The Orgins of the Infinitesimal Calculus Book

	Preface	vii
	Introduction	1
Chapter 1.	Greek Mathematics	11
1.0	Introduction	11
1.1	The influence of Greek mathematics in the seventeenth century	14
1.2	A brief chronology of Greek mathematics	15
1.3	Early Greek mathematics and the physical world	18
1.4	The axiomatisation of Greek mathematics	25
1.5	The theory of proportion and means	27
1.6	The squaring of the circle	30
1.7	The method of exhaustion	34
1.8	The discovery method of Archimedes	46
1.9	Curves, normals, tangents and curvature	51
Chapter 2.	The Transition to Western Europe	60
2.0	Introduction	60
2.1	On Hindu mathematics	61
2.2	The Arabs	66
2.3	The influence of Aristotle	69
2.4	The continuum, indivisibles and infinitesimals	71
2.5	The growth of kinematics in the West	75
2.6	The latitude of forms	81
2.7	The function concept in the fourteenth and fifteenth centuries	87
2.8	Conclusion	89
Chapter 3.	Some Centre of Gravity Determinations in the Later Sixteenth Century	90
3.0	Introduction	90
3.1	Francesco Maurolico (1494-1575)	91
3.2	Federigo Commandino (1509-1575)	94
3.3	Simon Stevin (1548-1620)	96
3.4	Luca Valerio (1552-1618)	101
Chapter 4.	Infinitesimals and Indivisibles in the Early Seventeenth Century	108
4.1	Johann Kepler (1571-1630)	108
4.2	Indivisibles in Italy	116
4.3	Bonaventura Cavalieri (1598-1647)	122
4.4	Gregoire de Saint-Vincent (1584-1667)	135
Chapter 5.	Further Advances in France and Italy	149
5.0	Introduction	149
5.1	The arith metisation of integration methods	151
5.2	First investigations of the cycloid	156
5.3	Another integration method	162
5.4	The concept of tangent	163
5.5	The composition of motions	174
5.6	The link between differential and integral processes	177
5.7	Evangelista Torricelli: tangent and quadrature	182
Chapter 6.	Consolidation of Gains: France, England and the Low Countries	195
6.0	Introduction	195
6.1	Blaise Pascal (1623-1662)	196
6.2	Infinitesimal methods in England	205
6.3	Infinitesimal methods in the Low Countries	214
6.4	The rectification of arcs	223
6.5	James Gregory (1638-1675)	228
6.6	Isaac Barrow (1630-1677)	239
Chapter 7.	Epilogue: Newton and Leibniz	253
7.0	Introduction	253
7.1	Isaac Newton (1642-1727)	255
7.2	Gottfried Wilhelm Leibniz (1646-1716)	268
	Bibliography	291
	Index	299