Larismethique nouellement composee par maistre Estienne de La Roche dict Villefra[n]che natif de Lyo[n] sus le Rosne diuisee en deux parties dont la p[re]miere tracte des p[ro]prietes p[er]fectio[n]s et regles de la dicte scie[n]ce: come le no[m]bre entire, le no[m]bre rout, le regle de troys, la regle d'une faulse position, de deux faluses position[n]s, d'apposition et remotio[n], de la regle la chose, et de la qua[n]tite des p[ro]gressio[n]s et p[ro]portio[n]s. La seco[n]de tracte de la practique dicelle applicquee en fait des mo[n]oyes, en toutes marcha[n]dises comme drapperie, espicerie, mercerie et en toutes aultres marcha[n]dises qui se vendent a mesure au pois ou au nombre, en co[m]paignies et en tro[n]ques, es changes et merites, en

THE FIRST PUBLISHED WORK ON ALGEBRA IN FRENCH. First edition, extremely rare, of the first published work on algebra in French. This is a fine copy in a beautiful contemporary binding. Born in Lyon, then the principal commercial centre of France, La Roche was a student of Nicolas Chuquet and published for the first time in the present work large sections from Chuquet's Le Triparty en la Science des Nombres, the most original mathematical work of the fifteenth century. Chuquet's work, of which a single manuscript survives (BNF Fonds français 1346), remained unpublished until 1881. La Roche's work thus printed for the first time several important innovations in arithmetic and algebra introduced by Chuquet: the use of exponents to denote powers of a number, often credited to Descartes who introduced them in his Géométrie more than a century later; the use of the 'second unknown' (see below) in the solution of systems of linear equations, which was an important step towards the invention of symbolic algebra by Viète; the use of negative numbers in the solution of equations; and the introduction of our terms 'million', 'billion' and 'trillion' for powers of 106. La Roche also includes Chuquet's 'règle des nombres moyens,' according to which a fraction could be found between any two given fractions by taking the sum of their numerators and dividing by the sum of their denominators; this rule could be used to find the solution of any problem soluble in rational numbers, once an upper and a lower bound for the solution had been found. La Roche intended his work to serve the mercantile class, and his account of commercial arithmetic goes considerably beyond Chuquet. "The second, and greater, part of La Roche's work has, apart from some geometrical calculations at the end, a commercial character. The author states that as a basis he used 'the flower of several masters, experts in the art' of arithmetic, such as Luca Pacioli, supplemented by his own knowledge of business practice . [La Roche's work] presented an outstanding view of contemporary methods of computation and their applications in trade" (DSB). OCLC lists copies at Columbia and Harvard only in North America. ABPC/RBH list only the Macclesfield copy (rebound in the 19th century) since Honeyman (Sotheby's, April 14, 2005, lot 1204, £19,200 = $36,409). The present copy was offered by Librairie Thomas-Scheler in 1996 (Catalogue Nouvelle Série No. 15, n. 296, 120,000F). "We do not know much about de la Roche (c. 1470-1530). Tax registers from Lyon reveal that his father lived in the Rue Neuve in the 1480s and that Estienne owned more than one property in Villefranche, from which he derived his nickname. De la Roche is described as a 'master of argorisme' as he taught merchant arithmetic for 25 years at Lyon. He owned the manuscript of the Triparty after the death of Chuquet (1488). It is therefore considered that de la Roche was on friendly terms with Chuquet and possibly learned mathematics from him. "The importance of the Larismethique has been seriously underestimated. There are several reasons for this. Probably the most important one is Aristide Marre's misrepresentation of the Larismethique as a grave case of plagiarism. Marre discovered that the printed work by Estienne de la Roche, contained large fragments that were literally copied from Chuquet's manuscript (Marre, Le Triparty . par Maistre Nicolas Chuquet (1881), introduction)" (Heeffer, pp. 1-2). But Barbara Moss argues that "the charge of plagiarism against Estienne de la Roche is largely an anachronism . Before the spread of printing, academic knowledge had been disseminated through the copying of manuscripts, and Chuquet, like many of his contemporaries, must have written down for reference a large number of examples from the work of others, with or without a note of their source . De la Roche's use of citations and sources is similar to that in a number of printed arithmetics of that period. Following the usual com.…