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 “ 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 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 
“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. 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 
