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Cuvier’s History of the Natural Sciences

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Georges Cuvier

2. Scientific Impact of Isaac Newton & Gottfried Wilhelm Leibniz

2. Observation and Experimentation, the Contributions of Isaac Newton

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Portrait of Isaac Newton. Oil on canvas (1702) by Godfrey Kneller. Trustees of the National Portrait Gallery.

1Messieurs,

2In the previous session, after an overview of the major discoveries marking the seventeenth century, I presented the favorable drivers of observations, which were as important, or at least multiplied, in the eighteenth century. These observations form the body of useful sciences we have today. Now, I would like to present the history of these various observations and their relationships and connections.

  • 1 [For Cartesian philosophy, see Lesson 1, note 72, above.]

3This history is divided into two clearly distinct periods. During the first period, naturalists, chemists, and physiologists simply pursued the process followed in the seventeenth century. In a way, natural history was only a secondary subject of study, a fragment of general physics. Methods, classifications, and nomenclatures were not considered as important as they are today. Cartesian hypotheses1 continued to dominate the part of natural history closest to physics, preventing another approach to explain facts.

4Of special note is the case of geology during this first period. There were no studies on the structure and layers of the Earth. Hypotheses were drawn on its origin and the potential modifications leading to its current state.

5The study of chemistry was even more imperfect. Substances were not weighed before an experiment to verify if the combination of products had the same weight as before. Changes in matter were not taken into account. In short, mathematical accuracy, as applied today, was not considered necessary.

  • 2 [Georg Ernst Stahl, see Volume 2, Lesson 9, note 90.]

6Physiology was almost in the same situation. A few physical and mechanical hypotheses were competing against other hypotheses based on the action of the soul, even to explain bodily phenomena. Stahl’s system2 was influential and only counterbalanced by systems that admitted, without exact experimentation, a mechanical structure involving physical or chemical means.

7Sciences that specifically constitute natural history —zoology, botany, and mineralogy— were secondary. No one found the courage to establish a general system to include the three kingdoms of nature, using a common method or a set nomenclature that could be adopted by all countries. Characteristics were vaguely defined, except in botany, which dominated the other sciences: a vague method was applied but without a regular, set, and convenient nomenclature. Sentences were used to designate species within the various genera. The simple names we have today did not exist. The structure of the characteristics was described in plethoric details.

8Mineralogy used neither chemical processes nor the mechanical analysis of crystals. There was not the slightest knowledge of crystallography. This was the state of sciences at the beginning of the eighteenth century. While the general principles were well known, they were not applied in a scientific way.

  • 3 [Carolus Linnaeus, see Volume 2, Lesson 2, note 112; see also Volume 1, Lesson 7, note 34.]
  • 4 [Georges-Louis Leclerc, Comte de Buffon, see Volume 2, Lesson 4, note 57; see also Volume 1, Lesso (...)
  • 5 [Albrecht von Haller, see Volume 2, Lesson 1, note 16.]
  • 6 [Charles Bonnet (born 13 March 1720, Geneva, Republic of Geneva; died 20 May 1793, Genthod near Ge (...)
  • 7 [Torbern Olaf Bergman, see Volume 2, Lesson 9, note 1.]
  • 8 [Joseph Black (born 16 April 1728, Bordeaux, France; died 6 December 1799, Edinburgh, Scotland), a (...)
  • 9 [Johan Gottschalk Wallerius (born 11 July 1709, Stora Mellösa, Närk, Sweden; died 16 November 1785 (...)
  • 10 [Carl Wilhelm Scheele (born 9 December 1742, Stralsund, Swedish Pomerania; died 21 May 1786, Köpin (...)
  • 11 [Albrecht von Haller, see Volume 2, Lesson 1, note 16.]
  • 12 [Geogony (or Geogeny) is an antiquated, nineteenth-century term used to refer to the speculative s (...)

9The influence of the century’s major doctrines that I am going to recount was gradually felt, thanks to the works of a few great men. This occurred mainly from 1740 or 1750 to 1760 or 1770. The sciences underwent a complete revolution and made rapid advances. Linnaeus,3 Buffon,4 Haller,5 and Bonnet6 initiated this happy revolution, followed by the works of Bergman,7 Black,8 Wallerius,9 and Scheele10 on chemistry and mineralogy. Once the momentum generated, good results were quickly attained. Haller’s works gave a scientific orientation to physiology.11 Chemical and mechanical hypotheses as well as systems based on a spiritual principle were abandoned. Buffon spread the taste for science despite the inaccuracy of his hypotheses. His eloquent speeches gave an unequaled charm to natural sciences. Many people, who would not have otherwise been involved, adopted better methods. When I say that his methods were poor, I only mean his systems related to geogony12 and physiology. There was nothing wrong with his descriptions that he even perfected. He was the first to adapt the rules of criticism to fact-finding in natural history, or at least, it occurred rarely before, particularly among those naturalists who defined systems. Bonnet made a subject of meditation out of natural history by relating it to metaphysics or even morals or theology. He contemplated natural history with a perspective that was previously neglected. His ideas on motion are related to those of Leibniz. He tried to reach a level of accuracy uncommon for inexperienced researchers and made some errors. Linnaeus will have an everlasting merit with the positive determinations of species. While he did not exactly reach that goal, he charted the course. There was no complete catalog before Linnaeus; each author focused on the species most interesting to him. Only generic names were used; designating a species required a specific sentence consisting of a series of adjectives, each attributed to a characteristic. Linnaeus based his new nomenclature on two principles. He first established that characteristics and distribution patterns should only be taken from the structure or organization of the objects. Secondly, each genus should have an invariable name and each species under this genus should receive a trivial and simple name, therefore giving a set designation to each object. Thanks to this nomenclature that uses one noun for the genus and one adjective to describe the species, memorizing names became extremely easy even for people with a bad memory. Naturalists found a ground for agreement. For example, everybody knew exactly which species of plant was designated by the name Tulipa gesneraria, which was difficult before the introduction of this binary nomenclature. Before, it was even impossible to understand the characteristic sentences for species without reading books. Furthermore, the sentences had to be modified each time new discoveries were made. The permanence of the trivial or specific name established by Linnaeus has the advantage of allowing the identification of any species, placed under any genus as required by scientific progress. These ideas, which seem so simple but did not occur to anyone before, were the most valuable in Linnaeus’s work.

