Protomathesis opus uarium, ac scitu non minus utile quàm iucundum, nunc primùm in lucem foeliciter emissum: cuius index uniuersalis, in uersa pagina continetur

Paris: Impensis Gerardi Morrhij & Ioannis Petri, 1532. FIRST AND SOLE EDITION. Hardcover. Fine. Bound in contemporary quarter pigskin and wooden boards with intact clasps. Inscription on title: “Est Adolfi Glauburg, Johannis Adolfi Glauburg, Jacobi Maquardi Glauburg.” An extremely fine, crisp, bright copy with broad margins. There is some minor damp-staining to a few gatherings, a few insignificant blemishes, and a short worm-trail in the inner margin of the title page, just touching the printed border. Profusely illustrated. Divided into four parts, Oronce Finé’s monumental ‘Protomathesis’ presents the various branches of scientific knowledge: mathematics (truncated) (De arithmetica practica libri IIII), theoretical and practical geometry (De geometria libri II), cosmography -that is, astronomy and geography- (De Cosmographia, sive sphaera mundi libri V), and horology and gnomonics (measuring time, constructing clocks, sundials, etc.) (De solaribus horologiis et quadrantibus libri IIII). Mixing theoretical and practical knowledge (from Euclidean geometry and the theory of the sphere to the construction and use of surveying instruments and sundials), the publication of the ‘Protomathesis’ was important for the new image it provided of mathematics, in France and beyond.

In the ‘Protomathesis’, the understanding and application of this knowledge is facilitated by the use of instruments, and Finé’s technical drawings of astronomical, geodetic, and horological instruments in the volume are so accurate that, as Catherine Eagleton has shown, they could be copied to make actual instruments and could themselves be used as paper instruments.

The ‘Protomathesis’ is also a universally acclaimed monument of book production and design. The book is introduced by a fine architectural title page border with a lunette of Hercules defeating the Lernean Hydra. This is followed by the well-known image of the goddess of astronomy (Urania) lecturing Finé, who holds a book and an astrolabe, beneath a spherical model of the solar system. This magnificent woodcut is repeated in Book I of the second part (De Cosmographia). There are an additional 280 woodcuts in the text, including geometric figures, polyhedra, models of the geocentric solar system, diagrams of eccentric orbits, Finé’s “octant mesh” for mapping an eighth of the globe, and detailed renderings of numerous instruments: quadrants, cross-staves, sundials, geometrical squares, the shaped rectilinear dial, astronomical rings, astrolabes, and the hydraulic astronomical clock.

De solaribus horologiis et quadrantibus libri IIII

“Given Finé’s interest in instruments, and his statements about the need to ground practical mathematics in theoretical understanding, it is perhaps no surprise that the fourth book ‘Concerning sundials and quadrants’ includes descriptions on how to make and use a variety of sundials. (Catherine Eagleton, Oronce Finé’s Sundials, in The Worlds of Oronce Finé, p. 85)

An ivory dial made in 1524 and signed by Finé (preserved in the Museo Poldi Pezzoli, Milan) testifies to Finé’s skill as a maker of horological instruments. Among the many instruments described and illustrated in the fourth part is the ship-shaped rectilinear dial, a cousin of Regiomontanus’ universal dial; a combined sun and moon dial, and the hydraulic clock.

“The first book of ‘De solaribus horologiis’ covers dials that tell the time by measuring the direction in which the sun is observed, and begins with a diagram and description of the basic geometry underpinning a sundial for the latitude of Paris. Finé then explains how this geometry can be applied to make a variety of dials, including horizontal dials (proposition 2) and vertical dials (proposition 3). Later in Book 1, Finé moves on to talk about dials that are portable, and can be used at more than one latitude, and gives examples of dials for various latitudes, aligned in various ways, and constructed on various surfaces and shapes. The first book ends with instructions for how to make and use a nocturnal, for telling the time by the stars, a moon dial, and a dial for hours counted from dawn or dusk rather than from midnight or midday, based on the same geometry as the earlier, simpler examples in the book. Book 2 deals mainly with dials that tell the time from the altitude at which the sun is observed, including quadrants as well as the cylinder dial, ring dials, a universal astrolabe and universal ring dial. At the end of the second book, just before the description of the hydraulic clock, Finé includes the universal rectilinear dial (proposition 15) and the ship-shaped dial (proposition 16). In the text, he explicitly links the two similar instruments, and the ship­shaped dial is described as an alternative version of the preceding instrument, although Finé also points out that this version is more useful than the universal rectilinear dial…. Added to these is a hydraulic clock that Finé himself claims to have developed. The third and fourth books describe the construction and use of an astrolabe quadrant.”(Catherine Eagleton, “Oronce Finé’s sundials: the sources and influences of De Solaribus Horologiis,” in The Worlds of Oronce Finé: Mathematics, Instruments, and the Book in Renaissance France, ed. Alexander Marr (2009), pp. 83–99;

See also, Anthony Turner, 'Dropped Out of Sight: Oronce Finé and the Water-Clock in the Sixteenth and Seventeenth Centuries', in Marr 2009, 191–205.

The polymath Oronce Finé was born in Briançon in 1494. His grandfather Michel and his father François were also physicians; we also have Oronce’s testimony that his father was skilled in astronomy. Oronce studied at the College of Navarre, Paris, where, beginning in 1516, he also taught mathematics. On March 27, 1531, François I (to whom the ‘Protomathesis’ is dedicated) made Finé first regius professor of mathematics at the Royal College. In 1532, he was entrusted with a house located in rue des Lavandières. Around 1535 Finé married Denise Blanche, with whom he had six boys and a girl. Oronce died on October 6, 1555 and was buried in the Carmelites of Place Mauber.

“Finé’s contemporaries considered him to be as well-versed in art as in the sciences. His work as a designer is closely related to his major fields of mathematics, astronomy, geography, and horology and gnomonics and his contribution to book production is particularly interesting in extending beyond the illustration to the ornamentation of scientific texts.”(Mortimer 225). (Inventory #: 5240)