كتاب Strength of Materials and Theory of Elasticity
منتدى هندسة الإنتاج والتصميم الميكانيكى
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منتدى هندسة الإنتاج والتصميم الميكانيكى
بسم الله الرحمن الرحيم

أهلا وسهلاً بك زائرنا الكريم
نتمنى أن تقضوا معنا أفضل الأوقات
وتسعدونا بالأراء والمساهمات
إذا كنت أحد أعضائنا يرجى تسجيل الدخول
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 كتاب Strength of Materials and Theory of Elasticity

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أخواني في الله
أحضرت لكم كتاب
Strength of Materials and Theory of Elasticity
in 19th Century Italy
A Brief Account of the History of Mechanics of Solids and Structures
Danilo Capecchi, Giuseppe Ruta

كتاب Strength of Materials and Theory of Elasticity  S_o_m_16
و المحتوى كما يلي :


Contents
1 The Theory of Elasticity in the 19th Century 1
1.1 Theory of Elasticity and Continuum Mechanics . 1
1.1.1 The Classical Molecular Model 3
1.1.1.1 The Components of Stress . 7
1.1.1.2 The Component of Strains
and the Constitutive Relationships 8
1.1.2 Internal Criticisms Toward the Classical
Molecular Model 13
1.1.3 Substitutes for the Classical Molecular Model 17
1.1.3.1 Cauchy’s Phenomenological Approach . 17
1.1.3.2 Green’s Energetic Approach 22
1.1.3.3 Differences in the Theories of Elasticity 24
1.1.4 The Perspective of Crystallography 25
1.1.5 Continuum Mechanics in the Second Half
of the 19th Century . 31
1.2 Theory of Structures 35
1.2.1 Statically Indeterminate Systems 37
1.2.2 The Method of Forces . 39
1.2.3 The Method of Displacements . 42
1.2.4 Variational Methods 47
1.2.5 Applications of Variational Methods . 50
1.2.5.1 James Clerk Maxwell
and the Method of Forces 50
1.2.5.2 James H. Cotterill and the Minimum
of Energy Expended in Distorting 54
1.2.6 Perfecting of the Method of Forces 56
1.2.6.1 Lévy’s Global Compatibility 56
1.2.6.2 Mohr and the Principle of Virtual Work 59
ix1.3 The Italian Contribution 66
1.3.1 First Studies in the Theory of Elasticity . 70
1.3.2 Continuum Mechanics . 71
1.3.3 Mechanics of Structures 73
References 76
2 An Aristocratic Scholar 83
2.1 Introduction 83
2.2 The Principles of Piola’s Mechanics . 86
2.3 Papers on Continuum Mechanics . 89
2.3.1 1832. La meccanica de’ corpi naturalmente
estesi trattata col calcolo delle variazioni . 93
2.3.2 1836. Nuova analisi per tutte le questioni
della meccanica molecolare . 100
2.3.3 1848. Intorno alle equazioni fondamentali
del movimento di corpi qualsivogliono . 104
2.3.4 1856. Di un principio controverso della
meccanica analitica di lagrange e delle
sue molteplici applicazioni 109
2.3.5 Solidification Principle and Generalised Forces 109
2.4 Piola’s Stress Tensors and Theorem . 113
2.4.1 A Modern Interpretation of Piola’s Contributions 114
2.4.2 The Piola-Kirchhoff Stress Tensors 116
References 119
3 The Mathematicians of the Risorgimento . 123
3.1 Enrico Betti 123
3.1.1 The Principles of the Theory of Elasticity . 127
3.1.1.1 Infinitesimal Strains 127
3.1.1.2 Potential of the Elastic Forces . 129
3.1.1.3 The Principle of Virtual Work . 131
3.1.2 The Reciprocal Work Theorem . 132
3.1.3 Calculation of Displacements 135
3.1.3.1 Unitary Dilatation and Infinitesimal
Rotations . 135
3.1.3.2 The Displacements . 137
3.1.4 The Saint Venant Problem 138
3.2 Eugenio Beltrami 141
3.2.1 Non-Euclidean Geometry . 144
3.2.2 Sulle equazioni generali della elasticità . 146
3.2.3 Papers on Maxwell’s Electro-Magnetic Theory 149
