Contents 18.Mathematics as of 1700,391 IThe Transtormation of Mathematics.391 2 Mathematics and Scienc.394 19.Calculus in the Eighteenth Century,400 1 Inuoduction.400 2 The Function Concept,403 3 The'Techniqueof Integratior and Complex Quantitics.406 4 Elliptic Integrals,411 Further Spccial Functions 422 6 The (akulus of Functions of Several Variables,425 Supply Rigor in the Calculus,426 20.Infinite Series,436 1 Introduction,436 2 Initial Work on Infinite Series.436 3.The Expansion of Functions,440 4 'I he Manipulation of Series,422 5 Trigonometric Serics,454 6 Continued hractions,459 7 The Problem of Convergence and Divergence,460 21.Ordinary Differential Equations in the Eighteenth Century,468 cond Order Ea tations,484 6 The Method of Series,488 7 Systems of 22.Partial Differential Equations in the Eighteenth Century,502 6 heory.52 Monge and the haxtemo Systems of Fi Mathematical Subject,542 23.Analytic and Differential Geometry in the Eighteenth Century,544 5.555 6