A Posteriori Deductions Dynamical Conception of Matter And, 126

Home , Absolute rotation, Bucket argument

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INDEX

a posteriori deductions An Account of Sir Isaac Newton’s dynamical conception of matter and, Philosophical Discoveries 126–128 (MacLaurin), 300–301, 308–317 geometrical conception of matter Acta eruditorum (Leibniz), 39 and, 116–119, 134–136 action at a distance, 192–194, 347–348 aprioriassumption active force, Leibniz’s concept of, 40–41 causation and, 270–279 air resistance, laws of motion and, 171, Locke’s discussion of nature and, 366 265–266 alchemy, Newton’s interest in, 3nn7–8, spacetime theory and, 197 107–111 absolute motion d’Alembert,J.L.R.,109, 192, 195, 282, definitions of, 199 285n15, 378–379 DiSalle’s discussion of, 215–217 algebra dispositional account of mass and, as analysis, 223–224 329–331 curves expressed in, 225–226 Newton’s concept of, 196–218 Algebra (Kinckhuysen), 226 Scholium discussion of, 206–215 Analogies of Experience, Kant’s space-time theories and, development of, 355 200–206 analysis. See also theoretical analysis absolute rest influence of Principia on, 361–364, absolute motion and, 209–215 366–371 Euler’s theories on time and space Newton’s discussion of, 224–229, and, 173–175 250–253 absolute rotation, 204–206 terminology and definitions of, absolute space 221–224 Kant’s discussion of, 342–359 Analysis per Quantitatum, Series, Newton’s definition of, 200–206, Fluxiones, ac differentias cum 208–209, 211–215, 347–359 Enumeratio Linearum Tertii absolute velocities, Newtonian Ordinis (Newton), 8 space-time theory and, 202–206 Anstey, P. R., 57–58, 58n18 abstract quantity, fluxions theory and, apogee, mean motion of, 377–383 224 approximations acceleration Newton’s research and, 394n22 centripetal force and, 372–377 successive approximation, 100 force and, 163–167 area rule of Kepler, 156–158, 160–162 universal law of gravitation and, planetary bodies and, 162, 164, 162–167 179n20, 364–366

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420 index

areas for curves, Cartesian Bacon, Francis, 57–59, 59n21, 62n27 co-ordinates, 220–221 Barber,K.F.,16n10, 17n11 argument for universal gravitation Barrow, Isaac, 8 (AUG). See universal gravitation composition of motion theory, Aristotle 236–239, 238n26–27, 239n29, analysis methods of, 221–226 245, 247 causation and, 85 on De Analysis, 224–229 Locke’s discussion of, 52–53 Geometrical lectures of, 236 metaphysics of, 320–321 geometrical objects defined by, model of science and mathematics, 71–77 70, 74–77, 77n17, 80, 82 justification of postulates by, 77–82 on motion, 213, 249 on mathematics as science, 70–71 teleology of, 345–346 on mechanics in geometry, 83–85 unities of form and matter of, 39 on nature and mathematics, 69–101 astronomy physical significance of mathematics influence of Principia on, 360–364, and, 96–97 393–395 on postulates as practice of natural philosophy and, 61–68, mechanics, 97–100 61n26, 65n31 Bayesian theory, models and Newton’s discussion of, 65n31, hypotheses in, 91n41 67–68 Bayle, Pierre, 310 simultaneity theory in, 368 Belkind, Ori, 6, 138–168, 210–211 atheism, 350 Bennett, Jonathan, 24–25 atomism, Newton’s discussion of, Bentley, Richard, 3, 87n32, 130n24, 29n30 285, 286n17, 291, 347–348 attraction Berkeley, George, 304–305, 308, 333 force proportional to mass, 175 Bernoulli, Johann, 40 hypotheses concerning, 139–146, Biener, Zvi, 6–7, 105–137 177–183 Blancanus, Josephus, 72n4, 75n11, Kant’s discussion of, 342, 355–356 77n17 lunar precession and, 193–194 Blay, Michel, 3n6 as matter property, 280–298 Bloch, Leon,´ 3n6 Maupertuis’s defense of, 286–298 bodies in motion motion and, 85–89, 88n34 bodies plural, Cartesian concept of, postulates of mathematical/physical 14n5 distinction, 89–91 “body in general,” Cartesian concept s’Gravesande’s defense of Newton’s of, 14–16, 14n4 theories concerning, 283–286 Boyle’s dispositional theory and, structural assumptions and, 320–326 146–156 closed systems of interacting bodies, third law of motion and, 121–124, 183–185 175–185 Descartes’s discussion of, 13–20, attraction-at-a-distance, Locke’s 16–17 concept of, 64–65 dispositional account of mass and, AUG (argument for universal 327–331 gravitation). See universal dynamical conception of matter and, gravitation 111–116 Axioms of Intuition, 353n17 Euler’s theories on time and space Ayers, Michael, 266n21, 284n14 and, 173–175

index 421

geometrical conception of matter Cambridge Companion to Newton, and, 116–119 3n9 gravity and, 128–130 Cambridge Platonism, 343, 357n25 Huygens’s rules for, 169–170, Carnap, Rudolf, 204–205 188–190 Cartesian co-ordinates Leibniz on force and, 33–41 areas for curves and, 220–221 Locke’s discussion of, 263–269 polynomial equations and, 234–236 mechanical aether principle, quadrature rules and, 226 107–111 Cassini, G. D., 191, 393n20 natural philosophy and role of, Cauchy, A.-L., 116n13 57–62, 85 causation Newtonian space-time principles deductive reasoning and, 140–146 and, 203n9 discrepancy as measurement and, Newton’s account of, 7, 13–32, 91–97 24n21 force and, 96n50 Newton’s divine phenomenalism Hume’s Newtonian ideal of, and, 335–338 269–279 Newton’s laws and force of, 42–47 Kant’s discussion of, 354–355 “problem of bodies” principle, mathematical/physical distinction 16–32 and, 85–89 proportionalities and, 130–136 mathematics and, 71–77 quantity of motion and, 151–156 Maupertuis’s discussion of, 287–288 solid bodies, Descartes’s discussion metaphysics of space and, 349–359 of, 18n12, 28–29 postulates of mathematical/physical space and, 111n9 distinction, 89–91 third law of motion and, 121–124 Cavendish, H., 194, 206n12, 363 Bonneau, François de (Sieur de Celestial Mechanics (Laplace), 361, Verdus), 239–241 394n23 bootstrap confirmation, laws of celestial mechanics, Newton’s influence motion and, 179n20 on, 382–383 Boscovichian point-particles, 116, 136 centrifugal force, Newtonian Boulliau, Ismael,¨ 364 space-time and, 206 Boyle, Robert centripetal force on bodies in motion, 7, 262 Area Law of Kepler and, 156–158 dispositional theory of, 320–326 Cotes’s commentaries on, 119–121 Locke and, 263 gravitation and, 142, 143n12 natural philosophy and work of, inverse-square measurements and, 49–51, 57–68, 58nn18–19, 59n21, 369–371 59n23, 60nn24–25, 62n27, 66n32 planetary bodies and, 179n20 Newtonian and Humean approaches chemistry, Newton’s legacy and history to problems of, 332–335 of, 2 Brading, Katherine, 7, 13–32 Child, J. M., 236, 238n26 Brahe, Tycho, 391 Christensen, David, 179n20 Brown, Harvey, 197 Clairaut, A. C., 192, 378–383, 391–392 bucket argument Clarke, Samuel, 109, 213, 285–286, 291 absolute vs. relative motion and, co-linearity, Newtonian space-time 207–208, 214–217 theory and, 202–206 Newtonian space-time and, 204–206 Cogitata physico mathematica Burtt, E. A., 2 (Mersenne), 240n34

