**Claude Dechales**became a Jesuit at the age of 15 and was educated within the Jesuit Order. The Jesuit Order had been created about eighty years before Dechales was born and from the very beginning education and scholarship became the principal work of the Order. By the time Dechales entered the Order it contained over 16,000 men. The main task of the Jesuits was education, but the next most important task was missionary work throughout Europe, Asia, and Africa. Dechales participated in these two major roles of the Jesuits, for in addition to a life spent in education, he was, for a time, a Jesuit missionary in Turkey.

Dechales lectured at Jesuit colleges, first in Paris where for four years he taught at the Collège de Clermont, then at he taught at Colleges in Lyons and Chambéry. From Chambéry he went to Marseilles where King Louis XIV appointed him Royal Professor of Hydrography. In Marseilles he taught navigation, military engineering and other applications of mathematics. From Marseilles he moved to Turin where he was appointed professor of mathematics.

Dechales is best remembered for *Cursus seu mundus mathematicus* Ⓣ published in Lyons in 1674, a complete course of mathematics. Topics covered in this wide ranging work included practical geometry, mechanics, statics, magnetism and optics as well as topics outwith the usual topics of mathematics such as geography, architecture, astronomy, natural philosophy and music. Nardi writes [5]:-

The book was widely used but it reflects his ability to teach rather than a research ability and fails to use the mathematical advances of the day. It is old-fashioned in its coverage: in algebra, for example, it owes more to Diophantus than to the algebraists of its day. Hutton wrote that the book:-Dechales adopted Galileo's theory of motion, where he introduced several original views and developments. He attaches a preponderant significance to the experimental foundation of Galileo's main theorems and, in his opinion, the proportionality of velocity and time is first an expression of Nature(ex natura rei), then a logical assignment. Dechales anticipates some aspects of Newton's natural philosophy by emphasising questions depending on dynamics such as the concept of gravity(related to the free fall of bodies)and the mathematical treatment of air friction. ... Dechales'[offers]apology of Galileo's times-squared law of uniformly accelerated motion, which is maintained by Dechales in opposition to rival explanatory attempts developed - or even simply proposed - by contemporary scientists like the Jesuit professors Fabri and Le Cazre ...

As Moritz Cantor points out in [3] Dechales rarely mentions the work of Mydorge, Desargues, Pascal, Fermat, Descartes, or Wallis [1]:-... is of a very old-fashioned sort, considering the time when it was written.

Other work by Dechales included... while according Dechales due credit for his efforts, Cantor is nevertheless critical of much of the mathematical content of his work, deploring Dechales's failure to make full use of such available contemporary source materials as the first-hand works of mathematicians, their correspondence, and so on.

*L'art de fortifier, de défendre et d'attaquer les places, suivant les méthodes françoises, hollandoises, italiennes et espagnoles*Ⓣ (Paris, 1677), and

*L'art de naviger demontré par principes et confirmé par plusieurs observations tirées de l'experience*Ⓣ (Paris, 1677). In 1678 he published in Lausanne his edition of Euclid,

*The Elements of Euclid Explained in a New but Most Easy Method: Together with the Use of Every Proposition through All Parts of the Mathematics, written in French by That Most Excellent Mathematician, F Claude Francis Milliet Dechales of the Society of Jesus*. This work covers Books 1 to 6, together with Books 11 and 12, of Euclid's

*Elements*. A second edition was published in 1683, then an edition revised by Ozanam was published in Paris in 1753. An English translation was published in London by M Gillyflower and W Freeman, the translation being by Reeve Williams. A second edition of this English translation appeared in 1696. Schaap writes [1]:-

Dechales's separate edition of Euclid, long a favourite in France and elsewhere on the Continent, never became popular in England.

**Article by:** *J J O'Connor* and *E F Robertson*