Jacques Alexandre Le Tenneur

Born: 1610 in Paris, France
Died: 1660 in France

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Little is known of the life of Jacques Le Tenneur (even the dates given for his birth and death are uncertain) except that he was a friend of Mersenne and that he corresponded with Gassendi. What little we do know about his life comes from this correspondence. It is thought that he spent the first 30 or so years of his life in Paris where he was almost certainly educated. We know from his letters that he was proud to describe himself as an amateur and a self-educated person. At one point in his correspondence with Mersenne, he firmly denies that he was taught by Roberval. In this he is countering a comment by Mersenne who seemed to believe that Roberval had been his teacher. Paolo Galluzzi writes [6]:-
He has carefully studied Galileo's 'Dialogues' and 'Two new sciences', while he acutely and passionately defends the 'De motu' by Torricelli from Roberval's objections (Le Tenneur to Mersenne, 9 July 1647). 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. In 1651 he was counsellor to the provincial senate of Guyenne. At this time the Fronde, a civil war in France, was taking place and 1651 is the year Louis XIV lifted the siege of Cognac and assured the obedience of Guyenne. It is highly likely that Le Tenneur was involved with the political feuding of the Fronde.

Galileo wrote down his ideas on falling bodied in Du Motu around 1590 but never published them. In 1646 Honoré Fabri published Tractatus physicus de motu locali 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. however, spotted that Fabri's own theory, despite his belief to the contrary, also required mathematical instants. Le Tenneur then argues that Galileo's theory is superior to that of Fabri since it did not depend of the unit of time used for measurements. He points out the invariance in Galileo's theory that (see for example [7]):-

... 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. .... But all is found to cohere and agree marvellously.
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. Palmerino writes [7]:-
He finally declared that he had entered into the controversy on the insistence of a few friends and of Mersenne, and not because he had any faith in the possibility of changing the opinions of his stubborn interlocutors
Mersenne sent Le Tenneur's letter to Fabri without disclosing its author. Fabri then wrote to his own pupil Pierre Mousnier in May 1647, saying that the views expressed by the anonymous critic were powerful ones. 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 , 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. There was also a belief that all bodies have an innate speed of a certain determinate degree. Le Tenneur's argument against this is put at follows (see for example [7]):-

It must needs be the case that the first space is to the second space like the two first spaces to the two subsequent ones, as has been shown against Fabri, because we obviously need a principle of uniformity in natural events as these need to proceed in an uninterrupted course. The consequence of this is that heavy bodies have no innate speed, but that in falling, they pass through all degrees of slowness and speed.
Another important topic causing much controversy at this time was the vacuum. Around 1644, Evangelista Torricelli was the first to conduct experiments with a column of mercury in a tube which he inverted and created a vacuum. Le Tenneur had been present in 1647 when Florin Périer, Pascal's brother-in-law, repeated Torricelli's experiment in Clermont. This did not convince some who witnessed the experiment that a vacuum had been created. 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. There continued to be much argument and later a suggestion was made to see whether the column of mercury would reach the same height at the top of a mountain as at the foot. Mersenne wrote to Le Tenneur in January 1648 suggesting he carry out such an experiment on the Puy-de-Dôme. Le Tenneur replied on 18 January (see for example [3]):-
I tell you that I think, along with Roberval, that it would be entirely useless, and that the same thing found below would be the same high up.
Of course Le Tenneur was wrong in his belief. However, he had other objections to Mersenne's suggestion, saying that he was no longer living in the Auvergne but had moved to Tours. Also, he wrote:-
... do you think that carrying a glass tube and 20 pounds of mercury up a mountain that high is easy?
In an earlier letter Le Tenneur had asked Mersenne how the cost of such an expedition might be met. Mersenne had suggested he apply for financial assistance to "a great lady of my acquaintance". In his letter of 18 January 1648, Le Tenneur guesses that Mersenne is referring to:-
... the fat Marquise d'Effait, who gladly dances with anyone, but would not consider spending a penny for the advancement of science.
In fact the Puy-de-Dôme experiment was carried out by Florin Périer in October 1648.

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'. Le Tenneur replies that [3]:-

... he accepts the view common among his contemporaries that light is something corporeal. 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 (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 . 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.

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

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JOC/EFR April 2009
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