Arithmetrice introductor [Arithmetica]. Philippi Calandri ... de Arimethrica [sic] opusculum.
Florence: Bernardo Zuchetta, 1518 [colophon].
Extremely rare second edition of the first illustrated Italian arithmetic, containing the first printed example of the modern method of long division, and the first printed use of the word ‘zero’. Calandri’s work was used to teach elementary mathematical techniques necessary for business, both for craftsmen and merchants. This edition follows the first of 1491, with the same illustrations (although there are some reversals and rearrangements) but a different printer. A richly illustrated manuscript of the work is preserved in the Biblioteca Riccardiana in Florence.
One of the earliest printed works to teach commercial arithmetic, it gives the leading rules for integers and for lire, soldi and denari. Calandri is the first to give long division in the modern form, known to the Italian writers by the name ‘a danda’. “Indeed Calandri gives only the ‘a danda’ method, omitting the galley forms, and is therefore fully a century ahead of his time” (Smith).
On the page facing the preface there appears a majestic, seated teacher in a classroom with students. The scene is labelled, ‘Pythagoras, Inventor of Arithmetic’" The book then begins with a salutation that embedded the title of the work in a supposed network of patronage: “A small work of Filippo Calandri on Arithmetic, [dedicated] to Giuliano di Lorenzo de' Medici.” The preface goes on to claim pre-eminence in commerce for Florence and to claim that the author went to a great deal of trouble to ensure that the book was printed in ‘the Florentine style.’ The exact meaning of lo stile fiorentino is unclear, but it may have to do with the elegant appearance of the book by comparison to the simple look of earlier printed arithmetics. Calandri is also given to dressing up his exposition with classical and patristic citations: thus, he cites Fibonacci (1170-1250), the usual source, on the subject of Arabic numerals, but he also refers to St. Jerome and Juvenal.
Born in Florence in 1467, Filippo Calandri was, like his grandfather, father and brother, an abacist (a book-keeper or accountant in modern terms). Almost nothing else is known of his life. Apart from his Arithmetic, he also composed a work on probability and games of chance entitled Varie ragioni tratte de vari luogi; this was never published, but the manuscript survives in the Biblioteca Communale in Siena.
This second edition is even rarer than the first: only one copy has appeared at international auctions in the last 50 years (Honeyman, lot 568).
Brunet I:1468 (ed. 1491); Klebs: 236.2; De Morgan, Arithmetical Books from the Invention of Printing to the Present Time, p. 1 (listing Calandri's work as the first printed Arithmetic); Riccardi I 208 (giving the date incorrectly as 1515 and nor mentioning the title, suggesting that he has not seen a copy); Smith, Rara Arithmetica, pp. 47-49 (describing the book as a quarto, suggesting that he has not seen a copy); Sotheran 6673 (‘of excessive rarity... whereas 6 copies of the edition of 1491 have been sold in the last 10 years, no copy of the present one can be traced at all’).
8vo, ff.  (a4, b-n8, o4, without signatures or pagination). Title-page in gothic type; text in roman type, largely in two columns within ruled frames, with numerous woodcut diagrams and illustrations as well as arithmetical schemata and symbols throughout the text. Contemporary vellum (one leaf with light brown stain, small area of damp-staining affecting two other leaves), a very good, genuine copy in its original state.