Newe geometrische und perspectivische Inventiones etlicher sonderbahrer Instrument …. Johann FAULHABER.
Newe geometrische und perspectivische Inventiones etlicher sonderbahrer Instrument …
Newe geometrische und perspectivische Inventiones etlicher sonderbahrer Instrument …
Newe geometrische und perspectivische Inventiones etlicher sonderbahrer Instrument …
The First Illustrations in Print of Galileo's Sector
Forerunner of the Pocket Calculator
Frankfurt am Main, Richter and Anthonius Humm, 1610.

Newe geometrische und perspectivische Inventiones etlicher sonderbahrer Instrument ….

38 pp., (1) f. integral blank, (3) folding plates, with engraved title, half-page engraved arms at dedication, and three engravings lettered A-C in the text (first two being half-page and the third full-page). Quarter bound in modern tan calf and pasteboards, title gold tooled on spine, red sprinkled edges. Very minor rubbing to binding. Small printer’s crease to corner of title, some dampstaining at pp. 19-33, an occasional minor spot in the margin, small tear where third plate connects to binding. Overall excellent.

Rare first edition of this illustrated treatise on instrument making by the Ulm mathematician and military architect Johann Faulhaber (1580-1635), a work principally important in the history of science and technology for its engraved technical illustrations of Galileo Galilei’s (1564-1624) famous ‘proportional compass’ – the first such illustrations to appear in print – and for its revealing anecdote of how Faulhaber came to learn of the instrument and of its inventor, “Gallileus de Gallilei Professor zu Padua.” This device – more usefully described as ‘Galileo’s Sector’ to distinguish it from the various ‘compasses’ which appeared in the late sixteenth century – has been called the forerunner of the pocket computer, and so revolutionary was its utility that it “suddenly made it possible for nearly everyone to deal effectively with almost any [mathematical] problem arising in practical matters by following rather simple instructions” (Drake, p. 10).

Galileo invented his remarkably useful instrument around 1596, calling it the geometrical and military compass. The device bears nine sets of lines or scales for calculating square and cube roots, determining interest rates, making monetary exchanges, squaring the circle, performing trigonometric calculations for surveying, and determining specific weights of metals and stones (essential for artillery). Galileo first described this instrument in 1606 in a privately printed user’s guide La Operazione del Compasso... (printed in only 60 copies in his house) to accompany the instrument but without illustrating it so as to minimize the risk of piracy, a serious and chronic problem for him at the time. In the present work, Faulhaber explicitly credits Galileo with being the instrument’s first inventor (“and not I”), and illustrates the two sides of the proportional compass for the first time in print, on separate folding plates, with his calibrations stressing its mercantile qualities with adjustments for the measuring standards of Ulm. He includes a summary of the instrument’s wider uses and marvels at its flexibility, noting that his good friend, the excellent painter Georg Brentel of Lauingen (1581-1634) has already devised a way to use it for recalibrating sundials (Brentel would publish on Galileo’s invention in 1614).

The Galileo scholar Stillman Drake tells us that Faulhaber’s text relates (p. 27) “that his acquaintance with [the instrument] dated from a visit paid to him (probably in 1603) by Mathias Bernegger en route from Austria to Strasburg. Faulhaber had recognized the value of the instrument, although he considered some of its scales less useful than others that he put in their places. He said further that before publishing he had made careful inquiries to determine the name of the original inventor and had learned that this was Galileo Galilei, professor of mathematics at Padua. Because Bernegger seems never to have visited Italy, it is probable that he had seen the silver example of the instrument sent by Galileo to the Archduke of Austria and in that way knew of its inventor. Faulhaber’s inquiries were probably made because of other claimants who appeared in the meanwhile” (S. Drake, p. 26), professing to be the author and/or maker of Galileo's remarkable device.

In two further sections of the present volume, Faulhaber discusses his improvements to several (non-Galilean) instruments used in the accurate construction of pictorial perspective and presents a secret invention (newe geheime Invention) for land surveying which employs magnets. The Ulm mathematician offers a summary of the perspective devices published by Albrecht Dürer, Walter Hermann Ryff, Heinrich Lautensack, Wenzel Jamnitzer, Daniele Barbaro, and Johannes (Hans) Lencker, and he illustrates three of his adaptations in charming pictorial engravings (executed by the Nuremberg artist Hans Carl). A large folding plate illustrates a circular multi-purpose instrument derived from the inventions in Tyco Brahe’s Astronomiae instauratae mechanica (1598). Also of note is the handsome engraved title to Faulhaber’s treatise, which depicts dozens of astronomical, surveying, and perspectival instruments presumably invented or developed by the author. Faulhaber apparently intended his book to be of interest outside Germany, as he immediately released a Latin translation (also now very rare) under the title Mathematici tractatus duo nuper germanice editi Johannis Faulhaberi (Frankfurt, 1610).

OCLC locates U.S. copies at NYPL, Yale, Michigan, New Hampshire, Wisconsin, Brown; The Latin translation is held at Yale, NYPL, and Brown.

* Poggendorf, I, 725; Zin S. Drake, Galileo Galilei: Operations of the Geometric and Military Compass, 1606; E. Tomash and M. R. Williams, The Erwin Tomash Library on the History of Computing: An Illustrated and Annotated Catalogue, vol. 1, p. 436, no. F22; K. Hawlitschek, Johann Faulhaber, 1580-1635: Eine Blütezeit der mathematischen Wissenschaften in Ulm.

Price: $35,000.00

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