Inertia and scientific law in sixteenth-century commentaries on Lucretius.

When Newton was planning a second edition of the Principia, he considered adding to the work some passages indicating his belief that the theory of inertia was known in antiquity. He intended to include several selections, ninety verses in all, from Lucretius's De rerum natura to illustrate that point.(1) In the end, however, he decided against incorporating the material in the new edition, probably because Richard Bentley, the master of Trinity College Cambridge, considered Epicurean thought, of which Lucretius's work is the chief example, to be an attack on religion. Bentley had written to Newton that he planned to base a refutation of Epicurean atheism on Newton's Principia and asked him for clarification of several points.(2) Newton did not throw his comments on antiquity away but allowed some excerpts from them to be used by a friend, and Newton's manuscript has recently been published.(3)

Is there any indication that Newton's assumption of a connection between ancient authors and the theory of inertia might have any basis in fact? Although reevaluations of our knowledge of late sixteenth-century views of motion have begun to challenge the traditional belief that the theory of inertia developed out of medieval impetus theories, evidence that the concept grew out of non-Aristotelian sources like Lucretius is, as yet, slender.(4) In this paper I should like to call attention to a work that seems to indicate a relationship between Lucretius's De rerum natura and the concepts of inertia and scientific law.

The most curious feature of the theory of inertia is the idea that a moving body will persevere in a straight line at constant velocity forever unless some force intervenes to change that motion.(5) The assertion is, as N. R. Hanson said, "not axiomatic in the sense of self-evident."(6) The ancient Greeks, observing that carts kept moving only because horses exerted a force on them to pull them forward, concluded that it was necessary to apply force continuously to keep a body in horizontal motion. This was "forced" or "violent" motion, as distinct from rectilinear vertical motion, which was considered "natural." Motion downward for Aristotle comes to a stop when the object reaches the center of the universe, or as close thereto as it can get.

Epicurean cosmology, which Lucretius follows, describes an infinite universe in which atoms, regardless of size or weight, are falling straight downward at the same speed.(7) Newton apparently assumed that these atoms, falling at a constant speed, are moving in an inertial motion. He believed that the theory of inertia was known to those ancients "who attributed to atoms in an infinite vacuum a motion which was rectilinear, extremely swift, and perpetual because of the lack of resistance."(8)

Modern historians have generally either ignored or disagreed with Newton's contention.(9) Whether or not the ancients believed in inertia, however, there is evidence to suggest that there might well have been a relationship between Lucretius's poem and the concept. The one historian who seems to have taken the suggestion seriously, I. Bernard Cohen, identified a link between Lucretius's poem De rerum natura and the concept of inertia based on his discovery that the phrase "quantum in se est" was used not only by Newton and Descartes in their discussion of the theory of motion but also by Lucretius.(10) In addition, the first annotated edition of De rerum natura, published by Joannes Baptista Pius (Giovanni Battista Pio) in 1511, contains comments on motion that seem to be a step on the road to the theory of inertia and, more generally, to a modern concept of scientific law.

Cohen agreed with Alexandre Koyre that Newton undoubtedly learned about inertia from reading Descartes.(11) The theory that all bodies persevere in the state of rest or of motion at uniform speed in a straight line unless acted on by an external force was proposed by both men. In his Principia philosophiae, for example, Descartes gives as a lex naturae the following: "Quod unaquaeque res, quantum in se est, semper in eodem statu perseveret; sicque quod semel movetur semper moveri pergat. "(12) Newton's own statement in the Principia mathematica of the law, which he lists as one of the axioms or leges motus, is: "Corpus omne perseverare in statu quo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum ilium mutare. "(13) He supplements this axiom in the section on definitions by the further explanation that a "materiae vis insita," or innate force of matter is "potentia resistendi, qua corpus unumquodque, quantum in se est, perseverat in statu suo vel quiescendi vel movendi uniformiter in directum."(14)

The resemblance between Descartes and Newton is found, therefore, not only in the similarity of the idea involved but also in the language used to describe it. Cohen points out, in addition, that both considered motion to be a state, that both spoke of the theory of inertia as a "law," and that both made use of the qualifying phrase "quantum in se est" in describing it.(15) It is this last phrase that Cohen found in Lucretius's De rerum natura and that made him pay more serious attention to Newton's interest in the work.

