LEONARDO DA VINCI 1452-1519

Leonardo da VINCI Vinci, 1452–Amboise, 1519 Squaring the Lune; Various Attempts at Squaring Pen and brown ink About 1505 The term squaring refers to the construction, with a straightedge and compass, of a square with the same surface area as a given figure. Squaring is the very basis of the calculation of surfaces, as any polygon can be reduced to a square; but the squaring of curvilinear figures poses infinitely complex problems.The Greek mathematician Hippocrates of Chios succeeded in squaring the lune (a figure bounded by two circular arcs of different radii). Biblioteca Ambrosiana, Milan, Codex Atlanticus, fol. 389r. Leonardo da VINCI Vinci, 1452–Amboise, 1519 Various Attempts at Doubling the Cube. The Extension of the Pythagorean Theorem to the Power of 3. Attempt at the Geometri- cal Construction of Square Roots from 1 to 9 Pen and brown ink About 1505 Here again, Leonardo endeavours to double the cube by various means – including applying the Pythagorean theorem to volumes rather than surface areas. Biblioteca Ambrosiana, Milan, Codex Atlanticus, fol. 428R 112 113