**Florimond de Beaune** was a French jurist and amateur mathematician who produced the first important introduction to Descartes' cartesian geometry.

- He was born in Blois, which is in central France on the Loire River and, at the time de Beaune was born there, it was almost a second capital of France.
- Florimond de Beaune senior was a squire with an estate being the Seigneur de Goulioux.
- De Beaune was educated in Paris where he went on to study law although his status meant that he had no need to take a degree.
- De Beaune bought the office of counselor to the court of justice in Blois, and was only an amateur mathematician.
- As we noted, his second marriage brought de Beaune a substantial amount of money.
- The classification by authors shows that de Beaune possessed all the works by Kepler, Galileo, Descartes and J-B Morin published at that time, and most of those of Mersenne and Gassendi.
- The places of publication show the facility of obtaining works published outside of France.
- It is unfortunate that little of de Beaune's mathematical work survives although Paul Tannery was able, from correspondence of de Beaune's that he discovered, to come to interesting conclusions.
- This statement, which is not easily justified except in the language of differential and integral calculus, was fifty years ahead of scientific developments and - by itself - reveals Debeaune's singular ability to translate physical questions into the abstract language of mathematical analysis, despite the inadequacies of the operative means of his time.
- De Beaune did, however, publish some work for he produced the first important introduction to Descartes' cartesian geometry.
- He wrote Notes brièves Ⓣ(Brief notes) which was published in 1649 as part of the first Latin edition of Descartes' La Géométrie.
- Two other papers by de Beaune on algebra appeared as part of the second edition of La Géométrie.
- De Beaune and Descartes were good friends and corresponded frequently on mathematical topics.
- When he was very ill near the end of his life, de Beaune entrusted Bartholin with several manuscripts and asked him to arrange for their publication.
- 'Doctrine de l'angle solide construit sous trois angles plans' for posthumous publication, but the treatise never found its way into print because of the complexity of its accompanying diagrams.
- The treatise is of interest chiefly because it is a work of pure synthetic geometry consisting of some 125 propositions composed in the style of Euclid by one of the ablest practitioners of the new analytical art typified by the works of Descartes and Fermat.
- And while he built on results found in works on trigonometry by Snell, Girard, and Briggs, de Beaune avoided the numerical methods employed by these and other mathematical practitioners of the period in favour of pure geometry, indicating that he distinguished clearly between two genres of mathematics.
- De Beaune was also interested in mechanics and optics and wrote on these topics.
- We do know from Mersenne that de Beaune wrote Méchaniques Ⓣ(Mechanics) and we know from Frans van Schooten that he wrote Dioptrique Ⓣ(Dioptrics).
- De Beaune gained the reputation of being the finest instrument maker of his day which is why Descartes wrote to de Beaune in March 1639.
- Descartes had designed a machine for grinding hyperbolic lenses that he described in La Dioptrique and he asked de Beaune if he could make the instrument.
- De Beaune became obsessed with the idea of making Descartes' machine to grind lenses and devoted his whole time to the project.
- Descartes knew that de Beaune was the only person who had the technical proficiency, a deep understanding of mathematics and a fascination with astronomy.
- However in January 1640, despite his expertise, de Beaune cut his hand badly on a piece of roughly shaped glass which he was trying to cut into a hyperbolic shape.
- When Descartes heard about the accident he seemed pleased that his scientific imagination went beyond what the best technician could make.
- Several years after the accident, de Beaune returned to the topic of lenses but by this time he was more interested in the theory than in grinding lenses.
- However, his failing eyesight deteriorated rapidly, and he died shortly after having a foot amputated.

Born 7 October 1601, Blois, France. Died 18 August 1652, Blois, France.

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Analysis, Astronomy

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