Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

By Paolo Mancosu | Go to book overview
INDEX
acute hyperbolic solid, 129-131, 243
definition of, 132
paradoxical nature, 137, 239
philosophical relevance, 136-149
proof of finiteness by exhaustion, 134-135
proof of finiteness by indivisibles, 133-134
algebra, 56, 84-85, 86, 88, 90; see also negative numbers
and arithmetic, 85, 89, 227
and geometry, 57, 82, 227
of segments in Descartes, 66-68
algebraization of geometry and mathematics, 9, 84-86, 87
Alsted, J. H., 86
analysis
and synthesis, 3, 83-84, 100, 227
initesimal, 159, 162
Andersen, K., 35, 39, 40, 219, 220, 239
Anderson, A., 38
Angeli, S. degli, 220, 239
Apollonius, 10, 68
Archimedes, 10, 26, 29, 34-35, 38, 57, 58, 59, 60, 79, 94, 96, 97, 134, 171, 224
Aristotle, 6, 8, 16, 17, 94, 230, 240
no proportion between curve and straight, 77, 225
no proportion between finite and infinite, 139-140, 141, 214, 239
on direct proofs, 27
on proofs by contradiction, 115
on scientific knowledge, 10-12, 22, 64, 83, 103, 105
on uniqueness of definitions, 21, 98
arithmetic, 16, 17, 56; see also algebra and geometry, 66-67, 86-87, 145
of fractions, 85
Arnauld, A., 99
on congruency, 219
on demonstration, 7, 92, 93, 100-103, 106, 232, 234
on indivisibles, 237
on knowledge of infinity, 137, 142-143, 241
on negative numbers, 88-90, 228
Arndt, H. W., 227, 232
Auger, L., 230, 237
Averroës, 12, 17
axiom, 20, 21, 22, 129, 140
Barnes, J., 214
Baron, M., 230
Barozzi, F., 13, 15, 24, 25, 214, 215, 217
Barrow, I., 160
on algebra, 86, 87, 227
on causality in mathematics, 13, 19, 20-24, 26, 92, 93, 216
on congruency, 29, 56, 217, 219
on genetic definitions, 98-99
on mathematical existence, 20, 140-141, 215
on motion in geometry, 94, 95, 96-97, 230, 231
on ratios, 88, 228
on Tacquet's paradox, 124-125, 236
on Torricelli's acute hyperbolic solid, 138, 139-141, 240, 241
Bartholinus, E., 65
Bayle, P., 19, 24, 32, 143, 239

-267-

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Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
Table of contents

Table of contents

  • Title Page iii
  • Preface vii
  • Contents *
  • Introduction 3
  • 1 - Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century 8
  • 2 - Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity 34
  • 3 - Descartes' Géométrie 65
  • 4 - The Problem of Continuity 92
  • 5 - Paradoxes of the Infinite 118
  • 6 - Leibniz's Differential Calculus and Its Opponents 150
  • Appendix 178
  • Notes 213
  • References 249
  • Index 267
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