[Footnotes]

[Footnotes]
1
J.L. Heilbron, Electricity in the 17th and 18th centuries (Berkeley, 1979), 60–61
T.L. Hankins, Science and the Enlightenment (Cambridge, 1985), 39–40.
Johann Ber- noulli addressed Euler as "prince of mathematicians," in P.H. Fuss, ed., Correspondance mathematique et physique de quelques celehres geometres du XVIIIeme siecle (2 vols., St. Petersburg, 1843), 2, 88, 91.
2
M.S. Mahoney, "Diagrams and dynamics: Mathematical perspectives on Edgerton's thesis," in J.W. Shirley and F.D. Hoeniger, eds., Science and the arts in the Renaissance (Washington, 1985), 198–220
"Infinitesimals and transcendent rela-
tions: The mathematies of motion in the late seventeenth century," in D.C. Lindberg and R.S. Westman, eds., Reappraisals of the Scientific Revolution (Cambridge, 1990), 461–491
M. Blay, "Varignon, ou la theorie du mouvement des projectiles 'comprise en une proposition generale'," AS, 45 (1988), 591–618.
3
A. Koyre and LB. Cohen, "The case of the missing tanquam: Leibniz, Newton and Clarke," Isis, 52 (1961), 555–566
"Newton and the Leibniz-Clarke correspon- dence," Archives internationales d'histoire des sciences, 15 (1962), 63–126
K.P. Wikler, "Berkeley, Newton and the stars," Studies in history and philosophy of science, 17 (1986), 23–41.
L. Sklar, Space, time and spacetime (Berkeley, 1974)
J. Earman, Worlds enough and space-time (Cambridge, MA, 1989).
4
L. Euler, "Reflexions sur l'espace et le terns," MASB, 4, 1748 (1750), 324-333
Y. Elkana, "Scientific and metaphysical problems: Euler and Kant," R.S. Cohen and M.W. Wartofsky, eds., Boston studies in the philosophy of science, 14 (Dordrecht, 1971), 277– 305
A. Clairaut, "Sur quelques principes qui donnent la solution d'un grand nombre de problemes de dynamique," MASP, 1742 (1745), 1–52, on 2.
5
E. Mach, Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit (Prague, 1872)
Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt, Ith edn. (Leipzig, 1883), chapt. 2.
6
C. Truesdell, Essays in the history of mechanics (Berlin, 1968), 112, 131
Truesdell, "Introduction," EOO, II, 72, ix, xlii
H.J.M. Bos, "Mathematics and rational mechanics," in G.S. Rousseau and R. Porter, eds., The ferment of knowledge (Cam- bridge, 1980), 327–355.
7
J.L. Lagrange, Mecanique analitique (Paris, 1788), 164–165
L. Euler, Theoria motus corporum rigidorum seu solidorum (Rostock and Greifswald, 1765), in EOO, II, 3, and 4, 38
Truesdell, Essays (ref. 6), 170, n. 6
EOO, II, 11, 185–186.
8
Johann Bernoulli, "Solutiones quorundam problematum mathematicorum," CASP, 5, 1730/1 (1738), 11–25
Bernoulli, Opere Omnio (4 vols., Lausanne and Geneva, 1742), 3, 365–375
"Problema statico-dynamicum," "Continuatio tracta- tionis de descensu corporis gravis, super hypothenusa trianguli rectanguli mobilis super piano horizontali immobili," ibid., 4, 332–341, 341–347
P. d'Arcy, "Probleme de dynamique," MASP, (1752), 344-361
ibid., 1750 (1754), 107–108.
Jean Le Rond d'Alembert, Traite de dynamique (Paris, 1743), 72– 80
Clairaut's; Fuss (ref. 1), 2, 64ff., 479ff.
Mach, Mechanik (ref. 5), chapt. 3, §3
Lagrange (ref. 7), 185–188
D. Bertoloni Meli, "The relativization of centrifugal force," Isis, 81 (1990), 23–43, §4.
9
Clairaut (ref. 4)
EOO, II, 11, 222–223, n. R. Dugas, History of mechanics (Neuchatel, 1955), 370–373.
10
Bertoloni Meli (ref. 8), §4.
11
Clairaut (ref. 4), 24–26 and 48–52.
12
Ibid., 42–52.