Lucretius based his poem on the Epicurean argument that the world is made of eternal atoms moving in an infinite void.(16) In discussing this flow of atoms, Lucretius explained on at least four occasions that atoms, "quantum in se est," fall straight downward at the same speed in the void.(17) Having recognized the use of the same expression "quantum in se est" in Lucretius, Descartes, and Newton, Cohen set out to see how the phrase had been interpreted by the editors of De rerum natura over the centuries.

The poem had been lost from view during the Middle Ages, undoubtedly because of its negative religious connotations since Lucretius argues that although there are gods, they dwell in a distant part of the universe in a state of tranquility, paying no attention to what man is doing in his own world; that after death the atoms that constitute people are simply recycled into something else; and that there is no individuality left. For these reasons, he proposes that man should have no fear either of the gods or of any punishment after death. Despite this impiety, manuscript copies of De rerum natura were preserved during the Middle Ages, and one was discovered in a German monastery in 1414 by Poggio Bracciolini, an apostolic secretary to the Council of Constance, who sent it to a friend in Florence, Niccolo Niccoli, who never returned it.(18) The first published editions were made from Niccolo's copy, and numerous other editions appeared during the sixteenth and seventeenth centuries. As well, the poem has also been translated many times over the centuries.

Cohen examined several of these editions and translations, contemporary as well as modern, in order to determine how the phrase "quantum in se est" has been interpreted. However, the only sixteenth century annotated version of Lucretius that Cohen looked at in any detail, was that of Dionysius Lambinus (Denys Lambin), published in 1563-64.(19) Lambinus's efforts to correlate various manuscripts of De rerum natura and his careful job of editing were so successful that his work is still consulted by twentieth-century scholars.(20)

Lambinus considered the phrase "quantum in se est" to mean sponte sua, "by itself unaided," which, Cohen tells us, "in the context of the traditional Aristotelian physics, connoted 'natural' as opposed to 'violent' motion." Such "natural" motion "does not result from the application of an external force."(21) For Cohen a significant change in the meaning of natural motion came about when Descartes "altered the sense of the phrase 'quantum in se est' by implying that what is 'natural' is that a body maintain its state of rest or of uniform rectilinear motion," whether it was moving horizontally or vertically. Cohen concludes that Descartes's and Newton's description of bodies persevering in the same state "was a revolutionary new concept," and that A. Motte, who made an English translation of Newton's Principia, translated the phrase "quantum in se est" by "as much as in it lies," an expression Cohen says that was meant to include the concept of "natural" motion.(22)

In seeking the sixteenth-century understanding of the phrase "quantum in se est," Cohen allowed himself to be too swayed by the attitude of modern Lucretian scholars toward Lambinus's commentary and relied solely on it for an early interpretation of the phrase before turning to various seventeenth-century commentators and translators. "In 1661," according to Cohen, "the only edition of Lucretius available with a commentary was that of Lambinus."(23) C.A. Gordon, the bibliographer of Lucretius's poem, however, lists four commentaries in addition to that of Lambinus before that date.(24) Cohen knew that others existed, however, for he refers in passing to that of J. B. Pius published in Bologna in 1511 and republished in Paris in 1514, but he apparently did not consult it.(25)

Pius's edition does not seem to be much appreciated by modern scholars. Perhaps, as Gordon tells us, this is because the text "is surrounded by a sea of comment or consists sometimes of solid comment with no text at all," and it was supplanted by the more thorough work of Lambinus.(26) Pius's work, the first commentary edition, nevertheless, remained the only annotated version of De rerum natura until the Lambinus edition appeared fifty-two years later.(27) All in all, Lucretian scholars have not found as much of interest in Pius's edition as in the later one. When seen in the light of the discussion of the theory of inertia and the origin of the modern concept of scientific law, however, the Pius commentary acquires a different value.

Cohen skipped too swiftly from Lucretius to Descartes and Newton and left the impression that the terms "natural motion" and "violent motion" as applied to De rerum natura carried the same implications as when used by Aristotle, for whom the natural motion of earthly objects would come to an end when they reached the center of the universe or as close to it as they could get. However, the Epicurean view of an infinite universe, which had no one center but contained multiple worlds and was adopted by Lucretius, assumes principles of motion different from those of Aristotle.

