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The Principle of Inertia in the History of Classical Mechanics

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Abstract

Making a history of the principle of inertia, as of any other principle or concept, is a complex but still possible operation. In this work it has been chosen to make a back story which seemed the most natural way for a reconstruction. On the way back, it has been decided to stop at the 6th century CE with the contribution of Ioannes Philoponus. The principle he stated, although very different from the modern one, is certainly associated with it. Going back in time it is still possible and of course one could proceed to the origins of the homo sapiens who perhaps posed the problem of why a club thrown with his hand could go so far from him. But the similarities that one can find with the modern principle are very vague, too perhaps. Without going so far one could see an embryonic idea of the principle of inertia in the atomistic theory of Democritus in the 5th century BCE. The motion of atoms whirling with no apparent reason can suggest the idea that a body can also move with no reason. But the transition from the atom, a metaphysical being, to the body, an empirical being, is far from immediate.

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Notes

  1. The argument has been considered both from a historical and epistemological points of view. No comprehensive study exists, for what I know, on the history of the principle of inertia, but very interesting suggestions can be found in Koyré (1978), Maier (1982) and Westfall (1971). Interesting epistemological considerations can be found in Nagel (1961) and Mach (1883).

  2. I adopt the same term used by Maier (1982, p. 78).

  3. For an in depth discussion on the logical status of classical mechanics see the still topical text by Nagel (1961).

  4. p. 65.

  5. p. 3.

  6. p. 10.

  7. pp. 1–3.

  8. f. 61r, translation into English in Patrizi and Brickman (1943).

  9. f. 65r-v. English translation in Patrizi and Brickman (1943).

  10. f. 61r.

  11. f. 62r.

  12. f. 62v.

  13. f. 64v.

  14. p. 29.

  15. p. 187.

  16. Dialogue 5, p. 93. My translation.

  17. p. 13. Translation into English in Newton (1999).

  18. p. 530.

  19. p. 18.

  20. pp. 30–35.

  21. Scholium to definitions; p. 6.

  22. Notice that both and Gassendi were influenced by Patrizi, thus one can say Newton derived his ideas on space from Patrizi. The role of Henry More for Newton’s conception of space is discussed in depth in Hall (1990).

  23. p. 528.

  24. p. 2. Translation into English in Newton (1999).

  25. p. 2. Translation into English in Newton (1999).

  26. Footnote 10, pp. 514–515.

  27. Translation into English in Westfall (1971).

  28. p. 82.

  29. p. 54.

  30. p. 55.

  31. p. 85.

  32. pp. 46–47.

  33. p. 53. My translation.

  34. p. 24.

  35. p. 225.

  36. p. 155.

  37. p. 42; II 25.

  38. vol. 5, p. 440.

  39. p. 227.

  40. pp. 55.

  41. p. 254.

  42. p. 256.

  43. pp. 81–82.

  44. p. 94.

  45. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, p. 355a. Translation into English in Charleton (1654).

  46. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, p. 345a. Translation into English in Charleton (1654).

  47. To signal that Gassendi quoted Patrizi and also named Campanella—who was one of his correspondent—and Telesio (Gassendi, 1658), vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, p. 246a,b.

  48. p. 213.

  49. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, pp. 246v.

  50. pp. 244–245.

  51. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, pp. 183a,b. Translation into English in Capek (1976).

  52. pp. 244–245.

  53. Epistola 1, p. 62; vol. 3, p. 495b.

  54. Epistola 1, pp. 39–40.

  55. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, p. 354a. Translation into English in Charleton (1654).

  56. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, p. 355a.

  57. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, p. 355a. Translation into English in Charleton (1654).

  58. Vol. 1.

  59. pp. 149–152.

  60. p. 264.

  61. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, p. 338a. Translation into English in Lolordo (2007).

  62. p. 75.

  63. Vol. 1, Syntagma philosophicum, Physica, sec. 1, book 3, p. 354a, b. Translation into English in Charleton (1654).

  64. Epistola 1, pp. 141–142; vol. 3, p. 515b.

  65. p. 173. Translation into English in Galilei (1967).

  66. p. 207. Translation into English in Galilei (1974).

