JAMES MUNROE AND COMPANY. NEW YORK: COLLINS, BROTHER, AND COMPANY. Entered according to Act of Congress, in the year 1837, by JAMES MUNROE AND COMPANY, in the Clerk's office of the District Court for the District of Massachusetts. 05-8-45 ADE THE use of infinitely small quantities, which was first introduced into the higher departments of Mathematics, has been gradually creeping downwards, and elementary writers are rapidly becoming reconciled to it. But at the same time, the uncompromising advocates of the ancient rigor of demonstration have, by their attacks, induced some mathematicians to waste much time in disguising the principles of the Differential Calculus under a form of words, in which the term "infinitely small" does not occur. The value of this labor may be duly estimated from the inconsistency of one, who has ostensibly discarded the infinitesimal doctrine from his theory of the Calculus, and introduced it into his treatise of Geometry. With all its boasted rigor, the ancient Geometry can indeed lead to no result more accurate, none more to be depended upon, than those of the infinitesimal theory; and I doubt if any well constituted mind, well constituted at least for mathematical investigations, ever reposes with any more confidence upon the one than upon the other. If there were |