Jean-Louis Calandrini

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30 August 1703
Geneva, Switzerland
29 December 1758
Geneva, Switzerland

Jean-Louis Calandrini was a mathematician working in Geneva, Switzerland in the first half of the 18th century. A great supporter of Newton's theories, he was a major contributor, along with Thomas Le Seur and François Jacquier, to an highly annotated edition of Newton's Principia.


Jean-Louis Calandrini was the son of the Calvinist pastor, also called Jean-Louis Calandrini (1677-1718), and his wife Michée Du Pan (1678-1750) who were married in Geneva on 3 March 1701. The Calandrini family were originally from Lucca (now in the north of Italy), but being Protestants in a Roman Catholic district they went, probably for their own safety, to live in the city of Geneva, a stronghold of Calvinism. In fact the Geneva Academy, at which Calandrini studied and later worked, had been founded in 1559 by Jean Calvin for training ministers. Jean-Louis Calandrini, the subject of this biography, was the great-nephew of Benedict Calandrini (1639-1720), who was both a Calvinist pastor and a professor of theology at the Geneva Academy. Benedict Calandrini was the son of another Jean-Louis Calandrini (1585-1656), who was a merchant and trader.

Calandrini moved rapidly through his education at the Académie de Calvin in Geneva, and in 1722 while he was still only eighteen years old he was awarded a doctorate having submitted a thesis Disquisitio Physica de Coloribus [4] on the theory of colours [8]:-
The 'Disquisitio Physica de Coloribus' opened with a two-page dedication addressed to a select group of pastors and senators with family ties with the young 'respondent'. Indeed, it is thanks to this political patronage that the young man was able to obtain a position at the Academy.
There is an important fact to note about this thesis on colour, namely that it was based on Isaac Newton's theory of colour. Even at this early stage in his career, Calandrini was an avid follower of Newton and he would continue to work to bring Newton's ideas to as wide an audience as possible.

Two years after the award of his doctorate, he was competing for the chair of philosophy at the Académie de Calvin in Geneva. The competition for the chair was between three men; the eldest was Amédée de la Rive while the other two were both young men, Calandrini who was twenty-one years old and Gabriel Cramer who was one year younger. The magistrates who were making the appointment favoured the older man with more experience but they were so impressed with the two brilliant young men that they thought up a clever plan to enable them to acquire the services of all three. Clearly they were looking to the future and seeing in Cramer and Calandrini two men who would make important future contributions to the Academy.

The scheme the magistrates proposed was to split the chair of philosophy into two chairs, one chair of philosophy and one chair of mathematics. De la Rive was offered the philosophy chair, which after all was what he had applied for in the first place, while Cramer and Calandrini were offered the mathematics chair on the understanding that they shared the duties and shared the salary. The magistrates put another condition on the appointment too, namely that Cramer and Calandrini each spend two or three years travelling and while one was away the other would take on the full list of duties and the full salary. It was a good plan for not only did it successfully attract all three men to the Academy, but it also gave Calandrini the opportunity to travel and meet mathematicians around Europe and he was to take full advantage of this which both benefited him and the Academy.

In 1724 Calandrini set out for his three years of travelling, first going to Basel in Switzerland where he studied with Johann Bernoulli, then to Leiden in the Netherlands where he studied with Willem 'sGravesande who was a strong supporter of Newton, next to Paris and finally to London. In London he met with William Whiston and got to know fellows of the Royal Society. During his time there, he published a paper about the aurora borealis observed at Geneva in the Philosophical Transactions (1726) of the Royal Society. He writes [3]:-
... the northern lights are produced by the reflection of the sun's light from the northern frozen parts of the atmosphere, but I do not see how such remarkable flames can be explained. If this phenomenon be supposed to arise from the ascension of exhalations, the aurora borealis that accompanies the phenomenon, the columns, the duration of the appearance, and its continuing in the same place, will be the grand difficulty.
He certainly saw both sides of the Newton debate on this trip, with pro-Newton supporters in Leiden and London, and anti-Newtonians in Basel and in Paris.

