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GENERAL VIEW OF MATHEMATICAL ANALYSIS 45
THE TRUE IDEA OF AN EQUATION 46 Division of Functions into Abstract and Concrete 47 Enumeration of Abstract Functions 50
DIVISIONS OF THE CALCULUS 53 The Calculus of Values, or Arithmetic 57 Its Extent 57 Its true Nature 59 The Calculus of Functions 61 Two Modes of obtaining Equations 61 1. By the Relations between the given Quantities 61 2. By the Relations between auxiliary Quantities 64 Corresponding Divisions of the Calculus of Functions 67
ORDINARY ANALYSIS; OR, ALGEBRA. 69
Its Object 69 Classification of Equations 70
ALGEBRAIC EQUATIONS 71 Their Classification 71
ALGEBRAIC RESOLUTION OF EQUATIONS 72 Its Limits 72 General Solution 72 What we know in Algebra 74
NUMERICAL RESOLUTION OF EQUATIONS 75 Its limited Usefulness 76 Different Divisions of the two Systems 78
THE THEORY OF EQUATIONS 79
THE METHOD OF INDETERMINATE COEFFICIENTS 80
NEGATIVE QUANTITIES 81
THE PRINCIPLE OF HOMOGENEITY 84