In his commentary on De rerum natura Pius considers the differences in views of motion a subject worth emphasizing.(28) For the Peripatetics, he says, there are three kinds of natural motions: (1) circular motion, like that of the heavenly bodies, (2) motion toward the center, like that of earth and water, and (3) motion away from the center upwards, like fire and air.(29) Natural motion in such a cosmos is defined as motion of a sublunar substance toward its natural place, either up or down, or of heavenly bodies in a circular path. This was undoubtedly the analysis of motion that Pius had learned in school and he favored, even though a different view of motion applies in the Epicurean world that Lucretius describes.

Pius also divides Lucretian motion into three: (1) "natural" motion, in which things fall toward the center, (2) "violent" motion in which heavy bodies are moved upward, and (3) a swerve, in which some atoms deviate from their rectilinear fall.(30) Pius's presumption that all things would fall toward a center shows the influence of his Aristotelian education. Although he was explicating Lucretius's point of view, there is no indication that he adopted it himself. If bodies were to fall naturally toward the center, they would collide in the process and there would be no need for the swerve. On the other hand, Pius does recognize that in an infinite Lucretian universe there is no center.(31)

Unlike Aristotle who argued that fire moved upward because it was light and was moving toward its natural place, Lucretius believed that lighter atoms are forced upward, being squeezed out by heavier ones.(32) He compared them to pieces of wood that have been pushed under water and are forced up to the surface when released. This upward motion of fire as well as wood is for Lucretius "violent," not "natural." In Lucretius's system flames rise upward, squeezed out by air, though their weight "quantum in se est" strives to draw them down. Pius explains that "quantum in se est" means "by its own nature if not disturbed by another force" ("suapte natura si non ab aliena vi turbentur").(33) In line 247 he interprets "quantum in se est" to mean "from natural motion, not violent" ("ex naturali motu non violento"). Cohen would have been helped in his understanding of the phrase "quantum in se est" if he had looked at Pius's commentary. However, although Pius tries to understand vertical motion in the Aristotelian sense of motion toward the center, he recognizes that that was not Lucretius's opinion. The latter subscribed to the view that atoms falling straight downward in an infinite universe could, in effect, continue forever at the same speed unless disturbed by an outside force. Pius's explanation that the motion continues in a straight line "if not disturbed by another force" ("si non ab aliena vi turbentur") is similar to Newton's explanation that a body moves in a straight line "unless it is compelled to change that state by forces impressed upon it" ("nisi quatenus a viribus impressis cogitur statum mutare").(34) The De rerum natura, especially with Pius's comments, does seem to contain some of the elements of the theory of inertia.

Lucretius, however, says nothing about bodies remaining at rest. In fact, he says, atoms never rest, and Pius explains that all things are in perpetual motion.(35) Modern historians have, therefore, rejected Newton's claim that Lucretius was aware of the theory of inertia. Before Lucretius's view could approximate Newton's, the kind of motion described by the former would apparently have to be united to Kepler's theory of "inertia," which held that an object at rest would remain at rest unless acted on by an outside force.(36)

In the course of his discussion of Newton's theory of inertia, Cohen commented, "I do not know who first wrote of a 'law of motion,' a lex motus, but I believe that no one before ever held that such laws are axioms."(37) He may well be right in his observation about Newton's use of the term "axiom," but the phrase "law of motion" is associated with De rerum natura by Pius's commentary, even though neither the expression lex naturae used by Descartes nor lex motus used by Newton in their discussions of inertia was used by Lucretius in De rerum natura.

As careful as he was to explicate the meaning of "quantum in se est," Cohen did not emphasize the importance of Lucretius's work as an alternative to Aristotle. Nor did he recognize Pius's commentary as an important step in the direction of the Cartesian and Newtonian views of motion. But there is more of interest in Pius's commentary.