10Linnaeus’s second merit was to define scientific terms in a fixed manner. Before him, no one had clearly defined sufficient technical terms to represent the variations of the different parts of species. Descriptions remained vague. An author would describe the organization and the structure of a plant in one way; another would proceed differently.

11All existing methods before Linnaeus were more or less vague and not always perfectly understood. Indications were too brief; naturalists succeeded one another and did not follow the same limits in forming genera and classes. Linnaeus’s third merit was to determine kingdoms, classes, orders, genera, and species, using characteristics in a way that the nuances in each subdivision were clearly defined. Through all these works, Linnaeus had to make a clear distinction between artificial systems and the natural method. This had not been done because the classification methods were muddled. To the extent possible, every one tried to connect plants, animals, and minerals that presented some resemblances, but there was no attempt to systematically simplify and refine such relationships. Linnaeus adopted the artificial system but declared it to be only adequate to easily determine species. He judged that further work should be done to discover a natural method based on the true relationships between objects.

12Linnaeus defined his classifications based on noteworthy characteristics, irrespective of spiritual consideration and nuances in relationships between beings. His sexual system, determined for many classes and based on the number of stamens, is rigorous. Classes are positively recognized as all this recognition requires is counting the stamens of flowers. A similar approach, based on the number of distinct stigmas and styles, was applied to orders. He applied another principle to genera, which he believed had to be natural. They were defined based on flower characteristics and fructification but remained a bit artificial and rigorous.

  • 13 [René Antoine Ferchault de Réaumur, see Volume 2, Lesson 16, note 31.]

13Without any other method, Linnaeus’s method is a source of distortion, as it does not represent the relationships among, and the true nature of, objects. However, it is obvious that for beginners, for people undertaking an independent study of botany, his method is much easier than the previous vague ones. It is easy to count parts of flowers, to observe the position of a style and other small details I do not have to enumerate. The method became a trend everywhere. Many men and women, who would not have otherwise paid attention to botany, eagerly applied his method. Before botany was made easy, only those who needed the knowledge because of their profession —such as doctors and apothecaries— studied it. The same applied to mineralogy, studied only by metallurgists. Zoology was almost entirely ignored as it had fewer lucrative links compared to the other branches of natural history. However, after the publications of Linnaeus, Bonnet, Buffon, men of all classes increasingly studied these sciences. Some, like Réaumur,13 focused on the details of insect behavior. Others studied the link between anatomy and physiology. Natural history became popular, leading to further progress. The higher the number of people who focus on sciences, the better chances there are for new discoveries.

  • 14 [Alchemy, see Volume 2, Lesson 10.]
  • 15 [The philosophers’stone or stone of the philosophers, a legendary alchemical substance said to be (...)
  • 16 [Robert Boyle, see Volume 2, Lesson 12, note 32.]

14As we saw, chemistry remained restricted to a few men as it required more complicated work and did not stir the imagination of most people, particularly because of the contempt for alchemy.14 The great lords who focused on chemistry in the Middle Ages and in the seventeenth century were hoping to discover the philosophers’stone.15 Some pursued this chimeric quest in the eighteenth century but as alchemy improved and as principles excluding any possibility of metal transmutation were introduced, many abandoned chemistry. This science used to be studied for medical purposes. Almost all publications on chemistry in the seventeenth century, with the exception of those of Boyle16 and his school, only dealt with medicine and were written by pharmacists or physicians. With the simplification of therapeutics and pharmacopoeia, men who studied chemistry were exclusively those who considered it as a branch of physics and tried to find a link to other sciences or their systems. We will see Black, Bergman, and other contemporary chemists applying this philosophical perspective and making major discoveries, leading to a change in theory and giving this science the same accuracy as in mathematics and physics.

15Physiology and natural history registered a faster progress, the most significant between 1750 and 1780.

16Messieurs, these are the various phases of sciences in the eighteenth century that I would like to discuss with you. We will start the first period with geology, or rather cosmogony, as geology was only cosmogony in the first age. I will discuss cosmogony first since it includes all other sciences. The ideas that had the greatest influence on scientific doctrines emerged from the efforts made to explain the formation of the Earth. We will examine the numerous systems imagined to rationalize the creation of organized beings, resuscitated from time to time for the same objective. We will see how such systems grew depending on the minds in which they fell. It seems to me that these cosmogony systems should still be at the forefront as they are more directly linked to metaphysics, the science of the human mind and, thus, the science of sciences, which guides and governs all sciences.

17After geology, I will address the gradual progression of ideas in chemistry, in parallel with other sciences. Mineralogy will follow as the most immediate application of chemistry. It will be divided into chemical mineralogy and mineralogy based on the representation of elementary bodies. Finally, we will see how dogmas from chemistry and physics were applied to life phenomena or physiology. The study of physiology first focused on humanity but physiology also includes plants and animals. Therefore, related research concerned all organized beings. However, the prerequisite for physiology is the knowledge of the structure of beings or anatomy. We will therefore study in parallel the history of anatomy and physiology, for plants, animals, and humans.

