6.5 X 11 Threelines.P65

Cambridge University Press 978-0-521-64066-4 - Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736 Niccolo Guicciardini Index More information

Index

Airy, George B., 68 Borelli, Giovanni A., 53 Aiton, Eric, 9, 14, 49, 57, 95, 147–54, 209, 218, 244 Bos, Henk J. M., 9, 14, 98, 118, 120, 127, 138, 141, Albouy, Alain, 207 143, 144, 148, 157, 159, 259 Alembert, Jean le Rond d’, 93, 95, 152, 154, 257, 259 Brackenridge, Bruce, 7, 12, 14, 50, 52, 55, 97, 108, analytical method of ﬂuxions, 17–27, 97–8, 108–15 112, 218 Analytical Society of Cambridge, 258 Bragelogne, Christophe B. de, 204 Anaximander, 101 Brahe, Tycho, 151, 165 ancient geometry, 27–32, 101–4, 164–6, 193, 254 Breger, Herbert, 120, 144, 162, 246 Anderson, Robert, 81, 173 Brinkley, John, 237 Aoki, Shinko, 93 Brougham, Henry, 7, 97 Apollonius, 29, 30, 32, 52, 53, 106, 118, 166, 183, Buffon, George-Louis Leclerc, Comte de, 202 190, 193, 254 Archimedes, 5, 30, 107, 118, 162, 165, 166, 198, 215, Cajori, Florian, 13, 40, 83, 90 255 Calandrini, Jean-Louis, 248 Aristarchus of Samo, 101 Caldo, Lorenzo, 63 Aristotle, 101 Callippus, 101 Arithmetica universalis, 36, 37 Campbell, Colin, 175 Arnol’d, Vladimir I., 55, 218 Carr, John, 191 Arthur, Richard T. W., 14, 28 Carre,´ Louis, 201, 204 Asclepiades, 101 Casini, Paolo, 102, 103 Ashmole, Elias, 31 Cassini, Gian Domenico, 165, 178, 203 Axtell, J. L., 170, 175, 176 Castel, Louis-Bertrand, 202 Cauchy, Augustin Louis, 44 Ball, W. W. Rouse, 90, 202 Cavalieri, Bonaventura, 142 Barrow, Isaac, 28, 29, 53, 103, 124, 215 Chandler, Philip P., 63, 93 Belaval, Yvon, 165 Chandrasekhar, Subrahmanyan, 7, 11, 57, 63, 65, 245, Bennett, Jim A., 171 257 Bentley, Richard, 100, 124, 175, 176, 184 Charles II, 174 Berkeley, George, 199, 254, 263 Cheyne, George, 189, 251 Bernoulli, Daniel, 94, 208, 248, 257, 259 Clairaut, Alexis-Claude, 92, 93, 95, 152, 196, 208, Bernoulli, Jacob, 137, 162, 178, 196, 199, 205, 216, 257, 259 240, 248, 250, 252 Clarke, John, 190, 191 Bernoulli, Johann, 5, 15, 56, 88, 89, 91, 106–8, 115, Clerke, Gilbert, 175 116, 120, 137, 144, 149, 154, 159, 177, 185, Cluver,¨ Detleff, 119, 162, 164, 199, 252 194–202, 204–7, 216–8, 221, 223–34, 236, 237, Cohen, I. Bernard, 1, 7, 10–14, 39, 40, 91, 99, 154 240–5, 247, 248, 250, 257, 260 Collins, John, 37, 256 Bernoulli, Niklaus, 88, 89, 196, 233, 236, 237, 242–4, Commandino, Federico, 254 259 convergence of series, 20 Bertoloni Meli, Domenico, 9, 14, 146, 147, 149, Cook, Alan, 170 151–5, 157, 158, 161, 165, 208 Copernicus, 102, 165 binomial series, 18–20, 63, 79–80 Costabel, Pierre, 9, 108, 112 Blay, Michel, 14, 82–4, 147, 200, 201, 203, 244 Cotes, Roger, 5, 89, 100, 104, 116, 184–6, 191, 193, Blondel, Franc¸ois, 173 202, 206, 218, 226, 228, 237, 254, 255, 258

