The beginning of the seventeenth century was a period when mathematicians began to see the benefits of knowing about the work of others and a network grew up in France of mathematicians meeting, corresponding, and generally motivating each other to make further discoveries. Beaugrand was certainly part of this network from a very early stage which, after 1619, became centred around Mersenne and he frequently attended meetings in Mersenne's cell in Paris.
In Bordeaux there was a small circle of lovers of mathematics with men like d'Espagnet, Philon and Prades all being mentioned in Fermat's correspondence. Étienne d'Espagnet was the son of Jean d'Espagnet, the president of the Bordeaux parliament, and was a friend of Viète. Beaugrand, as a pupil of Viète, would have known of d'Espagnet and the Bordeaux group, and afterwards he became friends with d'Espagnet. Fermat probably met Beaugrand for the first time in Orléans in August 1626. It is thought that he advised Fermat to settle in Bordeaux because of the mathematical life of the city. Beaugrand corresponded frequently with Fermat after he was in Bordeaux and it is through this correspondence that Fermat's work became known in Paris. Certainly Beaugrand always acted as if he had discovered Fermat and proudly reported his achievements to Mersenne and he also reported on Fermat's work when he travelled to Italy and met many Italian mathematicians. We know that at least five years before this Italian trip of 1635 Beaugrand had made a visit to England.
In 1630 Beaugrand became a Court Official, being named mathematician to Gaston duc d'Orleans. Gaston, the third son of King Henry IV, had been made Duke of Orleans in 1626 after his marriage to Marie de Bourbon-Montpensier. However he soon came into conflict with Louis XIII and a military conflict resulted. He fled to Lorraine in 1631, then to the Spanish Netherlands in 1632. As with many mathematicians in this period Beaugrand's life was greatly affected by wars and the fate of his employer. Certainly he moved in high political circles in Paris, and was considered highly for his mathematical abilities. In 1634 he was appointed to the committee which was set up by Cardinal Richelieu to evaluate Jean-Baptiste Morin's solution to the longitude problem by measuring absolute time from the position of the Moon relative to the stars. Étienne Pascal, Mydorge, Hérigone, J C Boulenger and L de la Porte served on the committee along with Beaugrand and they were in dispute with Morin for the five years after he made his proposal.
Beaugrand met Hobbes on a number of occasions, and Descartes records that the two met in Mersenne's cell in Paris in 1634 and 1637. Between these two dates, in 1635, Beaugrand went to Italy along with the French ambassador Bellièvre and his party. At this time Beaugrand was holding the office of secretary to the king. As always when he was travelling, he made a special effort to meet with mathematicians. He visited Cavalieri in Bologna, Castelli in Rome, and Galileo in his home at Arcetri near Florence. He corresponded with all three of these mathematicians after he returned to Paris in February 1636.
Beaugrand published Geostatique in 1636 and also published on mathematics. As well as mathematics, he was interested in astronomy. He observed eclipses and other astronomical events. By the time he published Geostatique, however, he was out of favour with most of the French mathematicians although the work was well received by the Italian mathematicians who seemed particularly impressed with him. There is little wonder that he was not in favour among the French mathematicians for he had attacked the work of Desargues and published a series of pamphlets attacking the work of Descartes. In fact earlier he had been a friend of Desargues before he had a dispute with him. By this time even his close friend Fermat had become rather distant.
Beaugrand claimed that Descartes' work was copied from Harriot. It seems unlikely that this claim is true although many historians still argue over how much Harriot influenced the work of others. It was not the custom of the time to acknowledge sources of ideas as it is today so it is possible that Beaugrand's claim is at least in some small degree true. A letter from Beaugrand to Desargues written on 25 July 1639 defended the classical methods.
Article by: J J O'Connor and E F Robertson