**Estienne de la Roche** as a French mathematician who published an arithmetic book with good notation for powers and roots.

- Because of where he lived when young, La Roche was sometimes known as 'Villefranche.' This is almost the total information about his life which is known.
- It comes from the Lyon tax register of 1493, which also describes de la Roche as a qualified master of 'argorisms.' This is a rather unusual spelling of 'algorisms,' but de la Roche uses the same spelling 'argorisms' in his book.
- De la Roche's date of birth is unknown, and the date we have given of 1470 is simply a guess based on the fact that he had to be old enough to be described as a qualified master of 'argorisms' by 1493.
- At the time when de la Roche lived in Lyon it was the commercial capital of France so it is natural that someone living there would become interested in the mathematics of the time relevant to commerce.
- La Roche taught commercial arithmetic in Lyon for 25 years.
- This fact is known since a number of copies of Chuquet's manuscripts still exist which have marginal annotations in de la Roche's handwriting.
- See the end of this article for a description of the route the manuscripts took to reach us today.
- De la Roche published Larismetique nouellement composée Ⓣ(Arithmetic newly presented) in 1520 which was considered an excellent arithmetic book with good notation for powers and roots.
- However in 1880 Aristide Marre published Chuquet's Triparty Ⓣ(The science of numbers in three parts).
- It was immediately discovered that the first part of de la Roche's Larismetique Ⓣ(Arithmetic newly presented) is essentially a copy of Chuquet's Algebra.
- It is to be regretted that Chuquet did not have in de la Roche an interpreter acting with sympathy and full understanding.
- It was thought at this time that de la Roche was simply a plagiarist.
- However more recent work has come to a less harsh conclusion about de la Roche.
- It now appears that de la Roche was trying to teach important mathematics which was not available to the French public.
- that the charge of plagiarism against Estienne de la Roche is largely an anachronism, and that the difference in emphasis may be explained by the readers he had in mind and by the climate of mathematical opinion, while the similarities are close enough to indicate how far his potential readership would have been receptive to a more faithful presentation of Chuquet's ideas.
- If de la Roche had been more faithful to Chuquet's notation and terminology and had used it consistently, and especially if this had given rise to some controversy in the literature, then Bombelli's work, at least, might have been enhanced.
- In this sense, and in this sense only, can de la Roche be held responsible for Chuquet's ideas remaining in obscurity.
- Let us now look at some examples of notation from de la Roche's Larismetique nouellement composée Ⓣ(Arithmetic newly presented).
- This strange use of a square to denote the cube only appears in de la Roche, not being followed by anyone else.
- Here is his description of numbers, powers and the unknown (a thing).
- Now, as one of the sides is a radical, multiply each side by itself.
- De la Roche was writing a commercial arithmetic, and as such it was highly successful.
- Nicolas Chuquet from Paris, Philippe Friscobaldi from Florence, and Luca Pacioli from Burgo.
- This statement itself suggests that de la Roche was not trying to hide his dependence on others, for many mathematicians of this period would have made no acknowledgement to others at all.
- Indeed de la Roche took parts of Chuquet, parts of Pacioli and parts of Philippe Friscobaldi, a French banker who is considerably less well known as a mathematics writer than the other two.
- The unfortunate part is that de la Roche lacked any real skill in forming them into his teaching book.
- It then passed into the famous library of Jean Baptiste Colbert (1619-1683), the finance minister of King Louis XIV who was also the founder of the French Academy ...
- As de la Roche's birth date is unknown, so is his death date.
- It appears he was still alive when his Larismetique nouellement composée Ⓣ(Arithmetic newly presented) was published in 1520, but since Gilles Huguetan revised the work for publication in 1538, de la Roche must have died a few years before 1538.

Born about 1470, Lyon, France. Died about 1530, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive