Index

``Account ofthe Commercium empiricisim and, 80, 88 Epistolicum'' ,), 169 moon's variation and, 139±155 Adams, John C., 201, 335 navigation and, 325, 328, 335 Algebra syzygy and, 146±149, 152±154, 199± apsidal motion and, 156±167, 170, 200 173±181 Clairut and, 215±217 Babbage, Charles, 98 curvature method and, 193±200 Babson College, xvii d'Alembert and, 215±217 Background to Newton's Principia ®rst-order in®nitesimals and, 227±232 ,Herivel), 105 hourly apogee and, 208±214 Bacon, Francis, 80±81, 91±92 incremental velocity and, 238±243 Ball, W. W. Rouse, viii, 105 moon's variation and, 141±152 Banks, Sir Joseph, 97 Newton on, 168±169 Barbour, Julian, 113 pendulum decay and, 259±261 Bechler, Zev, 22 Portsmouth method and, 203±204 Bentley, Richard, 36, 93 radial perturbation and, 205±208 Berlin Academy, 153, 177 resistance force and, 251±257 Bernoulli, Daniel, 284 second-order in®nitesimals and, 233± Bernoulli, Johann, 171 238 Blay, Michel, xiv, xvi, xix, 225±248 American Historical Association, 317 Boyle, Charles, 93 Angle ofin¯ection, 56, 58, 61±62 Boyle, Robert, 3, 91±92 Apogee, 191, 193 Boyle, Thomas, 81 hourly motion of, 208±214 Brackenridge, J. Bruce, xiv±xv, xix, Apsidal motion, 139±140 105±137 Clairaut on, 173±176 Bradley, Richard, 96 d'Alembert on, 179±182 Brahe, Tycho, 141, 189, 328 di½culty of, 170 Brewster, David, vii±viii, xii Euler on, 176±179 Browne, Sir William, 97 moon's variation and, 141±155 Brydges, James, 96 Newton on, 155±168 Buchwald, Jed, vii±xix, 98 Arbuthnot, John, 87 Budenz, Julia, 299 Arithmetica Universalis ,Newton), 26±27 Burndy Library, xvii, 29 missing author of, 35±37 Ashra®, Babak, 288 , xiii, xvi, 17, 20, 140, 170 Aston, Francis, 85±86 apsidal motion and, 157±161, 164± Astronomy 167, 173, 177, 180 apsidal motion and, 155±182 Clairaut and, 215±216 Index 342

Calculus ,cont.) on Huygens, 30±35 curvature method and, 195, 198±199 Newtonian style and, 249±250 d'Alembert and, 215±216 on , 15±29, 32±33, 37±41 hourly apogee and, 208±209, 212±213 on Westfall, 317±319 incremental velocity and, 241±243 Collegio alle Acque, 322 moon's variation and, 144, 147±148 Collier, Jeremy, 90 motion and, 238 Collins, John, 168 pendulum decay and, 259 Collisions, 106±108, 112 perturbational and, 172±173, 205±206 Color. See also Light Portsmouth method, 203±204 di¨raction and, 49, 60, 70 ``Calculus ofthe Trigonometric fringes and, 47±48 Functions, The'' ,Katz), 172 Newton on, 3, 23, 83±84 Cambridge University, viii, x, xiv±xv, quality of, 25 36, 105, 189 rubriform, 25 Cartography, 333 thick plates and, 49, 52 mappaemundi and, 325±326 Commercium Epistolicum,9 Florentine archives and, 327±328 Comparison theorem, 117 mathematics and, 328±329 Compendium ,Sanderson), 10 Ptolemy and, 326±327 Comte, Auguste, 243 Scienti®c Revolution and, 328 Conduitt, John, viii, 105 Cassini, Gian Domenico, 328 Continuity, 225 Castelli, Benedetti, 323 ®rst-order in®nitesimals and, 227±232 Celestial vortices, 112±113, 249, 282± Law 2 and, 226±227 283 second-order in®nitesimals and, 233± Centrifugal force, 113 238 Centripetal force, 11 Correspondence ,Newton), xi apsidal motion and, 162, 171 Croone, William, 94 Huygens and, 33 Curvature, 105±106 Newtonian sytle and, 250±251, 266 offorce,117±119 second-order in®nitesimals and, 234± incremental velocity and, 238±243 235 measurement of, 113±119 vs. centrifugal, 113 methodology and, 193±200, 214 Chandrasekhar, S., xiv, 199 moon's variation and, 147±150 Cheyne, George, 19±20 Principia revisions and, 119±133 Circular orbit, 134, 152 revolving bodies and, 228±232 apsidal motion and, 155±182 moon's variation and, 139±155 d'Alembert, Jean le Rond, xvi Clairaut, Alexis-Claude, xvi apogee and, 214 apogee and, 214 apsidal motion and, 179±182 apsidal motion and, 173±177, 179±182 curvature method and, 195 curvature method and, 195, 200 ideal ¯uid and, 285±286 methodology of, 139±140 methodology of, 139±140 pertubations and, 191, 193 pertubations and, 191, 193 theory of, 215±217 theory of, 215±217 Cohen, I. Bernard, xi, xv, xix, 3, 42± Danti, Egnatio, 331±332 45, 288, 299 Daston, Lorraine, 98 on Arithmetica, 35±37 De Borda, 283±284 Index 343

De®nitions, 5, 8 Edleston, J., vii de Gandt, FrancËois, xiv E¿ux problem, 266, 268±269 De Gravitatione et Aequipondio Fluidorum Ehrlichson, Herman, xiv ,Newton), x, 8 Eizat, Sir Edward, 89 De Humoribus ,Lister), 92 Elliptical motion, 105±106, 133±134. de La Hire, Philippe, 328 See also Motion Delisle, 172 apsidal motion and, 155±182 De Methodis Serierum et Fluxionum curvature measure and, 113±119 ,Newton), 147, 168 moon's variation and, 139±155 De Motu Corporum ,Newton), x, 26, perturbation methods and, 189±224 236, 253, 259 Empirical law. See Laws Densmore, Dana, xiv Empiricism, 80, 88 Desaguliers, J. T., 21±22, 272, 276 EnestroÈm, G., viii Descartes, ReneÂ, x, xii±xiii, 4 Engineering, 321, 329 analysis and, 9±10 hydraulic, 322±323 celestial vortices and, 112±113, 249, military, 323±325, 332±333 282±283 Enumeration Linearum Tertio Ordinis ether and, 266 ,Newton), 17 Newton on, 168±169 Equations. See Formulae rules and, 5 Essay ,Ball), 105 Dialogi Physici ,Fabri), 48 Ether, 52, 266 Dibner Institute, xvii, 317 Euler, J. A., 139, 153 Dictionary of Scienti®c Biography, 329, 332 Euler, Leonhard Di¨raction, 20, 71±76 apsidal motion and, 171, 176±182 angle ofin¯ection and, 58 curvature method and, 200 dark/light bands and, 67 hourly motion and, 211 error in model of, 47±48 methodology of, 139 fringes and, 47±52 moon's variation and, 152±153, 191 Grimaldi and, 48 periodic solution of, 214 hair and, 52±56, 59±61, 63, 67±68 perturbational problem and, 172±173 knife edges and, 60, 63±66 Experimentum crucis, 250 law and, 61±63 Newton's explanation of, 68±70 Fabri, HonoreÂ,48 Digges, Leonard, 327 Feingold, Mordechai, xv, xix, 77±102 Digges, Thomas, 332 Fell, John, 86 Discours de la cause de la pesanteur Feynman, Richard, 257 ,Huygens), 225 FineÂ, Oronce, 331 Discours de la meÂthode ,Descartes), 5 Flamsteed, John, 92, 334 Dobbs, Betty Jo Teeter, xiv, 112 apsidal motion and, 155, 167 Drag coe½cient, 255±256 lunar motion and, 190 , 105, 134 Royal Society and, 85±86 curvature measure and, 113±119 vs. Newton, 95 force measurement and, 117±119 Fluids, 265 parabolic method and, 108±113 continuous, 267±270, 284 polygonal measure and, 106±108 density and, 264 Principia revisions and, 119±133 e¿ux problem and, 266 three techniques for, 106±119 elastic, 267, 299±302 Index 344

Fluids ,cont.) resistance and, 251±257, 269±271, ideal, 285, 287 283, 288±298 rare®ed, 267±268 second-order in®nitesimals and, 233± resistance and, 251±257, 271, 283±311 238 stagnation and, 269 stagnation and, 269 vertical fall and, 272±282 uniform circular motion and, 105, 107 vortex theory and, 282±283 vertical fall and, 272±282, 286 , 20. See also Calculus viscosity and, 285 Fluxionum Methodus Inversa ,Cheyne), 20 vortex theory and, 282±283 Folkes, Martin, 77, 96 Formulae Force Clairaut and, 215±217 apsidal motion and, 139±182 curvature method and, 193±200 central, 239, 241±243, 266 d'Alembert and, 215±217 centrifugal, 113 di¨raction and, 56, 58 centripetal, 11, 33, 113, 162, 171, hourly apogee and, 208±214 234±235, 250±251, 266 inverse square, 142 Clairaut and, 215±217 moon's variation and, 142±151 continuous infringement model and, Newton's law, 226 284 pendulum decay and, 259 curvature measure and, 113±119, 193± Portsmouth method and, 203±204 200 radial perturbation and, 205±208 d'Alembert and, 215±217 resistance force, 252 elliptical orbits and, 105±106, 113± Fortezza da Basso, 323 119, 133±134, 139±182, 189±224 Friction. See Resistance ®rst-order in®nitesimals and, 227±238 Fringes, 47±48 ¯uids and, 251±257, 267±271, 283± dark/light bands and, 52, 67 298 hair and, 52±56, 59±63, 67±68 gravity and, 225 ,see also Gravity) knife edge and, 49±51, 60, 63±66 hourly apogee and, 202, 208±214 law and, 61±63 impulsive, 8, 107±108 Newton's explanation of, 68±70 incremental velocity and, 238±243 Frisius, Gemma, 328 and, 227, 254, 267±268, 270, Fundamenta Opticae ,Newton), 18, 48 272, 283±287 Kepler and, 189±190, 249 Galileo, 110, 249, 319 Law 2 and, 226±227 gravity and, 225, 241 lunar motion and, 189±224 Gascoigne, William, 155 macroscopic, 265 Geography, 325±329 mathematics and, 225±248 Geography ,Ptolemy), 326±327 Newtonian style and, 250±298 Geometria Curvilinea ,Newton), 169 orbital motion and, 107±108 Geometrie ,Descartes), xii±xiii parabolic method and, 108±113 , xii±xiii, 10, 81±82, 335 pendulum decay and, 257±264, 311± Clairaut and, 215±217 313 curvature method and, 194±199 polygonal measure and, 106±108 d'Alembert and, 215±217 Portsmouth method and, 201±204 di¨fraction and, 53 radial perturbation and, 204±208 hourly apogee and, 208±213 rare®ed ¯uids and, 267±268 incremental velocity and, 238±240 Index 345

Newton on, 95, 169 Hair, light experiments on Portsmouth method and, 201±204 angle ofin¯ection and, 56, 58, 61±62 radial perturbation and, 205±208 di¨raction and, 52±56, 67±68 revolving bodies and, 228±232 formulae and, 71 second-order in®nitesimals and, 233± fringe measurement, 55, 58±61 238 laws and, 62±63 value of, 87 points ofin¯ection of,55 God, 21, 27, 29 Hales, Stephen, 22 Goddard, Jonathan, 94 Hall, Marie, x±xi Grace K. Babson Collection of Hall, Rupert, ix±xi, 18, 317 Newtoniana, xvii, 29 Halley, Edmond, xvii, 26, 36, 115 Graunt, John, xvii apsidal motion and, 182 Gravity, 225 background of, 334 apsidal motion and, 139±182 mathematics and, 335 Clairaut and, 215±217 Principia and, 84 curvature measure and, 113±119, 193± Royal Society and, 84±87 200 Harris, John, 87, 96 d'Alembert and, 215±217 Harvard University, 33 elliptical orbits and, 105±106, 113± Harvey, William, 80, 81, 88 119, 133±134, 139±182, 189±224 Hauksbee, Francis, 274 ®rst-order in®nitesimals and, 227±238 Heath, Thomas Little, viii hourly apogee and, 202, 208±214 Heiberg, J. L., viii incremental velocity and, 238±243 Heilbron, John, 78 inertia and, 275, 286 Herivel, John, xi, 105, 113±114 inverse-square law and, 249, 251 Herschel, Sir William, 33 Kepler and, 189±190, 249 Herstine, Michael, 182 Law 2 and, 226±227 Hill, G. W., 214 measurement of, 251±252 elliptical orbit and, 149 Newtonian style and, 250±298 hourly motion and, 211 parabolic method and, 108±113 lunar motion, 192 pendulum decay and, 257±264, 311± methodology and, 139, 153 313 perturbation and, 200 perturbation methods and, 189±224 Hill, John, 97 quadrature and, 146±154 Historia Piscium ,Willughby), 86 second-order in®nitesimals and, 233± History ofScience Society, 317 238 History ,Sprat), 82 syzygy and, 146±149, 152±154 Homogeneity, 6±7 universal, 33 Hooke, Robert, xv, 19, 69±70, 78 vertical fall and, 272±282, 300 criticism ofNewton and, 83±84 Gregory, David, 19±20, 36, 67, 116, curvature measure and, 114±115, 196 272 di¨raction and, 48 Gregory, James, 168 Royal Society and, 87 Grenville, Sir Richard, 333 Horblit, Harrison D., 33 Gresham College, 91±92 Horne Library, xvii Grimaldi, Francisco Maria, 48 Horologium Oscillatorium ,Huygens), 32, Grinnell College, 317 225 Guicciardini, NiccoloÁ, xiv Horrocks, Jeremiah, 154, 190 Index 346

Horrocks ,cont.) Katz, Victor, 172 apsidal motion and, 155±156 Keill, James, 89 curvature method and, 196 Keill, John, 87 hourly motion and, 212 Kepler, Johannes, xv, 249 Horsley, Samuel, 97 law of, 130 Houghton Library, 33 motion and, 189±190 Hourly motion, 202, 208±214 3/2 power rule of, 250 Hunter, Michael, 82, 98 vortex theory and, 283 Hurstbourne Castle, viii Keynes, John Maynard, ix Huygens, Christiaan, xiii, xv, 225, 254 Knife edge experiments missing authorship of, 30±37 di¨raction and, 49±51, 63±66 Newton and, 41 formulae and, 56 Opticks and, 32±33 fringes measurement and, 56, 60 Royal Society and, 81, 82 Knudsen, Ole, 288 Hydraulics, 322, 323 KoyreÂ, Alexandre, xiii, 319, 321 Hydrodynamica ,Bernoulli), 284 Hydrodynamics. See Fluids Lagrange, 214 lunar motion and, 191 Ili¨e, Rob, 98 perturbing function, 174 Inertia, 227, 254 Laplace, 169, 214 continuous infringement model and, curvature method and, 199 284 lunar motion and, 191 ¯uids and, 267±271, 283±298 tables of, 182 non-inertial components and, 286 Laurd, H. R., 201 spherical resistance and, 269±271, 283 Laws, 4±5 vertical fall and, 272±282, 286 ofareas, 228±232 viscosity and, 285 ofconnection, 7 In®nitesimals continuous action and, 226±227, 237± ®rst-order, 227±232 238, 243 second-order, 233±238 di¨raction and, 59, 61±63 In¯ection. See Di¨raction empirical, 59 Institutions astronomiques ,Le Monnier), ofharmony, 6 182 inverse-cube, 196 Introductio in Analysin In®nitorum ,Euler), inverse square, 142, 162±163, 171, 171, 173 176, 192, 196, 249, 251, 266 Inverse-cube law, 196 Kepler's, 130 Inverse square law, 192 medicine and, 89 apsidal motion and, 162±163, 171, 176 Newton's methods and, 49 curvature and, 196 ofunity, 6±7 gravity and, 249, 251 Lectiones Opticae ,Newton), 3, 18 moon's variation and, 142 Lee, Richard, 332 Newtonian style and, 266 Leeghwater, Jan, 322 Italy, 321±322, 327, 331±332 Leibniz, Gottfried Wilhelm, xvi, 17, 19 apsidal motion and, 140 Jansen, Willem, 288 calculus and, 169±170 Jurin, James, 77 curvature method and, 195 Index 347

Newton and, 92, 168 193±200, 203±217, 227±243, 251± Le Monnier, 182 257, 259±261 Lex connexionis, 7 analysis and, 9±10 Lex harmoniae, 6 apsidal motion and, 159±182 Lex unitatis, 6±7 Arithmetica Universalis and, 35±37 Life and Times of ,Cohen & binomial theorem, 142±143 Hall), 317 calculus, xiii, xvi, 17, 20, 140, 144, Light, 23. See also Opticks ,Newton) 147±148, 157±161, 164±167, 170, angle ofin¯ection and, 56, 58, 61±62 172±173, 177, 180, 195, 198±199, as a body, 24±26 203±206, 208±209, 212±213, 215± dark/light bands and, 52, 67 216, 238, 241±243, 259 di¨raction and, 20, 47±76 circular orbit and, 132 fringes and, 47±52 Clairaut and, 139, 173±174, 215±217 Grimaldi and, 48 continuous action and, 225±248 hair and, 52±56, 59±63, 67±68 curvature and, 113±119, 193±200, knife edges and, 49±51, 60, 63±66 228±232 law and, 61±63 d'Alembert and, 139, 179±182, 215± Newton's explanation and, 68±70 217 rectilinear propagation and, 47±76 de®nitions and, 8 refraction and, 70 di¨raction and, 49, 51±63 Lister, Martin, 84±86, 92±93, 95 elliptical orbit and, 133 Liveing, G. D., 201 engineering and, 321±325 Locke, John, 115, 134 Euler and, 139, 172±173, 176±179 Logarithms, 115, 170 ®rst-order in®nitesimals and, 227±232 Logic, 4, 8 ¯uid resistance and, 299±311 analysis and, 9 geometry, xii±xiii, 10, 53, 81±82, 87, methodology and, 10±12 95, 169, 194±217, 228±240, 335 Logicae Artis Compendium ,Sanderson), history and, 321±339 4±7 hourly apogee and, 208±214 Lucasian Professor, 36 logarithms and, 115, 170 maps and, 325±329, 333 Machin, John, 95 medicine and, 88±89 Mahoney, Michael, 319 moon's variation and, 139±155 Mamiani, Maurizio, xix, 3±14 motion and, 225±248 Manuel, Frank, 78 naturalists and, 77±102 Mappaemundi, 325±326 nature and, 321±339 Maps, 333 Newton's methods and, 49 Florentine archives and, 327±328 optics and, 22, 49, 51±63 mappaemundi and, 325±326 parabolic method and, 108±113 mathematics and, 328±329 pendulum decay and, 259±261, 262± Ptolemy and, 326±327 264 Scienti®c Revolution and, 328 physics and, 3 Mathematical Papers of Isaac Newton polygonal measure and, 106±108 ,Whiteside), xii Portsmouth method and, 201±204 Mathematics Principia revisions and, 119±133 algebra, 141±152, 156±170, 173±181, radial perturbation and, 204±208 Index 348