422 index

Cohen, I. B. Corollary VI, 203n9, 216 on discrepancy as measurement, corpuscular hypothesis 92n42, 93n43 Boyle’s dispositional theory and, on dynamical conception of matter, 320–326 125 Newton’s concept of mass and, on force and motion theory, 326–331 44–47 Cotes, Roger, 6, 105–107 on Newton’s definitions, on attraction, 295n37, 297n41 198n2 on dynamical conception and status on Newton’s theories, 2–5 of laws, 124–128 Collins, John, 224–227, 239–240n34 on gravity as essential property, collisions 128–130, 276n29, 357n23 Huygens’s rules concerning, “invisible hand” commentaries of, 169–170, 188–190 119–130, 136–137 third law of motion concerning, Newton’s Challenge and, 307–308 146–147, 152–156, 171, on proportionalities, 130–136 178–183 third law critiqued by, 175–185 color, Boyle’s dispositional theory on third law of motion, 121–124 concerning, 320–326 critical philosophy, Kant and evolution common cause principle, of, 352–359 demonstrative induction and, Critique of Pure Reason (Kant), 144n14 300–301, 350n14 composition of motions. See rule of curves composition in De Methodis, 245, 247–251 of Barrow, 236–239 method of tangents and, 240–247 cycloids, 240–243 perihelion of Mercury and, 384–389 in De Methodis, 245, 250–253 squaring of, 225–226 ellipse and, 243, 245 Van Heuraet’s theorem and, 232, general law for, 243–248 235–236 quadratrix, composition of motion Cutting-off of a Ratio (Apollonius), for, 243, 245 222n5 speeds and, 253 cycloid, composition of motions for, spirals and, 243–245 240–243 theory of, 229 universal gravitation and, 155–156, data, evidence and, 361–364 161–162, 167–168 De Analysis per Aequationes Numero “Confesio naturae contra atheistas” Terminorum Infinitas (Newton), (Leibniz), 34 222, 224–229 conservation, of momentum, 150–151, “De Arcanis Motus et Mechanica ad 154–156, 158, 166–167 puramGeometriamreducenda” constant ratio, speeds of motions and, (Leibniz), 36n11 239n30 De Corpore (Hobbes), 34 continuum mechanics, Newtonian de Gandt, François, 3n6 theory and, 116 De Gravitatione et Aequipondio Copernicus, N., 361–362 Fluidorum (Newton), 4, 7, 15 Corollary II, 171–172 absolute space discussed in, Corollary IV, 170n4 210–215, 342–347 Corollary V, spacetime definitions and, criticism of Descartes in, 109–111 173n11, 202–203 DiSalle’s discussion of, 217

index 423

dispositional account of mass in, dynamical conception of matter and, 327–331 112–116 divine phenomenalism in, 336–338 on essence of bodies, 292n30 dynamical conception of matter and, on force, 34, 43 111–116 on geometry, 84–85, 223–224, geometrical concepts in, 106–107 229–239 motion discussed in, 151, 206 Leibniz’s critique of, 345–346 “problem of bodies” principle in, Locke’s discussion of, 51–52 20–25, 117–118 MacLaurin’s discussion of, 310–311, relational accounts of motion in, 315–319 175 mechanical aether principle and, De Methodis, 8 107–111, 259 ﬂuxions discussed in, 219–221, neo-Platonic tradition and, 343–345 224–229 Newton’s criticisms of, 21–23, motions discussed in, 233–234, 245, 24n21, 69–70, 109–111, 200, 247–252 342–343 De Motu (Berkeley), 304–305 Newton’s research and work of, 2, 4, De Motum Corporum in Gyrum 7, 9, 106–107, 116–117, 142 (Newton), 107, 131, 364–365, problem of bodies and, 13–20, 32, 392–395 39 “De mundo praesenti” (Leibniz), 39 vortex theory of, 52n11 De Pierris, Graciela, 9, 257–279 determination of motions, theories dead force, Leibniz’s concept of, concerning, 232–239 40–41 DI. See demonstrative induction deduction Dialogues Concerning Natural Religion Locke’s model of, 266n21 (Hume), 307–308 OED deﬁnition of, 178n19 DiSalle, Robert, 349n12 “A Defense of the Doctrine Touching on absolute motion, 208, 212n22, the Spring and Weight of the Air” 215–218 (Boyle), 59 on natural philosophy, 302n9 demonstrative induction (DI) on Newton’s methodology, 5, 8 argument for universal gravitation on spacetime theory, 197, 199–201, and, 156–167 205, 349n12 Dorling’s concept of, 142–146, Discours (Maupertuis), 280–282, 144n14 286n19, 295–296 structural assumptions and, Discourse on Metaphysics (Leibniz), 39 167–168 DiscourseontheCauseofGravity derivative force, Leibniz’s concept of, (Huygens), 390 40–41 dispositions Descartes, Rene´ Boyle’s philosophical theory of, 7, absolute vs. relative motion and, 320–341 206–215, 211n19, 215 Humean and Newtonian approaches air resistance and motion theory of, to, 332–335 366 Newton’s account of mass and, on analysis, 223 326–331 Cotes’s comparison of Newton with, Newton’s divine phenomenalism 119–130 and, 335–338 determination of motions theory, divine omnipresence, Kant’s discussion 233 of, 353n18, 359

