代微积拾级/说明

ALGEBRAIC GEOMETRY，WITH DIFFERENTIAL AND INTEGRAL CALCULUS

The present work, which is a translation of Loomis' ANALYTICAL GEOMETRY, AND DIFFERENTIAL AND INTEGRAL, CALCULUS, is issued in pursuance of a project formed some time since, as the continuation of a course of mathematics, the first of which, a Compendium of Arithmetic, was published by the undersigned in 1854. The next in order is a Treatise on Algebra, which should have preceded this, but in consequence of unavoidable delays in the publication, it will not be issued till some weeks later. A tolerable acquaintance with the last-named treatise will put the student in a position to understand the work now presented to the public. Although this is the first time that the principles of Algebraic Geometry have been placed before the Chinese (so far as the translator is aware), in their own idiom, yet there is little doubt that this branch of the science will commend itself to native mathematicians, in consideration of its obvious utility; especially when we remember the readiness with which they adopted Euclid's Elements of Geometry, Computation by Logarithms, and other novelties of European introduction. A spirit of inquiry is abroad among the Chinese, and there is a class of students in the empire, by no means small in number, who receive with avidity instruction on scientific matters from the West. Mere superficial essays and popular digests are far from adequate to satisfy such applicants; and yet when anything beyond that is attempted, the want of a common medium of communication at once appears as an insuperable obstacle; and it is evident that how clearly soever we may be enabled to lay results before the native mind, yet until they understand something of the processes by which such results are obtained, thinkers of the above class can scarcely be supposed to appreciate the achievements of modern science, to repose absolute confidence in the results, or to rest satisfied till they are in a position to some extent to verify the statements which are laid before them. It is hoped that the present translation will in some measure supply what is now a desideratum; and the translator, while taking this opportunity to testify to the exceeding care and accuracy displayed in the work of Professor Loomis, considers it is but justice to the native scholar Le Shen-lan, who has assisted in the translation throughout, to state that whatever degree of perfection this version may have attained, is almost entirely due to his efforts and talents.

A list of technical terms used in the works above-named is subjoined.