Mathematics ,cont.) resolution and, 5±6, 8 resistance and, 251±257 vertical fall and, 272±282 second-order in®nitesimals and, 233± Methods of Series and Fluxions ,Newton), 238 115 spiral orbit and, 132 Middleton, Benjamin, 334±335 tangents and, 105±106 Military engineering, 323±325, 332±333 trigonometry, 140, 142±144, 148, 151, Minute Book of the Sessions of the AcadeÂmie 157±160, 163±167, 173±174, 194± Royale des Sciences, 238 199, 203±216, 227±238 Molyneux, William, 85 vertical fall and, 272±282 Moon Mather, Cotton, 91 apsidal motion and, 155±182 Mead, Richard, 88±89 perturbation methods and, 189±224 Mechanica ,Euler), 172 quadrature and, 20, 146±150, 152±154 Medicine, 88±89, 91±92 syzygy and, 146±149, 152±154 Meditations ,Descartes), 9 variation of, 139±155, 171, 250±251 Meli, Domenico Bertoloni, 113 Moore, Jonas, 333±334 MeÂmoires de l'AcadeÂmie Royale des Sciences, Morals, 21 238±239 Moray, Sir Robert, 81 Methodology, 4, 7, 10±12 More, Louis Trenchard, viii analysis and, 9 Mos geometricus,5,8 apogee and, 208±214 Motion apsidal motion and, 155±182 apsidal, 139±140, 155±182 Clairaut and, 139, 176, 215±217 Clairaut and, 215±217 comparison theorem and, 117 curvature measure and, 113±119, 193± composition and, 5 200 curvature and, 113±119, 193±200 d'Alembert and, 215±217 d'Alembert and, 139, 179±182, 215± elliptical, 105±106, 113±119, 133± 217 134, 139±182, 189±224 di¨raction and, 47±76 ®rst-order in®nitesimals and, 227±238 doctrine and, 5, 8±9 ¯uid resistance and, 299±311 Euler and, 139, 172±173, 176±179 hourly apogee and, 202, 208±214 force measurement and, 117±119 incremental velocity and, 238±243 geometrical, 5 Keplerian, 189±190, 249 invention and, 5, 8±9 Law 2 and, 226±227 moon's variation and, 139±155 lunar, 189±224 Newton on, 168±169 mathematics and, 225±248 parabolic, 108±113 Newtonian sytle and, 250±300 pendulum decay and, 257±264, 311± orbital, 107±108 313 parabolic method and, 108±113 perturbations and, 189±224 pendulum decay and, 257±264, 311± polygonal measure and, 106±108 313 Portsmouth, 201±204 polygonal measure and, 106±108 Principia Book II and, 249±313 Portsmouth method and, 201±204 Principia revisions and, 119±133 quantity of, 107±108 quadratures and, 20, 146±150, 152± radial perturbation and, 204±208 154, 199±200 second-order in®nitesimals and, 233± radial, 204±208 238 Index 349