424 index

divine phenomenalism, dispositional hypothetico-deductive vs. theory and, 335–338 demonstrative induction methods Dobbs, Betty Jo Teeter, 3n8 and, 144–146 Domski, Mary, 9, 48–68, 84–85 influence of Principia on, 361–364 Dorling, Jon, 142 “invisible hand” commentaries of double reduction, analysis of curves Cotes and, 120–121 and, 228 laws of motion supported with, Downing, Lisa, 9, 280–298 169–195 Ducheyne, Steffen, 155n20 Newton–Cotes discussion of Duhem, Pierre, 2n2, 140, 371, 373 attraction and, 177–183 Dunlop, Katherine, 8, 69–101 Newton’s conceptions of matter and, dynamical conception of matter, 6–7, 8 105–137 force measurements and, 105–107 Newton’s space and time definitions geometrical concepts vs., 111–116, and, 200–201 136–137 projectile and pendulum laws of motion and, 124–128 experimentsofNewtonand, 170–171 Earman, J., 203 An Enquiry Concerning Human EI (eliminative induction), 143–146 Understanding (Hume), 258, Einstein, Albert, Newton’s theories and 271–279 transition to, 1–2, 6, 180–183, An Enquiry Concerning the Principles of 197, 383–385 Morals (Hume), 273–274 Elémens de la philosophie de Neuton entelechy, Atristotelian concept of, (Voltaire), 293 345–346 Elements (Euclid), 73, 79, 90n39, 223 epigenesis of pure reason, 353n18 Elements of Natural Philosophy (Locke), epistemology, metaphysics and, 17n11 64 equality, composition of motion and, “elimination argument” of Descartes, 236–239 110–111 equality of action and reaction. See eliminative induction (EI), 143–146 third law of motion ellipses equilibrium, Newton’s argument composition of motion for, 242, 245 concerning, 184–185 inverse-squared centripetal force An Essay Concerning Human and, 373–377 Understanding (Locke), 9, 48–50, Kepler’s laws and, 364–366, 392–395 49n3, 63–68, 263, 271, 284, Newton’s consideration of, 94n46, 288–289 140n6 essences, real vs. nominal, 288–296 theory-mediated measurement and, “The Establishment of the Mechanical 368–371 Philosophy” (Boas), 4 empirical research Euclid, 73, 79, 90n39, 159, 210–212, absolution motion and, 213–215 353n17, 358n26 action at a distance debate and, Euler, L., 172–175 192–194 on action at a distance, 192–195 Euler’s time and space theories and, on attractive forces proportional to 172–175 mass, 175 evidence from machines and, fluxions analysis and, 220–221, 171–172 224 Huygens’s rules for motion of bodies natural philosophy and mechanics and, 169–170, 187–190 vs. metaphysics and, 302–303

index 425

“Newton’s Challenge” and work of, third law of motion and, 121–124, 301–303 147–148 on precession, 378–383 Force in Newton’s Physics (Westfall), evidence 3n9, 4 complexity and parochialism of, Foucault’s pendulum experiment, 364–366 206n12 data and, 361–364 French Academy of Sciences, 86 parochialism and continuity of, French Enlightenment, 8 383–389 Friedman, Michael, 5, 9–10, post-Principia logic of, 377–383 342–359 in Principia, 371–377 functions, Newton’s theory of, 224 theory-mediated measurement and, 368–371 Gabbey, Alan, 83 exact-approximate duality, structural Galileo assumptions and, 161–162 on air resistance and theory of exceptionless universality, Locke and motion, 366 Newton on, 267–269 dynamical conception of matter and experimental method work of, 125 Locke’s concept of, 267 on force, 7, 47 Newton’s development of, 178–185, geometry and work of, 76, 78n18, 366 84, 375–377 extension on gravity, 387–389 dynamical conception of matter and, influence on Newton, 2 111–116 mathematics used by, 369–370 geometrical conception of matter on planetary motion, 162 and, 134–136, 343 spacetime transformations and, 197, as structural assumption, 148–149 202, 203n9, 204–206, 213 Garber, Daniel, 7, 10, 17, 18nn13–14, Fermat,P.de,233 19–20, 33–47 Flamsteed, J., 394n23 general relativity, curve-fitting theory fluxions and, 384–389 introduction in De Methodis of, geocentric systems, 141n8 249–251 Geometria (Newton), 83–85, 90–91, Newton’s theory of, 8 98–100, 99n54 velocity and, 219–254 geometrical conception of matter force Newton’s development of, 114–116, absolute, accelerative, and motive, 136–137 163 a posteriori characterization of, attractive force proportional to 116–119 mass, 175 proportionality and, 134–136 autonomous models of, 155n20 Geometrical lectures (Barrow), 236, dynamical conception of matter and, 238n26, 240n34 113–116 Géométrie (Descartes), 85, 224, 229 Leibniz on nature of, 33–47 geometry mathematical investigation of, 71, absolute space and, 358n26 93–97 analysis and, 222–224 Newton on nature of, 7, 41–47, Barrow’s views on, 70–101 367–371 conjectural history in Geometria of, quantity of motion and, 149n19 99n54

426 index

geometry (cont.) Newton’s “divine phenomenalism” definition of geometrical objects, and, 337–338 71–77 “sensorium” of absolute space and, discrepancy transformed into 211, 343–347 measurement, 91–97 s’Gravesande, Willem Jacob Van, 9, dynamical conception of matter and, 280–286, 289n27, 291 105–107, 111–116 gravitation (gravity). See also Euclid’s principles of, 79 attraction; universal gravitation justification of postulates in Area Law derivation of centripetal (Barrow), 77–82 force and, 156–158 mathematical/physical distinction bodies and universality of, 29n30 and, 85–89 Cotes’s commentaries on, 119–121 mechanics and application of, defense of Newton’s theories on, 83–85 280–281 motions and, 229–239 demonstrative induction and, natural philosophy and, 69–101 145–146 in Newton’s Principia, 8 derivation of universal nature of, postulates and mathemetical/ 162–167 physical distinction and, 89–91 Einstein’s general relativity and, practice of measurement and, 385–389 97–100 as essential property, 128–130 Glymour, Clark, 179n20 Euler–Newton debate concerning, God 192–194 attraction as action of, 90–91, force and, 42–47, 162–167, 286–288, 289n26, 293–294 263n15 Barrow on power of, 74–78, 90 Harmonic Rule and inverse-squared Descartes’s natural philosophy and, distance nature of, 158–162 16–17, 47 Hume’s discussion of, 274–279 dispositional theory and, 327–328, Huygens’s proposals for, 66n33, 138, 335–336 187–190 emanative effect of, 343n3 “invisible hand” commentaries of essentialist view of, 283–284 Cotes and, 120–121 gravity as agent of, 348–349 Kant’s discussion of, 342, 355–359 Hobbes’ physics and, 34–35 Kepler’s rules and, 373–377 Hume’s exclusion of, 340–341 Locke’s discussion of, 51–56, 64–68, Kant’s pre-critical divine 65n31, 66n33, 263n14 omnipresence theory and, Maupertuis’s discussion of, 287–296 353n18 measurements of discrepancies in, law-constitutive approach to bodies 100 and, 24n21 mechanical aether principle and, laws of motion and, 82, 127–128, 107–111 343–345 methodological research of Newton Leibniz on power of, 36–37 and, 6, 65n31, 87–89, 87n32 Locke on power of, 64–65, 263n14, pendulum experiments involving, 266–267 116–119 MacLaurin’s discussion of, 312–313 perihelion of Mercury and materialization of, 350–359 falsification of Newton’s theory of, natural philosophy and existence of, 383–389 143n13, 304, 306–308 relativity theory and, 180n21

