**Michel Chasles** worked on algebraic and projective geometry.

- Epernon, the town where Chasles was born, is in the region of Chartres lying about one third of the way from the town of Chartres to Paris.
- Chasles was christened Floréal Chasles by his parents after the month of the Republican calendar.
- This calendar fell out of use and a court order was obtained to change his name from Floréal to Michel a few days after his sixteenth birthday.
- Chasles attended the Lycée Impérial for his secondary education.
- Chasles was called up to take part in the defence of Paris in early 1814.
- Chasles was able to return to his studies at the École Polytechnique.
- Having obtained a place in the engineering corps, Chasles decided not to accept it but to give his place to one of his fellow students who was in financial difficulties.
- However, Chasles was interested in history and in mathematics and he was not successful as a trainee in the firm.
- In 1837 Chasles published his first major work Aperçu historique sur l'origine et le développement des méthodes en géométrie Ⓣ(Historical overview of the origin and development of methods in geometry) which quickly made his reputation as both a mathematician and as an historian of mathematics.
- In Aperçu historique Ⓣ(Historical overview) Chasles studied the method of reciprocal polars as an application of the principle of duality in projective geometry; in the same way the principle of homography leads to a great number of properties of quadric surfaces.
- The Académie des Sciences wanted to publish the work which Chasles submitted to them but he asked to be able to add to the historical introduction as well as to add further historical notes to the text and include some new material and notes.
- This work in many ways is the crucial one for Chasles's future research since almost all of the many works he produced throughout the rest of his career elaborate on points discussed in these notes he added to the Aperçu historique Ⓣ(Historical overview).
- This was that Chasles could not read German so he was not so familiar with the recent results published in that language.
- On the strength of his fine work Chasles became professor at the École Polytechnique in Paris in 1841, at the age of nearly 48.
- In his text Traité de géométrie Ⓣ(Treatise on geometry) in 1852 Chasles discusses cross ratio, pencils and involutions, all notions which he introduced.
- One of the results for which Chasles is well known is his enumeration of conics.
- Questions of this type go back to Apollonius, but such questions had arisen while Chasles was working on geometry, in particular the Steiner "problem of five conics" was posed in 1848.
- Chasles solved this problem correctly in 1864 when he gave the answer of 3264.
- Chasles received many honours for this highly original work.
- The London Mathematical Society was founded in 1865 and it elected Chasles in 1867 as its first foreign member.
- There is one aspect of Chasles's life which seems so out of character with the brilliant man that he was that it caused him great distress.
- Chasles collected autographs and manuscripts but appears to have displayed a naiveté which is almost unbelievable.
- Chasles bought thousands of manuscripts from Denis Vrain-Lucas between 1861 and 1869.
- Vrain-Lucas sold Chasles documents which purported to be part of correspondence between Newton, Pascal, and Boyle.
- Chasles presented the letters to the Académie des Sciences in 1867 for they "proved" that Pascal was the first to propose the universal law of gravitation, and not Newton.
- Chasles argued strongly that the letters were genuine.
- However Vrain-Lucas was tried in 1869-70 for forging the documents and Chasles had to appear at the trial.
- It was an extremely uncomfortable experience for Chasles since he had to admit in court that he had purchased documents supposedly written by Galileo, Cleopatra and Lazarus and how someone of Chasles's intelligence and a deep interest in history would have believed that these all these wrote in French is beyond belief! Vrain-Lucas was found guilty and Chasles, although 77 by this time, must have looked extremely silly.

Born 15 November 1793, Epernon, France. Died 18 December 1880, Paris, France.

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Algebra, Astronomy, Geometry, Physics

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