uniform circular, 105, 107 Regulae Philosophandi and, 3±14 vertical fall and, 272±282 Royal Society and, 77±102 ``Motion ofBodies in Mobile Orbits; sale ofpapers of,ix and the Motion ofthe Apsis, The'' Westfall and, 317±319 ,Newton), 196 Newtonian style, 250. See also Moyle, Walter, 91 Methodology Book II aftermath, 282±287 Natural philosophy Book II, Section 7 and, 264±272 color and, 25 ¯uid resistance, 299±311 light as a body and, 24±26 motion and force, 251±257 mathematics and, 77±102 pendulum decay, 257±264, 311±313 methodology and, 4±12 ,see also vertical fall, 272±282 Methodology) Nicholson, William, 93 Newton's reluctance and, 18 North, Roger, 90 Nauenberg, Michael, xiv±xvi, xix±xx, No slip hypothesis, 254 71, 182, 189±224 NunÄez, Pedro, 331 curvature and, 134 methodology and, 114±115 Oldenburg, Henry, 82±84 Navigation, 325±329 On Circular Motion ,Newton), 108, 111± Neile, William, 82 112, 115, 133±134 Never at Rest ,Westfall), xiv, 318 Optice ,Newton), 29 ``New Theory ofLight and Colors'' Opticks ,Newton), xi, xv ,Newton), 3 aborted edition of, 23±26 New Theory of Physick and Diseases, di¨raction and, 47±76 Founded on the Principles of the Huygens and, 30±33, 35 Newtonian Philosophy, A ,Robinson), imperfect science of, 18±23 89 Lister on, 93 Newton, Isaac, 335±336. See also missing author and, 15±18, 38 Principia ,Newton) North on, 90 on analysis, 168±169 perfectionism and, 27, 29 apsidal motion and, 155±172, 176, publication of, 87 180±182 special copy of, 37±41 Arithmetica Universalis and, 35±37 Optics Bible and, xiv angle ofin¯ection and, 56, 58, 61±62 continuity and, 225±248 as a body, 24±26 di¨raction and, 47±76 dark/light bands and, 52, 67 Hooke and, 19, 48, 69±70, 78, 83±84, di¨raction and, 20, 47±76 87, 114±115, 196 fringes and, 47±52 on mathematics, 168±172 Grimaldi and, 48 mature dynamics and, 105±137 hair and, 52±56, 59±63, 67±68 moon's variation and, 139±155 knife edges and, 49±51, 60, 63±66 Opticks and, 15±76 law and, 61±63 as perfectionist author, 26±29 mathematics and, 22 perturbation methods of, 189±224 Newton's explanation and, 23±26, 68± Principia Book II and, 249±313 70 public's view of, vii±xvii rectilinear propogation and, 47±76 publishing controversies of, 18±26 refraction and, 70 Index 350

Opuscula Varii Argumenti ,Euler), 172 di¨raction and, 20, 47±76 Oreper, Gregory, 288 elliptical orbits and, 105±106, 113± Oxford Philosophical Society, 86 119, 133±134, 139±182, 189±224 empiricisim and, 80, 88 Palazzo Vecchio, 332 ®rst-order in®nitesimals and, 227±238 Parabolic method, 108±113, 133±134 ¯uids and, 251±257, 267±271, 283± Paris Academy, 173 311 Parker, Samuel, 90 force measurement and, 117±119 Pendulum decay fringes and, 47±52 Book II and, 265, 289, 311±313 gravity and, 225 ,see also Gravity) failure of, 272 Grimaldi and, 48 and, 311±313 hair and, 52±56, 59±63, 67±68 resistance studies and, 257±264 hourly apogee and, 202, 208±214 Pepys, Samuel, 86 impulsive, 8, 107±108 Perturbation incremental velocity and, 238±243 apogee and, 208±214 inertia and, 227, 254, 267±268, 270, Clairaut and, 173±176, 215±217 272, 283±287 curvature method and, 193±200 Kepler and, 189±190, 249 d'Alembert and, 215±217 knife edges and, 49±51, 60, 63±66 Euler on, 172±173 law and, 61±63, 226±227 Portsmouth method, 201±204 light experiments and, 24±26, 52, 67 radial, 204±208 mathematics and, 22 ,see also three-body problem and, 189±224 Mathematics) Petty, Sir William, xvii, 82±83, 94 moon's variation and, 139±155, 189± Philomats, 77, 91 224 Philosophical Transactions, 15, 17±18 navigation and, 325, 328, 335 optics and, 23±24 Newton's explanation and, 23±26, 68± Royal Society and, 77, 83±84, 97 70, 250±298 Philosophy, natural orbital motion and, 107±108 color and, 25 parabolic method and, 108±113 light as a body and, 24±26 pendulum decay and, 257±264, 311± mathematics and, 77±102 313 methodology and, 4±12 ,see also polygonal measure and, 106±108 Methodology) Portsmouth method and, 201±204 Newton's reluctance and, 18 Principia revisions and, 119±133 Physics, 3 radial perturbation and, 204±208 angle ofin¯ection and, 56, 58, 61±62 rare®ed ¯uids and, 267±268 apsidal motion and, 139±182 resistance and, 251±257, 269±271, central force and, 239, 241±243, 266 283, 288±311 centrifugal force and, 113 second-order in®nitesimals and, 233± centripetal force and, 11, 33, 113, 162, 238 171, 234±235, 250±251, 266 stagnation and, 269 Clairaut and, 215±217 syzygy and, 146±149, 152±154 continuous infringement model and, three techniques for, 106±119 284 uniform circular motion and, 105, 107 curvature measure and, 113±119, 193± vertical fall and, 272±282, 286 200 viscosity and, 285 d'Alembert and, 215±217 vortex theory and, 282±283 Index 351