  67. p. 236. Translation into English in Galilei (1974).

  68. p. 56. Translation into English in Galilei (1967).

  69. Second day.

  70. p. 180.

  71. Vol. 10, p. 170. Letter of Benedetto Castelli to Galileo, 1st April 1607.

  72. Vol. 5, p. 134. Letter of Galileo to Mark Welser, 14th August 1612.

  73. p. 495.

  74. p. 174.

  75. p. 53.

  76. pp. 154–155

  77. p. 289.

  78. p. 447.

  79. p. 169.

  80. pp. 206–209.

  81. pp. 243–244.

  82. p. 244. Translation into English in Galilei (1974).

  83. Vol. 8, pp. 336–337. Translation into English in Galilei (1974)

  84. p. 57. The letter to Galileo is of 19 August 1639, see Galilei (1890–1909), vol. 18, p. 88.

  85. pp. 154–157. My translation.

  86. p. 201.

  87. Published as a part of Opera geometrica in 1644 but almost certainly based on a manuscript dating at least to 1641.

  88. De motu proiectorum, p. 156.

  89. pp. 80–81.

  90. Book 12, question 9, f. 73r. Translation into English in Maier (1982).

  91. Book 12, question 9, f. 73r. Translation into English in Maier (1982).

  92. p. 180. Translation into English in Clagett (1959).

  93. pp. 96–112.

  94. p. 35.

  95. pp. 235–236.

  96. pp. 505–515.

  97. pp. 22–23.

  98. p. 510. See also Franco (2003).

  99. p. 42.

  100. Book 4, Question 7, f. 73v. Translation into English in Duhem (1985).

  101. Buridan introduced the term impetus only after 1352 in his final reading of the Quaestiones super octo phisicorum libros Aristotelis. This is most probably the reason for the absence of the term in Albertus de Saxonia(and Oresme)’s commentaries on Aristotle’s Physica written before this date (Thijssen, 2004).

  102. Book 8, Question 12, ff. 120v–121r. Translation in Clagett (1959).

  103. Book 8, Question 12, f. 120v. Translation into English in Clagett (1959).

  104. p. 44.

  105. Book 8, Question 12, f. 121r. Translation into English in Clagett (1959).

  106. p. 92, footnote 15.

  107. Book. 8, Question 12, f. 120v–121r. Translation into English in Clagett (1959).

  108. 642-1.

  109. pp. 497–499; 271–293.

  110. See for instance the argumentations of Franciscus de Marchia quoted in Clagett (1959, p. 529).

  111. p. 181.

  112. 693,28, p. 180.

  113. 642-1, 642-10.

  114. 642-10.

  115. 642-20.

  116. p. 517.

  117. p. 125.

  118. p. 269.

  119. 215a.

  120. 644-17, 644-20.

  121. p. 169.

  122. pp. 140–145.

  123. pp. 112–113.

  124. p. 87. Simplicius, commentary on De caelo.

  125. p. 89. Cicero, De finibus.

  126. pp. 93–97.

  127. It should be noticed that according to some interpretations Democritus probably could not conceive atoms immersed in an empty space as a container but rather he thought about an alternation of void and atoms; where void had some form of reality for Democritus, and both atoms and void were in a place (Jammer, 1993; Sedley, 1982), p. 11; pp. 179-182.

  128. Johannes Stobaeus (after 5th century CE) stated however: “And he [Democritus] said that it was possible for an atom to be as big as a world” (Taylor, 1999, p. 88). Note that Democritus did not use the very word atoms, but rather solids, beings, substances; see Pagano and Pagano (2022, p. 7).

  129. pp. 70–71. Simplicius, commentary on De caelo.

  130. 1071b.

  131. p. 89. Simplicius, commentary on De caelo.

  132. p. 91. According to Alfieri there are no reason to believe in atoms embedded in vast empty spaces; atoms could be quite close to each other. That is Democritus’ universe would be not so empty of matter as one is led to think.

  133. pp. 84–85.

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Capecchi, D. The Principle of Inertia in the History of Classical Mechanics. Found Sci (2023). https://doi.org/10.1007/s10699-023-09902-3

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