Four theorems complete the trigonometric properties of triangles: one decomposes each side into the projections of the other two, two give the area and the last, the law of tangents, relates sums and differences of sides to sums and differences of angles. The story The law of tangents was published by the Danish Thomas Fincke in 1583, in the same book in which he named the tangent (see chapter VIII), and François Viète also used it at the same time. It became very practical in the era of logarithm tables: as it only involves quotients and products, it allows you to solve a triangle knowing two sides and the angle between them without adding squares, which the law of cosines would require. With logarithms, each multiplication or division became an addition or subtraction of numbers taken from the table.