281

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-64066-4 - Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736 Niccolo Guicciardini Index More information

282 Index

Couzin, Robert, 165 fluent (definition of), 21 Craig, John, 104, 175, 179, 181, 183 fluxion (definition of), 21 Cushing, James T., 55, 218 Fontaine, Alexis, 259 Fontenelle, Bernard Le Bovier de, 2, 3, 5, 196, 197 Dahr, Abhishek, 232 force (representation of central force), 50–1, 104–6 Dawson, John, 193 Force, James E., 32, 188 De analysi per aequationes numero terminorum Forsyth, A. R., 89 infinitas, 20–1 Fraser, Craig, 154, 259 De Gandt, François, 7, 14, 42, 96, 219, 255 French, A. P., 208 De methodis serierum et fluxionum, 21–6 Frost, Percival, 191 De Moivre, Abraham, 5, 104, 116, 186, 189, 193, 194, Fueter, E., 216 226, 227, 236, 243, 258 De quadratura curvarum, 35–6 Galilei, Galileo, 47, 79, 95, 104–6, 117, 124, 165, Democritus, 101, 102 173, 198, 239, 245, 253 Densmore, Dana, 7, 14, 90 Galloys, Jean, 200 Desaguliers, John T., 92, 176, 192 Galuzzi, Massimo, 29, 86, 233, 235, 236 Descartes, Rene,´ 17–19, 28–30, 43, 79, 81, 117–9, Gascoigne, John, 32, 102 121, 126, 127, 165, 166, 173 Gaukroger, Stephen, 102 Dhombres, Jean, 204 Geometria curvilinea, 33–5 Di Sieno, Simonetta, 29 Giuntini, Sandra, 225 differential and integral calculus, 142–5 Giusti, Enrico, 126 Diodorus, 101 Glanville, Joseph, 102 direct problem of central forces, 41, 51–4 Goldstine, Herman H., 89 Ditton, Humphry, 189, 190 Gouk, Penelope, 102 Dobbs, Betty J. T., 30, 31 Gowing, Ronald, 185, 186, 205 Domcke, George P., 191 Grabiner, Judith V., 259 Dortous de Marain, Jean B., 92 Grandi, Guido, 206 Dupont, Pascal, 107, 198 Gravesande, Willem J. ’s, 191, 192, 248 Greenberg, John L., 91, 92, 197, 201, 202, 204 Eagles, Christina M., 179, 181, 184, 188, 250 Gregoire´ de Saint-Vincent, 53, 84, 183 Echelle, Abraham de l’, 53 Gregory, David, 5, 29, 59, 89, 90, 99–101, 103, 104, Ecphantos, 101 112, 113, 116, 119, 120, 123, 169, 177, 179–84, Edleston, Joseph, 100, 177, 180, 184, 185, 253 187–9, 193, 202, 203, 223, 227, 248, 250, 254, Edwards, C. H., 27 255 Einstein, Albert, 6, 7 Gregory, James, 81, 179, 181 Emerson, William, 192 Grosholtz, Emily R., 127 Empedocles, 101 Guicciardini, Niccolo,` 14, 92, 108, 109, 164, 191–4, Epicurus, 101 201, 211, 212, 214, 217, 227, 258, 260 Erlichson, Herman, 14, 49, 59, 82, 83, 98, 134, 155, 172, 209, 218, 222, 234, 245 Halifax (Earl of), 175 Euclid, 29, 30, 62, 103, 104, 106, 107, 118, 124, 125, Hall, Rupert, 1, 4, 10, 81, 99, 114, 158, 178, 185, 200, 166, 183, 190, 191, 254 236 Eudoxus, 101 Halley, Edmond, 53, 104, 169–75, 186, 189, 191, 193, Euler, Leonhard, 5, 6, 10–12, 93–5, 115, 152, 196, 227, 254, 255 197, 205, 208, 231, 232, 241, 247, 248, 257, 259, Harris, John, 252 260 Harrison, John, 53 Evans, J. H., 191 Hayes, Charles, 90, 182, 190 Hearne, Thomas, 181 Farrell, Maureen, 188 Heinekamp, Albert, 119, 120, 198 Fatio de Duillier, Nicolas, 5, 89, 90, 104, 116, 119, Heraclides, 101 120, 123, 177–9, 193, 200, 248 Hermann, Jacob, 5, 15, 49, 115, 138, 194–7, 199, 201, Feigenbaum, Lenore, 198, 201 204, 205, 217, 223–5, 228, 229, 232, 233, 241, Feingold, Mordechai, 28 244, 247, 248 Fellmann, Emil A., 216 Phoronomia, 205–6 Fermat, Pierre de, 23, 29, 118 and geometrical method, 207 Feynman, Richard, 10 and the inverse problem of central forces, 206–7 Fichant, Michel, 147 his proof of Proposition 1, Book 1, 211–6 Figala, Karin, 30, 31 life, 205 first and ultimate ratios, 32–6, 43–51, 96–7 Herschel, John F. W., 68 Flamsteed, John, 171, 181 Hiscock, W. G., 29, 189, 203 Fleckenstein, Joachim O., 108, 201, 217 Hofmann, Joseph E., 15, 140, 141