In those sections of De rerum natura in which the phrase "quantum in se est" is used, we find in Pius's commentary other terms that are associated with the new theories of Descartes and Newton. Descartes considered his theory of inertia to be a "law of nature," and while that expression is not used in De rerum natura, Pius uses it in his commentary on the text, explaining that the "decrees of rite" (fati foedera) to which Lucretius refers in describing filling atoms are laws (leges naturales), and later, where Lucretius alludes to "laws of nature" (foedera natural) Pius refers to leges naturae.(38) Thus Pius adds another meaning to an expression that was just coming into use, as we shall see below. Pius also explains in his commentary that the regularity of motion referred to in the text is a "law of motion" (lex motus), the category to which Newton ascribed his theory of inertia.(39) An atom filling in the void, says Pius, "perseveres" (perseveret) in its motion (Lucretius had said pergat).(40) "Persevere" is the word used by both Descartes and Newton to describe inertial motion. The atom is carried downward by its "weight" according to Lucretius, who often used the word pondus for weight. In his explanatory comment Pius sometimes preferred the word gravitas, explaining, for example, that all things fall because of natural gravity and suggesting an association of terms and ideas that would eventually grow into the Newtonian laws of inertia and of gravitation.(41) Pius's commentary, however, contains no reference to a "state" of motion, which like the word "inertia" itself was apparently a later development.

There is, then, some justification, it would seem, to Newton's assumption of a connection between inertia and the Lucretian poem. Although Pius's commentary was available in Cambridge libraries while Newton was a student there, Cohen and Koyre assure us that it was from Descartes that Newton got the theory of inertia rather than from Lucretius directly.(42)

Both Descartes and Newton also employ another concept that is found in Pius's work. This is the use of the term law in a scientific sense. The concept of a scientific law as a law of nature was apparently not used in antiquity, and a debate has arisen as to when the term "law" was first applied to the physical world. In an article published in 1942, Edgar Zilsel argued that the concept of a natural law, as it is used in modern science, originated in juridical metaphor, that is, when "the observable recurrent associations of physical events. . . were interpreted as divine commands."(43) He set out to trace the evolution of the concept of natural law from the theological idea of God as a lawgiver to its eventual application to nature as a scientific law. He claimed that the concept of physical law was unknown until its adoption in the seventeenth century by Descartes, Hooke, Boyle, and Newton, and he said that "Democritus and Lucretius, who consistently advocated causal explanations of nature, did not use the law metaphor. . . . Whereas modern translations of Lucretius speak of physical laws again and again, the term law was unknown to Lucretius himself. . . . In Epicurean philosophy, there can be no laws of nature, since the gods do not take care of the world."(44) Not until Descartes, he concluded, did the fully developed concept of natural law occur.

Zilsel was seemingly unaware that modern editors of De rerum natura translate the term foedus, which in antiquity meant a legal contract, as "law" in the modern sense of "law of nature." His belief that natural law implied "divine commands" presumably kept him from considering the possibility of its existence in the Epicurean philosophy of Lucretius, since the Epicurean gods did not interfere in earthly events and Epicureans are often accused of atheism for that reason.

In his Discourse on Method (1637) Descartes informs us that he has found the "laws which God put into nature," explaining that "God, after the creation of matter, let nature develop from chaos in accordance with these laws. Even if God had created several worlds, the laws of nature ('les loix de la nature') would be valid in all of them."(45) The context of original chaos and multiple worlds with which Descartes associates his laws of nature is reminiscent of Lucretius's description of the clash of atoms that occurred as a result of a slight swerve on the part of some of them causing random clashes of atoms in which many stick together and eventually produce a multiplicity of worlds. These worlds then operate in a way which Zilsel himself admits is seen by modern translators as lawful.(46) One might wonder whether there is a connection between the expression "law of nature" and De rerum natura.

Zilsel's thesis that the concept of scientific law developed in the seventeenth century has been contested recently (1986) by Jane Ruby in an article in the Journal of the History of Ideas in which she argues that while the idea of legislation by God or Nature does account for much of the ancient use of "law," the modern usage emerged through different processes at different times in three distinct fields.(47) First, she accepts Alistair Crombie's contention that Roger Bacon in the thirteenth century used the term law (lex) in optics in a modern way in referring to the "law of refraction" rather than the more general "law of nature."(48) Secondly, she insists that in the fifteenth century the word "law" appeared "in a recognizably modern sense" in mathematics. And thirdly, she says, it was used in a modern way in astronomy by 1514. In the fifteenth century, Regiomontanus used the term lex, not only in optics but also in astronomy and mathematics, although not quite in its modern sense.(49) Nevertheless, she says, despite their ambiguity Regiomontanus's phrases became part of the scientific vocabulary and were employed by Copernicus in his Commentariolus when he referred to the "fixed laws of motion" (motuum leges) of the planets in the firmament.(50) It is a usage that, she insists, echoes ancient uses derived from the Stoic concept of the law of nature. Copernicus, however, did not assert that God brought the whole of the universe under law. He spoke of God not "as a legislator, but as the wisest and most orderly of craftsmen."(51) Sixteenth-century astronomers, she concludes, "used lex as Regiomontanus and Copernicus did, without reference to God."(52)