18Once I finish presenting the history of general life science, I will move on to the sciences related to organized beings: botany and zoology. As these sciences became more significant in our century of focus, we will have to divide them. Zoology in particular became so rich that it was not possible for the same individuals to explore it in its entirety.

19Once the history of the first half of the eighteenth century is covered, we will pause to present the history of the great naturalists at the origin of the scientific revolution during that period. We will show how they managed to induce such revolution. We will then follow the same process as for the first half of the century: we will show successively how each science reached its state at end of the eighteenth century.

  • 17 [Sir Isaac Newton, see Volume 2, Lesson 11, note 37.]
  • 18 [Baron Gottfried Wilhelm von Leibniz, see Volume 1, Lesson 6, note 22.]

20Beforehand, I need to talk about two men whose influence was felt on all sciences and research even if they did not belong to the eighteenth century: Newton17 and Leibniz.18 As I previously described, Newton was the representative of peripateticism, or the method starting from specific facts to lead to general ideas or abstractions. Leibniz represented the opposite method, starting from general ideas, supported by hypotheses, and applying them to specific phenomena in order to find an explanation. Not that Leibniz relied entirely on hypotheses and did not see the merit of experimentation, but the metaphysical process was more dominant in his work. His ideas had such an influence in Germany that all sciences ended up reflecting his hypotheses.

  • 19 [Hannah Ayscough (born 1623, Market Overton, Rutland, England; died 4 June 1679, Colsterworth, Lin (...)
  • 20 [The King’s School, a British grammar school with academy status for boys, in the market town of G (...)
  • 21 [Isaac Barrow (born October 1630, London; died 4 May 1677, London), an English Christian theologia (...)

21Newton (Isaac) was born in 1642 in Woolsthorpe in Lincolnshire, from an old family but not of fortunate means. However, they owned some land. Almost since his childhood, Newton had enjoyed copying machines, drawing, and tracing geometric figures. His mother,19 a widower, withdrew him, despite his inclinations, from the school of Grantham20 where he was sent at the age of twelve. She wanted him to manage her possessions, a work he was extremely reluctant to undertake. One of his uncles found him one day, sitting under a hedge and solving a mathematical problem. Struck by this irresistible vocation, the uncle convinced the mother to let him follow his inclinations and return to Grantham. He remained there until the age of eighteen and then moved to Cambridge University where he was admitted at Trinity College. He was fortunate to have Isaac Barrow21 as professor, a great geometrician whose ideas on tangents he reproduced. Newton was so precocious that in 1665, at the age of twenty-three, he went further than his teachers in his study of some branches of algebra. He discovered a calculus he called fluxions, now called differential based on the prevailing denomination by Leibniz. Newton postponed by several years the publication of his discovery, a decision resulting, as we will see later, in major quarrels between him and Leibniz on the ownership of the infinitesimal calculus.

  • 22 [The Great Plague, lasting from 1665 to 1666, was the last major epidemic of the bubonic plague to (...)
  • 23 [Johannes Kepler, see Volume 2, Lesson 12, note 5.]

22Following a plague outbreak in London in 1665,22 Newton returned to the countryside of Woolsthorpe. It was there, under an apple tree still exhibited today, that the famous apple that led to his discovery of the universal theory of gravitation fell on his face. He wondered why the force of attraction that caused the apple to fall would not extend to the moon and, if it were the case, if that power would not be enough to maintain this planet in orbit around the Earth. He thought that if the moon was held around the Earth by gravity, planets circling around the sun should similarly be held in orbit. But if such gravity existed, its stability or variability and the energy of its power at different distances from the center should be reflected in differing speed of circular motions. Therefore, its law could be expressed by comparing such motions. There is indeed a remarkable relationship between them, recognized by Kepler23 through studies and expressed with the following formula: the period of a planet’s orbit squared is proportional to its distance from the sun cubed. From this law, Newton calculated that the force of the sun is inversely proportional to the square of the distance. In 1666, at the age of twenty-four, Newton seemed to have conceived the fundamental ideas of the universal system and started the calculation demonstrating that universal gravity is a property of all matter.

  • 24 [Descartes, see Volume 1, Lesson 6, note 7.]

23He wanted to apply this principle to chemical phenomena. Before and long after him —as discoveries did not spread as fast as today— chemical phenomena were not clearly explained. As you know, Descartes24 imagined that acids could be sharp corpuscles penetrating other bodies under the influence of subtle matter. This mechanical theory was not sustainable as sharp bodies can only go one way while chemical forces act in all directions. However, Newton’s new ideas took long to settle and became generalized only in the first third of the eighteenth century.

  • 25 [John Collins (born 25 March 1625, Wood Eaton, Oxfordshire, England; died 10 November 1683, London (...)
  • 26 [Isaac] Barrow [see note 21, above], his professor, had [in 1669] generously passed his professors (...)
  • 27 [Royal Society of London, see Volume 2, Lesson 8, note 96.]
  • 28 [The catoptric telescope or “Newtonian reflector,” was built by Isaac Newton as a solution to the (...)
  • 29 As we know, they [the phenomena of diffraction] were discovered in 1665 by [Francesco Maria] Grima (...)
  • 30 [Robert Hooke, see Volume 2, Lesson 12, note 66.]