Index 283

Hooke, Robert, 113, 170–2 life, 136–7 Hoskin, Michael, 176 publication policy, 164–8 Hospital, Guillaume F. A. de l’, 2, 107, 119–21, 123, representation of trajectories, 152–6 137, 157, 177, 190, 196–9, 201, 202, 204, 216, transmutation theorem, 141–2 251, 252 Leybourn, Thomas, 258, 260 Hudde, Johann, 18, 23, 120 Locke, John, 176, 257 Huygens, Christiaan, 2, 3, 6, 9, 26, 29, 30, 81, 89, 105, 106, 109, 110, 137, 147, 149, 152, 166, MacDonald Ross, George, 165 171–3, 175–82, 185, 187, 188, 192, 198, 203, Machin, John, 175, 191 204, 206, 215, 216, 248 Maclaurin, Colin, 94, 169, 193, 202, 248, 251, 254, and proportion theory, 124–7 255, 258, 259 his criticism to Proposition 6, Book 1, 129–35 MacPike, Eugene F., 172, 174 his mathematical work, 118–20 Maffioli, Cesare, 206 his reception of the Principia, 120–4 Mahoney, Michael, 51, 219 Huygens, Constantijn, 120 Malebranche, Nicolas, 177, 180, 198, 201, 202 Hyppocrates, 180, 181 Mamiani, Maurizio, 14, 31 Mancosu, Paolo, 162, 197, 199, 200 Iliffe, Robert, 104 Mandelbrote, Scott, 31, 32 infinitesimals Manfredi, Eustachio, 206, 248 calculus of, 142–5 Manfredi, Gabriele, 137 foundation of, 159–63 Manuel, Frank E., 32 geometry of, 138–42 Marie, Maximilien, 2, 3 inverse problem of central forces, 54–6, 58–60, Mariotte, Edme, 122 217–33 Martins, Roberto de A., 121 Maupertuis, Pierre de, 91, 92, 197, 248 James II, 173 Mazzone, Silvia, 199, 205, 207, 241 Jenisch, Philipp Jacob, 164 McGuire, J. E., 101, 102 Jesseph, Douglas M., 127 Mede, Joseph, 31 Jones, William, 90, 180, 197, 202, 252 Mencke, Otto, 147 Jourdain, Philip E. B., 7 Metrodorus of Chios, 101 Jurin, James, 248 Michelotti, Pier A., 206, 248 Mignard, François, 122 Keill, John, 5, 15, 90, 116, 149, 186, 187, 191, 193, Milnes, James, 190, 191 194, 200, 201, 211, 216–8, 226–30, 233, 237, Molieres,` Joseph Privat, Abbe´ de, 201 243, 244, 248, 253, 260 moment (definition of), 21 Kepler, Johannes, 41, 165, 183, 203 Monroe, J., 202 Kirsanov, Vladimir S., 184 Montmort, Pierre R., 198, 201, 204, 244 Kitcher, Philip, 164 More, Henry, 31 Knobloch, Eberhard, 10, 14, 164, 165 Moschus the Phoenician, 101 Krauss, Johann H., 229 motion in resisting media, 81–90, 147–9, 185–6, Kuhn, Thomas, 169 203–4, 233–44

