Hamish Riley-Smith

Rare Books And Manuscripts

Pietro Borgo

Libro de Abacho 1540

The second Italian commercial arithmetic – a practical book for the use of merchants


Libro de Abacho.

Venice,Bernardino de Bindoni 1540

Quarto, 20.0 x 15.5 cm, contemporary vellum, yapped edges, later endpapers, 99 leaves [leaves 1, 68-69, 88, 91 and 100 are unnumbered; no leaves for 7 and 8; leaf 80 is misnumbered 74, leaf 86 misnumbered 8], woodcut initials, rinted mathematical calculations in the margins throughout, old worm holes on the inner margin of last four leaves unaffecting the text.

Rare. Wellcome Library 986. Copac: Oxford and Wellcome only. Riccardi I.164. Smith, Rara Arithmetica pp.12-22. Not in Adams,Cambridge Libraries (1 copy only University Library 1509). This edition not in Kress (1533 only). No edition in Goldsmith.


The Venetian arithmetician Pietro Borgo’s commercial arithmetic. First published in Venice in 1484 it was the second commercial arithmetic published in Italy and more than any other book it set a standard for the arithmetics of the 16th century and had a far greater influence on education and none of the early textbooks deserve more careful study. All early editions are rare. The text of this 1540 and all early editions are substantially the same as the first edition of 1484.
“Borgo first treats of notation carrying his numbers as high as ‘numero de million de million’, and making no mention whatever of the Roman numerals. In the same spirit he eliminates all of the medieval theory of numbers, asserting that he does this because he is preparing a practical book for the use of merchants…multiplication is the first operation treated. First comes the table, arranged in column form, unlike the Boethian type of arithmetic, which preferred the square array…The author then gives the method of checking by casting out 7’s and 9’s…Then follow multiplication ‘per colonna’…Division is explained by the galley form…then known as the method of giving, ‘a danda’, and described by Pacioli and Calandri. Then follow addition (although this was used in multiplication), subtraction, denominate numbers, common fractions, rule of three, partnership, barter, alligation and false position…The problems are generally practical for the time, and they reveal some interesting facts concerning business customs at the close of the 15th century”. Smith, Rara Arithmetica.

Pietro Borgo - Libro de Abacho 1540
Pietro Borgo - Libro de Abacho 1540
Pietro Borgo - Libro de Abacho 1540
Pietro Borgo - Libro de Abacho 1540

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