Ptolemaeus, Claudius (Federico Commandino, comm.)

Ptolemaei Planisphaerium. Iordani Planisphaerium. Federici Commandini Urbrinatis in Ptolemaei Planisphaerium commentarius. Venice: [Paulus Manutius], 1558



2 parts in one volume, 4to (8 x 5 7/8 in.; 203 x 150 mm). Aldine device on both titles and both final pages, numerous woodcut text diagrams, historiated woodcut initials; first title and leaves E2-3 lightly browned, old shelfmark in ink on both titles. Antique half vellum over boards decorated with a leaf from a sixteenth century edition of German official documents, red sprinkled edges.

unidentified purple oval French library stamp obscured on title — unidentified stamped monogram "GPF" on title

EDIT 16, CNCE 28281; Renouard 1558/4; UCLA 449; Houzeau & Lancaster 769; Riccardi I, 360, 1;  see K. Andersen, The Geometry of an Art (2006), pp. 138-145

First edition of Commandino's commentary.

While the Greek text of Ptolemy's Planisphaerium is no longer extant, it was translated into Arabic, and from Arabic into Latin. This Latin version, along with Jordanus de Nemore's work on the same topic, were printed in Basel in 1536. That edition is here edited by Federico Commandino (1509-1575) with his own commentary. Commandino, who was physician to the Duke of Urbino at his household in Rome, is the author of several translations of ancient Greek mathematical treatises and commentaries thereon.

The Planisphaerium concerns the stereographic projection of the celestial sphere on a plane with the south celestial pole at the center, a technique which Ptolemy used for mapping points in the heavens on the plane of the equator. In working with this projection and conic sections, Commandino noticed that conic sections can be considered sections in visual cones or perspective images. This inspired him to include in his work a study of perspective which occupies the first nineteen leaves of his commentary, and represents one of the earliest mathematical formulations of a method already widely employed by artists.