La Hire, Philippe de, 183, 191, 200 Nagel, Fritz, 15, 197 Lagrange, Joseph L., 257 Nauenberg, Michael, 11, 14, 49, 93, 108, 112, 116, Lai, Tyrone, 164 209, 257 Lalande, Jerome J., 258 Needham, Tristan, 50 Landen, John, 193, 258, 260 Nieuwentijt, Bernhardt, 119, 164, 165, 199 Laplace, Pierre-Simon de, 39, 95, 231, 232 notation Laugwitz, Detlef, 259 Leibniz’s, 142–5 Lees, Stephen, 15 Newton’s, 22, 80 Leibniz, Gottfried W., 2–6, 8–10, 14, 15, 27, 31, 35, translations between Newton’s and Leibniz’s, 37, 49, 89, 90, 100, 104, 106, 112, 114, 115, 250–3 117–23, 169, 177, 178, 180, 181, 185, 187, 190, Numa Pompilius, 101, 165 194–200, 202–6, 216, 227, 236–8, 241, 243, 244, 246, 250–7, 259, 263 Oldenburg, Henry, 37, 256 and inﬁnite series, 137–8 Omerique, Hugo de, 30 application of calculus to dynamics, 145–52 Orpheus, 102 approach towards the Ancients, 164–6 Oughtred, William, 17, 18, 40 differential and integral calculus, 142–5 foundations of calculus, 156–63 Palmieri, Paolo, 14, 95 geometry of inﬁnitesimals, 138–42 Pappus, 28, 29, 32, 43, 53, 101, 103, 254

284 Index

Pascal, Blaise, 118, 138 2nd edn, 237–40 Pasini, Enrico, 14, 160, 161, 166 Propositions 15–18, 88 Peiffer, Jeanne, 200, 201, 252 Propositions 25–31, 89 Pemberton, Henry, 29, 30, 124 Proposition 34 (= 35 1st edn), 89–90 perturbations of planetary orbits, 60–8, 92–4 Principia, Book 3 Pez´ enas,´ R. P., 202 Moon theory, 92–4 Philolaus, 101 shape of planets, 91–2 Pitcairne, Archibald, 179, 183, 189 tides, 94–5 Plato, 101 Proudman, J., 95 Playfair, John, 258 Pycior, Helena M., 18, 37 Poincare,´ Jules Henri, 39 Pythagoras, 25, 101, 102, 104 Poleni, Giovanni, 206, 248 Politella, Joseph, 165 Rattansi, Piyo´ M., 101, 102 Popkin, Richard H., 32 Rau, Christian, 53 Pourciau, Bruce, 14, 43, 55, 218 Reyneau, Charles-Rene,´ 201, 202 Principia Riccati, Jacopo, 89, 137, 206, 207, 225, 244, 248 commented edition by Le Seur and Jacquier, 248–9 Richer, Jean, 122 translation by the Marquise du Chastelet, 249 Rigaud, Stephen P., 174, 177, 178, 180, 181, 197, 202 Principia, Book 1 Roberval, Gilles Personne de, 103, 118, 215 Lemmas 1–11 (Section 1), 43–47 Robinet, Andre,´ 31, 199, 201 Proposition 1, 48–9, 209–11 Roero, Clara S., 107, 198, 199, 205, 207, 241 Proposition 2, 48 Rolle, Michel, 199 Proposition 6, 50–1, 128–9 Romer,¨ Olaus,¨ 123 curvature method (2nd edn), 108–12 Ronan, Colin A., 172, 174 Proposition 7, 51 Rossi, Mary Ann, 12 Proposition 9, 52 Routh, Edward J., 7, 97 Proposition 10, 52–4 Corollary 1, 56 Sageng, Erik, 254, 264 Proposition 11, 54 Saulmon (alias Saumon), 204 Proposition 12, 54 Saunderson, Nicholas, 180, 255 Proposition 13, 54 Saurin, Joseph, 201 Corollary 1, 54–6, 217–8 Sauveur, Joseph, 201 Proposition 17, 56–8 Schmitt, Charles B., 165 Corollaries 3–4, 58 Schneider, Ivo, 158, 186, 254 Proposition 41, 58–9, 218–22 Scriba, Christoph J., 254 Corollary 3, 59–60, 222–3 series, 18–20, 63–4, 79–80, 97, 137–8, 235–6, 239–40 Proposition 43, 60–1 Sigurdsson, Skuli, 10, 158 Proposition 44, 61–3 Simpson, Thomas, 157, 192–4, 258, 260 Proposition 45, 63–5 Simson, Robert, 254 Proposition 66, 65–8 Sluse, Rene´ Franc¸ois W. de, 18 Corollaries 2–4, 66 Snelders, H. A. M., 120–2 Corollaries 10–11, 67 solid of least resistance, 89–90, 178, 183–4 Corollaries 18–22, 67 Speiser, David, 120 Proposition 70, 68 Spence, William, 260 Proposition 71, 69–71 Stewart, Matthew, 193, 254 Proposition 73, 71–2 Stone, Edmund, 196, 202, 251 Scholium, 68 Strabo, 101 Proposition 90, 73–4 Stukeley, William, 104 Proposition 91, 74–5 Sylla, Edith, 127, 175 Corollary 1,75–7 synthetic method of ﬂuxions, 27–37, 96–7, 112–5 Corollary 2, 77–8, 184–5 Proposition 93 Taylor series, 80, 235–6, 239–43 Scholium, 79–80 Taylor, Brook, 197, 201, 254 Principia, Book 2 Thales, 102 Lemma 2 (Section 2) 85–6 Thorp, Robert, 191 Proposition 1, 82 time (geometrical representation of), 42, 245–6 Proposition 2, 82–4 Todhunter, Isaac, 259 Proposition 5, 84–5 Toplis, John, 258 Proposition 8, 86–8 Torricelli, Evangelista, 165, 173 Proposition 10, 88 transcendental quantities, 144, 246 1st edn, 233–6 Trompf, Garry W., 102

