The positive philosophy of Auguste Comte;

Auguste Comte

Language:

English

Status:

Complete work

Authorship:

Written by the author

BOOK I. MATHEMATICS. CHAPTER I. mathkmatics, abstract and concrete. Description of Mathematics Object of Mathematics General Method E.xamples ..... True Definition of Mathematics Its two parts 37 37 38 38 40 41 C0^• TENTS. Their difterent oLjects Their different natures Concrete Mathematics Abstract Mathematics Extent of its domain Its Universality Its limitations . XXXlll PAGE 42 43 43 44 45 45 46 CHAPTER II. 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 ' . 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 valu

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