3.2.4 Compatibility Equations 153
x Contents3.2.5 Beltrami-Michell’s Equations 155
3.2.6 Papers on Structural Mechanics 156
3.2.6.1 A Criterion of Failure . 156
3.2.6.2 The Equilibrium of Membranes 158
3.3 The Pupils . 160
3.3.1 The School of Pisa . 160
3.3.2 Beltrami’s Pupils 168
References 174
4 Solving Statically Indeterminate Systems . 179
4.1 Scuole d’applicazione per gl’ingegneri 179
4.1.1 The First Schools of Application for Engineers 182
4.1.1.1 The School of Application in Turin and
the Royal Technical Institute in Milan . 182
4.1.1.2 The School of Application in Naples 184
4.1.1.3 The School of Application in Rome . 185
4.1.1.4 Curricula Studiorum 186
4.2 The Teaching . 188
4.3 Luigi Federico Menabrea . 191
4.3.1 1858. Nouveau principe sur la distribution
des tensions 194
4.3.1.1 Analysis of the Proof . 195
4.3.1.2 Immediate Criticisms
to the Paper of 1858 . 197
4.3.1.3 The Origins of Menabrea’s Equation
of Elasticity . 200
4.3.2 1868. Étude de statique physique . 204
4.3.2.1 The ‘Inductive’ Proof of the Principle . 207
4.3.3 1875. Sulla determinazione delle tensioni e
delle pressioni ne’ sistemi elastici . 208
4.3.4 Rombaux’ Application of the Principle of Elasticity 210
4.3.4.1 Condizioni di stabilità della tettoja della
stazione di Arezzo . 211
4.3.4.2 The Question About the Priority . 213
4.4 Carlo Alberto Castigliano . 214
4.4.1 1873. Intorno ai sistemi elastici 217
4.4.1.1 The Method of Displacements . 217
4.4.1.2 The Minimum of Molecular Work 218
4.4.1.3 Mixed Structures 220
4.4.1.4 Applications . 224
Contents xi4.4.2 1875. Intorno all’equilibrio dei sistemi elastici 227
4.4.2.1 Mixed Structures 228
4.4.3 1875. Nuova teoria intorno all’equilibrio
dei sistemi elastici 229
4.4.3.1 The Theorem of Minimum Work
as a Corollary 230
4.4.3.2 Generic Systems 231
4.4.4 1879. Théorie de l’équilibre des systémes
élastiques et ses Applications 233
4.4.4.1 Flexible Systems 236
4.4.4.2 The Costitutive Relationship 237
4.4.4.3 Applications: The Dora Bridge 238
4.4.5 A Missing Concept: The Complementary
Elastic Energy 242
4.5 Valentino Cerruti 246
4.5.1 Sistemi elastici articolati. A Summary 247
4.5.1.1 Counting of Equations and Constraints . 247
4.5.1.2 Evaluation of External Constraint Reactions.
Statically Determinate Systems 249
4.5.1.3 Redundant and Uniform
Resistance Trusses . 250
4.5.1.4 Final Sections 250
4.5.2 Trusses with Uniform Resistance . 252
4.5.3 Statically Indeterminate Trusses 255
4.5.3.1 Poisson’s and Lévy’s Approaches 255
4.5.3.2 Cerruti’s Contribution to Solution
of Redundant Trusses . 257
References 261
5 Computations by Means of Drawings . 267
5.1 Graphical Statics . 267
5.2 Graphical Statics and Vector Calculus 271
5.3 The Contributions of Maxwell and Culmann . 273
5.3.1 Reciprocal Figures According to Maxwell . 273
5.3.2 Culmann’s Graphische Statik 278
5.4 The Contribution of Luigi Cremona . 287
5.4.1 The Funicular Polygon and the Polygon
of Forces as Reciprocal Figures 289
5.4.1.1 The Funicular Polygon and the Polygon
of Forces . 289
5.4.1.2 The Null Polarity 294
5.4.1.3 Reciprocity 296
5.4.1.4 Cremona’s Diagram 298
xii Contents5.4.2 The Lectures on Graphical Statics . 302
5.4.3 Cremona’s Inheritance . 305
5.4.3.1 Carlo Saviotti 305
5.4.3.2 The Overcoming of the Maestro . 312
References 314
Appendix A: Quotations 317
A.1 Quotations of Chap. 1 317
A.2 Quotations of Chap. 2 332
A.3 Quotations of Chap. 3 342
A.4 Quotations of Chap. 4 354
A.5 Quotations of Chap. 5 375
Index .