Picard, Jean, 328 2 and, 227±228 Pitcairne, Archibald, 88±89 3 and, 226 Plot, Robert, 86 4 and, 142, 145 Polygonal measure, 106±108 6 and, 117±120, 130±131, 234, 236 Portsmouth method, viii, xvi, 214, 215 7 and, 130, 132, 171 apogee and, 211 8 and, 171, 226±227, 266 elliptical motion and, 191±192 9 and, 120±121, 130, 132, 171, 271± perturbation and, 201±204, 207±208 272 Portugal, 325, 331 10 and, 10, 121±123, 130, 132±133, Price, Derek, 23, 26 171 Principia Book II ,Newton), 250 11 and, 130, 132±133, 171 aftermath of, 282±287 12 and, 171, 229 central concern of, 251±257 13 and, 171 ®rst edition of, 257±264, 299±311 17 and, 190, 201±202 second and third editions of, 272±282, 25 and, 141, 196 311±313 26 and, 139, 141, 143±144, 196 section 7 of, 264±272 28 and, 139, 141, 150, 160, 163, 197, Principia ,Newton), x±xi, xiii±xvi, 4, 7, 199 9±10, 336 29 and, 139, 141 algebra and, 169 30 and, 259 apsidal motion and, 140, 161 35 and, 140, 190, 212 Book II and, 249±313 36 and, 271, 278, 299±302 continuous action and, 226 37 and, 278, 302±304 curvature measure and, 115±117, 133± 38 and, 269±270, 278, 304±309 134, 194 39 and, 278, 309±310 di¨raction and, 47±48, 51±52 40 and, 271, 310±311 dynamics and, 105±106 41 and, xiii, 249 fault of, 40 43 and, 161, 196 hourly motion and, 211±213 44 and, 161, 196 incremental velocity and, 241 45 and, 161±163, 192, 196±197, 204± Law 2 and, 226±227 205, 207±208, 213 lunar motion and, 189±192 66 and, 154, 189 mathematical nature of, 22±23 75 and, 266 moon's variation and, 139±155 76 and, 266 motion and, 236 ,see also Motion) Ptolemy, 326±327 parabolic method and, 111±112 perfectionism and, 27 Quadrature, 20, 199±200 polygonal measure and, 108 moon's variation and, 146±150, 152± Portsmouth method and, 201, 215 154 publication of, 26, 86±87 Quanti®cation, 88 Queries and, xi, 21±22, 48, 87, 90 Queries, xi, 21±22, 48, 87, 90 radial perturbation and, 204 Quincy, John, 88 revisions of, 119±133 variorum edition, 299 Ramists, 4 Pringle, Sir John, 97 Ray, John, 89 Propogation. See Light Rectilinear propagation. See Light Propositions, 5±6 Reductionsim, 88 1 and, 130, 228, 231, 233±234, 249 Refraction, 70 Index 352

Register Book ,Royal Society), 115 Sanderson, Robert, xiv, 4±5 Regulae Philosophandi,3±9,13±14 analysis and, 9 conceptual sources and, 10±12 laws and, 7 ``Researches in the Lunar Theory'' methodology and, 10±12 ,Hill), 153 propositions and, 6 Resistance resolution and, 8 ¯uids and, 251±257, 268±271, 283± Scarburgh, Sir Charles, 94 311 Schliesser, Eric, 288 inertia and, 267±268, 270±272, 283± Scholastics, 4 287 Science and Religion in Seventeenth Century pendulum decay and, 257±264, 311± England ,Westfall), 317 313 Scienti®c ideas, 3 rare®ed ¯uids and, 267±268 analysis and, 9 spherical, 251±257 conceptual entities and, 8 stagnation and, 269 rules and, 4±8 vertical fall and, 272±282 Scienti®c Revolution, 321, 328 vortex theory and, 282±283 Sensorium, 21, 27, 29 Reynolds number, 256, 274, 276, 283 Shapiro, Alan E., xiv±xv, xvii, xx, 81 Rhetoric, 4, 8±12 Newton's di¨raction experiments and, Richardson, Richard, 77, 91 47±76 Robinson, Nicholas, 89 Opticks and, 18±22 Robinson, Tancred, 85±86, 89 Shaw, Peter, 92 Rotz, Jean, 333 Sherard, William, 77, 91 Royal Society, ix, xi, 18±19, 22, 334± Simplicity, 6 335 Six Philosophical Essays ,Parker), 90 body ofknowledge of,94±95 Sloane, Sir Hans, 77, 85, 91, 96 constricted atmosphere of, 91 Smith, George E., xiv, xvi±xvii, xx, debates over mathematics and, 80± 182, 249±313 83 Smith, India, 288 De Motu and, 26 Smith, Thomas, 90, 93 di¨raction and, 48 Snel, Willibrord, 328 Halley and, 84±87 Socrates, 171 later dissensions of, 97±98 Somers, Lord John, 92 medicine and, 88±89, 91±92 Sprat, Thomas, 79, 82 mission of, 79±80 Stevin, Simon, 323, 332 Newtonian in¯uence, 94±96 Stokes, G. G., 201 Philosophical Transactions and, 24 Stukeley, William, 96 presidency battle of, 77±78 Summus, 33 Principia and, 84, 86 Syzygy Register Book and, 115 moon's varation and, 146±149, 152± satire of, 93 154 secretary battles of, 84±85 perturbation methods and, 199±200 stagnation of, 78±79 vertical fall and, 274 Tangents, 105±106 violence and, 93±94 Tannery, Paul, viii Rubriform, 25 Tanquam, 27 Rules, 4±8 Techtonicon ,Digges), 327 Index 353

