**Jacques Le Tenneur** was a French amateur mathematician who published a work on dynamics following Galileo's point of view.

- What little we do know about his life comes from this correspondence.
- We know from his letters that he was proud to describe himself as an amateur and a self-educated person.
- M Le Tenneur appears as a convinced "Galilean" full of admiration for Gassendi's atomism.
- Of Gassendi he particularly appreciates the insertion of scientific ideas into an organic philosophical background as well as his talent as experimenter.
- As many others in those years, Le Tenneur was fascinated by Descartes' physics, but, as he wrote to Mersenne, he admired Descartes' insightful arguments, but did not find them at all convincing ...
- (Le Tenneur to Mersenne, 9 July 1647).
- It is known for certain that by 1646 Le Tenneur was in Clermont in the Auvergne region of central France.
- Clermont was the town that Pascal had been born in 23 years before.
- Galileo wrote down his ideas on falling bodied in Du Motu Ⓣ(On movement) around 1590 but never published them.
- In 1646 Honoré Fabri published Tractatus physicus de motu locali Ⓣ(Treatise on local physical movement) which set out to refute Galileo's theory of motion of falling bodies and to substitute a theory of his own.
- Mersenne, clearly aware that Le Tenneur was a firm believer in Galileo's theory, wrote to him late in 1646 asking him to support Galileo's theory against the attacks by Fabri.
- In January 1647 Le Tenneur corresponded with Gassendi who also encouraged him to argue the case for Galileo.
- Le Tenneur replied with a long letter to Mersenne written on 13 April 1647.
- As Zeno's paradoxes had shown in antiquity, the idea of a mathematical instant led to difficulties.
- Fabri had argued that mathematical instants do not exit and hence Galileo's theory breaks down immediately since he assumes their existence.
- Le Tenneur then argues that Galileo's theory is superior to that of Fabri since it did not depend on the unit of time used for measurements.
- The multiplication of times according to any proportion whatsoever always confirms the uniform proportion among the spaces, and it does not happen that you get a larger or a smaller space if the equal times get longer or shorter ....
- Nor will there be a larger ratio between four spaces and two spaces, than between two spaces and one space; nor will there occur a larger or smaller space.

- Another part of Fabri's argument was that it was impossible for a body sliding down an inclined plane and another body in free fall to both pass through an infinite number of velocities.
- This argument really claims that two lines of different lengths cannot both contain an equal number of points.
- Le Tenneur essentially refutes this by showing that in a right-angled triangle every point on one of the shorter sides corresponds to a point on the hypotenuse by drawing a line parallel to the other short side, and visa-versa.
- Fabri asked Mousnier to reply which he did in a letter to Mersenne on 1 October 1647.
- Le Tenneur's letter to Mersenne formed the basis of his most important work De motu naturaliter accelerato tractatus physico-mathematicus Ⓣ(Physico-mathematical treatise on naturally accelerated motion), published in 1649, where he showed that he understood Galileo's arguments for free falling objects while Fabri and others did not.
- Most people at that time believed that the speed of a body in free fall was proportional to the distance it had fallen.
- Someone said that they would only believe in a vacuum if a hole was made in the tube and the mercury seen to fall.
- Le Tenneur offered a 100 to 1 bet that it would fall, but attempts to make a small hole in the glass failed.
- Mersenne wrote to Le Tenneur in January 1648 suggesting he carry out such an experiment on the Puy-de-Dôme.
- Of course Le Tenneur was wrong in his belief.
- In an earlier letter Le Tenneur had asked Mersenne how the cost of such an expedition might be met.
- Mersenne had expressed other thoughts about the vacuum in his January 1648 letter.
- He presented an argument, first made by Étienne Noël: the fact that light can pass freely through the glass suggests that other 'subtle matter' might also be able to pass through.
- Perhaps above the column of mercury there is not a vacuum but this 'subtle matter'.
- But since he believes that it is a limited 'horror of vacuum' that holds up the column of mercury, he argues that if light or subtle matter could simply enter and fill the empty space, then the column in the tube would fall.
- Le Tenneur also published Traité des quantités incommensurables Ⓣ(Treatise on irrational quantities) (1640) which is a work on the foundations of algebra.
- The full title of the work is Traité des quantites incommensurables ou sont decidees plusieurs belles questions des nombres rationaus et irrationaus, l'erreurs de Stevin refutées, le dizieme livre d'Euclide illustre de nouvelles demonstrations Ⓣ(Treatise on irrational quantities in which several beautiful questions on rational and irrational numbers are answered, errors of Stevin are refuted and the tenth book of Euclid is illustrated with new demonstrations).
- Le Tenneur clearly was trying to argue against the notions current at the time on using algebra to study geometry.
- He wished geometry to be Greek style, not in the style of Descartes and his followers.

Born 1610, Paris, France. Died 1660, France.

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