Index
A
Abel, Niels Henric (1802–1829), 142, 343
Alembert, Jean Baptiste le Ronde D’ (1717–
1783), 23, 39, 68, 86–88, 90, 334, 338
Almansi, Emilio (1869–1948), 190
Amici, Giovanni Battista (1786–1863), 85,
123
Angiulli, Vincenzo (1747–1819), 68
Araldi, Michele (1740–1813), 68, 83
Arzelà, Cesare (1847–1912), 84, 161
Ascoli, Giulio (1843–1896), 161
Avogadro, Amedeo (1776–1856), 70
B
Barilari, Pacifico (1813–1896), 39
Battaglini, Giuseppe (1826–1894), 162, 171,
246
Bauschinger, Johann(1834–1893),268,270,
312, 313
Belanger, Jean Baptiste (1790–1874), 310
Bellavitis, Giusto (1803–1880), 272, 273
Belli, Giuseppe (1791–1860), 70
Belluzzi, Odone (1892–1956), 299
Beltrami, Eugenio (1835–1900), 72, 73,
141–144, 146–150, 152–156, 158–
160, 168, 171, 173, 345
Benedetti, Giovanni Battista (1530–1590),
271
Benvenuto, Edoardo (1940–1998), 201
Bernoulli, Daniel (1700–1782), 68
Bernoulli, Johann (1700–1782), 69
Bertelli, Timoteo (1826–1905), 39
Bertini, Eugenio (1846–1933), 161, 305
Bertot, Henri, 41
Bertrand, Joseph Louis François (1822–
1900), 124, 193, 200 , 358
Bessel, Friedrich Wilhelm (1784–1846), 34
Betti, Enrico (1823–1892), 34, 72, 75, 84,
123–144, 160–162, 164, 168–170,
172, 173, 188, 215, 305, 343
Boggio, Tommaso (1877–1963), 161
Boltzmann, Ludwig (1844–1906), 164
Bolyai, Janos (1802–1860), 143, 145
Bongiovanni, Margherita, 74
Borchardt, Carl Wilhelm (1816–1880), 27,
146
Bordoni, Antonio (1789–1860), 83, 84, 105
Borelli, Alfonso (1608–1679), 143
Born, Max (1882–1970), 31
Boscovich, Ruggero Giovanni (1711–1787),
2
Boussinesq, Valentin Joseph (1842–1929),
32, 86
Bravais, Auguste (1811–1863), 16, 25, 30,
322
Bresse, Jaques Antoine Charles (1822–
1883), 280, 377
Brioschi, Francesco (1824–1897), 84, 85,
89, 109, 123, 124, 141–143, 180, 181,
184, 287, 289, 302, 355
Brunacci, Vincenzo (1768–1818), 83–85,
88, 89, 332
Bunsen, Robert Wilhelm (1811–1899), 35
Burali-Forti, Cesare (1861–1931), 273
C
Caparrini, Sandro, 271
Capelli, Alfredo (1855–1910), 171
Carnot, Lazare Nicolas Marguérite (1753–
1823), 108, 339
Casati, Gabrio (1798–1783), 69, 74,
Casorati, Felice (1835–1890), 84, 123, 124,
168
Castelnuovo, Guido (1865–1952), 164, 305
Castigliano, Carlo Alberto (1847–1884), 26,
37, 50, 54, 55, 73–75, 86, 153, 157,
179, 181, 189–191, 197, 198, 210–
225, 227–247, 256, 257, 349, 355,
367
Cattaneo, Carlo (1801–1869), 183
Cauchy, Augustin Louis (1789–1857), 3–20,
22–27, 30, 83–86, 90, 98–100, 104,
107, 109–111, 114, 115, 139, 149,
234, 286, 319, 321, 333, 360
Cavalieri, Bonaventura (1598–1647), 85
Cavalli, Giovanni (1808–1897), 71
Cavour, Camillo Benso count of (1810–
1861), 192
Cayley, Arthur (1821–1895), 252, 254, 258
Ceradini, Cesare (1844–1935), 190
Cerruti, Valentino (1850–1909), 73–75, 162,
179, 214, 246–261
Cesaro, Ernesto (1859–1906), 86, 144, 152,
154, 155, 168, 171–174
Chasles, Michel (1793–1880), 245, 268,
272, 288
Clapeyron, Benoit Paul Emile (1799–1864),
33, 39, 41, 42, 48–51, 54, 65, 225,
226, 232, 268, 327, 365
Clausius, Rudolph Julius Emmanuel (1822–