24Once the plague was over, Newton returned to Cambridge and was named fellow of the university. He shared with Collins25 his discovery of the method of fluxions, which proves its priority. At the age of twenty-four, he had also studied light refraction through prisms. In 1669, he gave lectures26 on optics, sharing part of his immortal discoveries on this branch of physics although nothing had been published yet. At the age of twenty-nine, this young man who held in his hands twenty-five centuries of science and the key of the universe, so to speak, only presented for his candidacy at the Royal Society of London27 a telescope of his invention, or rather an improved version of the catoptric telescope.28 The improved version did not turn out to be an improvement and was never used. Newton became a member of the Royal Society of London at the age of thirty and only then shared his works on light. In March 1674, he read an essay on the fundamental phenomena of diffraction.29 More remarkably, he announced a principle now extensively applied in optics, the principle of interference: colors appear when two rays of light arrive at the eye from almost the same directions so that this organ considers there is only one ray. This theory was heavily contested. Robert Hooke,30 who perfected the microscope before Newton, presented so many arguments against his discoveries —they now appear ridiculous but garnered then a general agreement— that Newton was revolted and dissuaded to present new ones and retreated to Cambridge.

25Newton defined his theory of optics in 1704. It was only in 1684, at the age of fortytwo, that he shared his ideas on gravity. He is vivid proof of this truth: genius is a combination of patience of steel and ingenious ideas. Without patience, the most remarkable ideas remain sterile. Anyone else would have been eager to enjoy the glory of discovery. This great man, who primarily focused on solid truths, kept his ideas, gave them his thoughts, verified them with calculation and observation, and kept them secret until they were sound enough to resist the attacks of those who would see their own hypotheses fall apart.

  • 31 [Philosophiae naturalis principia mathematica (Mathematical principles of natural philosophy), oft (...)

26The first two books of the Natural Philosophy were shared with scholars in 1686; the full treatise, called the Principles of Natural Philosophy, was printed at the expense of the Royal Society in 1687.31 It was so above the ideas of the time, and so inaccessible to his contemporaries that no more than eight to ten men could understand it. However, hundreds of champions fought against it without understanding, as it is always the case for great discoveries.

  • 32 The dog, named Diamond, climbed on his master’s desk and overturned a candle, setting the manuscri (...)

27Since then, Newton published very little despite his numerous experiments in chemistry. He started to focus on chemistry from the moment he expressed the idea of molecular attraction of matter particles. Among other things, he noticed that metal oxides produced the brightest colors and that colors depended a lot on ray thickness. He also experimented extensively on color changes induced by chemical phenomena. Unfortunately, the related manuscripts were set on fire by a dog he loved and had left in his room.32 Newton was only forty-five but this accident gave him an affliction leading to insanity, from which he eventually recovered. He remained discouraged and wrote only works of minor importance afterwards. He performed his thermometric experimentation on dilatation, from ice to fusion, in 1701. He published other experiments that were not new discoveries but related to earlier ideas. It can be said that Newton had reached the end of his scientific career at the age of forty-six.

  • 33 [Charles Montagu, 1st Earl of Halifax (born 16 April 1661, Horton, Northamptonshire, England; died (...)

28However, it was only then when he received universal praise, honor, and fortune. In 1688, he was elected a member of the Parliament, representing Cambridge University. In 1696, he was offered the important position of Warden of the Mint. The Earl of Halifax, Chancellor of the Exchequer,33 had conceived the general coinage plan for gold and silver. Selecting a mathematician to lead this operation was natural. Moreover, the choice of Newton is justified by the fact that he was also a great chemist: he carried out experiments on metal alloys for his works on the catoptric telescope. In 1699, he was named Master of the Mint, a more lucrative position that greatly changed his fortune. His wealth was previously so limited that in 1674, he had to ask the Royal Society for an exemption of member contribution —the Society was not supported by the government and relied on its members.

  • 34 [The French Academy of Sciences, founded in 1666 by Louis XIV, see Volume 2, Lesson 8, note 86.]
  • 35 [Queen Anne, see Volume 2, Lesson 16, note 48.]

29Newton’s reputation spread overseas. In 1699, he became a foreign associate of the Paris Academy of Sciences.34 In 1701, he was reelected in Parliament representing Cambridge University. In 1703, he received the highest honor from the Royal Society of London: he was appointed its president, a title he kept until his death. Finally, in 1705, Queen Anne35 knighted him.

  • 36 It is fortunate that [Robert] Hooke [see Volume 2, Lesson 12, note 66] died before him. For fear o (...)
  • 37 [Samuel Clarke (born 11 October 1675, Norwich, English; died 17 May 1729, London), an English phil (...)
  • 38 [Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light (London: (...)
  • 39 [Arithmetica universalis; sive de compositione et resolutione arithmetuca liber, ciu accessit hell (...)

30His works were consecutively published36 and gradually received the reputation they deserved in Europe. His treatise on optics, written in 1704, was translated in Latin by Dr. Clarke37 and published in 1706.38 His student Whiston published in 1707, without his consent and maybe even without his knowledge, his universal arithmetic,39 which seems to be the algebra lectures delivered by Newton in Cambridge.

31His quarrels with Leibniz on the ownership of the discovery of the infinitesimal calculus only started in 1699. Newton made his discovery in 1666 and Leibniz probably a little later. Dates are unimportant; it is enough to know that each of these two great mathematicians made the discovery separately.

  • 40 [Brothers Jacob (born 6 January 1655, Basel; died 16 August 1705, Basel) and Johann Bernoulli (bor (...)
  • 41 [Guillaume François Antoine, Marquis de l’Hôpital (born 1661, Paris; died 2 February 1704, Paris), (...)