index 427

rule of composition and, 155–156, Huggett, Nick, 7–8, 196–218, 212n22 161–162 human nature, Hume’s discussion of, scientific method of Newton and, 258n4 138–168 Hume, David, 9, 309–310 third law of motion and, Boyle’s dispositional theory and, 121–124 332–335 gravitational constant, 122n15 on causation, 269–279 Greene, Robert, 131n28 gravitation (gravity), discussion of, Guicciardini, Niccolo,´ 84–85 274–279 on human nature, 258n4 Hall, A. Rupert, 4, 4n13, 87n31 on impenetrability of bodies, Hall, Marie Boas, 4, 4n13 274–279 Halley, Edmond, 191, 306 legacy of, 338–341 Halley’s comet, 377, 383 Newton’s legacy to, 338–341 Hanson, Norwood Russell, 4, 141–142, on scientific method, 258–259, 141n8 269–279 Harmonic Rule of Kepler, 156, Huygens, Christiaan, 6, 35n6, 66n33 158–162, 164 geometric principles and work of, Harper, William 84, 369–370, 375 on causation, 93 on gravitation, 66n33, 138, 187–190, dynamical conception of matter and, 387–391 6–8, 106, 125–126 laws of motion and, 124, 152, 190, on empirical support for laws of 213n23, 305 motion, 169–195 MacLaurin and, 317 on gravitation, 143, 156 rules for motion of bodies, 169–170, gravitational theory transition to 170n3 relativity discussed by, 180n21 theory-mediated measurement and on mathematics as science, 71 work of, 368–369 weak equivalence principle discussed on velocity, 203 by, 181n22 hylomorphism, dynamical conception HD. See hypothetico-deductive (HD) of matter and, 112–116 reasoning hypotheses heliocentric systems, 141n8 absolute motion and, 208 Hempel, Karl, 382 attraction and, (Newton–Cotes Henry, John, 87n31 exchange) 139–146, 177–185 Hill-Brown theory of the Moon, hypothetico-deductive (HD) 383 reasoning and, 140–146, 141n8 historical observation, natural Locke’s attitudes concerning, philosophy and, 57–62 63n28 “History of Astronomy, The” (Smith), models and, 91–92, 91n41, 92n42 308 postulates and, 80–82 History of Particular Qualities (Boyle), scientific method and, 138–146, 325–326 260–269 Hobbes, Thomas, 2, 34–35, 38–39, 43, third law of motion as, 147–148 233, 240n34 universal law of gravitation and, Hooke, Robert, 364–365 166–167 Horologium Oscillatorium (Huygens), “Hypotheses non fingo” (Newton), 305 124, 177–183, 263n15 Horrocks, J., 364 Hypothesis physica nova (Leibniz), 35

428 index

hypothetico-deductive (HD) reasoning gravity and, 128n21 discrepancy as measurement and, laws of motion concerning, 147, 91–97, 92n42 154–156 hypotheses and, 140–146 linear acceleration and, 216–217 influence of Principia on, 363–364 motion and, 110n5 laws of motion and, 148–156 proportionality of, 133–136 Newton’s research methodology “inference-tickets” theorems, and, 6, 391 centripetal force and, 371–377 orbital phenomena and, 190–192 inherent force, Newton’s concept of, structural assumptions and, 44–47, 288–296 161–162 instantaneous velocity force and quantity of motion and, identity, Descartes’s discussion of 149n19 bodies and, 18–20 inverse-squared centripetal force impenetrability of bodies, 23–25 and, 159–162 Hume’s discussion of, 274–279 Introductio in analysin infinitorum Kant’s discussion of, 356–359 (Euler), 224 Maupertuis and, 292n30 inverse-squared centripetal force universal gravitation and, 261–269 Cotes’s commentaries on, impressed force, 44–47, 122–124, 119–121 346–347 gravitation and, 142, 143n12 Inaugural Dissertation (Kant), Harmonic Rule and, 158–162 351–352, 353n18 Keplerian ellipse and, 373–377, Individuation and Identity in Early 392–395 Modern Philosophy (Barber and lunar precession and, 192–194 Gracia), 16n10 measurement theory and, 369–371 individuation, Descartes’s discussion of precession theorem and, 182–183 bodies and, 16–20, 16n10, 18n14, solar gravity and, 378–379 19n15 “invisible hand” commentaries of inductive reasoning. See also Cotes, 106, 119–130, 121–124, demonstrative induction; 136–137 hypothetico-deductive (HD) Isaac Newton’s Papers and Letters, 3 reasoning Isaac Newton’s Philosophiae Naturalis EI (eliminative induction) and, Principia Mathematica (Cohen & 143–146 Koyre),´ 3 Hume’s Newtonian ideal of isochronous motion, pendulum causation and, 269–279 experiments concerning, 387–389 hypotheses and rule of, 139–146 hypothetico-deductive reasoning Jammer, Max, 4n14 and, 140–146 Janiak, Andrew, 88nn34–35, 89, 96, scientific method and, 259–269 287n21, 350n13 structural assumptions and, Joy, Lynn, 7, 320–341 146–156 universal law of gravitation and, Kant, Immanuel, 132n29, 172n9 164–167 on gravitation, 347, 352–359 inertia metaphysics of, 350–359 Area Law derivation of centripetal metaphysical deduction of, 352–353 force and, 156–158 Newton and, 9–10, 299–301 dynamical conception of matter and, philosophy and science and, 114–116 302–303