1888), 12
Clavius, Cristophorus (1538–1612), 143
Clebsch, Adolf (1833–1872), 15, 16, 24, 26,
27, 34, 35, 37, 44, 45, 47, 56, 73, 131,
138–140, 156, 168, 217, 225, 257,
268, 310, 347
Clerk Maxwell, James (1831–1879), 32, 33,
36, 50–53, 66, 134, 143, 144, 149,
151–153, 161, 168, 170, 273–278,
284, 289, 311, 331, 379
Clifford,WilliamKingdon(1845–1879), 173
Colombo, Giuseppe (1836–1921), 216
Colonnetti, Gustavo (1886–1968), 190, 191
Cosserat, Eugéne Maurice Pierre (1866–
1931), 112
Cosserat, François (1852–1914), 112
Cotterill, James Henry (1836–1922), 39, 50,
54, 55, 278
Cournot, Antoine-Augustin (1801–1877),
196, 201–203, 252, 360
Cousinery, Barthelemy Edouard (1790–
1851), 268, 271, 273
Cremona, Luigi (1830–1903), 37, 84, 124,
125, 142, 143, 187, 213, 245, 267–
270, 274, 277, 278, 280, 281, 284,
287–289, 294–296, 298–303, 305,
306, 308, 311–313, 378, 379, 381,
387
Croce, Benedetto (1866–1952), 163
Crotti, Francesco(1839–1896), 50, 158, 233,
243–246
Culmann, Carl (1821–1881), 36, 37, 245,
267–269, 273, 277–279, 281–286,
298, 302, 306, 309, 311, 312, 375,
377, 381, 385
Curioni, Giovanni (1831–1887), 179, 182
D
Da Vinci, Leonardo (1542–1519), 271
Delanges, Paolo (1750?–1810), 39, 69
Dini, Ulisse (1845–1918), 84, 125, 161
Di Pasquale, Salvatore (1931–2004), 170
Dirichlet Lejeune, Peter Gustav (1805–
1859), 124, 161, 170
Dorna, Alessandro (1825–1887), 39, 71,
196, 201, 203
Dove, Heinrich Wilhelm (1803–1879), 34
Duhamel, Jean-Marie Constant (1797–
1872), 7
Duhem, Pierre Maurice Marie (1861–1916),
32
E
Engesser, Friedrich (1848–1931), 50, 66
Enriques, Federigo (1871–1946), 84, 305
Euclide (IV sec. a.C.), 145, 344
Euler, Leonhard (1707–1783), 3, 19, 37–39,
54, 68, 86, 90, 93, 95, 101, 110, 190,
252, 275, 296, 334, 338, 380
F
Favaro, Antonio (1847–1922), 269
Finzi, Bruno (1899–1974), 71
Flamant, Alfred Aimé (1839–1914?), 32, 35
Fleming Jenkin, Henry Charles (1833–
1885), 37, 53, 274, 278
Fontana, Gregorio (1735–1803), 39, 83
Fossombroni, Vittorio (1754–1844), 68, 83
Frankel,Wilhelm (1841–1895), 50
Fredholm, Erik Ivar (1866–1927), 161
Fresnel, Augustin Jean (1788–1827), 3
Frisiani, Paolo (1797–1880), 85
Fusinieri, Ambrogio (1775–1852), 39Index 391
G
Galois, Evariste (1811–1832), 124
Gauss, Carl Friedrich (1777–1855), 48, 124,
142, 143, 145, 146, 161, 343, 350
Gibbs, Josiah Willard (1839–1903), 272
Giorgini, Gaetano (1795–1874), 123
Giulio, Ignazio Carlo (1803–1859), 71, 74,
182
Grashof, Franz (1826–1893), 34, 233
Grassmann, Hermann Génter (1809–1877),
272, 273
Green, Gorge (1793–1841), 16, 17, 22–26,
31, 48, 72, 104, 114, 117, 127, 130,
131, 133, 134, 136, 137, 143, 152,
159, 161, 170, 231, 234, 235, 243,
320, 321, 343, 350, 366–368, 371
Guidi, Camillo (1853–1941), 172, 190, 313
H
Hadamard, Jacques (1865–1963), 161
Hamilton, William Rowan (1805–1865), 18,
271, 272
Heaviside, Oliver (1850–1925), 272, 273
Hellinger, Ernst (1883–1950), 27, 116
Helmholtz, Hermann Ludwig (1821–1894),
35
Hermite, Charles (1822–1901), 124
Hodgkinson, Eaton (1789–1861), 16, 32
