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2018 July Jacques Rohault

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Jacques Rohault


The Book of the Month for July 2018 is Oeuvres posthumes de M. Rohault, a collection of the work of Jacques Rohault (1618-72), published posthumously in 1690, nearly 20 years after his death.

Jacques Rohault, Oeuvres Posthumes (The Hague, 1690), title pages of the first and second volumes.


Jacques Rohault was a French mathematician, philosopher and physicist. Born in Amiens, Rohault was the son of a wealthy wine merchant. He studied in the Jesuit College where he lived and eventually became a professor after moving to Paris, which, along with Lyon, was the hub of mathematical development in France at the time. He married the daughter of Claude Clerselier (1614-84), the man who edited all of René Descartes’ unpublished work, and through this relation Rohault became a very enthusiastic follower of Descartes‘ work and he was very influential in the dissemination of Cartesianism in France. Some of Rohault’s other works included Traité de physique (1671) which was actually used as a standard textbook for fifty years. He ran “Wednesday Meetings” in Paris where he did demonstrations and discussed Descartes’ work and philosophy, also drawing from his experiments and further popularizing his work. Rohault’s work really advocates for the power of observation and experimentation.


Rohault lived during the seventeenth century, towards the end of the Renaissance, a time of a great resurgence in mathematics and a revival of ideas and thinking. Many new discoveries were taking place which lead to even greater achievements: for example, Descartes’ discovery of the Cartesian coordinate system allowed the orbits of suns and planets to be mapped out and studied, yielding further developments in the field of astronomy.


The work contained in Oeuvres posthumes was done during this marvellous period for maths but what is interesting about this book, and something one might find unusual, is the great scope or variety of the topics discussed. Not only is there work on mathematics but there are also chapters about fortification and mechanics, which could be unexpected to some readers who anticipate to see a book of work by a mathematician and philosopher, and this gives us a great insight into the things with which Rohault concerned himself.


Jacques Rohault, Oeuvres Posthumes (The Hague, 1690), ii, p. 14: A page explaining terms relating to fortification.

The book is published in two volumes. The first volume has three chapters which include Rohault’s work on the translation of Euclid’s Elements, some trigonometry in relation to triangles and some practical geometry. The second volume has five chapters and a wider range of subjects, the chapters being: Les fortifications, Les méchaniques, La perspective, La résolution des triangles sphériques and L’arithmétique.


Jacques Rohault, Oeuvres Posthumes (The Hague, 1690): tables of contents of both volumes.


The book was translated into English in 1723 by the Newtonian, Samuel Clarke (1675-1729), and his brother John (1682-1757). However, this translation came some time after the work had been published, and there had been several developments in maths which saw the diffusion of Cartesianism at the end of the seventeenth century and the emergence of Newtonian concepts. This ensured that the English translation of Oeuvres posthumes had a strong Newtonian aspect due to the corrections, by the Clarkes, of Rohault’s Cartesian errors, which even Cartesians themselves admitted were mistakes. The English translation is a good example of the conflict between two huge mathematical movements.


Although Rohault was dedicated in his Cartesian patronage, there were matters in which Rohault and Descartes diverged. Rohault was far more interested in experimentation, even inventing instruments with which to implement his demonstrations, whereas Descartes’ mind was more satiated by pure reason; so, in a way, Rohault could almost be considered a different type or a new breed of Cartesian. A good example of this may be seen in their approaches to the question of the void. Descartes rejected the idea of a void or a vacuum entirely giving the example: if a jug which is designed to have water in it, has no water, then the jug is not “empty” it’s actually full of air. Throughout his work, Descartes’ provides three arguments against the existence of the void. The first is his claim that “nothing can have no properties” giving an example in a letter to Marin Mersenne (1588-1648), that a mountain could not exist without the existence of a valley also. Secondly he draws on the impossibility of an empty space, i.e. one cannot imagine a vacuum therefore it cannot exist. And thirdly he asserts that our ideas of space and substance are actually the same so any space must be full of matter.


Rohault likewise was very interested in the idea of the void and experimenting with it. Like any good Cartesian, he agreed with the idea that “nothing” cannot have any properties for where there are properties they must belong to something. Despite this, Rohault still proceeded to execute several experiments to test it. Not just inspired by Descartes but also Blaise Pascal (1623-62), he recreated Pascal’s Puy-de-Dôme experiment from 1648 when Pascal asked his brother-in-law to climb to the top of Puy-de-Dôme, the highest mountain in the area, with a tube of mercury, checking and comparing the height of the mercury along the way. To their surprise the level of the mercury decreased in the tube as they ascended the mountain, and this experiment assisted in the investigation of the weight of air. Rohault extended this experiment for his research on the void using a tube containing mercury, which was sealed at one end and submerged in mercury at the other. The Cartesians’ answer of course was still to claim that there was no void but instead somehow some matter had entered because otherwise the inside of the tube would be touching the mercury if there was no matter to keep them apart.


Jacques Rohault, Oeuvres Posthumes (The Hague, 1690), I, p. 3: Rohault’s work on Euclid’s elements.


Jacques Rohault was an important character in seventeenth century maths, and a key personality in the promotion, transmission and circulation of the principles and philosophy of René Descartes. This work by Jacques Rohault was printed in French, the vernacular, which meant that it extended the reach of the knowledge because it was readily available to a broader public and not just to those who could read Latin, the language of learning and academics.




Mihnea Dobre, ‘Rohault’s Traité de physique and its Newtonian reception’, in Antoni Roca-Rosell (ed). The Circulation of Science and Technology, Proceedings of the 4th International Conference of the ESHS, Barcelona, 18-20 November 2010, pp 389-394. (SCHCT-IEC, Barcelona, 2012).

Thomas Gale, Rohault, Jacques (1620-1672). (, 2006).

Simone Mazauric, Histoire des sciences à l’époque modern. (Armand Colin, Paris, 2009).

Aaron Spink, “Cartesian Method and Experiment” (Doctoral dissertation, University of South Florida, 2017).

David Wootton, The Invention of Science (Penguin UK, 2015).


Text by Ms Rachel Fitzgerald, final year BA student at Dublin City University.

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