32Newton communicated his discovery using an anagram, as it was customary, in a letter to the secretary of the Royal Society of London, then intended for Leibniz. He only presented the results he obtained, without unveiling his method. To his credit, Leibniz shared his discovery openly in 1677, and therefore, he could not have stolen it from Newton. Leibniz’s discovery was understood by the Bernoulli Brothers40 and the Marquis de l’Hôpital.41 Every great geometrician subsequently adopted and perfected Leibniz’s method.

  • 42 [Nicolas Fatio de Duillier (born 26 February 1664, Basel; died 12 May 1753, Maddersfield, near Wor (...)
  • 43 [Around the end of the year 1712, the Royal Society of London published Commercium epistolicum D. (...)

33This state of affairs remained without disagreement until 1699. Everyone knew that Leibniz discovered the differential and no one contested Newton’s invention of fluxions. The imprudence of a young man from Geneva, Fatio de Duillier,42 was the source of the quarrel between the two scholars. The English took Newton’s side and accused Leibniz of plagiary. German geometricians and the rest of the continent defended Leibniz. The latter asked the Royal Society of London to be the judge. From a factual point of view, the Society demonstrated a great loyalty: all trial materials were printed under the title of Commercium epistolicum in 1712.43 For the question of law, however, the Society relied on arbitrators it nominated, who were unknown and for the choice of whom Leibniz was not consulted. The arbitrators decided in favor of Newton. However, it is certain that Newton’s light presentation would not have led to the same advances in transcendental mathematics. In the end, all scholars in Europe adopted Leibniz’s formulae while Newton’s were only used in England.

  • 44 [Caroline of Ansbach (born 1 March 1683, Ansbach, Germany; died 20 November 1737, St. James’s Pala (...)
  • 45 [Commercium epistolicum D. Johannis Collins et aliorum de analysi promota, jussu Societatis regiae (...)
  • 46 [Newton’s Philosophiae naturalis principia mathematica, see note 31, above.]
  • 47 [The General Scholium, an essay written by Isaac Newton, appended to his Philosophiae naturalis pr (...)

34Newton and Leibniz had other discussions on metaphysical questions. Their letters, shared with the Princess of Wales,44 reflected the animosity over their disagreement on the infinitesimal calculus. Newton harbored some resentment even after Leibniz’s death in 1716. As soon as he learned about it, he printed two letters written by Leibniz the year before and attached a very bitter refutation, stating that he only delayed this publication to spare Leibniz. Six years later, in 1722, he had a new edition of the Commercium epistolicum printed,45 preceded by a very partial extract. In his weakness, he removed, or accepted the removal, from the third edition of his Principia46 in 1725, the famous scholium in which he recognized the rights of his rival.47

  • 48 [Johann Bernoulli, also known as Jean or John (born 6 August 1667, Basel, Switzerland; died 1 Janu (...)
  • 49 [Princess of Wales, see note 44, above.]

35Not to excuse such behavior but to make it more understandable, I would like to point out that Leibniz was as passionate and unfair as Newton. Hurt by the unexpected publication of the Commercium epistolicum and offended by the ruling of unknown judges who did not wait for his defense, he called upon opposite testimonies that were as unreasonable. He printed and disseminated all over Europe an anonymous letter, later known as written by Jean Bernoulli.48 The letter was injurious for Newton, saying that he based his method of fluxions on differential calculus. Even more serious, in his correspondence with the Princess of Wales,49 whom he knew showed kindness towards Newton, Leibniz attacked Newton’s philosophy as false in terms of physics, and dangerous in terms of religion. In fact, there was reason for jealousy between these two great men because the major mathematical discovery in contention was the foundation of advances in astronomy and of the theory of universal system exposed by Newton.

  • 50 [Spheres of Eudoxus, the earliest, general, geometrical model of celestial motion, devised by Eudo (...)
  • 51 [The quest of the Argonauts, see Volume 1, Lesson 4, notes 7, 25, and 27, and Lesson 12, note 54.]
  • 52 [The Trojan War, see Volume 1, Lesson 4.]
  • 53 [The Book of Revelation, often known simply as Revelation or The Apocalypse of John, is a book of (...)

36Newton wrote about subjects other than physics and mathematics. He particularly focused on chronology and even theology. His chronology was mainly based on the Spheres of Eudoxus50 and presented new ideas on the age of society. According to his chronology, the quest of the Argonauts51 was 500 years closer to Trojan War.52 In his works on theology, Newton’s comments on the Apocalypse53 were in line with the thoughts of the Protestants but this point of view was as ridiculous as the others.

  • 54 [Newton held the title of president of the Royal Society of London (see Volume 2, Lesson 8, note 9 (...)

37Since the time of his appointment as president of the Royal Society of London,54 Newton lived the happiest part of his life. The challenges he previously faced disappeared and he only had admirers until his eighty-fifth year, his last one. He died quietly, from a bladder disease, as a benefactor of humanity.

38From the few facts I mentioned, you can note that Newton’s scientific process was to accurately observe the facts; clearly define them; establish a comparison among them to determine commonalities; set formulae expressing relationships; and assess if specific cases other than the ones he started with exactly fit the general formulae. Newton’s theory of gravitation was the simplest among his works: gravity acts on celestial bodies and combined with their force of projection, or their tendency for linear motion, produces an ellipse or a parabola that is their trajectory path. But what is the cause of gravity? What makes sublunary bodies fall because of gravity? Newton did not look for, or at least did not imagine any cause. This is the difference between peripateticism and the Cartesian approach. Descartes invented a subtle matter that pushed the bodies towards the Earth but it was only a hypothesis, improper for calculation and not yielding any useful result.

