The positive philosophy of Auguste Comte;

BOOK I. MATHEMATICS. mathkmatics, abstract and concrete. Description of Mathematics Object of Mathematics General Method E.xamples ..... True Definition of Mathematics Its two parts C0^• TENTS. Their difterent oLjects Their different natures Concrete Mathematics Abstract Mathematics Extent of its domain Its Universality Its limitations . XXXlll general view of mathematical analysis. Analysis . True idea of an equation Abstract functions . Concrete functions . Two parts of the Calculus Algebra . Arithmetic Its extent . Its nature . Algebra . Creation of new functions . . • • Finding equations between auxiliary quantities Division of the Calculus of functions . . Section 1. Ordinary Analysis, or Calculus of Direct tions ....•••• Its object ...••••• Classihcation of Equations .... Algebraic equations Algebraic resolution of equations . Om- existing knowledge . . . . • Numerical resolution of equations . The Theory of equations . _. _ . Method of indeterminate coefficients • , , • Section 2. Transcendental Analysis, or Calculus Functions . . Three principal views History ' . Method of Leibnitz . Generality of the formulas Justification of the Method Newton's Method. Method of Limits Fluxions and Ihients. Lagkange's Method . Identity of the three methods Their comparative value . - The Differenti.al and Integral Calculus Its two parts I. C of Indirect Tlieir mutual relations Cases of union of the two. Cases of the Differential calculus alone Cases of the Integral calculus alone. The Differential Cdlculus. Two ])ortions .... Subdivisions .... Reduction to the elements Transformation of derived functions for new variables Analytical applications . The Integral Caleulus Its divisions .... Subdivisions .... One variable or several Orders of differentiation . Quadratures .... Algebraic functions . Transcendental functions . Singular Solutions .…