Triangles Sphericques. Valentin MENNHER de KEMPTEN.
Triangles Sphericques.
Triangles Sphericques.
Triangles Sphericques.
Triangles Sphericques.
Triangles Sphericques.
Triangles Sphericques.
Triangles Sphericques.
Triangles Sphericques.
Spherical Geometry in Vernacular, with Practical Applications to Astronomy and Horology.

Triangles Sphericques.

First Edition. Valentin Mennher, a member of the St. Ambrose guild of schoolmasters, was born in Bavarian Swabia c1521, and became a well-known editor and writer of mathematical textbooks.1 After travels in Italy, Germany, and Austria, he settled in Antwerp in 1549, where he produced a number of works, including our book on spherical triangles (which were later known as Euler triangles).2 The mathematical discipline of spherical geometry was of extreme practical importance in the emerging sciences of geodesy, astronomy, and navigation; it stands to reason that the present work was composed in vernacular, where it would have had wider use among students and practicing scientists in France and in the French-speaking Low Countries. Indeed, Mennher discusses the application of spherical geometry to astronomy,  geography, and to the design of sundials.  The last chapter is devoted to multifaceted sundials "pour calculer les heures sur divers horloges solaires sur chacun pais que lon veult…"; the second to last page is illustrated with an impressive woodcut of a multifaceted dial. Mennher apologizes in the foreword of the book for his limited French, explaining that it is not his mother tongue, and also complains about the issues he had with the "Corrector," illustrating the age-old technical problems between mathematicians and the printers of their texts. An important and well-produced vernacular work, whose calculations, mathematical problems, and ingenious proofs were painstakingly accomplished by the author himself. Illustrated throughout with typographic diagrams. A very good exemplar, bound in contemporary calf. Only the Columbia copy located in American libraries.

Antwerp: Coppens van Diest, 1564.

Octavo, 162 x 105 x 18 mm (binding), 161 x 104 x 15 mm (text block). A-I8, K4 [K4 ?blank or ?errata wanting]; 75 of 76 ff. Contemporary Belgian calf, unlettered. Leather cracked on both boards; some invisible restorations; joints and hinges firm and sound; ?later endpapers. Interior: Soiling to tail margin of title; minimal dustiness passim; paper flaw to head margin of I6. A good antiquarian copy in its original binding.

Provenance:

Acquired by W. S. Cotter Rare Books from bookseller Massimo Caputi, February 2021. A bookseller's modern penciled stock number to lower pastedown: MC0308, likely Caputi's notation.

BT 2089 or 2090; BB IV M181; Smith, D.E. Rara arithmetica, p. 249-50 (noting that it is bound with other works by Mennher; the Columbia copy); Kheil, Carl Peter. Valentin Mennher und Antich Rocha 1550-1565, p. 8, No. 3 (with notes on Mennher's introduction); Hoogendoorn, K. Bibliography of the Exact Sciences in the Low Countries From c1470 to the Golden Age, MENNH04 1.2, p. 639 (noting two issues, with distinct fingerprints, the second issue printed with a list of errata, though this assertion is unconfirmed).   


1Mennher is also remembered as an early pioneer of double-entry accounting in Belgium, where an expanding trade market demanded more refined and accurate bookkeeping techniques.


2Spherical triangles are defined as figures formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices whose interior angles total at least 180˚ but less than 540˚. 


3A second issue of the book is known, which bears a list of errata; the issues have a distinct fingerprints. Ours is 156408 - bi A2 .64 : b2 K2 000.

Item #100

Price: $5,200.00