39In truth, Newton is criticized for having left Aristotle’s occult qualities in his system. While he does not explain gravity, he does not prevent the search for explanation. As far as he was concerned, and because he could not discover more, he just admitted it as a fact that reflected ancient known phenomena but also rigorously explained newly discovered ones. Newton also did for optics what he did for astronomy: he observed facts and generalized them without looking for a cause that was not reflected by observation or experimentation. It took a long time to apply this method to other sciences, but as this application became generalized, progress accelerated. In the next session, I will talk about Leibniz and Bonnet.

Notes

1 [For Cartesian philosophy, see Lesson 1, note 72, above.]

2 [Georg Ernst Stahl, see Volume 2, Lesson 9, note 90.]

3 [Carolus Linnaeus, see Volume 2, Lesson 2, note 112; see also Volume 1, Lesson 7, note 34.]

4 [Georges-Louis Leclerc, Comte de Buffon, see Volume 2, Lesson 4, note 57; see also Volume 1, Lesson 7, note 39.]

5 [Albrecht von Haller, see Volume 2, Lesson 1, note 16.]

6 [Charles Bonnet (born 13 March 1720, Geneva, Republic of Geneva; died 20 May 1793, Genthod near Geneva, Republic of Geneva), naturalist and philosopher, born of a French family driven out of France by the religious persecution in the sixteenth century (see Lesson 1, note 80, above). Although a lawyer by profession, his favorite pursuit was natural science, concentrating first on entomology and later on botany. Among other important contributions, he is credited with the discovery of parthenogenesis (reproduction without fertilization) and for developing the catastrophe theo-ry of evolution, which maintained that the Earth has been affected in the past by sudden, short-lived, violent events, possibly worldwide in scope, in contrast to uniformitarianism, in which slow incremental changes, such as erosion, created all the Earth’s geological features.]

7 [Torbern Olaf Bergman, see Volume 2, Lesson 9, note 1.]

8 [Joseph Black (born 16 April 1728, Bordeaux, France; died 6 December 1799, Edinburgh, Scotland), a Scottish physician and chemist, known for his discoveries of magnesium, latent heat, specific heat, and carbon dioxide. Beginning in 1756, he was professor of anatomy and chemistry at the University of Glasgow for 10 years, and then professor of medicine and chemistry at the University of Edinburgh from 1766, teaching and lecturing there for more than 30 years.]

9 [Johan Gottschalk Wallerius (born 11 July 1709, Stora Mellösa, Närk, Sweden; died 16 November 1785, Uppsala, Swe-den), a Swedish chemist and mineralogist, regarded as the founder of agricultural chemistry, mainly based on the significance of his widely disseminated work Agriculturae fun-damenta chemica (Uppsala: Gustavus Adolphus Gyllenborg, 1761, [4] + 321 + [1] p.), published in Swedish the same year as Åkerbrukets chemiska grunder and later translated into many other languages. He published several other studies on chemical, mineralogical and geological subjects.]

10 [Carl Wilhelm Scheele (born 9 December 1742, Stralsund, Swedish Pomerania; died 21 May 1786, Köping, Sweden), a Swedish pharmaceutical chemist who unfortunately made a number of important chemical discoveries before others who are generally given the credit. For example, Volume 2, Lesson 13, note 88) published his findings he discovered oxygen, although Joseph Priestley (see first, and he identified molybdenum, tungsten, barium, hydrogen, and chlorine before Humphry Davy (a Cornish Cornwall, England; died 29 May 1829, Geneva, Switzer-chemist and inventor, born 17 December 1778, Penzance, land), among others.]

11 [Albrecht von Haller, see Volume 2, Lesson 1, note 16.]

12 [Geogony (or Geogeny) is an antiquated, nineteenth-century term used to refer to the speculative science of the Earth’s formation and history. The term was used in Elementary Geology an early geology text published in 1847 by Edward Hitchcock (an American geologist, born 24 May 1793, Deerfield, Massachusetts; died 27 February 1864, Newman & Company, 361 p Amherst, Massachusetts), eighth edition, New York: Mark H..]

13 [René Antoine Ferchault de Réaumur, see Volume 2, Lesson 16, note 31.]

14 [Alchemy, see Volume 2, Lesson 10.]

15 [The philosophers’stone or stone of the philosophers, a legendary alchemical substance said to be capable of turning base metals such as lead into gold or silver, see Volume 2, Lesson 10, note 4.]

16 [Robert Boyle, see Volume 2, Lesson 12, note 32.]

17 [Sir Isaac Newton, see Volume 2, Lesson 11, note 37.]

18 [Baron Gottfried Wilhelm von Leibniz, see Volume 1, Lesson 6, note 22.]

19 [Hannah Ayscough (born 1623, Market Overton, Rutland, England; died 4 June 1679, Colsterworth, Lincolnshire England), mother of Sir Isaac Newton (see Volume 2, Lesson 11, note 37). Widowed three months before her son’s birth, she remarried and went to live with her new husband, the Reverend Barnabas Smith (born 1582; died 1653, North Witham, Lincolnshire, England), leaving her son in the care of his maternal grandmother, Margery Ayscough (born about 1585, Stroxton, Lincolnshire, England; death unknown). The young Isaac disliked his stepfather and maintained some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed by him up to the age of 19: “Threatening my father and mother Smith to burn them and the house over them.”]