Index 285

Truesdell, Clifford, 9, 12, 108, 199, 259 Tschirnhaus, Ehrenfried W. von, 145, 178

Vailati, Enrico, 162, 199, 200 van Maanen, Jan A., 120 Van Schooten, Frans (the Younger), 18 Varignon, Pierre, 5, 49, 108, 115, 137, 154, 155, 163, 186, 194, 195, 199–206, 213, 217, 227, 232, 240, 241, 243, 244, 247, 248, 252, 257 Vermij, Rienk H., 120 Verzaglia, Giuseppe S., 196, 206, 241 Viete,` Franc¸ois, 17, 18, 40, 118, 166 Viviani, Vincenzo, 31 Vossius, Isaac, 173

Waff, Craig B., 63, 93 Wallis, John, 17–19, 21, 26–8, 30, 37, 97, 120, 170–2, 183, 203, 256 Walmesley, Charles, 193 Ward, Seth, 203 Waring, Edward, 258, 260 Westfall, Richard S., 1, 14, 20, 29, 32, 40, 154, 172 Whewell, William, 2, 3 Whiston, William, 53, 169, 188, 189, 191, 255 Whiteside, Derek T., 1–4, 7, 12, 14, 15, 17, 20–2, 25–8, 32, 33, 35–7, 49, 55, 73, 75, 76, 78, 89, 93, 97, 100, 103, 105–8, 200, 209, 218, 222, 227, 232, 234, 236, 237, 243 Whitman, Anne, 7, 12, 13, 39, 40, 45, 47, 61, 71, 72, 82, 85, 210 Wightman, William P. D., 179 Wilson, Curtis A., 65, 67, 93, 94, 151, 257, 259 Witt, Jan de, 183 Wolff, Christian, 207 Wollenschlager,¨ Kurt, 227, 236, 243 Woodhouse, Robert, 258 Wotton, William, 175 Wren, Christopher, 170–2 Wright, John M. F., 191

Yates, Frances, 102 Yoder, Joella G., 118, 120

Zehe, Horst, 178 Zenocrates, 101