Ruby seems puzzled, however, by Philip Melanchthon's strongly anti-Epicurean dedication of the Sphere of Sacrobosco, where he refers to the "laws (leges) of the great orbes and stars" and to man's knowledge of the "laws of motion" (motuum leges) as proof of man's immortality.(53) Since Melanchthon presumably did not know Copernicus's writings, she speculates that there may have been a connection between Copernicus and Melanchthon via a third party, such as Rheticus. The fact that Melanchthon uses the term "law" in an anti-Epicurean attack, however, suggests another source for it.

That Melanchthon was familiar with the Epicurean point of view seems apparent from a reading of his Initia doctrina physicae, written as a textbook for use in the new Lutheran educational curriculum. Melanchthon's book frequently attacks many of the basic Epicurean ideas from eternal atoms to the existence of a void and of a multiplicity of worlds.(54) While it is possible that Melanchthon had read the recently published letters of Epicurus in Greek, he certainly quotes a few lines from the Latin poem of Lucretius.(55) It is conceivable, therefore, that he may have read the annotated edition of De rerum natura by J. B. Pius.

The problem that worried Lucretius about atoms falling eternally in a straight path was that effect would then follow cause in an undeviating order. In order to "break" these "bonds of fate," ("fati foedera rumpat") Lucretius supposed that some of the falling atoms swerved slightly.(56) Breaking the bonds of fate, Pius explains in his comments, meant "altering the natural laws" ("mutat leges naturales").(57) No power can change the sum total of things according to Lucretius, for there is no place into which any kind of matter could escape from the universe. A new power could not burst into the universe and change the whole nature of things by "turning [vetere] their motions," or in Pius's words "by changing the laws of motion" ("leges motus alterare").(58)

Plus has thus introduced both the terms "laws of motion" and "laws of nature" in discussing the rectilinear motion of falling atoms. He uses them to describe the regular order of nature in a context where God, as a supreme legislator, has no relevance, since Lucretius's gods stood apart in a distant region of the universe and paid no attention either to man or his world. Laws for him express the eternal necessity of fate and the chain of cause and effect. For him, therefore, law was not derived from a juridical metaphor, since there was no divine lawgiver to establish such regularity in nature. Instead, "law" signified the connection of cause and effect in nature. This is a use of the term "law" very early in the sixteenth century in a new context beyond those of optics, mathematics, and astronomy discussed by Ruby.

Although Lucretius did not use the term "law" in the text of De rerum natura, as Zilsel pointed out, he nevertheless employed a concept of cause and effect relationships that modern scholars. translate by that word. It is presumably Pius, then, who in his commentary makes use of a new and more modern terminology for the poem, introducing "lex" for "foedus" and applying it to motion and nature.

How much impact did Pius's commentary have on discussions of physics during the sixteenth and early seventeenth centuries? It is difficult to tell. For approximately half a century it remained the only attempt to comment on De rerum natura and was republished in Paris in 1514.(59) Philip Melanchthon reacted strongly against the Epicurean world view and condemned many of its basic ideas. It is quite possible, however, that Pius's comments are the source of at least some of his references to laws of nature and of motion.

How much Epicurean ideas, and in particular Lucretius's poem, may have influenced scientists in the sixteenth and early seventeenth centuries remains to be determined. If Pius's commentary is any indication, however, the usual assumption that the theory of inertia must have developed from medieval discussions of impetus needs to be reexamined. The comparison of Pius's commentary with the works of Descartes and Newton suggests instead that the theory of inertia is associated with the adoption of an Epicurean cosmology.