20 [The King’s School, a British grammar school with academy status for boys, in the market town of Grantham, in Lincolnshire, England. Although its history can be traced back to 1329, the school has an unbroken history on the same site since its re-endowment in 1528.]

21 [Isaac Barrow (born October 1630, London; died 4 May 1677, London), an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent.]

22 [The Great Plague, lasting from 1665 to 1666, was the last major epidemic of the bubonic plague to occur in England. It happened within the centuries-long time period of the Second Pandemic, an extended period of intermittent bubonic plague epidemics that began in Europe in 1347, the first year of the Black Death, an outbreak which included other forms such as pneumonic plague, and lasted until 1750. The Great Plague killed an estimated 100,000 people, almost a quarter of London’s population. Plague is caused by the Yersinia pestis bacterium, which is usually transmitted through the bite of an infected rat flea. The 1665-1666 epidemic was on a far smaller scale than the earlier Black Death pandemic; it was remembered afterwards as the “great” plague mainly because it was the last widespread outbreak of bubonic plague in England during the 400-year timespan of the Second Pandemic.]

23 [Johannes Kepler, see Volume 2, Lesson 12, note 5.]

24 [Descartes, see Volume 1, Lesson 6, note 7.]

25 [John Collins (born 25 March 1625, Wood Eaton, Oxfordshire, England; died 10 November 1683, London), an English mathematician best known for his extensive correspondence with leading scientists and mathematicians, providing important details of many of the discoveries and developments made in his time.]

26 [Isaac] Barrow [see note 21, above], his professor, had [in 1669] generously passed his professorship [the Lucasian Chair at Cambridge University] to him. [M. de St.-Agy]

27 [Royal Society of London, see Volume 2, Lesson 8, note 96.]

28 [The catoptric telescope or “Newtonian reflector,” was built by Isaac Newton as a solution to the problem of chromatic aberration exhibited in dioptric telescopes, which use lenses as objectives.]

29 As we know, they [the phenomena of diffraction] were discovered in 1665 by [Francesco Maria] Grimaldi [an Italian Jesuit priest, mathematician, and physicist who taught at the Jesuit college in Bologna; born 2 April 1618, Bologna; died 28 December 1663, Bologna]. [M. de St.-Agy]

30 [Robert Hooke, see Volume 2, Lesson 12, note 66.]

31 [Philosophiae naturalis principia mathematica (Mathematical principles of natural philosophy), often simply called the Principia, London: Benjamin Motte, 1687, [12] + 510 + [2] p.]

32 The dog, named Diamond, climbed on his master’s desk and overturned a candle, setting the manuscripts on fire. [M. de St.-Agy]

33 [Charles Montagu, 1st Earl of Halifax (born 16 April 1661, Horton, Northamptonshire, England; died 19 May 1715, London, England), an English poet and statesman. In 1691, having become a member of the House of Commons, he rose quickly, becoming one of the Commissioners of the Treasury and a member of the Privy Council. In 1694, he became Chancellor of the Exchequer, a reward for having helped to establish the Bank of England.]

34 [The French Academy of Sciences, founded in 1666 by Louis XIV, see Volume 2, Lesson 8, note 86.]

35 [Queen Anne, see Volume 2, Lesson 16, note 48.]

36 It is fortunate that [Robert] Hooke [see Volume 2, Lesson 12, note 66] died before him. For fear of Hooke’s attacks, Newton would not have published if Hooke had still been alive. [M. de St.-Agy]

37 [Samuel Clarke (born 11 October 1675, Norwich, English; died 17 May 1729, London), an English philosopher and Anglican clergyman, considered a major figure in British philosophy.]

38 [Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light (London: printed for Samuel Smith and Benjamin Walford, printers to the Royal Society, at the Prince’s Arms in St. Paul’s Church-yard, [4] + 144 + 211 p. + not paginated pls, in-quarto) a book by English natural philosopher Isaac Newton that was published in English in 1704; a scholarly Latin translation appeared in 1706 (Optice: sive de reflexionibus, refractionibus, inflexionibus & coloribus lucis libri tres, auctore Isaaco Newton equite aurato, Latine reddidit Samuel Clarke, Londini: Impensis S. Smith & B. Walford, xi + 415 p.) The book analyzes the fundamental nature of light by means of the refraction of light with prisms and lenses, the diffraction of light by closely spaced sheets of glass, and the behavior of color mixtures with spectral lights or pigment powders. It is considered one of the great historical works of science.]

39 [Arithmetica universalis; sive de compositione et resolutione arithmetuca liber, ciu accessit helleiana aequationum radices arithmetice inveniendi methodus (London: Benjamin Tooke, 343 p.), a mathematics text by Isaac Newton. Written in Latin, it was edited and published in 1707 by William Whiston (an English theologian, historian, mathematician, and a leading figure in the popularization of the ideas of Isaac Newton; born 9 December 1667, Twycross, England; died 22 August 1752, London), Newton’s successor as Lucasian Professor of Mathematics at the University of Cambridge. It was based on Newton’s lecture notes but he was so unhappy with the publication that he refused to have his name appear as author. In fact, when Whiston’s edition was published, Newton was so upset he considered purchasing all of the copies so he could destroy them.]

40 [Brothers Jacob (born 6 January 1655, Basel; died 16 August 1705, Basel) and Johann Bernoulli (born 6 August 1667, Basel; died 1 January 1748, Basil), prominent mathematicians in the prosperous Bernoulli family of traders and scholars from the free city of Basel in Switzerland, were early proponents of Leibnizian calculus and had sided with Leibniz during the Leibniz-Newton calculus controversy.]