index 429

Kargon, R., 84n25 evidentiary complexity concerning, Keill, J., 282 364–366 Kepler, Johannes, 2n2 force and, 34–41, 42–47, 45–47, 3/2 power rule of, 371 122–124 Area Law of, 156–158, 179n20 force and quantity of motion and, dynamical conception of matter and, 149 125–128 geometry and, 229–239 ellipse theory of, 364–366, 392–395 Huygens’s rules concerning, 124, geometrical conception of matter 152, 169–170 and, 116–119 Kant’s discussion of, 342–359 gravitation and, 145–146 Leibniz’s interest in, 35–41 Harmonic Rule of, 156, 158–162 machines as evidence for, 171–172 laws of, 94, 361–364 mathematics and science of, 8 mechanical aether principle and laws matter theory and, 7–8 of, 107–111 method of tangents and, 239–245 on orbital motion, 162, 164, Newton’s deﬁnitions, 198–199, 190–191, 364–366, 375–377 215–217 Keynes, John Maynard, 3, 3n7 Newton’s laws, 7–8, 13–32, 86–89, al Khwar¯ ¯ızm¯ı, M. ibn Musa, 120–124, 128n21, 129–130, 223n10 146–156 Kinckhuysen, G., 226 “problem of bodies” principle and, knowledge, Locke’s discussion of, 26–32 266–267 projectiles and pendulum Koyre,´ Alexandre, 2–3, 87n31, 198n2, experiments and, 170–171 260n9, 262n13, 273 Scholium discussion of, 206–215 s’Gravesande’s defense of, 284–286 Lacaille, N. L., 192, 195 spacetime theories and, 196–197, Lambert, 191 203n9 Laplace, P.-S., 191–192, 361–362, 383, as structural assumptions, 146–156 394n23 structural assumptions concerning, law-constitutive solution to “problem 146–156 of bodies,” 20–24, 24n21, 28–32, systematic dependencies for, 179n20 30n31 third law, 120–124, 128n21, laws of motion 129–130, 146–156 autonomous models and, 155n20 least-squares curve ﬁts, Newtonian conventionalist approach to, idealizations and, 384–389 147–148 Leibniz, G. W., 4, 7, 10 Descartes’s discussion of bodies and, Clarke correspondence with, 213 15–20, 16n9 Descartes critiqued by, 345–346 Descartes’s work critiqued by differential calculus of, 224 Newton and, 21–23, 22n19, on force, 33–41 24n21 Kant’s critique of, 350–354 dispositional account of mass and, MacLaurin and, 316n33, 318–319 328–331 mechanical aether principle and, dynamical conception of matter and, 109–111 111–116, 124–128 on motion, 213n23 empirical support for, 169–195 Newton’s theories critiqued by, Euler’s time and space theories and, 41–47, 138, 281n7, 355n20, 172–175 394n23

430 index

Leibniz, G. W. (cont.) dispositional property of, 326–331, on orbital phenomena, 363n4 333–335 on space, 347–348 Hume’s philosophy and concept of, Lewis, David, 204–205 339–341 light, Newton’s research on, 116–117, Newton’s definition of, 30, 180n21 367–371 limited physical theory, mathematics orbital phenomena and, 190–192 and, 370–371 parts and whole concepts and, line of nodes, mean motion of, 376–377 148n18 linear momentum, laws of motion and, proportionality and, 133n30 149–150 quantity of motion and, 151–156 linguistics, data and evidence in weight and, 170n3 research on, 361 Master-Builders, Locke’s concept of, living force, Leibniz’s concept of, 48–49, 66–68 40–41 material density, mechanical aether Locke, John principle and, 109–111 commentaries on Principia, 48–50 materialization of God, 350–359 correspondence with Stillingfleet, Mathematical Papers (1967–1981) 51–56, 51n9, 52nn11–12 (Newton), 219 mathematical natural philosophy mathematics embraced by, 63–68 analysis and, 221–224 Maupertuis and, 280, 290–296, Barrow’s lectures on, 71–77 293n33 Boyle’s discussion of, 60–62, on natural philosophy, 51–62, 60nn24–25 54n15, 66nn32–33, 257–259 constitutive role of physics and, Newton and, 8–9, 262–269 259n7 s’Gravesande’s theories and, discrepancy as measurement and, 284–286 91–97 lodestone experiments, 184–185 Kant’s critique of, 351–352 Logarithmotechnica (Mercator), Locke’s commentaries on Newton’s 224–225 work in, 49, 52n12, 63–68 Lorentz, H., 197 mathematical/physical distinction lunar precession, Newton–Euler debate and, 85–89 on, 192–194 Newton and Barrow on nature and, 69–101 Mach, Ernst, 200 Newton’s work on, 8–9 Machin, John, 378 physics and, 369–371 MacLaurin, Colin, 10, 282n15, postulates and mathematical/ 300–301, 308–319 physical distinction and, 89–91 Maglo, Koffi, 89 science as, 71–77, 72n4 magnetic attraction, Newton’s matter theory. See also dynamical discussion of, 184–185 conception of matter Mahoney, Michael, 187–188 attraction and, 280–298 Maizeaux, P. des, 213 Descartes’s discussion of, 14–16 Malebranche, N., 293, 294n35 dispositional account of mass and, man-pressing-a-stone argument, laws 328–331 of motion and, 334–335 empiricism of Newton and, mass 107–137 attractive force proportional to, 175 inherent force and, 44–47

index 431

mechanical aether principle, postulates and mathematical/ 107–111 physical distinction in, 85–91 Newton’s research on, 6–8, 107–119 practice of measurement and, “problem of bodies” principle and, 97–100 20–32 scientiﬁc method and, 259 proportionality and, 131–136 space-time theories and, 172–175, Maupertuis, Pierre Louis Moreau de, 9, 204–206, 212–215 280–281, 286–298, 306 Meditations (Descartes), 14 Mayer, J., 175, 192–194 Meli, Domenico Bertoloni, 41n23 McCann, Edwin, 266n21 Mercator, Nicolaus, 224–225, 364 McGuire, J. E., 4–5, 4n16, 26–27, 29 Mercury, perihelion of, 383–389 McMullin, Ernan, 4–5, 29, 87n31, Mersenne, M., 240n34 87n33 The Metaphysical Foundations of measurement Natural Science (Kant), 2, discrepancy and, 91–97 355–359 empirical success and, 169–170, metaphysics 194–195 absolute space and, 210–211, Newton’s theory of, 366–371 343–346 postulates and practice of, 97–100 Descartes’s discussion of bodies and, proportionality of matter and, 16–20, 17n11 132–136 Euler and, 302–303 mechanics, principles of Kant’s transformation of, 342, absolute motion and, 196–218 350–359 causation and, 270 Leibniz on body and force and, dynamical conception of matter and 33–41 laws of motion and, 124–128 Maupertius’s defense of attraction “dynamical” interpretation of, and, 297–298 200–201 Newton’s contributions to, 9–10 Euclidean frames for, 210–211 physics and, 301–303, 309–310 Euler and, 172–175, 302–303 “problem of bodies” and, 31–32 force and, 42–47 science as, 72–77 Galilean spacetime transformations Metzger, Hel´ ene,` 2 and, 202–206 Milton, J., 58 geometry and, 83–85, 90–91 mobility, bodies and, 23–25 Huygens’s work on, 188 momentum inﬂuence of Principia on, 366–371 Area Law derivation of centripetal intelligibility model and, 264 force and, 158 Kant’s metaphysics and, 355–359 conservation of, 150–151, 154–156, laws of motion and evidence of 158, 166–167 machines, 171–172 dynamical conception of matter and, Leibniz’s discussion of, 33–41 113–116 Locke’s concept of, 9, 262–269, exchange of, 349–350 266n21 monadic metaphysics, 350–354 mathematics and causation and, More, Henry, 343 85–89 motion See also laws of motion mechanical aether principle, internal principle of, 115n11 107–111 mutual autonomy, Hume’s Newtonian mechanics as practice and, 97n51 ideal and, 278–279 metaphysics of space and, 349–359 mutuality of force, 122–124, 169–170

