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BRAMER, Benjamin [INSTRUMENTS / GEOMETRY] Instrumentum Conicum Universale. Kassel  1627

Broadside [66 x 28 cm] printed on three sheets, text on outer leaves and one engraving [28 x 21 cm to plate mark] on central sheet. Toning on top and bottom leaf, waterstaining on central leaf, two tears in blank left margin, a good copy with a clear impression of the plate.

Very rare first and only edition of this separately published broadside, describing an instrument for drawing conic sections invented by one of the most prolific architects and mathematicians of early seventeenth-century Germany. The broadside, dedicated to William, Landgrave of Hessen, as a New Year’s gift on the eve of the year 1628 is divided into three sections. The first contains the dedication to the author’s patron and a brief introduction explaining the need for such an instrument in the fields of optics, mechanics, “and other mathematical guilds.” The central section consists of an engraved plate depicting the instrument with a small inset showing a right and an oblique cone. The bottom third is divided into two columns of text, the first giving instructions for the construction of the instrument, the second describing its use. The broadside could have functioned as an advertisement for the instrument as well as a set of instructions to owners. Bramer’s instrument is essentially an instrument for drawing conic sections. The instrument consists of a vertical structure which is affixed at right angle to a level plane with a circle on it (the base of the cone), with an adjustable arm holding an angled board over the circle. The angle and height at which the board is suspended above it determine the cross section that is to be studied or drawn: in a right cone, the board is parallel to the circle. From the arm, a thin rod juts up marking the point of the cone. The study of conic sections had been a preoccupations of artists as well as scientists for some time, essential for the study of perspective. Dürer devoted the first book of his Instruction in measurement with Compass and Ruler (1525) to conic sections. The first drawing instrument for this purpose was developed by Barozzi, followed in 1614 by a similar device invented by Christoph Scheiner and published that year by his student Johann Georg Schönberger in his Exegeses funamentorum gnomicorum Bramer’s invention “might have produced more accurate curves than Scheiner’s, which was unsuited for precise drawings, but was met with little applause because of the cumbersome use of it.” (Cantor, Vorlesungen, II, 692-693)The Instrumentum Conicum Universalis is a continuation of Bramer’s work on the study of angles and instruments for their measurement. In 1618 he had published a work presenting an instrument for making various geometric measurements, and in 1630 and 1648 he would publish further drawing instruments. In his Appolonius Cattus of 1684 (written in the 1630s), Bramer presents two variations on the present instrument.Bramer (1588-1652) was raised in the household of his elder sister, whose husband was the mathematician and instrument maker Joost Bürgi. The improved accuracy in the latter’s astronomical and surveying instruments led to his appointment in Prague, then a developing center of scientific research, where he worked closely with Kepler, and was responsible for the great astronomer's computations. Growing up in such a milieu, Bramer received an outstanding training in mathematics, and his gifts were apparent at an early age. He is best known for a work on sines, an apparatus to improve perspective sufficiently important to be included in Nicholas Bion’s Traité de la construction et principaux usages des instruments de mathématiques nearly a hundred years later, and his various works on surveying and calculating instruments. Bramer held a number of high-ranking posts as architect and engineer throughout Germany: concerned chiefly with fortifications, he had extensive practical experience using the instruments he devised and described in his books.Not in OCLC, KVK, VD17 or BL, and no copy at Wolffenbüttel.

* On Bramer see DSB I.419. See also Cantor, Vorlesungen über die Geschichte der Mathematik, II, (New York, Johnson Reprints, 1965), pp. 692-693.

$US6500

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