An important and early treatise on the table abacus

(Licht, Balthasar). Algorithmus linealis cum pulchris conditionibus regule detri [...].

Leipzig, Melchior Lotter, 1509.

4to. 15 ff. Marbled wrappers.


An important treatise on the line or table abacus, "one of the earliest of the type represented also by Huswirt" (Smith). Lotter published four editions between 1500 and 1515, all of which are rare (this is the second).

"Licht was a German rechenmeister from the Leipzig area. [The 1509] edition of this work is dedicated to his teacher, Udalricus Kalb, a professor of mathematics in Leipzig, perhaps suggesting he studied under Kalb’s direction. This is a short, but quite useful, book on arithmetic using the table abacus. The examples are limited but clear. They show the gathering together of jettons (after a calculation) into the canonical form and the spreading of them out on lower lines (borrowing) in preparation for a subtraction, duplation and mediation. After these basic operations, Licht deals with operations such as the rule of three and presents a small table of coins and weights" (Tomash & Williams).

Very little is known about Licht's origins: on fol. A1v he calls himself "Balthasar licht Greuentalensis", and Erler classes him as a Bavarian; he may hail from Gräfenthal near Saalfeld, now in Thuringia. "Balthasar Licht is a figure of early modern mathematics who may be called as well-known as he is unknown. He is frequently cited in studies on Leipzig mathematics, ca. 1500, and yet his only text with which we are in fact familiar is his 'Algorithmus linealis' (ca. 1500); his life is mostly shrouded in darkness. His book is remarkable for at least two reasons: for one, it was frequently reissued, although a whole series of mathematical treatises in Latin (such as those by Heinrich Stromer and Johannes Widmann) were published in Leipzig between 1490 and 1520. Also, this text is singled out by its emphasis on the methods and achievements of the Nuremberg 'rechenmeisters': Licht taught the doctrines of practitioners, previously transmitted verbally and in German, in writing and in Latin, at a time when Latin was still the language of university scholars" (cf. Gärtner, p. 13).


From an old Czech private collection.


Insignificant stains to title-page; generally very clean.


VD 16, L 1587. OCLC 165767079. Smith, Rara arithmetica, p. 70 (with illustration, fig. 40). Cf. Tomash & Williams L109 (1515 edition only). Barbara Gärtner, “Balthasar Licht", in: Rechenbücher und mathematische Texte der frühen Neuzeit, ed. Rainer Gebhardt (1999), pp. 13-20.