Description

MARCHELLI, Giovanni. Trattato del Compasso di Proporzione … ad Istruzione de’ Signori Convittori del Collegio de’ Nobili di Milano…. Milano, Giuseppe Galeazzi, 1759.

FIRST and ONLY EDITION. Large 8vo (20,2 x 14,4 cm), XXII, 352 pp., [8] ff., with 1 large (ca. 40 x 50 cm) folding plate containing 5 illustrations; title-page printed in red and black, beautiful engraved device on title. Bound in contemporary Italian cartonato binding. In cardboard case. Internally very fresh, clean and crisp, excellent copy.

Rare first and only edition of this treatise on Galileo Galilei\’s proportional compass, written by the Jesuit Giovanni Marchelli and dedicated to the Genoese Marquess Giacomo Maria Brignole.

“Giovanni Marchelli was a Jesuit priest born in Genoa who taught at the Jesuit college in that city. Through this work on the Galilean sector, Marchelli sought to instruct his pupils in the fundamentals of practical geometry. By 1759, knowledge and use of the sector had become widespread, and there was no longer a need for elementary books on the subject. Marchelli describes a sophisticated sector with a full complement of scales and a quadrant arc. The sector scales are well illustrated and the text includes tables giving the positions of the various markings. The large folding plate also provides full-sized diagrams that show exactly how the markings on the quadrant arm and tangent, chord and sine scales are created (see the illustration of the diagram for the tangent lines). The work has thirteen chapters of which all but the final one cover the sector; its description, construction and application. The last chapter deals with military problems, primarily those encountered in gunnery such as the determining of the caliber of cannonballs and properly aiming at targets” (Tomash).

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; Riccardi II, 105.

A really excellent copy with an outstanding plate (40 x 50 cm).