THE
PHILOSOPHY
OF
MATHEMATICS.
THEPHILOSOPHYOFMATHEMATICS;
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.
The pleasure and profit which the translatorhas received from the great work here presented,have induced him to lay it before his fellow-teachersand students of Mathematics in a more accessibleform than that in which it has hitherto appeared.The want of a comprehensive map of thewide region of mathematical science—a bird's-eyeview of its leading features, and of the true bearingsand relations of all its parts—is felt by everythoughtful student. He is like the visitor to agreat city, who gets no just idea of its extent andsituation till he has seen it from some commandingeminence. To have a panoramic view of thewhole district—presenting at one glance all theparts in due co-ordination, and the darkest nooksclearly shown—is invaluable to either traveller orstudent. It is this which has been most perfectlyaccomplished for mathematical science by theauthor whose work is here presented.
Clearness and depth, comprehensiveness andprecision, have never, perhaps, been so remarkablyunited as in Auguste Comte. He views his subjectfrom an elevation which gives to each part ofthe complex whole its true position and value,while his telescopic glance loses none of the needfuldetails, and not only itself pierces to the heart[Pg 6]of the matter, but converts its opaqueness intosuch transparent crystal, that other eyes are enabledto see as deeply into it as his own.
Any mathematician who peruses this volumewill need no other justification of the high opinionhere expressed; but others may appreciate thefollowing endorsements of well-known authorities.Mill, in his "Logic," calls the work of M. Comte"by far the greatest yet produced on the Philosophyof the sciences;" and adds, "of this admirablework, one of the most admirable portions is thatin which he may truly be said to have created thePhilosophy of the higher Mathematics:" Morell,in his "Speculative Philosophy of Europe," says,"The classification given of the sciences at large,and their regular order of development, is unquestionablya master-piece of scientific thinking, assimple as it is comprehensive;" and Lewes, inhis "Biographical History of Philosophy," namesComte "the Bacon of the nineteenth century,"and says, "I unhesitatingly record my convi