41 [Guillaume François Antoine, Marquis de l’Hôpital (born 1661, Paris; died 2 February 1704, Paris), a French mathematician whose name is firmly associated with l’Hôpital’s rule, which uses derivatives to help evaluate limits involving indeterminate forms. Although the rule did not originate with l’Hôpital, it appeared in print for the first time in his treatise on the infinitesimal calculus, entitled Analyse des infiniment petits, pour l’intelligence des lignes courbes, Paris: l’Imprimerie Royale, 1696, 9 + 181 + [1] p.]

42 [Nicolas Fatio de Duillier (born 26 February 1664, Basel; died 12 May 1753, Maddersfield, near Worcester, England,) was a Swiss mathematician known for his close relationship with Isaac Newton, for his role in the Newton versus Leibniz calculus controversy, and for originating the” push” or “shadow” theory of gravitation. He also developed and patented a method of perforating jewels for use in clocks.]

43 [Around the end of the year 1712, the Royal Society of London published Commercium epistolicum D. Johannis Collins, et aliorum, de analysi promota: jussu Societatis Regiae in lucem editum (London: typis Pearsonianis, 122 p.), a collection of correspondence relevant to the priority dispute between Newton and Leibniz regarding the invention of the Infinitesimal Calculus (called by Newton the “Method of Fluxions”). An “Account” of the Commercium epistolicum was subsequently published in the Philosophical Transactions of the Royal Society of London (issue for January and February, 1714, no 342, pp. 173-224). The “Account” appeared anonymously, but is known to have been written by Isaac Newton.]

44 [Caroline of Ansbach (born 1 March 1683, Ansbach, Germany; died 20 November 1737, St. James’s Palace, London), Princess of Wales from 1714, Electress of Hanover from 1727), and Queen Consort of England and Ireland from 1727), met Leibniz in the autumn of 1704, and thereafter the two enjoyed a close friendship, sharing a voluminous correspondence until the end of Leibniz’s life in 1716.]

45 [Commercium epistolicum D. Johannis Collins et aliorum de analysi promota, jussu Societatis regiae in lucem editum: et jam unà cum ejusdem recensione praemissa, & judicio primarii, ut ferebatur, mathematici subjuncto, iterum impressum, London: Jacob Tonson & John Watts, 1722, [8] + 250 + [2] p., in-8°.]

46 [Newton’s Philosophiae naturalis principia mathematica, see note 31, above.]

47 [The General Scholium, an essay written by Isaac Newton, appended to his Philosophiae naturalis principia mathematica, better known as the Principia (see note 31, above). It was first published with the second edition (1713) of the Principia and reappeared with some additions and modifications in the third edition (1726). It is best known for the “Hypotheses non fingo” (“I do not frame hypotheses”) expression, which Newton used as a response to some of the criticism received after the release of the first edition (1687). In the essay, Newton not only counters the natural philosophy of René Descartes (see Volume 1, Lesson 6, note 7) and Gottfried Leibniz, but also addresses scientific methodology and theological and metaphysical issues.]

48 [Johann Bernoulli, also known as Jean or John (born 6 August 1667, Basel, Switzerland; died 1 January 1748, Basel, Switzerland), a Swiss mathematician, one of the many prominent mathematicians in the Bernoulli family, known for his contributions to infinitesimal calculus.]

49 [Princess of Wales, see note 44, above.]

50 [Spheres of Eudoxus, the earliest, general, geometrical model of celestial motion, devised by Eudoxos of Knidos, born approximately 390 BCE and lived 53 years. A polymath, he made important contributions to geography, metaphysics, and ethics. However, his most important work was in geometry, the theory of proportion, and astronomy. Our principal source for his astronomy is Aristotle (see Volume 1, Lessons 7 and 8). Eudoxos started with five basic principles: (1) the earth is the center of the universe; (2) all celestial motion is circular; (3) all celestial motion is regular; (4) the center of the path of any celestial motion is the same as the center of its motion; and (5) the center of all celestial motion is the center of the universe. Since the apparent motion of all celestial bodies is neither circular nor regular, though it is about the earth, Eudoxos needed to construct models that preserved the five principles and the appearances. This means constructing the apparent motions as combinations of circular motions, the basic idea behind most subsequent Greek mathematical astronomy and the basis of mathematical astronomy from Ptolemy (see Volume 1, Lesson 1) up to Kepler (see Volume 2, Lesson 12, note 5).]

51 [The quest of the Argonauts, see Volume 1, Lesson 4, notes 7, 25, and 27, and Lesson 12, note 54.]

52 [The Trojan War, see Volume 1, Lesson 4.]

53 [The Book of Revelation, often known simply as Revelation or The Apocalypse of John, is a book of the New Testament that occupies a central place in Christian eschatology (the part of theology concerned with death, judgment, and the final destiny of the soul and of humankind). Its title is derived from the first word of the text, written in Greek: apokalypsis, meaning “unveiling” or “revelation.” The Book of Revelation is the only apocalyptic document in the New Testament canon, although there are short apocalyptic passages in various places in the Gospels and the Epistles.]

54 [Newton held the title of president of the Royal Society of London (see Volume 2, Lesson 8, note 96) from 1703 until his death in 1727. While the reputation of the society increased under his leadership, he arguably abused his authority. In the famous dispute between himself and Gottfried Leibniz over the invention of infinitesimal calculus, he used his position to appoint an “impartial” committee to decide it, eventually publishing a report written by himself in the committee’s name (see note 43, above).]

Table des illustrations

Légende Portrait of Isaac Newton. Oil on canvas (1702) by Godfrey Kneller. Trustees of the National Portrait Gallery.
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