**Gilles Roberval** was a French scientist who developed powerful methods in the early study of integration.

- The reason is that Gilles Roberval was named Gilles Personne and this was the name under which he was known for at least the first twenty-five years of his life, only adding the "de Roberval" after 1628.
- Pierre and Jeanne Personne were of humble origins, living in the village of Roberval, about 50 km north (and a bit east) of Paris.
- Gilles began to study mathematics at the age of 14 years when the parish priest of Rhuis, a village just 2 km to the north of Roberval, realised that young Gilles was highly intelligent and began to give him lessons.
- The parish priest was actually the chaplain to the queen, Marie de Médici, and he not only instructed Gilles Personne in mathematics but also in Latin and probably Greek.
- Gilles Personne, as he was still known at the time, studied both practical and theoretical aspects of the problems of fortifications and ballistics which resulted from this siege.
- At around this time, having received permission from the head of the village of Roberval, he added "de Roberval" to his name becoming Gilles Personne de Roberval.
- We will refer to him as Roberval from this point on.
- It had been founded in the 14th century for students from Bayeux but by the time Roberval was appointed it no longer had that restriction.
- Before we consider briefly what Roberval's life in these rooms was like, we need to understand a little of his character.
- This was a competitive appointment and Roberval had to compete for reappointment every three years.
- Roberval brought in extra income by leasing out small plots on his farm to individuals.
- Menerval is, like Roberval's birthplace, north of Paris, but it is further to the west about 80 km from Paris.
- It was well situated for its produce to be sold in Paris, and also near enough for Roberval to be able to make trips to the farm.
- Let us now look at Roberval's contributions to mathematics.
- Most of Roberval's material in this 1693 publication was at least fifty years old, so it did not have the impact that it would have done had it been published shortly after being written.
- Roberval developed powerful methods in an early study of integration, writing Traité des indivisibles Ⓣ(Treatise on indivisables) which he claimed was based on Archimedes and not Cavalieri.
- In addition to his discoveries on plane curves, Roberval is important for his method of drawing the tangent to a curve, already suggested by Torricelli.
- This method of drawing tangents makes Roberval the founder of kinematic geometry.
- Roberval wrote a treatise on algebra and one of analytic geometry which appeared in his posthumous 1693 publication.
- The treatise has never been found and probably was never written, but parts of each of the eight books exists in Roberval's manuscripts.
- We mentioned above that Le système du monde d'après Aristarque de Samos Ⓣ(The system of the world according to Aristarchus of Samos)(1644) was one of only two publications by Roberval in his lifetime.
- In 1666 Roberval was one of a group of scientists making astronomical observations from Jean-Baptiste Colbert's Paris residence.
- In addition to Roberval the others involved were Christiaan Huygens, Pierre de Carcavi, Adrien Auzout, Bernard Frénicle de Bessy and Jacques Buot.
- Again, when a German inventor approached Colbert in 1668 with the offer of a secret machine which would solve the problem of calculating the longitude, Roberval was one of a small committee appointed by Colbert to examine the claim (the others were Auzout, Carcavi, Huygens, Picard and a senior naval officer).
- In 1669 he invented the 'Roberval balance' which is now almost universally used for weighing scales of the balance type.
- Monsieur de Roberval also had a date in the same neighbourhood.
- They appeared to be joking with each other, but there was a bit of an edge to their humour, as Monsieur de Roberval confirmed after he returned from dinner ...
- We see from this letter the friction between Roberval and Descartes.
- As well as meeting with other scientists in Paris, Roberval also corresponded regularly with Pierre de Fermat and with Evangelista Torricelli until his death in 1647.

Born 9 August 1602, Noël-Saint-Martin, Villeneuve-sur-Verberie, Oise, France. Died 27 October 1675, Paris, France.

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Analysis, Number Theory, Special Numbers And Numerals

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