Families of Curves and the Origins of Partial Differentiation (Volume 93) (North-Holland Mathematics Studies, Volume 93)

This book provides a detailed description of the main episodes in the emergence of partial differentiation during the period 1690-1740. It argues that the development of this concept - to a considerable degree of perfection - took place almost exclusively in problems concerning families of curves. Thus, the book shows the origins of the ideas and techniques which paved the way for the sudden introduction of partial differential equations in 1750. The main methodological characteristic of the book is its emphasis on a full understanding of the motives, problems and goals of the mathematicians of that time. Content: Edited by Page iii Copyright page Page iv Acknowledgements Page v S.B. Engelsman Chapter 1 Introduction Pages 1-21 Chapter 2 Families of Curves in the 1690s Pages 22-58 Chapter 3 Orthogonal Trajectories 1694–1720 Pages 59-91 Chapter 4 Nicolaus I Bernoulli and Orthogonal Trajectories Pages 92-123 Chapter 5 Euler's Theory of Modular Equations in the 1730s Pages 124-160 Epilogue Pages 161-162 Footnotes Chapter 1 Pages 163-165 Footnotes Chapter 2 Pages 166-175 Footnotes Chapter 3 Pages 176-184 Footnotes Chapter 4 Pages 185-189 Footnotes Chapter 5 Pages 190-198 Appendix 1 Nicolaus I Bernoulli's “Demonstratio Analytica Constructionis Curvarum, Quae Alias Positione Datas Ad Angulos Rectos Secant, Traditae in Actis Lips. 1719 Pag 295 Et Seqq.” Pages 199-203 Appendix 2 Leonhard Euler's “De Differentiatione Functionum Duas Pluresve Variabiles Quantitates Involventi Um” Pages 204-222 Appendix 3 Newton's Rule for the Radius of Curvature of May 21st, 1665 Pages 223-226 Bibliography Review Article Pages 227-238