My rating: 5 of 5 stars

Another book on books, this time a rare treat for me that combines my bibliophilia with my love of mathematics. Rara Arithmetica is a detailed catalogue of arithmetic books and manuscripts in George Arthur Plimpton’s library that were written before 1601. It includes detailed bibliographic information, biographies of the authors and important facts about each book including its audience, reception and impact. It includes many reproductions of title pages and other pages within the books.

There were four types of arithmetic in the Middle Ages that were inherited by the Renaissance (pp. 4-7). They are theoretical, algorisms, abacus mathamatics and computi (computus). Theoretical works were based primarily on Boethius, a 6th century CE scholar who drew on Nicomachus and Euclid. Algorisms were practical works used by merchants and business for computations and weights, often using Hindu and Arabic number systems. Abacus arithmetics used roman numerals and were also used for commercial purposes. Computi were the arithmetics used for church calendars and various date calculations, especially for movable religious feasts.

Some highlights from Rara Arithmetica:

A book written in 1488 by the astronomer and poet Anianus, which also includes work by a 13th century astronomer, is a treat. Anianus has, for the first time in print, the Latin version of what we know in English as the 30 days hath September…’ (pp. 31-33):

Junius aprils september et ipse nouember Dant triginta dies reliquis supadditur vnus De quorum numero februarius excipiatur. (pp. 31-33)
Johann Widman’s arithmetic in German (2nd edition, 1500) is the first time that plus and minus signs were used in a printed work, although they weren’t used as addition or subtraction “but as symbols of excess or deficiency in warehouse measures” (p. 39).

The first modern encyclopedia in print was Gregorius Reisch’s Aepitoma omnis phylosophiæ (1504). It includes the trivium (grammar, logic, rhetoric) and quadrium (arithmetic, geometry, music and astronomy), along with the natural and moral sciences.

There were several books written on numerical finger and arm symbolism, i.e. how to use your hands and arms to display a number. One neat one was Johannes Aventinus’s 1532 book. It provided illustrations for how to represent numbers up to one million that was useful in both the East and the West during the Middle Ages (pp. 137-138).