Trigonometriae sive. De dimensione triangulorum libri quinque.

Augsburg, Michael Manger, Dominicus Custos, 1600.


FIRST EDITION. 4to. 2 parts in 1, continuous pagination, additional typographical t-p to second, pp. (viii) 213 (iii) 215 [217]-370 [372] (ii), variant probably, first issue, without errata. Roman letter, with Italic. Engraved t-p with four figures of mathematicians, woodcut geographical diagrams and tables, woodcut printer’s device to recto of penultimate leaf, decorated tailpieces. Slight marginal dust-soiling to t-p, edges untrimmed and a bit dusty, two sheets of early mathematical diagrams (loosely inserted). An excellent copy in carta rustica, lacking one of four ties, bookplates of Auersperg library and Erwin Tomash to front pastedown, autograph of Wolfgang Engelbrecht von Auersperg and his catalogue entry dated 1656 to lower and upper t-p respectively, occasional contemporary annotation based on printed errata. In modern folding box.

An excellent copy of this ground-breaking mathematical work. Bartholomaeus Pitiscus (1561-1613) was a German theologian, mathematician and astronomer, tutor to the young Frederick IV, Count Palatine, and court chaplain at Breslau. First published in 1595, ‘Trigonometriae’ introduced the neologism ‘trigonometry’ into the Latin and vernacular language of mathematics, with the opening statement: ‘Trigonometria est doctrina de dimensione Triangulorum.’ It was a subject dating back to antiquity which only expanded exponentially in the C16 due to the demands of navigation and cartography. Divided in five parts, the work is a very thorough and clear manual laying down point by point, through very short statements, the basics of the subjects of plane and spherical trigonometry—e.g., the geometrical nature of triangles, the workings of straight lines, the translation of triangles onto spherical surfaces, trigonometric functions, sinus and cosinus, illustrated with schemas and accompanied by mathematical tables. Pitiscus calls the following ‘the golden rule of arithmetic’—‘if we take four numbers which are proportional to one another, given three it is possible to find the fourth.’ The last part is concerned with the practical applications of trigonometry in the calculation of irregular geographical surfaces, of the height of a building given one’s distance from it, latitude and longitude, and the height of the sun in relation to the horizon. Although without the two leaves of errata, the contemporary annotator—a mathematician—appears to have had access to them as he marked a passage as ‘error’ and amended its complex calculation with a six-figure result. Probably the same annotator also left two paper slips with drawings and operations of spherical trigonometry.  

Wolfgang Engelbrecht (1610-73), Count of Auersperg, was an Austrian politician and patron of the arts.

USTC 615235; Adams 1331 (with errata); Brunet IV, 679. Not in Riccardi, Smith or BM STC It. C17.