Several Arab scholars, notably contains all the theorems needed to solve triangles, planar or spherical—although these theorems are expressed in verbal form, as symbolic algebra had yet to be invented.

In particular, the law of sines is stated in essentially the modern way.

Two developments spurred this transformation: the rise of symbolic algebra, pioneered by the French mathematician François Viète (1540–1603), and the invention of analytic geometry by two other Frenchmen, Pierre de Fermat and René Descartes.

The final major development in classical trigonometry was the invention of John Napier in 1614.His tables of logarithms greatly facilitated the art of numerical computation—including the compilation of trigonometry tables—and were hailed as one of the greatest contributions to science.In the 16th century trigonometry began to change its character from a purely geometric discipline to an algebraic-analytic subject.Of course, this distinction is not always absolute: the Pythagorean theorem, for example, is a statement about the lengths of the three sides in a right triangle and is thus quantitative in nature.Still, in its original form, trigonometry was by and large an offspring of geometry; it was not until the 16th century that the two became separate branches of mathematics.The notations for the five remaining trigonometric functions were introduced shortly thereafter.During the Middle Ages, while Europe was plunged into darkness, the torch of learning was kept alive by Jewish scholars living in Spain, Mesopotamia, and Persia.For example, two spherical triangles whose angles are equal in pairs are congruent (identical in size as well as in shape), whereas they are only similar (identical in shape) for the planar case.Also, the sum of the angles of a spherical triangle is always greater than 180°, in contrast to the planar case where the angles always sum to exactly 180°.For example, if the lengths of two sides of a triangle and the measure of the enclosed angle are known, the third side and the two remaining angles can be calculated.Such calculations distinguish trigonometry from geometry, which mainly investigates qualitative relations.

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How radiometric dating works in general Radioactive elements decay gradually into other elements. The original element is called the parent, and the.

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Trigonometry Trigonometry, the branch of mathematics concerned with specific functions of angles.