432 index

natural history Newton on Matter and Activity mathematical constructs and, 92–97 (McMullin), 5 natural philosophy and, 57–68, Newtonian idealizations 58n18 curve-fits and, 384–389 natural law deviations from, 381–383 demonstrative induction and, influence on physics of, 375–377, 142–146, 143n13 390–395 Descartes’s discussion of motion Newtonian mechanics, historical and, 16–20 evolution of, 1 Locke’s discussion of, 64–68, “Newtonian Space-Time” (Stein), 4–5, 267–269 200–206, 208, 214–215, 217 “problem of bodies” and, 21, 21n17 Newton’s Challenge scientific method and, 274–279 Berkeley and, 304–305 structural assumptions concerning, Euler and, 301–303 148–156 MacLaurin’s articulation of, natural philosophy 308–319, 317, 318n34 divisions of science within, 56–62, Newton’s role in, 305–308 59n20 Newton’s new way of inquiry, history dynamical conception of matter and of, 1–5, 2n1 laws of motion and, 124–128 Nicomachean Ethics (Aristotle), 221 Euler’s work and, 302–303 normals, polynomial equations and Locke’scommentson,49–68, 54n14, problem of, 236 65n31, 257–259 Norton, John, 143–144 MacLaurin’s discussion of, 308–310 mathematics and, 60–68, objects 60nn24–25 geometrical definition of, 70–77 Newton’s contributions to, 9, 53–56, universal properties of, 153–156 105–111 occult force, gravity as, 139n5 principles of mechanics and, 188 October 1666 tract on fluxions Rule 4 applications in, 185–187 (Newton), 219–220, 228–229, scientific method and, 257–259 234, 242, 247 s’Gravesande’s theories and, Of the Conduct of the Understanding 284–286 (Locke), 54, 64 structural assumptions and, “Of the Usefulness of Mathematicks for 153–156 Natural Philosophy” (Boyle), neo-Platonic tradition, influence on 60–61, 63 Newton of, 343–345, 357n25 Oldenburg, Henry, 4n13 Never at Rest (Westfall), 3n9, 4 “On the Method of Distinguishing Real Newcomb, Simon, 191–192, 384–385 from Imaginary Phenomena” Newton, Isaac, passim. See also (Leibniz), 38–39 Philosophiae naturalis principia Opticks (Newton), 306–308 mathematica “Aetherial Medium” discussed in, definitions of, 198–199 356n21 as Lucasian Professor of matter and space in, 348n10, Mathematics, 226 349n11 methodology of, 5–10 optics, Newton’s work in, 3n10 philosophical inquiry and legacy of, orbital phenomena 1–5 equilibrium argument concerning, scholarship on, 1–10 184–185

index 433

influence of Principia on theories defense of, 280–282 concerning, 361–364, 373–377, definitions contained in, 198–199 391–395 dispositional account of mass in, Kant’s discussion of, 355n20 326–331 laws of motion and, 179n20 draft editions of, 26–29, 26n27, perihelion of Mercury, 383–389 28n28 planetary motion and, 190–192 dynamical conception of matter in, Origin of Forms and Qualities (Boyle), 113–116, 125–128 320–321, 325–326 evidential reasoning in, 364–366, 371–377 pain, Boyle’s dispositional theory and, force discussed in, 41–47, 162–163 324–326 geometry and mechanics discussed Panza, Marco, 8, 219–254 in, 8, 69–101, 70n1 Pappus, 221–223 gravity as essential property in, parallelogram, rule of, cycloids and, 129–130, 347–348 240–243 Hume’s discussion of, 271, parochialism, continuity of evidence 276–279 and, 383–389 hypotheses discussed in, 138–139 part, concept of, laws of motion and, influence on physics of, 360–395 148–149 Kant’s work and influence of, passive force, Leibniz’s concept of, 299–300 40–41, 45–47 limit-case idealizations in, 387–389 Pemberton, Henry, 282, 298n43 Locke’scommentson,48–68, 50n7, pendulum experiments 66n33 collision research and, 152–156 mathematical/physical distinction isochronous motion and, 387–389 in, 85–91 laws of motion and, 170–171 measurement concepts in, 99–100 mechanical aether principle and, mechanical aether principle and, 108–111, 116–117 109–111 proportionalities and, 130–136 mechanics discussed in, 83–84 sidereal time and, 368 nature and concept of mass in, third law applied to collisions and, 105–107 178–183 Newton’s Challenge and, 305–308 universal law of gravitation and, 162 philosophical inquiry and legacy of, perpetual motion, Leibniz’s discussion 1–5 of, 36–37 “problem of bodies” principle in, 20, perturbations, orbital phenomena and, 21n17, 25–32, 29n30 190–192, 195 Rule 4 added to, 139–140 Peyrera, Benedictus, 72n4, 73n5, 77n17 second edition of, 6 Phemister, P., 54n15 status of laws of motion discussed in, Philosophiae naturalis principia 124–128 mathematica (Newton). See also structural assumptions in, 146–156 Scholium to the Principia theory concepts developed in, (Newton) 366–371 absolute motion discussed in, 201 third law of motion discussed in, absolute space discussed in, 121–124, 147–156 348–350, 349n11 philosophy, Newton’s new way of bodies in motion discussed in, 13, inquiry and evolution of, 1–5, 85–89 2n1

