**Claude Mydorge**trained as a lawyer but really had little need to work as he came from a wealthy family. He was able to devote most of his life to research in mathematics without having the problems of earning a salary. His father Jean Mydorge was a councillor in the Parlement in Paris and a judge in the Grande Chambre. His mother, Mme Lamoignon, was from another leading French family.

His first position was as a councillor at the Châtelet and then he was treasurer of the généralité of Amiens. A généralité was a French administrative unit, each under a "collector general" (giving the unit its name) who was a direct agent of the king with wide police, justice, and financial powers. The position of treasurer general was a later addition to the généralités which came about after 1577. This position was an ideal one for Mydorge for it was a high ranking important position, and therefore a worthy one for a member of a leading French family, yet it had light duties which meant that Mydorge could devote a large amount of his time to the subject he loved, namely mathematics. In 1613 he married Mme de la Haye, the sister of the French ambassador in Constantinople.

Mydorge studied geometry and physics. He published books on optics and conic sections, for example *De sectionibus conicis, libri quattuor* Ⓣ (Paris, 1644) contains a wealth of new examples and ideas which were used by many later geometers. Speziali writes in [1]:-

Mydorge's work simplifies many of Apollonius's proofs. However, it contains a new powerful idea, namely that of deforming figures. For example he shows how to deform a circle into an ellipse and proves other results on deforming conic sections. The technique was taken up by La Hire and Newton, then later by Poncelet and Chasles.A further portion of the work, in manuscript, is lost. It seems that two English friends of the Mydorge family, William Cavendish, Duke of Newcastle, and Thomas Wriothesley, Earl of Southampton, took it to England, where apparently it disappeared.

He was interested in mathematical recreations and edited *Récréations Mathématiques* Ⓣ. Mydorge's book *Examen du livre des récréations mathématiques* Ⓣ was published in 1630 and many later books, such as one by Denis Henrion *Les Récréations mathématiques avec l'examen de ses problèmes en arithmétique, géométrie, mécanique, cosmographie, optique, catoptrique *... Ⓣ (1659), were based on it.

Mydorge left an unpublished manuscript *Traité de géométrie* Ⓣ of over 1000 geometric problems and their solutions. The 363^{rd} problem gives a method to transform a square into a regular polygon of equal area and having an arbitrary number of sides. As an example of the type of problem in the manuscript we give the following example. Mydorge proposes a construction of a regular heptagon with a given side:-

However Mydorge does not state that the construction is only an approximation. In [2] Busard examines the magnitude of the error in this and other constructions of Mydore inUpon the given side ab, with midpoint g, construct the equilateral triangle abc and extend the altitude gc to point d such that cd is one-sixth ab. Then c is the centre of the circle circumscribing the desired heptagon, and the construction is easily completed.

*Traité de géométrie*Ⓣ.

It was not only mathematical problems which interested Mydorge. He also worked on light and refraction in particular. His interest in optics also fitted in with an interest in making astronomical observations. He was a close friend of Descartes and made a large number of optical instruments for him, the two shared a strong interest in explaining vision, and the instruments and lenses were to help develop theories.

One of Mydorge's most famous results was an extremely accurate measurement of the latitude of Paris. He was also interested in methods of determining longitude and was appointed to a committee to determine the whether Jean-Baptiste Morin's methods for determining longitude from the Moon's motion was practical. Hérigone and Étienne Pascal served with him on this committee.

Speziali writes in [1]:-

A friend of Descartes and an eminent geometer, Mydorge was also well versed in optics. He possessed a lively curiosity and was open to all the new ideas of his age. Like Fermat, he belonged to that elite group of seventeenth-century scientists who pursued science as amateurs but nevertheless made contributions of the greatest importance to one or more fields of knowledge.

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

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