Background
Chuquet was born in 1445, in Paris, France. He called himself a Parisian. He spent his youth in that city, where he was probably born and where the name is yet known. It is difficult to say more about his life.
Chuquet was born in 1445, in Paris, France. He called himself a Parisian. He spent his youth in that city, where he was probably born and where the name is yet known. It is difficult to say more about his life.
Chuquet pursued his extensive studies in Paris, up to the baccalaureate in medicine (which implies a master of arts as well).
Chuquet's book on the science of numbers, the “Triparty,” which as an entity has remained in manuscript, was published by Aristide Marre in 1880. The following year Marre published the statement of, and replies to, a set of 156 problems that follow the “Triparty” in the manuscript. The analysis of these problems remains unpublished, as do an application to practical geometry and a treatise on commercial arithmetic.
The conclusion of the “Triparty” indicates that it was composed by one Nicolas Chuquet of Paris, holder of the baccalaureate in medicine, at Lyons, in 1484. Only one copy of the book (the work of a firm of copyists) is known to exist; although it remained in manuscript until 1880, several passages from it were copied slavishly by “Master Étienne de la Roche, also called Villefranche, native of Lyons on the Rhone,” in his arithmetic text of 1520, of which there was a second edition in 1538.
Chuquet was living in Lyons in 1484, perhaps practicing medicine but more probably teaching arithmetic there as “master of algorithms.” The significant place given to questions of simple and compound interest, the repayment of debts, and such in his work leads one to suppose this. However, he used these questions only as pretexts for exercises in algebra.
As for his mathematical work, in order to judge it fairly, it must compared with the work of such contemporaries as Regiomontanus, whose De triangulis omnimodis was written twenty years earlier, in 1464 (although it was not printed until 1533), and most notably with that of Luca Pacioli, whose Summa de arithmetica, geometria proportioni et proportionalita was published ten years later, in 1494.
Chuquet made few claims of priority. The only thing that he prided himself on as his personal discovery was his “règle des nombres moyens.” On one further occasion he seemed also to be claiming for himself the “règle des premiers.” But he says no more on this point - where, as far as we know, his originality is obvious.
Chuquet engaged in very little controversy, contenting himself with twice criticizing a certain Master Berthelemy de Romans, also cited by a contemporary French arithmetician, Jehan Adam (whose arithmetic manuscript is dated 1475).
The “Triparty” is a treatise on algebra, although the word appears nowhere in the manuscript. This algebra deals only with numbers, but in a very broad sense of the term. The first part concerns rational numbers. Chuquet’s originality in his rules for decimal numeration, both spoken and written, is immediately obvious. He introduced the practice of division into groups of six figures and used, besides the already familiar million, the words billion (1012), trillion (1018), quadrillion (1024), etc.
Chuquet’s study of the rules of three and of simple and double false position, clear but commonplace, served as pretext for a collection of remarkable linear problems, expounded in a chapter entitled “Seconde partie d’une position.” Here he did not reveal his methods but reserved their exposition for a later part of the work, where he then said that after having solved a problem by the usual methods - double position or algebra - one must vary the known numerical quantities and carefully analyze the sequence of computations in order to extract a canon (formula). This analysis generally led him to a correct formula, although at times he was mistaken and gave methods applicable only for particular values.
(French Edition)
1979Chuquet’s mathematical learning was solid. He cites by name Boethius - whom everyone knew at that time - Euclid, and Campanus of Novara. He knew the propositions of Archimedes, Ptolemy, and Eutocius, which he stated without indicating his sources. In geometry his language seems to be that of a translator, transposing terms taken from Greek or Latin into French. By contrast, in the parts devoted solely to arithmetic or algebra there is no borrowing of learned terminology. Everything is written in simple, direct language, with certain French neologisms that have not been preserved elsewhere. The only exception is the ponderous nomenclature for the various proportions encumbering the first pages of the “Triparty,” for Chuquet was respecting a style that goes back to Nicomachus and his translator Boethius and that still infested the teaching of mathematics in the seventeenth century.
On the whole, Chuquet wrote a beautiful French that is still quite readable. His simple, very mathematical style does not lack elegance, although occasional affectation led to the use of three or four synonyms in order to avoid monotonous repetition. Marre purports to find many Italianisms in Chuquet’s French. He attributes this peculiarity to the close relations between Lyons and the cities of northern Italy and to its large and prosperous Italian colony. Upon examination, many of these so-called Italianisms appear to be nothing more than Latinisms, however, and the French used by Chuquet seems as pure as that of his contemporaries.