A UNIQUE COLLECTION OF ARITHMETICS 229 



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 " Eara 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 mathe- 

 maticians 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 arith- 

 metic 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 

 " Eara 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. Plimp- 

 ton. The work is strictly speaking an " algorism " since that title 

 implied the use of the Hindu-Arabic numerals for practical computa- 

 tion, 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 