434 index

Physices elementa mathematica, mechanical aether principle and, experimentis confirmata 107–111 (s’Gravesande), 280–286 Newton’sviewsofspaceandtime physico-theology, MacLaurin’s work and, 198–199 and, 309–310 Newton’s theories concerning, 9, physics 85–89, 181–183 Boyle’s research on, 67–68 non-Keplerian motion of Moon and, history of, 1 376 Leibniz’s early interest in, 35–41 post-Principia evidence concerning, Locke’scommentsonNewton’s 377–383 work in, 49–56, 55n16 precession theorem and, 182–183, mathematical/physical distinction 383–389 and, 85–91, 95–97, 259n7, sidereal time and, 368 369–371 third law of motion and, 121–124, metaphysics and, 301–303, 146–156, 190–192 309–310 universal gravitation and, 348–349 natural philosophy and, 56–62 points, absolute space and criteria for, Newton’s transformation of, 212n22 360–395 polynomial equations Newton’s methodology concerning, speeds of motions, Newton’s 5–6 algorithm for, 233–235 practice of measurement and, tangents and curves and, 249–251 97–100 Popper, Karl, 141n7 “problem of bodies” and, 31–32 positivist theory, Newton’s space and theory of measurement in, 367–371 time principles and, 201–206 time in relation to, 199 Posterior Analytics (Aristotle), 72, Piccolomini, Alessandro, 72n4, 73n5, 77n17 77n17 postulates (geometric) pin example, Boyle’s dispositional Barrow’s justification of, 77–82 theory and, 324–326 Euclid’s principles of, 79, 79n19 planetary motions. See also orbital mathematical/physical distinction phenomena and, 89–91 centripetal force and, 371–377 measurement practices and, 97–100 Cotes’s discussion of Newton’s work Pourciau, Bruce, 149n19, 330n31 on, 119–121 precession theorem equilibrium argument concerning, argument for universal gravitation 184–185 and, 125–128 evidential complexity concerning, centripetal force and, 371–377 364–366 laws of motion and, 181–183 Hume’s discussion of, 258n4 lunar apogee/perigee and, 377–383 inductive method and research on, perihelion of Mercury and, 383–389 141n8 “Preparative toward a Natural and inertial mass and, 100 Experimental History” (Bacon), influence of Principia on theories 58n18 concerning, 373–377, 392–395 primary-secondary qualities Kant’s discussion of, 356–359 Maupertuis’s discussion of, 296–297 Kepler’s laws and, 162, 164, 179n20, Newton and Locke on, 264–266 364–366 primitive force, Leibniz’s concept of, mathematical constructs and, 92–97 40–41, 45–47

index 435

“principe d’invention,” 240 definitions of, 367–371 Principia. See Philosophiae naturalis force and, 149–151, 149n19 principia mathematica (Newton) mass and, 151–156 Principles of Philosophy (Descartes), 13–21, 207, 375–376 rationalist philosophy prism experiments, Newton’s work on MacLaurin’s work and, 317–319 optics and, 116–117 Newton’s Rules and, 262–269 “problem of bodies” reality, mathematical reasoning and, Descartes’s laws of nature and, 81–82 16–20 reason, Kant’s preformation system of, Newton’s discussion of, 20–29 353n18 solution to, 29–32 Regulae philosophandi (Newton), problematic analysis, defined, 222 106 problems, geometrical, 90n39 Rule 3, 117–119, 129, 153–156 “Proemial¨ Essay” (Boyle), 59 Rule 4 and dynamical conception of projectiles, Newton’s laws of motion matter in, 128 concerning, 170–171 relative motion, absolute motion vs., proportionality 206–215 attractive force and mass, 175 relativity. See general relativity; special bodies in motion and, 130–136 relativity pendulum experiments and, religion 146–147, 152–156, 178–183 absolute space in relation to, 343 third law of motion and, 183 Descartes’s discussion of, 15n6 “Provisos: A Problem Concerning the divine phenomenalism and, Inferential Function of Scientific 335–338 Theories” (Hempel), 382 Leibniz on bodies and, 35–41 mathematics and, 74–77, 74nn7–8 quadratrix, composition of motion for, natural philosophy and, 307–310 242–245 Newton’s discussion of, 9–10 quadrature, rules of, 226 Religion Within the Limits of Reason polynomial equations and, 236 Alone (Kant), 359 Van Heuraet’s theorem and, Remnant, P., 24–25 231–232 repulsion, Kant’s discussion of, Wallis’ method of, 251–252 355–356 quam proxime principle, Newton’s resistance theorems and, 372–377, 380–383, force and, 36–41, 45–47 392–395 mechanical aether principle and, quantitative empiricism 107–111 dynamical conception of matter and, Roberval,Gillesde,8, 220–221, 114–116 239–245, 240n34, 250 geometric quantities and, 250–251 Rogers,G.A.J.,257 Newton’s research methodology rotational motion, 216–217 and, 6–7, 392–395 Rudolphine Tables (Kepler), 364 quantity of matter Rule 3, 117–119, 129, 153–156, definitions of, 367–371 161–162, 259n8, 260–269, proportionality and, 132–136 274–279 quantity of motion Rule 4 absolute motion and, 210–211, absolute vs. relative motion and, 215–217 207n15

436 index

Rule 4 (cont.) third law of motion in, 147 addition to Philosophiae naturalis science principia mathematica (Newton), mathematics as, 71–77, 72n4 139–140 natural philosophy and categories gravitational theory and, 180n21, of, 56–62 194 philosophy and, 302–303 Huygens’ rules concerning bodies postulates and mathematical/ and, 189–190 physical distinction and, 90–91 natural philosophy applications of, scientific method 185–187 argument for universal gravitation scientific method and, 260–269 and, 138–168 rule of composition, universal Hume’s discussion of, 258–259, gravitation and, 155–156, 269–279 161–162, 167–168 influence of Principia on, 363–364 Rules of Reasoning Locke and Newton on, 259–269 discrepancy as measurement and, natural philosophy and, 257–259 92–97 Scottish Enlightenment, Spinoza and, “problem of bodies” and, 28–29 310–311 Rynasiewicz, Robert, 208, 216 second law of motion definitions contained in, 215–217 Sargent, Rose-Mary, 59n21 dispositional account of mass and, scalar components, ratio of 330n31 field of analysis and, 251–252 force and, 42–47 method of tangents and, 245, senses, mathematical reasoning and, 247–248 80–81 Schaffer, Simon, 187–188 Sepkoski, David, 77n15 Schliesser, Eric, 10, 289n26, 299–319 sidereal time, Newton’s experiments Scholastic natural philosophy, Locke’s concerning, 368–371 discussion of, 52 Smeenk, Chris, 6–7, 105–137 Scholium to the Principia (Newton) Smith, Adam, 308 absolute and relative motion Smith, George E., 5n17, 360–395 discussed in, 206–217 dynamical conception of matter and, attraction discussed in, 177–185, 106, 125–126 347n9 influence on Newton scholarship, definitions in, 198–201 5n17 dynamical conception of matter and, on mathematical/physical 126 distinction, 87 ellipses discussed in, 94n46 on mathematics as science, 71, gravitation discussed in, 87, 138, 259n7 187, 356n21, 390–391 on nature and mathematics, 93–97, lunar precession discussed in, 96nn49–50 193–194 on physics, 5–8 mechanics and laws of motion in, on postulates and measurement, 172 100 “problem of bodies” principle and, on universal gravitation, 160–161 26 Smith, Norman Kemp, 310 space and time discussed in, Socratic problem, 300 196–197, 199–201, 367–371 MacLaurin and, 308–310 Stein’s analysis of, 201–206 Newton’s Challenge and, 301n4