Temkin, Oswei, 317 Clairaut and, 215±217 Teside, 114 curvature method and, 193±200 Theoria Motus Lunae Exhibens Omnes d'Alembert and, 215±217 Eius Inaequalitates ,Euler), 152±153, Portsmouth method and, 201±204 176 radial perturbation and, 204±208 Theory, 4, 7, 10±12 Time analysis and, 9 ®rst-order in®nitesimals and, 227±232 apogee and, 208±214 ¯uid resistance and, 303 apsidal motion and, 155±182 motion and, 227±238 Clairaut and, 139, 176, 215±217 revolving bodies and, 230 comparison theorem and, 117 second-order in®nitesimals and, 233± composition and, 5 238 curvature and, 113±119, 193±200 Tisserand, 190±191, 199 d'Alembert and, 139, 179±182, 215± Tractatus de Quadratura Curvarum 217 ,Newton), 17 di¨raction and, 47±76 Traite de la lumieÁre ,Huygens), xv, 225 doctrine and, 5, 8±9 missing author of, 30±32 Euler and, 139, 172±173, 176±179 Newton's modeling of, 41 force measurement and, 117±119 Opticks and, 32±33 ¯uids and, 284 two forms of title page and, 33±35, geometrical, 5 38 Horrocksian, 154, 156 Traite de MeÂcanique CeÂleste ,Tisserand), invention and, 5, 8±9 190±191 inviscid ¯uid ¯ow, 286 Transformations, 3 light and, 3 ,see also Light) methodology and, 4±12 lunar, 139±182 rules and, 4±5 medicine and, 89 Treatise on the Apocalypse ,Newton), 4± moon's variation and, 139±155 10 optics and, 22 Trigonometry, 140, 142 parabolic, 108±113 apsidal motion and, 157±160, 163± pendulum decay and, 257±264, 311± 167, 173±174 313 Clairaut and, 215±216 perturbations and, 189±224 curvature method and, 194±199 physics and, 89 ,see also Physics) d'Alembert and, 215±216 polygonal measure and, 106±108 ®rst-order in®nitesimals and, 227± Portsmouth method and, 201±204 232 Principia Book II and, 249±313 hourly apogee and, 208±213 Principia revisions and, 119±133 moon's variation and, 143±144, 148, quadratures and, 20, 146±150, 152± 151 154, 199±200 Portsmouth method and, 203±204 resolution and, 5±6, 8 radial perturbation and, 205±208 Royal Society and, 80, 82, 95 second-order in®nitesimals and, 233± vertical fall and, 272±282 238 vortex, 112±113, 282±283 Trinity Notebook, 4 Thick plates, 49, 52 Truesdell, Cli¨ord, 249, 265, 269 Three-body problem, 189±192, 250 Turriano, Juanelo, 333 apogee and, 208±214 Tyson, Edward, 86 Index 354

U½ziali dei Fiume, 322, 327 University Library, 27, 35 University ofNatal, 33 Unpublished Scienti®c Papers of Isaac Newton ,Hall & Hall), x±xi Utilitarianism, 80

Varignon, Pierre, xvi, 237±243 Vellum Manuscript ,Newton), 113 Velocity. See also Motion central force and, 241±243 incremental, 238±243 instantaneous, 238±241 Vermuyden, Cornelius, 322 Vertical fall, 300 experiment description, 272±276 inertia and, 275, 286 results of, 276±282 Vis centripeta, 33 Vortex theory, 112±113, 249, 282±283

Waller, Richard, 95 Wallis, John, 19, 70, 82, 87, 335 Wallop, Isaac Newton, 105 Ward, Seth, 81 Waste Book ,Newton), 105, 133±134 curvature measure and, 113±114, 116 dynamics and, 113 polygonal measure and, 106±108 West, James, 91 Westfall, Richard Samuel, xiii±xiv, xvii, xx, 78, 321±339 Cohen on, 317±319 Wheatland, David P., 33 Whiston, William, 27, 36 Whiteside, D. T., xii±xiii, 156, 169 curvature measure and, 113±114, 116 moon's variation and, 139±140 Whitman, Anne, 299, 319 Willughby, Francis, 86, 94 Wilson, Curtis, xiv, xvi, xx, 113, 139± 188 Woodward, John, 91, 93