Trattato del Compasso di Proporzione … ad Instuzione de’ Signori Convittori del Collegio de’ Nobili di Milano.
8vo (20.2 x 14.4 cm). XXII pp., 352, [16] pp., with [1] large (40 x 50 cm) folding plate containing 5 illustrations; title-page printed in red and black, engraved device on title. Bound in contemporary Italian cartonato binding, title in ink on spine. Minor edge wear, minor staining to lower cover. Quires C and E loosening, internally very fresh and clean, retaining deckle at fore-edge and bottom edge, toning to plate, marginal paper flaw and rear reinforcement of crease to plate, generally excellent. Rare first and sole edition of this treatise on mathematics and the use of Galileo’s proportional compass, written expressly for the use of his mathematics pupils in the Jesuit College of Milan, by the Jesuit mathematics professor Giovanni Marchelli, thus providing interesting evidence for the use of scientific instruments in Jesuit education for a young audience. The text offers an advanced understanding of Galileo’s landmark instrument, and, coming from a Jesuit, it is perhaps notable that Galileo’s “invention” of the instrument is so candidly celebrated. The proportional compass (or ‘sector’) in fact combines two separate instruments, one for making observations (by adding a quadrant to its arms), the other to calculate various measures like proportion, trigonometry, and squares and cube roots. Its several scales permit easy and direct solutions for problems in surveying, gunnery, and navigation. Conceived as a universal instrument, the device was adapted for a variety of pedagogical purposes far more diverse than Galileo’s sector, ranging from pure geometry to such practical operations as taking measurements for the architectural orders (p. 11), converting currency and calculating interest (p. 42), performing various ‘rule-of-three’ operations such as the dissolution of business partnerships (p. 53), surveying (passim), and the construction of Napier tables (p. 73). The compass scales are well illustrated, and the text includes tables giving the positions of the various markings. The large folding plate provides diagrams “for constructing Galileo’s quadrant” that show with great refinement exactly where the markings on the quadrant’s arm and tangent are to be engraved. The final chapter deals with military problems, such as the determination of the caliber of cannon balls.
* De Backer-Sommervogel V.525, 4; Cinti 177; Carli-Favaro 128; Tomash II.M34.
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