After these three years of travelling, Calandrini began his teaching at the Geneva Academy. Cramer and Calandrini divided up the mathematics courses each would teach. Cramer taught geometry and mechanics while Calandrini taught algebra and astronomy. The two had been paired in the arrangement and their friends joking called them Castor and Pollux. Had their personalities been different the arrangement might have presented all sorts of difficulties, but given their natures things worked out remarkably well [8]:-
In his lectures Calandrini sided with Newtonianism: he approached the theory of gravitation in mathematical terms. ... One was thus allowed to deal mathematically with gravitation accepting the fact that the causes of this force will remain unknown to us. Calandrini also presented Newton's theory in terms compatible with physico-theology: according to this viewpoint, the theory of gravitation reveals the visible effects of a continuous providential intervention of God in the natural phenomena. Without God's continuous 'reform', the 'system of the world' would be doomed to chaos and a progressive decrease of 'motion'. Calandrini and Cramer joined efforts at the Academy in promoting this pious view of Newtonian natural philosophy.
Calandrini's views on religion meant that he taught his physics in terms of a world rationally designed by God and continually kept in order by Him. He found his views very much in line with those who delivered the Boyle lectures. These had been set up through the will of Robert Boyle to consider the relationship between Christianity and the natural philosophy which was being put forward at this time. Two of the lecture series by Samuel Clarke, A Demonstration of the Being and Attributes of God (1704) and A Demonstration of the Being and Attributes of God (1705) particularly impressed Calandrini. Clarke's lectures of 1704 put strong arguments for natural religion while those of 1705 dealt with religious revelation. Calandrini used these lectures in teaching his students.

Charles Bonnet wrote in 1775 [12]:-
Both Cramer and Calandrini were faithful in heart and spirit to Revelation, and since they were laymen, and were enjoying the greatest fame in our Academy, what they said in favour of Revelation did not fail to impress the students, and contributed in no small degree to protect them against the dangerous sophisms of faithlessness.
Louis Bourguet (1678-1742) was Frenchman with an extremely broad range of interests who had travelled widely. Bourguet settled in Neuchâtel, Switzerland, in around 1715. He was friendly with Calandrini and, in 1728, together with Calandrini and a few other friends he founded the review journal Bibliotheque italique which aimed at making Italian science known to a French speaking audience. Bourguet had spent much time in Italy and had contacts with many of the leading Italian scholars. Calandrini, who was certainly always conscious of the Italian origin of his family, was keen to use the Bibliotheque italique to publish work promoting Newtonian thought, in particular to argue against those promoting the vortices of Descartes. This was an important venture for Calandrini since, as we will see below, it led to his connection with two friars of the Minim Order in Rome, Thomas Le Seur and François Jacquier.

When Calandrini had visited Leiden he had become friendly with Willem 'sGravesande and, three years later, Cramer had also made a visit to 'sGravesande who persuaded the two Geneva professors to publish in the Journal Historique de la République des Lettres. Two parts of this publication were planned:-
... to inform about the state of science and the work of scholars.
In fact three volumes were published, one in 1732 and two in the following year. The paper by Calandrini Dissertation sur la force des corps was published in the first of the two 1733 volumes. Actually the paper is anonymous but in a later paper by 'sGravesande in the same journal, he says that the earlier paper was by Calandrini. For details of Calandrini's paper and 'sGravesande's reply, see [9].

In 1734 Amédée de la Rive retired from the chair of philosophy at the Geneva Academy and Calandrini applied for the position. Again there was a competition for the chair but this time Calandrini was appointed. The arrangement to share the chair of mathematics between Cramer and Calandrini ended and Cramer became the only occupant of the chair of mathematics. This meant some changes in the courses that Calandrini taught for he now taught logic as well as theoretical physics. He also took on some private teaching, giving lessons in logic and philosophy to the sons of wealthy families.

