The art of the abacus

The first printed book on mathematics: on December 10th, 1478 the first printed book on mathematics was published in Treviso. It was called "l'arte dell'abaco" (the art of the abacus) and was written by an unknown author, probably a priest, and dedicated to some of his young friends who had consistently asked for it.

It is a basic study limited to the commercial applications of arithmetic. It follows the "Liber Abbaci" of Leonardo Pisano, also known as Fibonacci, written in 1202, which was a more complete work and remained fundamental for almost 300 years until surpassed by Luca Pacioli's book, published in Venice in 1494 with the title "Summa di Aritmetica, di Geometria, Proporzioni et Proporzionalità". The book printed in Treviso, written in Italian with use of many dialect terms, can still be easily read today and is one of approximately 30 books on arithmetic printed before the end of the 15th century, half of which were still in Latin.

During the period in which the book was published, the trading activities of the Serenissima Repubblica of Venice were particularly favourable and the conditions were ideal for the development of printing activities; of approximately seventy printers throughout Europe, fifty were situated in the Repubblica and out of these, thirteen worked within the city of Treviso. The printers at that time, only 26 years after the publication of the Mainz Bible, had already gained the necessary expertise as can be seen from "larte de labbacho", which is clearly printed, well impaginated and with very few printing errors.

The contents of the book are interesting considering the evolution of mathematical knowledge in the west: it uses Arabic numerals, having abandoned roman numerals which were recommended stil in 1348 by the Padua University for indicating the prices of books. The new numerals were already being used in the Liber Abbaci by Fibonacci, who, knowing their origin, called them "Indian".

The author teaches the four main operations, together with numerous examples and different techniques of notation, some of which are still in use today. He uses the concept of fraction, but not decimal numbers which were introduced about a century later.

He also shows how to calculate the date of the new Moon, starting from the astronomic number of the year, the age of the Moon at the beginning of the year and the length of the synodic lunar month, the latter being known to the author within half a second from the real value. All this whilst the Julian calendar was still in use, before beeing reformed by Pope Gregory XIII after long years of study in 1582.

Of the original book very few copies still exist: 8 listed in 1888 by Pichi and one mentioned by D.E.Smith in 1958 in America. During the 500 and more years from its publication, the book has been the subject of many studies and has recently been reprinted:

1969: Editore Zoppelli - Treviso, anastatic reprint, edited by Prof. G.Romano under a sponsorship by the Cassa di Risparmio della Marca Trevigiana.
1988: Open Court Publishing Company, in 'Capitalism and Arithmetic: The New Math of the 15th Century'. F.J.Swetz's book contains D.E.Smith's complete translation in English, written before the Great War and never published entirely (Sc.Am.: vol. 258-6, June 1988).
1995: new anastatic edition by Editrice Canova in Treviso, with notes updated by Prof. G.Romano.

The three figures taken from the original book represent in order: division worked by the galley (65284 : 594 = 109 remainder 538), five different methods for multiplication (56789 x 1234 = 70077626) and the calculation of the new Moon of December 24th, 1478 (at 21 hours and 121 puncti).

To announce the publication of the latest reprint, the Studio CaLion together with Translations '92, have prepared this page to inform the public "on the net" and to give everyone throughout the World the opportunity to possess a faithful reproduction of "larte de labbacho". For scholars and intellectuals this is a moment for appreciating a significant event which took place in our city.

The book, of 13.5 x 20 cm, 120 pages, with notes and introduction by Prof. G.Romano, can be found in book-shops, price 43.000 Italian Lire or can be ordered directly here for shipment C.O.D.