathematical astronomy.
In 1551 Rheticus produced a tract titled Canon of the Science of Triangles, the first publication of six-function trigonometric tables (although the word trigonometry was not yet coined). [10] This pamphlet was to be an introduction to Rheticus' greatest work, a full set of tables to be used in angular astronomical measurements. [16]
The word secant comes from Latin for "to cut", and a general secant line "cuts" a circle, intersecting it twice; this concept dates to antiquity and can be found in Book 3 of Euclid's Elements, as used e.g. in the intersecting secants theorem. 18th century sources in Latin called any non-tangential line segment external to a circle with one endpoint on the circumference a secans exterior.