Treviso Arithmetic

The Treviso Arithmetic, or Arte dell'Abbaco, is an anonymous textbook in commercial arithmetic written in a Venetian dialect of Italian and published in Treviso, Italy in 1478.

The author tells us his reason for writing his textbook:[1]
I have often been asked by certain youths in whom I have much interest, and who look forward to mercantile pursuits, to put into writing the fundamental principles of arithmetic, commonly called abacus.

The Treviso Arithmetic is the earliest known printed mathematics book in the West, and one of the first printed European textbooks dealing with a science.

the Arithmetic as an early printed book

There appears to have been only one edition of the work. David Eugene Smith translated parts of the Treviso Arithmetic for educational purposes in 1907. 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. Wodhull [2]. 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 Plimpton, a New York publisher, acquired the Treviso and made it an acquisition to his extensive collection of early scientific texts. Plimpton donated his library to Columbia University in 1936.[3]. Original copies of the Treviso Arithmetic are extremely rare.

There are 123 pages of text with 32 lines of print to a page. The pages are unnumbered, untrimmed and have wide margins. Some of the margins contain written notes. The size of the book is 14.5 cm by 20.6 cm.

The book included information taken from the 1202 Liber Abaci, such as lattice multiplication. George G. Joseph, "Crest of the Peacock' suggests that Napier read this book to create Napier's bones, or Napier's rods.

Why it was made

The Treviso Arithmetic is a practical book intended for self study and for use in Venetian trade. It is written in the Venetian dialect and communicated knowledge to a large population.

It helped to end the monopoly on mathematical knowledge and gave important information to the middle class. It was not written for a large audience, but intended to teach mathematics of everyday currency in Italy.

The Treviso became one of the first mathematics books that were written for the expansion of human knowledge. It gave opportunity for the common person to learn the art of computation instead of only a privileged few. The Treviso Arithmetic provided an early example of the Hindu-Arabic numeral system and computational algorithms. [4]

See also


1. ^ David Eugene Smith "The First Printed Arithmetic (Treviso, 1478)," Isis, 6 (1924): 311-331, at p. 314
2. ^ Swetz, Frank, J. 1987. Capitalism and Arithmetic. La Salle: Open Court.
3. ^ Swetz, 34
4. ^ Swetz, 26


  • Boyer, Carl. 1991. A History of Mathematics. New York City: Wiley.
  • Buck-Morss, Susan. "Envisioning Capital: Political Economy on Display." Critical Inquiry 21, no. 2 (1995): 434-436. (15 November 2006).
  • Carter, Baker. 2006. The Role of the History of Mathematics in Middle School. Presentation at East Tennessee University, August 28.
  • Gazale, Midhat, J. 2000. Number. Princeton: Princeton University Press.
  • Newman, J, R. 1956. The World of Mathematics. New York City: Simon & Schuster.
  • Peterson, Ivars. 1996. Old and New Arithmetic. Mathematical Association of America. (accessed October 11, 2006).
  • Swetz, Frank, J. 1987. Capitalism and Arithmetic. La Salle: Open Court.

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Country Italy
Region Veneto
Province Treviso (TV)
Mayor Gian Paolo Gobbo (since 2003)

Area km
 - Total (as of December 31, 2004)
 - Density /km
Time zone
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Il Canto degli Italiani
(also known as Fratelli d'Italia)

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David Eugene Smith, Ph.D., LL.D. (1860–1944) was an American mathematician and educator.

Born in Cortland, New York, he attended Syracuse University, graduating in 1881 (Ph. D., 1887; LL.D., 1905).
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George Ames Plimpton (March 18, 1927 – September 25, 2003) was an American journalist, writer, editor, and actor.


Plimpton was born in New York. He attended St. Bernard's School, Phillips Exeter Academy and Harvard University.
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Columbia University is a private university in the United States and a member of the Ivy League. Its main campus lies in the Morningside Heights neighborhood of the borough of Manhattan, in New York City.
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Liber Abaci (1202, also spelled as Liber Abbaci) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. Its title has two common translations, The Book of the Abacus or The Book of Calculation.
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Napier's bones are an abacus invented by John Napier for calculation of products and quotients of numbers. Also called Rabdology (from Greek ραβδoς [rabdos], rod and λóγoς [logos], word).
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Napier's bones are an abacus invented by John Napier for calculation of products and quotients of numbers. Also called Rabdology (from Greek ραβδoς [rabdos], rod and λóγoς [logos], word).
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Venetian or Venetan is a Romance language spoken by over five million people,[1] mostly in the Veneto region of Italy. The language is called vèneto in Venetian, veneto in Italian; the variant spoken in Venice is called
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Arabic numerals, known formally as Hindu-Arabic numerals, and also as Indian numerals, Hindu numerals, Western Arabic numerals, European numerals, or Western numerals, are the most common symbolic representation of numbers around the world.
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The Ars Magna (Latin: "Great Work") is an important book on mathematics written by Gerolamo Cardano. It was first published in 1545.

The book contains the first published solution to cubic equations and the first explicit calculation with complex numbers.
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