Clairaut (EOO, IV, 5, 146–148)
13
D. Bernoulli, "Nouveau Probleme de mecanique," MASB, 7, 1745 (1746), 54–70
DBW, 3, 179–196.
14
Fuss (ref. 1), 612–650, on 649
CASP, 10, 1738 (1747), 116–124
DBW, 3, 160–169
"Remarques sur le principe de la conservation des forces vives pris dans un sens general," MASB, 4, 1748 (1750), 356–364
DBW, 3, 197–206.
15
Euler, "De motu corporum in superficiebus mobilibus," Opuscula varii argumenti (Berlin, 1746), 1–136, E 86
EOO, II, 6, 75–174, on 118
16
EOO, II, 15, 163–164
EOO, II, 12, xliii–xliv
J. Ravetz, "The representation of physical quantities in eighteenth-century mathematical physics," Isis, 52 (1961), 7–20.
17
Euler (ref. 15), 118–120, 126.
E.J. Aiton, "The inverse problem of central forces," AS, 20 (1964), 81–99, on 94f
Clairaut to Euler, 23 Apr 1743, EOO, IV, 5 146–148.
18
. Euler, "De motu corporum in tubo rectilineo mobili circa axem fixum per ipsum tubum transeuntem," in Opera postuma in EOO, II, 7, 248–265, on 261–262
Curtis Wilson, "D'Alembert versus Euler on the precession of the equinoxes and the mechan- ics of rigid bodies," AHES, 37 (1987), 233–273, on 262–263.
19
T.L. Hankins, Jean d'Alembert (Oxford, 1970), chapt. 3, 239–240.
20
C. Waff, Universal gravity and the motion of the Moon's apogee: The establish- merit and reception of Newton's inverse-square law, 1687–1749 (Ph.D. thesis, Johns Hop- kins University, 1976)
P. Chandler, "Clairaut's critique of Newtonian attraction: Some insights into his philosophy of science," AS, 32 (1975), 369–378.
21
Truesdell (ref. 6), 114
E.G. Forbes, ed., The Euler-Mayer correspondence (Lon- don, 1971), vii
Curtis Wilson, "Perturbations and solar tables from Lacaille to Delam- bre: The rapprochement of observation and theory," AHES, 22 (1980), 54–304, on 122
"The great inequality of Jupiter and Saturn: From Kepler to Laplace," AHES, 33 (1985), 15–290, on 72
O. Wölk, "Eulers Beiträge zur Theorie der Bewegung der Himmelskörper," in Leonhard Euler: 1707–1783. Beiträge zu Leben und Werk (Basel, 1983), 345–362, on 346–348.
22
Wilson, "Perturbations" (ref. 21), 93–104.
23
P.S. Laplace, Oeuvres completes (14 vols., Paris, 1878–1912), 5, 13
G.J. Jacobi to P.H. von Fuss, 3 May 1841, in P. Staeckel and W. Ahrens, "Der Briefwechsel zwischen C.G.J. Jacobi und P.H. v. Fuss über die Herausgabe der Werke Leonhard Eulers," Bibliotheca mathematica, III, 8 (1907–1908), 233–306
Hankins (ref. 19), 63
Wilson, " Perturbations" (ref. 21), 191.
24
Wilson, "Perturbations" (ref. 21), 120, 193
Wolfgang Ludwig Krafft, and Johann Andreas Lexell in EOO, II, 22, 24–28
A. Gautier, Essai historique sur le probleme des trois corps (Paris, 1817), 75–76.
L. Euler, "De perturbatione motus terrae ab actione Veneris oriunda," NCP, 16 (1771), 426–427
Theoria motuum lunae nova methodo pertractata (St. Petersburg, 1772) in EOO, II, 22, 26–28
"Nova methodus planetarum principalium ad tabulas astronomicas reducendi," NCP, 18 (1773), 354–376.
25
Clairaut, "Du Systeme du monde," MASP, 1745 (1748), 329–364
"De l'orbite de la Lüne dans le Systeme de M. Newton," MASP, 1743 (1746), 17–32
"Avertissement de M. Clairaut sur le Systeme du monde, dans les principes de Fattraction," MASP, 1745 (1748), 577–580
"De l'orbite de la Lüne," MASP, 1748 (1752), 421–440
Theorie de la Lüne (St. Petersburg, 1752)
Gautier (ref. 24), 15–34, 100–101.