Hooke, Robert (1635–1703), 1, 18
Huygens, Christiaan (1629–1695), 162
J
Jacobi, Carl (1804–1851), 27, 34, 124, 142,
343
K
Kirchhoff, Gustav Robert (1824–1887), 16,
26–28, 34, 35, 71, 86, 116–118, 139,
153, 162
Klein, Felix Christian (1849–1925), 35
Korn, Arthur (1870–1945), 161, 173
Kronecker, Leopold (1823–1891), 124
Kummer, Ernest Eduard (1810–1893), 124
L
Lacroix, Sylvestre Franìois de (1765–1843),
105
Lagrange, Joseph Louis (1736–1813), 3, 4,
18, 19, 26, 47, 68, 69, 83–85, 87–93,
95, 96, 99–102, 104, 105, 108–114,
116, 118, 125, 126, 131, 158–160,
219, 220, 222, 248, 332–342, 349
Lambert, Johann Henrich (1727–1777), 145
Lamb, Horace (1849–1934), 34
Lamé, Gabriel (1795–1870), 4, 12, 14, 15,
20, 21, 25, 26, 35, 48, 49, 51, 130,
134, 146, 148, 231, 233, 234, 322,
366–368
Laplace, Pierre Simon (1749–1827), 1, 4,
133, 134, 143, 155, 161, 251, 350
Lauricella, Giuseppe (1867–1913), 161, 170
Lecornu, Léon (1854–1940), 158
Leibniz, Gottfried Wilhelm (1646–1716),
90, 92
Levi-Civita, Tullio (1873–1941), 143
Lévy, Maurice (1838–1910), 37, 56–58, 75,
213, 255, 257, 259
Libri, Guglielmo (1803–1869), 123
Lipschitz, Rudolf Otto Sigmund (1802–
1903), 134
Lobacevskij, Nikolaj Ivanovic (1792–1856),
143, 145, 146
Lorgna, Antonio Maria (1735–1796), 39, 68
Love, Augustus Edward Hough (1863–
1940), 12, 34, 35
M
Magistrini, Giovanni Battista (1777–1849),
87
Mainardi, Gaspare (1880–1879), 71
Marcolongo, Roberto (1882–1943), 27, 86,
273
Mariotte, Edme (1620–1684), 1
Martini, Francesco di Giorgio (1439–1501),
192
Mascheroni Lorenzo (1750–1800), 68
Matteucci, Carlo (1811–1868), 123
Menabrea, Luigi Federico (1809–1896), 37,
39, 50, 54, 74, 75, 162, 179, 189, 191–
210, 212–215, 219, 221, 227, 229,
230, 242, 243, 247, 252, 253, 256,
259, 311, 358, 366
Meyer, Franz (1856–1934), 158
Michell, John Henry (1863–1940), 156
Möbius, August Ferdinand (1790–1868), 36,
268, 271
Mohr, Christian Otto (1835–1918), 36, 37,
50, 52, 53, 56, 59–66, 233, 274, 285,
286, 330, 331
Monge, Gaspard (1746–1818), 268, 279,
376
Moseley, Henry (1802–1872), 36, 39, 54,
225392 Index
Mossotti, Ottaviano Fabrizio (1791–1863),
39, 70, 83–85, 123, 124, 158, 193,
201, 202, 310, 360
M’uller-Breslau, Heinrich (1851–1925), 53,
66
N
Navier, Claude Louis Marie Henri (1785–
1836), 3–5, 8, 12, 13, 15–17, 20, 24–
27, 36, 37, 39–44, 47, 56, 71, 131,
149, 161, 189, 194, 217, 252, 257,
311, 319, 321, 331, 350
Neumann, Carl Gottfried (1832–1923), 35,
134, 140, 141, 146
Neumann, Franz Ernst (1798–1895), 27, 34,
35
Newton Isaac (1643–1727), 1, 2, 25, 33, 86,
87, 126, 133, 332, 342, 343
O
Obici, Pietro (1804–1849), 123
Oersted, Hans Christian (1777–1851), 16
P
Pacinotti, Luigi (1804–1889), 70, 71, 123
Padova, Ernesto (1845–1896), 125, 161,
168, 173
Pagani, Gaspare Michele (1796–1855), 39,
70, 201, 360
Paoli, Pietro (1759–1839), 39, 68, 84
Pareto, Vilfredo (1848–1923), 164
Pearson, Karl (1857–1936), 32, 34, 38, 39,
47, 70, 71, 101, 117, 164
Piola Gabrio (1791–1850), 3, 26, 70, 71, 83–
89, 93, 95–116, 118, 126, 127, 139,
