4to. [23 x 17 cm], (4) ff., 80 pp., including numerous geometrical figures in text, and with 1 folding engraved plate. Bound in contemporary cartonnage with manuscript title on spine. An unpressed, partially untrimmed copy, pages clean and fresh, excellent.
A superlative copy of the scarce third edition of Le Operazioni del Compasso Geometrico, containing an enlarged illustration of Galileo’s sector for measuring and swiftly computing distances and mathematical problems. The original edition, published in 1606 and Galileo’s first printed book of significance, did not contain an illustration of his ‘proportional compass’, probably because of the likelihood that it would be pirated.
About 1596 Galileo invented a remarkably useful instrument, the geometrical and military compass. The device, a sort of primitive analog computer, bears nine sets of lines or scales for calculating cube roots, square roots, interest rates, circle squaring, etc. Its object was to greatly reduce computations in the measurement of distance, as well as to extract roots and perform other mathematical functions ‘on the fly’. Galileo envisaged his instrument as of use in both civil surveying and military fortification, and it was deliberately published in the Tuscan vernacular for the benefit of both audiences. The sector was particularly useful in ‘measurement by sight’ applications (described on pp. 62-80), allowing the user to compute heights and distances on the same instrument he used to sight them with. “One of the immediate consequences was that topographical surveying and mapping of terrain became possible for anyone interested, no longer requiring trained specialists” (Drake, p. 10).
The instrument proved to be much in demand, and the inventor established a workshop in his own house at Padova for its manufacture. As is well documented, the “compass” was copied and plagiarized by others, notably one Baldassare Capra, and in 1606 Galileo published Le Operazioni del Compasso to vindicate his claim to the invention by describing its construction and use. This was his first significant work to appear in print and is very rare. Only 60 copies of this first edition were printed and probably a dozen or so have survived.
It should be noted that Galileo’s “compass,” now called the sector, has been manufactured from Galileo’s day right up to the present time. No previously known device had accomplished anything quite like it, although mechanical aids to calculation had appeared earlier in various forms. Something of the importance to society of such an invention as Galileo’s, Stillman Drake once noted, can be grasped from the modern introduction of the electronic pocket computer. It completely revolutionized the way people, from princes to land surveyors, calculated complex mathematical problems without pencil and paper and, in so doing, democratized practical mathematics.
The plate in the 1640 second edition, the first appearance of the illustration, measures 11.9 x 34.5 cm to the plate mark. Frambotto re-engraved the plate for this third edition, enlarging it to 25 x 36.3 cm. While Cinti mentions a “n.1” engraved in the margin, this plate is not numbered, perhaps suggesting an early impression.
* Cinti 122; cf. also Drake’s translation with foreword and notes (Smithsonian Institution Press, 1978); Carli and Favaro 228.