Calandrini is best known for his work as an editor and commentator on Newton's Principia . This is not, however, immediately obvious since the annotated edition, published in Geneva in three volumes in 1739, 1740 and 1742, only gives Thomas Le Seur and François Jacquier as the editors on the title page. In fact the project was suggested by Calandrini, and although he is not listed on the title page, he was a major contributor to the annotations. Niccolò Guicciardini writes [8]:-
As to his authorial identification, it is to be noted that Calandrini did not add his name to those of Le Seur and Jacquier on the title-page. From this, one derives the impression that he wished to achieve recognition of authorship by more oblique means. It is because of his fame and prominent position in the 'république des lettres' that he expected to be recognised as the editor of the Genevan edition of the 'Principia' : he did not need a mention on the title-page, but rather he was keen on being the object of grateful recognition in the Monita signed by Le Seur and Jacquier.
There are natural questions regarding how Guicciardini cooperated with Le Seur and Jacquier in an era when communication between cities far apart was extremely slow and difficult. It is also interesting that it was a collaboration between Catholic and Protestant scholars [8]:-
How Calandrini, Le Seur and Jacquier planned to comment the 'Principia' in the 1730s is not known. Unfortunately, their correspondence is lost. It may well be that Calandrini came to know about the two Minims via his cooperation with Bourguet and the 'Bibliothèque Italique', which promoted many exchanges with the literati active in the peninsula. Be that as it may, a cooperation between scholars living in two cities as distant (geographically and culturally) as Geneva and Rome does not seem the easiest or most obvious choice, but Le Seur and Jacquier were amongst the few in all of Europe who possessed the competence and the stamina to carry out the first, complete, line-by-line, commentary of Newton's 'Principia' .
Le Seur and Jacquier fully acknowledge Calandrini's contribution, writing in the first volume:-
We do not wish to omit public evidence of our gratitude towards the illustrious Calandrini, Professor in the Academy of Geneva, very proficient in matters mathematical, who arranged that our edition of Newton's 'Principia' , enriched by many additions, would be readied to the elegant standard of the edition that appeared in London in the year 1726. Furthermore, that very learned man took upon himself the labour not only of checking carefully that the figures be engraved, and placed in the appropriate places, and that the typographical errors be corrected, but also of writing those elements of conic sections that we have already praised, and those things that appeared as not treated clearly enough by us, he occasionally elucidated with his own notes.
The commentary by Calandrini, Le Seur and Jacquier attempts to explain the basic mathematics and physics that Newton assumes his readers will know. They are therefore trying to make the task of understanding the Principia possible for those with much less background knowledge than Newton assumes. One typical example of this is the treatise by Calandrini on conic sections. If it looks strange to describe an annotation as a treatise, we should make it clear that this annotation is a major piece of work which fully deserves that description. Newton uses many properties of conic sections without giving proofs of them and Calandrini covers all this. But he also attempts to build on Newton's work and give further developments. An example of this is his attempt to extend Newton's lunar theory. This, however, is not entirely successful and was criticised by Alexis Clairaut.

In 1750 Calandrini retired from his chair of philosophy at the Geneva Academy and entered the world of politics. He was a Councillor of State on the Petit Conseil de Genève where one of his tasks was to arrange:-
... from 24 August to 7 September 1750, for the rental of the seats in the Auditorium, under the same conditions as the seats in the temple of St Germain.
The Petit Conseil of Geneva was one of two bodies which ran the city, the other being the Council of Two Hundred. The Petit Conseil had the executive power. In 1752 Calandrini became the treasurer of the city of Geneva, and five years later in 1757 he became a trustee of the city.

Let us note an error which occurs in some papers on Calandrini. In [16] William Watson writes:-
I very lately received a letter from the learned and ingenious Monsieur Calandrini, of Geneva, who has a considerable employment in the Ordnance in that city. In this letter Monsieur Calandrini tells me, that he had perused with attention a letter which I wrote to the late Lord Anson, which contained some suggestions tending, as I hoped, to prevent the mischiefs occasioned by lightning to ships at sea; and which likewise might, on the same account, be useful to powder magazines.
Monsieur Calandrini is indeed Jean-Louis Calandrini, but he is not the subject of this biography as mistakenly supposed by some. The first clue that this is not the mathematician Jean-Louis Calandrini is the date 1764 of Watson's paper. The mathematician Calandrini died in 1758 so receiving a letter from him shortly before 1764 seems unlikely (even if the post was slower in those times!). In fact the Calandrini who William Watson was corresponding with was a artillery general, which explains his concerns with lightning striking powder magazines.