143, 310, 331, 341
Poincaré, Henri (1854–1912), 27, 32, 238
Poinsot, Louis (1777–1859), 110
Poisson, Siméon Denise (1781–1840), 4–7,
12, 13, 15, 16, 25–28, 30, 34, 37, 39,
44–47, 56, 72, 75, 90, 98–101, 103,
104, 137, 140, 149, 158, 217, 234,
255–257, 261, 319, 321, 333, 337
Poncelet, Jean Victor (1788–1867), 245,
268, 279, 280, 376, 377
Pouchet, Louis Ézéchiel (1748–1809), 268
Promis, Carlo (1808–1873), 192
Prony, Gaspard Clair Franìois Marie Riche
(1755–1839), 83
Pullino, Giacinto (1837–1898), 190
R
Rankine, William John Macquorn (1820–
1872), 16, 28, 32, 36, 37, 268, 274
Rayleigh, John William Strutt (1819–1903),
32, 36
Regnault, Henry Victor (1810–1878), 16
Ricci-Curbastro, Gregorio (1853–1925), 18,
84, 125, 143, 152, 161
Richelmy, Prospero (1813–1884), 74, 180,
182, 183, 188, 355
Riemann, Bernhard (1826–1866), 36, 124,
125, 138, 143–146, 160
Ritter, Georg Dietrich August (1826–1908),
36, 66, 302, 310
Ritter, Karl Wilhelm (1847–1906), 36
Rombaux, Giovanni Battista, 210–213, 215,
229, 362
S
Sabbia, Emilio Francesco (1838–1914),
197–199, 358
Saccheri, Giovanni (1843–1925), 181, 210,
213, 355
Saccheri, Girolamo (1667–1773), 143, 145
Saint Venant, Adhémar J.C. Barré de (1797–
1886), 7, 12, 14–16, 22–26, 32, 35,
37–39, 41, 44, 45, 49, 50, 70, 71, 73,
117, 127, 138–141, 153, 155–157,
172, 189–191, 205, 225, 231, 272,
346–348, 366, 367
Saladini, Girolamo (1731–1813), 68, 69, 83
Saluzzo, Cesare (1837–1906), 192
Savart, Félix (1791–1841), 16
Saviotti Carlo (1845–1928), 269, 273, 281,
292, 293, 305, 306, 308–313
Sella, Quintino (1827–1884), 74, 182, 246
Severi, Francesco (1879–1961), 305
Sobrero, Ascanio (1812–1888), 182
Somigliana, Carlo (1860–1955), 71, 125,
161–163, 166, 168–170
Sophie Germain, Marie (1776–1831), 1
Staudt, Karl Georg Christian von (1798–
1867), 268, 280, 377
Stevin, Simon (1548–1620), 110, 268, 290,
291
Stokes, George Gabriel (1819–1903), 32, 33
T
Tait, Peter Guthrie (1831–1901), 32, 33, 48,
139
Taylor, Brook (1685–1731), 84
Tedone, Orazio (1870–1922), 125, 137, 161Index 393
Thomson, William (Kelvin) (1824–1907),
16, 26, 32, 33, 36, 48, 72, 126, 128–
131, 139
Todhunter, Isaac (1820–1884), 32, 38, 39,
47, 70, 71, 101, 117
Tortolini, Barnaba (1808–1874), 288
Toupin, Richard A. (1926-), 116
Truesdell, Clifford Ambrose (1919–2000),
86, 116
V
Varignon, Pierre (1654–1722), 268, 279,
291, 292, 294, 306, 310, 311
Venturoli, Giuseppe (1768–1846), 84, 310
Veronese, Giuseppe (1854–1917), 305
Villarceau,Yvon (1813–1883), 197, 199,
200, 358
Voigt, Woldemar (1850–1919), 18, 25–31,
34, 168, 321
Volterra,Vito (1860–1940), 84, 125, 161–
166, 168, 170, 171, 174, 191, 198,
350, 353, 354
W
Wallis, John (1616–1703), 143
Weierstrass, Karl Theodor Wilhelm (1815–
1897), 124
Weingarten, Leonhard Julius (1836–1910),
165, 166, 168, 171, 353, 354
Wertheim, Guillaume [Wilhelm] (1815–
1861), 13, 14, 16
Williot, Joseph Victor (1843–1907), 37
Z
Zucchetti, Ferdinando (1845–1883), 312


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