or what is certain) for mathematics, "natuurkunde" (the "art of nature") for physics, "scheikunde" (the "art of separation") for chemistry, "sterrenkunde" (the "art of stars") for astronomy, "meetkunde" (the "art of measuring") for geometry. Geometry, physics and trigonometry Stevin was the first to show how to model regular and semiregular polyhedra by delineating their frames in a plane. He also distinguished stable from unstable equilibria. Stevin contributed to trigonometry with his book, De Driehouckhandel. In THE FIRST BOOK OF THE ELEMENTS OF THE ART OF WEIGHING, The second part: Of the propositions [The Properties of Oblique Weights, Page 41, Theorem XI, Proposition XIX, he derived the condition for the balance of forces on inclined planes using a diagram with a "wreath" containing evenly spaced round masses resting on the planes of a triangular prism (see the illustration on the side). He concluded that the weights required were proportional to the lengths of the sides on which they rested assuming the third side was horizontal and that the effect of a weight was reduced in a similar manner. It's implicit that the reduction factor is the height of the triangle divided by the side (the sine of the angle of the side with respect to the horizontal). The proof diagram of this concept is known as the "Epitaph of Stevinus". As noted by E. J. Dijksterhuis, Stevin's proof of the equilibrium on an inclined plane can be faulted for using perpetual motion to imply a reductio ad absurdum. Dijksterhuis says Stevin "intuitively made use of the principle of conservation of energy ... long before it was formulated explicitly". He demonstrated the resolution of forces before Pierre Varignon, which had not been remarked previously, even though it is a simple consequence of the law of their composition. Stevin discovered the hydrostatic paradox, which states that the pressure in a liquid is independent of the shape of the vessel and the area of the base, but depends solely on its height. He also gave the measure for the pressure on any given portion of the side of a vessel. He was the first to explain the tides using the attraction of the moon. In 1586, he demonstrated that two objects of different weight fall with the same acceleration. Music theory The first mention of equal temperament related to the twelfth root of two in the West appeared in Simon Stevin's unfinished manuscript Van