Produced by Anna Hall, Albert László and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive) THE PHILOSOPHY OF MATHEMATICS. THE SCIENCE OF MATHEMATICS. | +----------------------+-------------------+ | | | | ABSTRACT MATHEMATICS. CONCRETE MATHEMATICS. | | | | | +-------+------+ | | | ANALYSIS; _or_, _The Calculus_. GEOMETRY. MECHANICS. | | | | +-------+----------+ +-------+---------+ | | | | =Ordinary =Transcendental =Synthetic= =Analytic= Analysis=; Analysis=; _or Special_ _or General_ _or_, _Calculus _or_, _Calculus =Geometry=. =Geometry=. of Direct of Indirect | | Functions_. Functions_. | | | | | | +--+--+ +-----+--+ +----+----+ +---+---+ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Algebra. | Calculus | Algebraic. | Of three | | of | Trigonometry. | dimensions. | | Variations. | | | | | | Arithmetic. Differential Graphical. Of two and Integral Descriptive dimensions. Calculus. Geometry. THE PHILOSOPHY OF MATHEMATICS; TRANSLATED FROM THE COURS DE PHILOSOPHIE POSITIVE OF AUGUSTE COMTE, BY W. M. GILLESPIE, PROFESSOR OF CIVIL ENGINEERING & ADJ. PROF. OF MATHEMATICS IN UNION COLLEGE. NEW YORK: HARPER & BROTHERS, PUBLISHERS, 82 CLIFF STREET 1851. Entered, according to Act of Congress, in the year one thousand eight hundred and fifty-one, by HARPER & BROTHERS. in the Clerk's Office of the District Court of the Southern District of New York. PREFACE.