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One of a large number of diagrams illustrating how to use an abbacus from a copy of Treviso's Arte dell' abbaco bequeathed to the Cambridge University Library by J.W.L. Glaisher in 1928.
A: Treviso, Veneto, Italy, B: Manhattan, New York, New York, United States
Page from Arte dell'Abbaco.
This unpretentious little book could almost be taken as a symbol of the third component in the collection of George A. Plimpton: "reading, writing and ‘rithmetic." It intends to teach commercial arithmetic, starting from the most elementary level to explain numbers and their positions as designators of units, tens, hundreds, and so forth. On the page shown, a reader has noted the method for calculating differences in income for those who invest varying amounts of money at different times. Graphically clear are the various earnings of Piero, Polo and Zuanne. Their names, and indeed the entire text, are in the local vernacular: Venetian dialect, not Italian. Abbacus, or commercial arithmetic, was solidly vernacular, Latin being reserved for the abstract studies of the universities.
Bequest of George Arthur Plimpton, 1936 to Columbia University.
The first dated book on arithmetic is the anonymous Arte dell’Abbaco ..., printed in Treviso, Italy, probably by Gerardus de Lisa, de Flandria on December 10, 1478. It is possible that some undated pamphlets on Algorithmus may predate this work.
"Frank J. Swetz translated the complete work using Smith's notes in 1987 in his Capitalism & Arithmetic: The New Math of the 15th Century. Swetz used a copy of the Treviso housed in the Manuscript Library at Columbia University. The volume found its way to this collection via a curious route. Maffeo Pinelli (1785), an Italian bibliophile, is the first known owner. After his death his library was purchased by a London book dealer and sold at auction on February 6, 1790. The book was obtained for three shillings by Mr. [Michael] Wodhull. About 100 years later the Arithmetic appeared in the library of Brayton Ives, a New York lawyer. When Ives sold the collection of books at auction, George [Arthur] Plimpton, a New York publisher, acquired the Treviso and made it an acquisition to his extensive collection of early scientific [i.e. mathematics] texts. Plimpton donated his library to Columbia University in 1936. Original copies of the Treviso Arithmetic are extremely rare" (Wikipedia article Treviso Arithmetic, accessed 01-10-2009).