index 437

Some Thoughts concerning Education force and gravitation and, 163–164 (Locke), 55, 65n31 on laws of motion, 330n32 space on mass and weight, 170n3 bodies and, 111n9 “Newtonian Space-Time” paper of, composition of motion and, 200–206, 202n8, 206n12, 247–251 208–210, 217–218 dispositional account of mass and, on Newton’s hypotheses, 178n19 327–331 on space and time in Newton’s work, Euler’s theories on time and, 4–5 172–175 spacetime theory and work of, 197 impenetrability of bodies and, structural assumptions about laws of 23–25 motion and, 146–148 Kant’s metaphysical deduction and, third law of motion and, 122 352–353 Stillingﬂeet, Edward, 49, 51–56, 51n9, Newton’s deﬁnitions of, 198–199, 64, 65n30, 66n32, 263n14 205n11 Streete, Thomas, 364 Newton’s views on, 7–8 structural assumptions, Newton’s part and whole and concept of, acceptance of, 6 148n18 argument for universal gravitation Scholium discussion of, 199–201, and, 156–167 367–371 deductive reasoning and, 167–168 Stein’s “Newtonian Space-Time” gravitational theory and, 145–146, discussion of, 200–206 164–167 theories of, 196–197 inductive reasoning and, 146–156 spatio-temporal framework substance, Aristotelian concept of, Kant’s metaphysical deduction and, 347 352–353 successive approximation, Smith’s Newtonian space-time and, concept of, 100 203–206 Sydenham, Thomas 49 special relativity System of the World (Newton), gravitational theory and, 180n21 122–123, 184 Minkowski geometry of, 197 perihelion of Mercury and, 383 Tamny, Martin, 5n16 Specimen dynamicum (Leibniz), 39–40, tangents, method of, 220–221 45 curves and, 240–245 speeds of motions, Newton’s algorithm Newton and Roberval’s method of, for, 233–234 239–245 composition of motion and, polynomial equations and, 236 247–251 “Tentamen de motuum caelestium Spinoza, de, B., 10 causis” (Leibniz), 41n23 MacLaurin’s criticism of, 310–319 Thabit¯ ibn Qurra, 223n10 Newton’s refutation of, 299 Thackray, A., 286 spirals, composition of motions for, Theological Political Treatise (Spinoza), 242–244 309–311, 313 Stachel, John, 302n9 theorems, geometrical, 90n39 Stein, Howard, 5, 66n32, 170n3 inverse-squared centripetal force on Cambridge Platonists, 343n3 and, 159–162 dynamical conception of matter and, laws of motion and, 179–183 8, 106, 125 tangents and normals and, 220

438 index

theoretical analysis true motion, absolute motion as, defined, 222 208–218, 211n18, 329–331 influence of Principia on, 361–364, Two New Sciences (Galileo), 375–376 366–371 Tycho’s variation, 376 Theoria motus abstractii (Leibniz), 35 Theory of the Moon’s Motion (Euler), “under-labourers” passage in Locke’s 380 Essay, 9, 48–49, 49n3, 67–68 third law of motion (equality of action Understanding Space-Time (DiSalle), and reaction), 120–124, 128n21, 199–201, 215–217 129–130, 146–156 uniformity constraint, proportionality attraction and, 175–177, 183–185 of matter and, 134–136 Cotes’s query about, 175–185 universal gravitation gravitational theory and, 166–167, Cotes’s discussion of, 119–130 183–185 derivation of, 162–167 lunar precession and, 192–194 dynamical conception of matter and projectile and pendulum laws of motion concerning, experiments and, 170–171 124–128 proportionality and, 183 Hume’s discussion of, 274–279 Thomson, James, 196 limit-case idealization concerning, tides, Newton’s gravitational theory 387–389 and, 180–183, 393–395 Locke’s discussion of, 268–269 time mechanical aether principle and, “apparent” to “mean” solar time, 107 199n3 orbital phenomena and, 191–192 Kant’s metaphysical deduction and, Rule 3 concerning, 260–269 352–353 scientific method of Newton and, Newton’s definitions of, 198–199, 138–168 205n11 structural assumptions concerning, Scholium discussion of, 199–201, 155–167 367–371 third law of motion and, 121–124 Stein’s “Newtonian Space-Time” universal validity discussion of, 200–206 Area Law derivation of centripetal theories of, 196–197 force and momentum Torricelli, E., 239n33, 240n34 conservation and, 158 Transcendental Aesthetic (Kant), gravitational theory and, 350n14 145–146 Transcendental Deduction (Kant), of laws of motion, 148–156 353n18 transformation, “problem of bodies” vacuum, Newton’s experiments and, 28–29, 29n30 concerning, 131–136 transmutation, “problem of bodies” Van Heuraet’s theorem, 229–232, and, 28–29 235 A Treatise of Human Nature (Hume), velocity. See also instantaneous velocity 258, 272n26, 333–335 absolute, 202–206 TreatiseoftheSystemoftheWorld dynamical conception of matter and, (Newton), 289n26 114–116 Treatise on Light (Huygens), force and quantity of motion and, 390 149n19

index 439

inverse-squared centripetal force weight and, 159–162 Huygens’s rules concerning bodies Newton on values of, 367–371 and, 187–190 proportionality of, 180–183 mass and, 170n3, 367–371 Verdus, Sieur de (Franc¸ois de Westfall, Richard, 3–5, 3n9 Bonneau), 239–241 Whiston, William, 285–286, 291 Viete,` F., 223 Whiteside, D. T., 219 Vietian analysis, 223–227, 229 Whitman, Anne, 3 vis agendi (force of acting), 37–38, whole, concept of, laws of motion and, 45–47 148–149 vis inertiae, 115n11, 131–132, 346–348, Wilson, Curtis, 107n1, 169n1, 191–192, 348n10 363n4, 365n8, 379n13, 380n14 vis insita Wilson, Kenneth, 393n21 dynamical conception of matter and, Wing, Vincent, 364 114–116 Winkler, Kenneth, 49–56, 51n9, 52n11, force and, 44–47 54n15, 55n16, 56n17, 58n18, vis viva (living force), Leibniz’s concept 65n30 of, 345–346 Worrall, John, 142 Voltaire,F.M.A.,282, 293, 297n40, Wren, Christopher, 35n6, 152, 306 169–170, 305 vortex theory, 187 Yolton, John, 257 Wallis, John, 152, 169–170, 251, 305 weak equivalence principle, 181n22 Zeteticorum Libri (Viete),` 223