Let us end with the following comment about Calandrini. Albert de Montet writes in [10]:-
Calandrini combined profound knowledge with brilliant qualities. Gifted with excellent judgment and a remarkable spirit of observation, his work put him among the most illustrious mathematicians of his time.

References (show)

  1. G Arrighi, Jean Louis Calandrini (1703-58) e il suo commento ai Principia di Newton, Physis-Riv. Internaz. Storia Sci. 17 (1-2) (1975), 129-137.
  2. P Bussotti and R Pisano, On the Jesuit Edition of Newton's Principia. Science and Advanced Researches in the Western Civilization, Advances in Historical Studies 3 (1) (2014), 33-55.
  3. J-L Calandrini, De Eodem Phaenomeno Genevae Viso, Epistola Viri Clarissimi Domini Johannis Ludovici Calandrini, Math. Prof. Ordinar. Genevae, ad Jac. Jurin, R. S. Secr., Philosophical Transactions of the Royal Society (1683-1775) 34 (1726-1727), 150-151.
  4. J L Calandrini, Disquisitio Physica de Coloribus quam Favente Divina Numinis Aura, et sub Praesidio D. S. Joh. Ant. Gauthier, Philosophiae Professoris, Publico Doctorum Examini Subjiciet Joh. Ludovicus Calandrini Genevensis Author & Respondens. Die Mensis Februar ii Horâ 1° Pomeridianâ Loco Solito (Gabrielis de Tournes & Filiorum, Genevae, 1722).
  5. Calandrini, Jean-Louis (1703-1758), Luières Lousanne.
  6. V P Dawson, Nature's Enigma: The Problem of the Polyp in the Letters of Bonnet, Trembley and Réaumur (American Philosophical Society, 1987).
  7. Eloge: Jean-Louis Calandrini, Journal Helvétique (January 1759), 30-34.
  8. N Guicciardini, Editing Newton in Geneva and Rome: The Annotated Edition of the Principia by Calandrini, Le Seur and Jacquier, Annals of Science 72 (3) (2015), 337-380.
  9. T L Hankins, Eighteenth-Century Attempts to Resolve the Vis viva Controversy, Isis 56 (3) (1965), 281-297.
  10. A de Montet, Jean-Louis Calandrini, Dictionnaire biographique des Genevois et des Vaudois 1 (Georges Bridel, Lausanne, 1877).
  11. R Pisano and P Bussotti, A Newtonian tale details on notes and proofs in Geneva edition of Newton's 'Principia', Journal of the British Society for the History of Mathematics 31 (3) (2016), 160-178.
  12. R Savioz (ed.), Mémoires Autobiographiques de Charles Bonnet de Genève (J Vrin, Paris, 1948).
  13. L Schelbert, Jean-Louis Calandrini, in Historical Dictionary of Switzerland (Rowman & Littlefield Publishers, 2014).
  14. J Senebier, Histoire Littéraire de Genève III (Barde, Manget et co., Geneva, 1786), 112-126.
  15. J A Serre, Theses physico-mathematicae de aere, Quibus nonnullae de usibus aeris adnexae sunt in gratiam Theologiae Naturalis, Quásque, Deo favente, Sub Praesidio d.d. Joh. Lud. Calandrini Matheseos Professoris Celeberrimi, Publicè defendere conabitur Joh. Adamus Serre Author & Respondens (Fabri & Barrillot, Genevae, 1727).
  16. W Watson, Observations upon the effects of lightning, with an account of the apparatus proposed to prevent its mischief to buildings, more particularly to powder magazines; being answers to certain questions proposed by M Calandrini of Geneva to William Watson, M.D. F.R.S., Philosophical Transactions of the Royal Society (1683-1775) 54 (1764), 201-227.

Additional Resources (show)

Other websites about Jean-Louis Calandrini:

  1. MathSciNet Author profile
  2. zbMATH entry

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update July 2022