History of Vector Analysis

I.Introduction......Page 18
II.The Concept of the Parallelogram of Velocities and Forces......Page 19
III.Leibniz' Concept of a Geometry of Situation......Page 20
IV.The Concept of the Geometrical Representation of Complex Numbers......Page 22
V.Summary and Conclusion......Page 28
Notes......Page 30
I.Introduction:Hamiltonian Historiography......Page 34
II.Hamilton's Life and Fame......Page 36
III.Hamilton and Complex Numbers......Page 40
IV.Hamilton's Discovery of Quaternions......Page 44
V.Quaternionsuntil Hamilton's Death(1865)......Page 50
VI.Summary and Conclusion......Page 58
Notes......Page 60
I.Introduction......Page 64
II.August Ferdinand Mobius and His Barycentric Calculus......Page 65
III.Giusto Bellavitis and His Calculus of Equipollences......Page 69
IV.Hermann Grassmann and His Calculus of Extension......Page 71
V.Grassmann's Theorieder Ebbeund Flut......Page 77
VI.Grassmann's Ausdehnungslehre of 1844......Page 80
VII.The Periodfrom 1844 to 1862......Page 94
VIII.Grassmann's Ausdehnungslehre of 1862 and the Gradual,Limited Acceptance of His Work......Page 106
IX.Matthew O'Brien......Page 113
I.Introduction......Page 126
II.Interest in Vectorial Analysis in Various Countries from 1841 to 1900......Page 127
III.Peter Guthrie Tait:Advocate and Developer of Quaternions......Page 134
IV.Benjamin Peirce:Advocate of Quaternions in America......Page 142
V.James Clerk Maxwell:Critic of Quaternions......Page 144
VI.William Kingdon Clifford:Transition Figure......Page 157
Notes......Page 161
II.Josiah Willard Gibbs......Page 167
III.Gibbs'Early Work in Vector Analysis......Page 169
IV.Gibbs'Elements of Vector Analysis......Page 172
V.Gibbs'Other Work Pertainingto Vector Analysis......Page 175
VI.Oliver Heaviside......Page 179
VII.Heaviside's Electrical Papers......Page 180
VIII.Heaviside's Electromagnetic Theory......Page 186
IX.The Reception Given to Heaviside's Writings......Page 191
X.Conclusion......Page 194
Notes......Page 195
I.Introduction......Page 199
II.The"Strugglefor Existence"......Page 200
III.Conclusions......Page 232
Notes......Page 238
I.Introduction......Page 242
II.Twelve Major Publicationsin Vector Analysisfrom 1894 to 1910......Page 243
III.Summary and Conclusion......Page 256
Notes......Page 260
SUMMARY AND CONCLUSIONS......Page 264
Notes......Page 272
Index......Page 277