Geometria prattica tratta dagl'Elementi d'Euclide et altri auttori da Giovanni Pomodoro Venetiano mathematico eccellentissimo descritta e dichiarata da Giovanni Scala matematico. Nella quale si vede in 50 tavole di rame scolpito tutto quello che ad un buon giometra s'appartiene di sapere et porre in uso. Opera non meno Vttile che necessaria, à Misuratori di terreni, di fabriche, et altri simmili, mà in'oltre ancora à Geografi, Cosmografi, Architetti Ciuili, et Milittari, à Bombardieri, Soldati priuati, à Capitani, Mastri di Campo et à si Voglia altra persona Virtuosa.

Rome: Apresso Stefano de Paulini, 1599.

First edition, first issue, of this finely illustrated manual of Euclidean geometry and its practical applications for surveyors, architects and others, unusual for being printed in folio, and a rather large folio for the period. The first plate illustrates surveying and measuring instruments; this is followed by a series of plates with Euclidean geometrical diagrams, and then by attractive plates of surveying and measuring problems, including architectural plans and elevations of buildings and streets. Many of the surveying scenes include figures in gentlemanly or military costumes or nude. The first 44 plates were designed by Pomodoro, but he died before the work was complete and the text was provided by Giovanni Scala (1547-1600), who also supplied a further seven plates. The fame of Pomodoro’s treatise is attested by the fact that, just one year after its publication, it was cited by the architect Giorgio Vasari the Younger (1562-1625) (the nephew of the art historian of the same name) in his manuscript Raccolto … di varii instrumenti per misurare con la vista: six of the 76 folios of the manuscript refer to Pomodoro, and Vasari traced illustrations from Tavolas I and XLI-XLIV (Brusaporci, p. 216). This is a very rare book: OCLC lists 5 copies in US (Burndy, Cornell, Harvard, Iowa State, Michigan); COPAC lists BL and Wellcome only; ABPC/RBH record only one copy sold at auction since the Honeyman sale (Christie’s, 6 June 2001, lot 384, £4230, modern binding).

The treatise begins with the description of the principal instruments for drawing, surveying and military planning: compass; ruler; square ruler; penknife; stiletto (to draw white lines, i.e., without ink); drawing pens; plumb-bob level; gun compass (to measure the diameter of the mouth of a cannon and of cannonballs); hinged rules with goniometer and magnetic compass; the surveyor’s cross; and the geometric square with quadrant (to measure distances, depths and lengths, with graduated alidade with viewfinder and a quarter of a circle inside the square). These are illustrated in Tavola I. The geometrical definitions and operations useful for solving surveying problems are illustrated on Tavolas II-XXX: triangles (II-XXV), circular figures (XXVI-XXIX), and solids (XXX). The solution of measurement problems is based primarily on the use of the Pythagorean theorem and similar triangles, as presented in Book VI of Euclid’s ‘Elements.’ The remaining Tavolas are devoted to applications. Tavolas XXXI-XXXIX are focused on the application of the surveyor’s cross to measuring of the area of streets, rivers, moats, lakes, woods, and of the bases of trees and mountains; Tavola XL describes a ‘lame square’ with movable angle which allows one to survey the interior and exterior angles of buildings; Tavolas XLI-XLIII deal with problems of distance measurement (Tavola XLIII is reproduced in Mortimer) and Tavola XLIV with the calculation of heights. Distances are usually calculated using similar triangles, while areas are determined by dividing them into simple geometric shapes, such as triangles and rectangles.

Pomodoro’s Tavolas are followed by seven by Scala devoted to the calculation of volumes of solids, especially parts of buildings such as columns, stairs and spires. He includes recommendations on the construction of foundations and retaining walls. Scala’s astronomical interests are apparent in the examples used in his studies of curved lines and their intersections: he cites the Sun’s path between the tropics and the intersection of the “Meridian with the Horizon, with the Equinox, with the Tropics, and with the Arctic and Antarctic circles” (Brusaporci, p. 207), as well as the ‘twisted’ form of comets’ tails. Scala is always careful to point out clearly which are his own contributions, and which are Pomodoro’s.

Virtually nothing is known about Pomodoro’s life, and everything that is known derives from the Foreword to the present work written by his brother Pietro and from the Introduction by Scala. Pomodoro died before this, his only published work, was completed, and probably many years before its publication, for Scala writes that “the work remained almost useless and abandoned … therefore for many years it has been buried, although M. Pietro Pomodoro, brother of M. Giovanni, tried … to find a virtuous person who wanted to work on it and fulfill what was missing, and explain what has been realized, and yet he (according to what he told me) didn’t find anyone who wanted to take charge of it” (Brusaporci, p. 203). This was possibly because of the practical nature of the work, which, ironically, was also the reason for the continued interest in it over the next two centuries. The first vernacular translation of Euclid by Niccolò Tartaglia (1499-1557) in 1543 had made the results of classical geometry available to practical men, but sixteenth-century treatises on surveying and other aspects of ‘practical’ geometry were almost exclusively written for university men. The prevailing attitude was explained by Geronimo Pico Fonticulano (1541-96) in his Geometria (1597): “If I describe the practice of fools, simply so that every mediocre talent can be used, I would do wrong to professors because I would facilitate the ignorant … who have only a naked practice that they do not know is right or not, but want to show that they do know, and presumptuously become professors” (quoted in Brusaporci, p. 218). Pomodoro’s was the first work on practical geometry that made a genuine attempt to render the subject accessible to practical men.

The first edition was re-issued in 1603 with a new engraved title page and the first gathering re-set, and further editions were printed in 1624, 1667, 1691 and 1772, all using the original plates. Riccardi I, 300; Mortimer, Harvard Italian 394; Honeyman 2512; Macclesfield 1655 (1667 edition). Brusaporci, ‘Giovanni Pomodoro (XVI Century),’ pp. 201-222 in Distinguished Figures in Descriptive Geometry and Its Applications for Mechanism Science: From the Middle Ages to the 17th Century, 2015.

Folio (345 x 240 mm), ff. [57], including engraved title within a scrollwork border with the coat of arms of the dedicatee, Cardinal Pietro Aldobrandini, and with 51 plates of diagrams and illustrations of measurement, of which 44 are by Pomodoro and the remaining 7 by Giovanni Scala; illustrated with historiated initials, vignettes and 6 different tailpieces. Contemporary vellum. Damp stain to lower inner margin of first two gatherings. A very nice and unrestored copy.

Item #3918

Price: $13,500.00

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