Centiloquium Circini Proportionum. Ein newer Proportional-Circkel, von vier, fünff, sechs oder mehr Spitzen, mit hundert schönen, ausserlesenen, nutzlichen Fragen und Exempeln gezieret und erkläret…wie auch Petri Apiani Organon Catholicum, &c.…

Each title within the same architectural woodcut border, two folding woodcut plates in the second part (the 2nd plate is numbered p. 33), & numerous woodcuts in the text of geometrical & surveying problems. 8 p.l., 88 pp.; 2 p.l., 33 pp. Two parts in two vols. Small 4to, modern vellum-backed paste-paper boards. Nuremberg: S. Halbmayer, colophon dated “1626.”

First edition, and complete with both parts, of this posthumously published work. Galgemair (1564-1619), who had been a student of both Apian and Mästlin at Tübingen, wrote a series of books on scientific instruments.

The first part of this book describes the precursor (truncated) to the sector and proportional compass that is today known as the reduction compass; a full-page woodcut of the instrument appears on A2r. There are 100 examples of the uses of the instrument, most with illustrations. The first examples provide geometric solutions to problems of a more abstract nature, while the latter address practical problems, such as how much gold foil a goldsmith needs to cover a round roof at the top of a tower, heights and distances of buildings, etc. The uses for the architect and cartographer are obvious.

Daniel Schwenter wrote the biographical preface and apparently thought very highly of the instrument. In Galgemair’s own preface, dated 1 April 1619, he explains how he discovered the instrument and its uses.

The second part contains Peter Apian’s Organon Catholicum, edited by Galgemair. The work describes an instrument for making astronomical and geographical observations and calculations. This work first appeared in Phillip Apian’s (Peter’s son and Galgemair’s teacher) Astrolabi (1580). It is interesting to note that the large folding diagram of the instrument is printed on the backs of sheets of paper that the printer evidently had left over from another book.

❧ Tomash & Williams G3 & 2. Galgemair: Zinner, Astronomische Instrumente des 11. bis 18. Jahrhunderts, p. 184. Apianus: Van Ortroy 116. (Inventory #: 6740)