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FIRST USE POST-KEPLER OF ELLIPTICAL ORBITS TO CALCULATE PLANETARY TABLES. First edition, very rare, of "the most important work on planetary systems between Kepler and Isaac Newton" (Robert Alan Hatch in Biographical Encyclopedia of Astronomers), "the first treatise after Kepler s Rudolphine Tables to take elliptical orbits as a basis for calculating planetary tables" (Cambridge Companion to Newton), and the first to state that the planetary moving force "should vary inversely as the square of the distance and not, as Kepler had held, inversely as the first power" (DSB). "An early Copernican and Keplerian, Ismael Boulliau was the most noted astronomer of his generation" (BEA). Newton read the present work closely and used it to rebut Robert Hooke s claim to have been the first to perceive the inverse-square law of gravity (see below). ABPC/RBH record only the Macclesfield copy in the last twenty years (a copy in a later binding with rust holes through the text). "Astronomiaphilolaica clearly extended awareness of planetary ellipses. Here Boulliau offered an entirely new cosmology, a "newer than new" alternative to Kepler s Astronomia nova. Boulliau began by attacking Kepler s cosmology at its very foundation, systematically undermining the physical principles on which Kepler based his calculations. Boulliau concluded that Kepler s celestial physics and calculational procedures were conjectural and cumbersome, unworthy of Kepler s genius. Critical of Kepler s assumptions and conclusions, Boulliau embraced elliptical orbits but insisted they could not be demonstrated by calculation alone. In place of Kepler s anima mortrix and "celestial figments," Boulliau argued it was simpler to assume that planets were self-moved, that their motion, imparted at creation, was conserved. In place of Kepler's indirect "a-geometrical methods" [the magnetic mechanisms hypothesized by Kepler to account for the eccentricity of the planetary orbits] Boulliau proposed direct calculation based on mean motion. "Boulliau s solution to the "problem of the planets" was the conical hypothesis [described in the present work]. Because circles and ellipses are conic sections, Boulliau imagined that the planets moved along the surface of an oblique cone, each revolving in an elliptical orbit around the Sun located at the lower focus. By construction, the axis of the cone bisected the base, which at once defined the upper (empty) focus of the ellipse as well as an infinite number of circles parallel to the base. The position of a planet on the ellipse at any given time (Kepler s problem) was thus defined by an intersecting circle, and hence, at any given instant, the motion of the planet was uniform and circular around its center (Plato s Dictum). Where Kepler invoked a complex interplay of forces, Boulliau explained elliptical motion by reason of geometry; the planets naturally accelerated or decelerated due to the differing size of circles. Where Kepler employed indirect trial-and-error methods based on physics, Boulliau provided direct procedures based on geometrical principles. In context, Boulliau s conical hypothesis was elegant and practical. Kepler s construction by contrast was ingenious but useless … "Boulliau s reputation reached its zenith during the 1660s in England … During this time Boulliau s Philolaic Tables were widely copied, adapted, or imitated. In England, Jeremy Shakerley, among others, believed they were more accurate than Kepler s, while in Italy, Riccioli demonstrated the claim for Saturn, Jupiter, and Mercury. Boulliau s modified elliptical hypothesis also received accolades. Although he had proposed his own method, Nicolaus Kauffman (Mercator) continued to praise Boulliau s model, claiming it could hardly be improved for accuracy. Not least, the "Ornament of the Century" offered praise. In his Principia (1687, Bk. III) Newton claimed that Kepler and Boulliau "above all others" had determined the periodic times of the planets with. Seller Inventory # 4954
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