Page:Popular Science Monthly Volume 77.djvu/235

Rh towards the end of the sixteenth century and he designed the famous clock of the Strassburg cathedral.

The unusually large number of physicians (eleven) appearing in the "Rara Arithmetica" is at first sight rather surprising, until we recollect that the scientific training of the time was largely confined to medicine. Some of these men might be counted among the best mathematicians of their day, notably the Italian Hieronymus Cardan (1501–1576) who attained fame as an algebraist, and the German Johann Widmann (fl. c. 1490), who wrote one of the first arithmetics in the German language. An English goldsmith is the author of a practical arithmetic, of which there were many designed especially for merchants and tradespeople. Jurists and numerous professors of Greek and Hebrew mingle here with priests and bishops and even two cardinals, Petrus de Alliaco and Nicolaus Cusa. The reckoning masters so frequently mentioned as authors remind us that for many years arithmetic had no place in the schools, and that the reckoning masters taught the art of reckoning outside of school hours very much as music and dancing are taught to-day.

Especial interest attaches, of course, to the first arithmetic to appear in print, the anonymous Treviso arithmetic of 1478. While there is no proper title page, the first page begins as follows: "Here commences a practical treatise, very good and very useful for any one who wishes to learn the art of merchants, vulgarly called the art of the abacus." The last page states that it was printed at Treviso (just north of Venice) on the tenth day of December, 1478. There are 124 unnumbered pages, running about 32 lines each. The first page is reproduced in the "Rara Arithmetica" in facsimile, together with three other pages. The author was evidently a teacher in Treviso, as he states that the book is written at the oft-repeated solicitation of his students; the printer's name is also unknown. Peculiarly enough this practical arithmetician applies four different names to the science, two as in the above title and further the art of "arismetrica" and algorism. This particular copy was in the Pinelli collection, and was acquired in 1790 by a Mr. Wodhull. Later it found its way into the library of Brayton Ives and at the sale of that library became the property of Mr. Plimpton. The work is strictly speaking an "algorism" since that title implied the use of the Hindu-Arabic numerals for practical computation, whereas "arithmetica" designated a theoretical treatise based largely on the work of Nicomachus and Boethius. An "abacus," strictly speaking, would be a work involving the use of some ruled surface or device to separate by columns (or rows) the units, tens, hundreds and thousands, etc., from each other. However these terms were not strictly applied, Leonard of Pisa's extended explanation of the Hindu reckoning appearing under the title "Liber Abbaci" or