26
T. Mayer, Theoria Lunae juxta systema newtonianum (London, 1767), 3, 6, and "Novae tabulae motuum Solis et Lunae," Akademie der Wissenschaften, Göttingen, Commentarii, 2, 1752 (1753), 383–430, esp. 384
Gautier (ref. 24), 102–103, 120–121.
Mayer to Euler, 4 Jul 1751 in Forbes (ref. 21)
27
G.W. Leibniz, "Tentamen de motuum coelestium causis," Acta eruditorum (1689), 89–96, in C.I. Gerhardt, ed., Leibnizens mathematische Schriften (7 vols., Halle-Berlin, 1849–56), 6, 150
E.J. Aiton, The vortex theory of planetary motion (Lon- don and New York, 1971), chapt. 6
Bertoloni Meli (ref. 8), sect. 2.
28
Bertoloni Meli, "Public claims, private worries," Studies in history and philosophy of science, 22 (1991), 415–419
Equivalence and priority: Newton versus Leibniz (Oxford, 1993).
29
J. Edelston, ed., The correspondence of Sir Isaac Newton and Professor Cotes (London, 1850), 311 (written around 1712)
Isaac Newton, Correspondence (7 vols., Cambridge, 1959– 1977), 6, 116–122 (written around 1714)
Newton, "An account of the book entitled Commercium epistolicum" Royal Society of London, Philosophical transactions, 29 (1715), 173–224, on 208–209
John Keill, "Reponse," Journal literaire, 4 (1714), 319– 358
Bertoloni Meli (ref. 8), § 2.
30
Schaffer, "Natural philosophy," in Rousseau and Porter (ref. 6), 55–91
Heil- bron, "Experimental natural philosophy," ibid., 357–387
R.W. Home, "Leonhard Euler's 'anti-Newtonian' theory of light," AS, 45 (1988), 521–533
Maclaurin, A treatise of fluxions (Edinburgh, 1742), 356
Thomas Simpson, Miscellaneous tracts (London, 1757), 137–138
Aiton, "The celestial mechanics of Leibniz: A new interpretation," AS, 20(1964), 111–123, on 123.
31
Wilson (ref. 21), 76.
32
Hankins (ref. 19), 78–80, 85.
33
E. Euler, "Recherches sur l'origine des forces," MASB, 6, 1750 (1752), 419–447, E 181
EOO, II, 5, 109–131, esp. 128–131.
34
EOO, IV, 6, 320–330 (correspondence with Frederick the Great in 1749)
P. Ar- telt, Die Wasserkünste von Sanssoucci (Berlin, 1893)
W. Kaiser and B. Thaler, eds., Johann Andreas Segner (1704–1777) und seine Zeit (Halle-Wittenberg, 1977)
Kaiser, Johann Andreas Segner (Leipzig, 1977)
K. Keller, "Johann Andreas Segner," Beiträge zur Geschichte der Technik und Industrie, 5 (Berlin, 1913), 54–72
EOO, IV, 1, passim.
35
L. Euler, "Recherches sur Feffect d'une machine hydraulique proposee par M. Segner, professeur ä Goettingue," MASB, 6, 1750 (1752), 311–354, E 179
EOO, II, 15, 1-40 (see also the preliminary attempt, ibid., 41–79)
Euler to d'Alembert, De- cember 1750, in EOO, IV, 5, 309–310
A. Segner, Theoria machinae cujusdam hydrau- licae (Göttingen, 1750)
Hannoveresche gelehrte Anzeigen, 35 (1750), 137–140, 55(1750), 149–150, and 60(1753), 881–888.
36
K. Le Demour, "Une machine ä elever des eaux," MASP (1732), 118
L. Euler, "Recherches sur une nouvelle maniere d'elever 1'eau proposee par M. de Mour," MASB, 7 (1751), 305–330, E 203
EOO, II, 75, 134–156.
37
Euler, "Theorie plus complette des machines qui sont mises en mouvement par la reaction de l'eau," MASB, 10, 1754 (1756), 227–295, E 222
EOO, II, 15, 157–218
Ostwald's Klassiker, no. 182
E.A. Brauer and M. Winkelmann, eds., Vollstänoligere Theorie der Machinen (Leipzig, 1911)
J. Ackeret, EOO, II, 15, xxxix
Truesdell (ref. 6), 131, 225.