The linguistic connections between Lucretian ideas and the concepts of inertia and scientific law are indicative of a change in the analysis of motion, set in the context of a non-Aristotelian view of the cosmos. It is generally assumed that seventeenth-century ideas of motion grew out of the work of the Merton school. However, both Charles Schmitt and Christopher Lewis warn that such work "was relatively little studied" in the late sixteenth and early seventeenth centuries. "After the first two decades of the sixteenth century, there seems to have been a drastic decline in the publication of the more important expositions of the Mertonian works . . . an indication of a real diversion of interest away from the Merton tradition."(60) If we take note of their conclusions and their warnings, it is possible to suggest that the theory of inertia, if not the concept of scientific law, may spring from a different source than the generally accepted medieval one. Perhaps the Epicurean tradition, which has long been virtually ignored, played a greater role in inspiring the Scientific Revolution than we have heretofore imagined. Newton's claim to see a connection between the writings of ancient authors and his own ideas may have some element of truth.

ATKINSON COLLEGE, YORK UNIVERSITY 

1 See Casini for these selections.

2 Bentley, 280-312.

3 Newton permitted David Gregory to publish selections from these notes in the "Preface" to his Astronomiae physicae. Newton's notes are published in Casini, 24-38.

4 For a criticism of the thesis that the theory of inertia grew out of medieval ideas of motion, see Lewis, 9, 18, 231, etc. and the foreword to Lewis's work by Charles B. Schmitt, xii-xvii.

5 Some scholars, like Alan Gabbey, prefer to refer to Descartes's development of this idea as the principle of the "conservation of motion" rather than inertia. To call such motion "inertia," he thinks, is anachronistic and a misrepresentation, arguing that the theory of inertia is a family of statements, definitions, and rules whose meaning depends on their context. Gabbey, 54-55.

6 Hanson, 107.

7 Furley, 582, explains that the Epicureans' downward motion is defined by assuming a basic straight line of free fall and asserting that "everything that falls freely, anywhere in the infinite universe, falls parallel to this line."

8 Hall, 310.

9 Ibid., 309, remarks that Newton's assumption of antecedents for the first law of motion in the ancients was "an historical impulse which he later overcame."

10 Cohen, 1964(1), 131-55. Also Cohen, 1964(2), 36-56. Gabbey, 32n, 6on, also considers the discovery important.

11 Cohen, 1964(1), 151, and 1964(2), 38. Koyre, 66-75.

12 Descartes, 1964, 8:62. I have underlined several terms in these quotations. "The first law of nature: that each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move" (Descartes, 1983, 59).

13 Newton, 1687, 12. "Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it" (Newton, 1962, 13).

14 Newton, 2, "a power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly forwards in a right line" (Newton, 1964, 2).

15 Cohen, 1964(1), 147-48; 1964(2), 46.

16 Lucretius, 1975, 2:201.

17 Ibid., 2:190, 201, 205, 247.

18 Monro, in Lucretius, 1905, 2:3.

19 Cohen, 1964(1), 146-47; 1964(2), 46.

20 Lambinus.

21 Cohen, 1964(1), 147.

22 Ibid., 148.

23 Ibid., 142.

24 Gordon, 76-88.

25 Cohen, 1964(1), 140.

26 Gordon, 73.

27 Gordon, for example, lists several copies if Pius's work in Cambridge Libraries, such as the 1514 edition in Clare College that was bound by John Siberch in Cambridge about 1521, and one in Trinity college bound in London between 1527 and 1544. Newton himself apparently used and annotated an edition of 1686, although he presumably would have had access to one of the Pius editions at Cambridge.

28 Lucretius, 1511, 51v.

29 Ibid., 49v.

30 Ibid., 57v.

31 Ibid., 49v.

32 Lucretius, 1975, 2:184-215.

33 Lucretius, 1511, 56v.

34 See footnote 13, above.

35 Lucretius, 1975, 2:308; idem, 1511, 54.

36 Rosen, 612.

37 Cohen, 1964(1), 136.

38 Lucretius, 1975, 2:254; idem, 1511, 57. Idem, 1975, 2:303; idem, 1511, 59.

39 Lucretius, 1511, 58, 59.

40 Ibid., 57v.

41 "Omnia moventur quae naturali gravitate descendunt." Ibid., 54.

42 Cohen. See footnote 11 above.

43 Zilsel, 247.

44 Ibid., 253.

45 See Descartes, 1964, 6:41. This translation of Descartes is quoted from Zilsel, 253.

46 Lucretius, 1975, 2:1048-76, 5:436-48. Zilsel, 253.

47 Ruby, 342-43.

48 Ibid., 342.

49 Ibid., 352-53.

50 Ibid., 354.

51 Ibid., 355.

52 Ibid., 355-56.

53 Ibid., 356-57.

54 Melanchthon, passim.

55 See, for example, Melanchthon, 301, where he quotes from Lucretius, De rerum natura, 2:1055 and uses both the expressions leges motuum and leges naturae but argues that such laws require a creative mind. He also refers to astronomical laws, leges motuum coelestium or equivalent in several places, e.g., 206, 221, 221, 228, 229, 232, 292.

