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Early Trigonometry

European Developments

Trigonometry Main Page

European Developments

Trigonometry reached Europe in the medieval times. Richard of Wallingford wrote a text on trigonometry, Quadripartium. He related the Indian sine to the ancient chords. He used Euclid's Elements as a basis for his arguments in plane trigonometry. Levi ben Gerson worked on plane trigonometry, particularly the laws of sines and cosines.

In the 16th century, trigonometry was incorporated into geography and navigation. Knowledge of trigonometry was used to construct maps, determining the position of a land mass in relation to the longitudes and latitudes.

Johannes Muller, or more popularly known as Regiomontanus, wrote a text On Triangles. He studied plane trigonometry, including results for solving triangles. He expanded on Levi ben Gerson's work. He proved the Sine Rule, and also considered the ambiguous case in using the rule.

Later works improved the tables of sines, which has been worked on extensively; as well as included tables for the other functions. Thomas Finck was the first to use the modern terms "tangent" and "secant".

The workd so far applied trigonometric concepts in astronomy. It was only until Bartholomew Pitiscus when there was a text considering the solving of a plane triangle on earth. He invented the word "trigonometry", in his title Trigonometriae sive, de dimensione triangulis, Liber (Book of Trigonometry, or the Measurement of Triangles). He developed his own sine and tangent tables. However, like all the tables that had been calculated before, the values are actually the lengths of certain lines in a fixed circle.

Later developments in trigonometry are mainly the use of trigonometric ratios in calculus; analysis, differential equations and integration, just to name a few.