38
L. Euler, "Principes generaux de Petat d'equilibre des fluides," E 225
"Principes generaux du mouvement des fluides," E 226
"Continuation des recherches sur la theorie du mouvement des fluides," E 227, MASB, 11 1755 (1757), 217–273, 274–315, 316-391
EOO, II, 12, 2–53, 54–91, 92–132.
39
Euler, Theoria motus corporum solidorum seu rigidorum, EOO, II, 3, 121–122.
40
Euler, "Decourverte d'un nouveau principe mecanique," MASB, 6 1750 (1752), 185–217, E 111
EOO, II, 5, 81–108.
Euler, "Continuation" (ref. 38), 108–109.
41
Truesdell, "Introduction"
42
Truesdell (ref. 6)
EOO, II, 11 and 12.
43
Wilson (ref. 18), 254, 263
Truesdell (ref. 6), 117–118
W. Habicht, "Einige grundlegende Themen in Leonard Eulers Schiffstheorie," (ref. 21), 243–270, on 261.
44
Truesdell (ref. 6), 163–164
Wilson (ref. 18), 255.
45
J. Bradley, "A letter to the honourable George Earl of Macclesfield concerning an apparent motion observed in some fixed stars," Royal Society of London, Philosophical transactions, 45 (1748), 1–43
J. d'Alembert, Recherches sur la precession des equinoxes, et sur la nutation de l'axe de la terre dans le Systeme newtonien (Paris, 1749)
EOO, IV, 5, 306 (7 Mar 1750)
Wilson (ref. 18), 259.
46
Euler (ref. 40)
E. Winter, ed., Die Registres der Berliner Akademie der Wissen- schaften 1746–1766.
Dokumente für das Wirken Leonhard Eulers in Berlin (Berlin, 1957), 153.
47
Euler, "Du mouvement d'un corps solide quelconque lorsqu'il tourne autour d'un axe mobile," MASB, 16, 1760 (1767), 176–227, E 336
EOO, II, 8, 316–356
Winter (ref. 46), 167
EOO, IV, 5, 307, n. 2
Wilson (ref. 18), 265.
EOO, IV, 315
E 177
E 292
Blanc, EOO, II, 9, xxiv
EOO, II, 3, xvi
EOO, II, 9, xxiii
Daniel Bernoulli, Traite sur le flux et reflux de la mer, in Newton, Philosophiae na- turalis principia mathematica, (3 vols., Geneva, 1739–42), 3, 133–246, on 136–137
d'Alembert (ref. 8), 53.
"Du mouvement d'un corps solide" (E 336)
"De motu corporum circa punctum fixum mobilium" (E 825)
Theoria motus of 1765 (EOO, II, 9, xxvii–xxviii).
E 336
E 825.
48
Euler, "Recherches sur la connoissance mecanique des corps," MASB, 14, 1758 (1765), 134–153, E 291
EOO, II, 8, 178–199
"Du mouvement de rotation des corps solides autour d'un axe variable," MASB, 14, 1758 (1765), 154–193, E 292
EOO, II, 8, 200-235
Winter (ref. 46), 240, 244.
49
Euler, Theoria motus, in EOO, II, 3, 8
Euler to Karsten, 20 Mar 1761 (EOO, IV, 1, 194)
Keller (ref. 34), 61–62.
Halle in 1761
Kaiser (ref. 34), 69–70
Wilson (ref. 18), 266.
51
Euler (ref. 39), EOO, II, 4, chapt. 15, on 85
P. Staeckel, in Enzyklopädie der mathematischen Wissenschaften, 4:1 (Leipzig, 1901–2), 583.
52
G.G. Coriolis, "Sur les equations du mouvement relatif des systemes de corps," Ecole Polytechnique, Journal, 15 (1835), 142–154, on 143, 147.
53
I. Szabö, Geschichte der mechanischen Prinzipien, 2nd edn. (Basel, 1979), chapt. 2
J.O. Fleckenstein's introduction to EOO, II, 5
P. Brunet, Etude historique sur le principe de la moindre action (Paris, 1938)
Lagrange (ref. 7), 188–189.
Hankins (ref. 1), 30–35, 194–195
L. Laudan, "The vis viva controversy, a post mortem," Isis, 59 (1968), 131–143
T. Frängsmyr, J.L. Heilbron, and R.E. Rider, eds., The quantifying spirit in the Enlightenment (Berkeley, 1990).
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