56 Lucretius, 1975, 2:253-54.

57 Lucretius, 1511, 58.

58 Lucretius, 1975, 2:304-07; idem, 1511, 59.

59 Lucretius, 1514. Gordon, 73, found two copies of the 1514 edition in Cambridge College Libraries.

60 Lewis, 18; Schmitt's foreword to Lewis's work, xvi.

Bibliography

Bentley, Richard. A Confutation of Atheism. In Isaac Newton's Papers and Letters on Natural Philosophy and Related Documents, ed. I. B. Cohen, 313-94. 2d ed. Cambridge, MA, 1978.

Casini, Paolo. "Newton: The Classical Scholia." History of Science 22 (1984): 24-38.

Cohen, I. B. "Newton's Concept of Inertia in Relation to Descartes and Lucretius." Royal Society of London, Notes and Records 19 (1964): 131-55.

-----. "'Quantum in se est:' Newton, Kepler, Galileo, Descartes and Lucretius." Proceedings of the American Catholic Philosophical Association for the Year of 1964 38 (1964): 36-46.

Descartes, Rene. Oeuvres de Descartes. Ed. Charles Adam and Paul Tannery. 8 vols. Paris, 1964.

-----. Principles of Philosophy. Trans. Valentine R. Mill and Reese P. Miller. Dordrecht, 1983.

Furley, David J. "Aristotle and the Atomists on Motion in a Void." In Motion and Time, Space and Matter, ed. P. K. Machamer and Turnbull, 83-98. Columbus, OH, 1976.

Gabbey, Alan. "Force and Inertia in Seventeenth-Century Dynamics." Studies in History and Philosophy of Science 2 (1971): 1-67.

Gordon, Cosmo Alexander. A Bibliography of Lucretius. Bury St. Edmunds, Suffolk, 1985.

Gregory, David. Astronomiae physicae et geometricae elementa. Oxford, 1702.

Hall, A.R. and Marie Boas Hall. Unpublished Scientific Papers of Isaac Newton. Cambridge, 1962.

Hanson, Norwood Russell. "The Law of Inertia: A Philosopher's Touchstone." Philosophy of Science 30 (1963): 107-120.

Koyre, Alexandre. Newtonian Studies. London, 1965.

Lewis, Christopher. The Merton Tradition and Kinematics in Late Sixteenth and Early Seventeenth Century Italy. Padua, 1980.

Lindberg, David C. and Robert S. Westman, ed. Reappraisals of the Scientific Revolution. Cambridge, 1990.

Lucretius. In Carum Lucretium poetam commentarii a Joanne Baptista Pio. Bologna, 1511.

-----. In Carum Lucretium poetam commentarii a Ioanne Baptista Pio editi. Paris, 1514.

-----. Titi Lucretii Cari De rerum natura libri sex. A Dionysio Lambino. Paris, 1563/64.

-----. T. Lucretius Cari De rerum natura. Ed. H. A. J. Monro. 4th ed. 2 vols. London, 1905.

-----. De rerum natura. Trans. W. H. D. Rouse. Rev. ed. Cambridge, MA, 1975.

Martels, Z. R. W. M. von, ed. Alchemy revisited. Leiden, 1990.

Melanchthon, Philip. Initia physicae. [Wittenberg, 1549.] Vol. 13 of Opera. Ed. Carolus Gottlieb Bretschneider. Halis Saxonum, 1846.

Newton, Isaac. Philosophiae naturalis Principia mathematica. London, 1687.

-----. Principia. Trans. Andrew Motte. Rev. Florian Cajori. Berkeley, 1962.

Rosen, Edward. "Kepler's Harmonics and His Concept of Inertia." American Journal of Physics 34 (1966): 610-13.

Ruby, Jane. "The Origins of Scientific Law." Journal of the History of Ideas 47 (1986): 341-59.

Zilsel, Edgar. "The Genesis of the Concept of Physical Law." The Philosophical Review 51 (1942): 245-79.