THE FIRST ARCHIMEDES
ARCHIMEDES, BOETHIUS, and CAMPANO da Novara; Luca GAURICO, editor.
Tetragonismus id est circuli quadratura per Campanum Archimedem Syracusanum atque Boetium mathematicae perspicacissimos adinventa.
Venice, [Giacomo Penzio for] Giovanni Battista Sessa, 28 August 1503.
4to, ff. 32; small woodcut Sessa device on title-page and different device below colophon, title with woodcut illustration of Archimedes standing on a map and looking up at the heavens, woodcut initials and diagrams; title-page slightly dust-soiled with small repair at foot, title tipped in and (conjoint) leaf a4 strengthened along gutter, a few headlines shaved, occasional light spotting, final verso with slight offsetting; a good copy in nineteenth-century boards, green morocco spine label, year of publication lettered to upper cover in manuscript, remains of index tabs; binding a little soiled; bookplate of ‘Progel’ (probably Joseph Bonaventura Progel, of Munich, d. 1851).
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Tetragonismus id est circuli quadratura per Campanum Archimedem Syracusanum atque Boetium mathematicae perspicacissimos adinventa.
The first appearance in print of any complete work by Archimedes, ‘generally regarded as one of the greatest mathematicians the world has ever known’ (PMM), including one of the earliest approximations of the value of pi.
This work contains Archimedes’ mathematical treatises Quadratura circuli and Quadratura parabolae, in the Latin translation of William of Moerbeke, which accompanied similar works on the quadrature of the circle by Campano da Novara and Boethius. In Quadratura circuli, Archimedes ‘calculated the ratio of circumference to diameter (not called π until early modern times) as being less than 3-1/7 and greater than 3-10/71. In the course of this proof Archimedes showed that he had an accurate measurement of approximating the roots of large numbers’ (DSB I, p. 222). Quadratura parabola proved that the area enclosed by a straight line and a parabola is equal to 4/3 the area of a triangle with equal height and base. ‘Archimedes demonstrated the quadrature of the parabola by purely geometric methods. In the first part of the tract he demonstrated the same thing by means of a balancing method. By the use of the law of the lever and a knowledge of the centers of gravity of triangles and trapezia, coupled with a reductio procedure, the quadrature is demonstrated’ (ibid., p. 219).
Tetragonismus represents the earliest appearance of any work by Archimedes in Latin, predated only by excerpts in Valla’s De expetendis et fugiendis rebus opus (Venice, 1501). The first printing of Archimedes in Greek was not until 1544, accompanied by Regiomontanus’s version of the Latin text. These publications, along with Tartaglia’s reprint of these two Archimedean texts in 1543, facilitated the use of Archimedes by Galileo, Torricelli, and Kepler.
BM STC Italian, p. 292; EDIT16 CNCE 8810; USTC 818222; Adams C-470; Graesse VII, p. 151; Riccardi I, col. 40, no. 1*.
