Page:The Sources of Standard English.djvu/461

24 A judicious combination of both methods is doubtless the best; and it is hoped that this result may be arrived at in some degree by the use of this book, which is simply a collection of examples, with helps for solution, ''arranged in progressive sections. The new edition has been enlarged by the'' addition of chapters on the straight line and plane, with explanatory dia&shy;grams and exercises on tangent planes, and on the cases of the spherical triangle.

The object of the author in writing on this subject has mainly been to place it on a basis altogether independent of the ordinary Cartesian system, instead of regarding it as only a special form of Abridged Notation. A short chapter on Determinants has been introduced.

The author has written this book under the conviction that the skill and power of the young mathematical student, in order to be thoroughly ''available afterwards, ought to be developed in all possible directions. The'' subject which he has chosen presents so many faces, that it would be difficult to find another which, with a very limited extent of reading, combines, to the same extent, so many valuable hints of methods of cal&shy;culations to be employed hereafter, with so much pleasure in its present ''use. In order to understand the work it is not necessary to have much'' knowledge of what is called Higher Algebra, nor of Algebraical Geometry of a higher kind than that which simply relates to the Conic Sections. From the study of a work like this, it is believed that the student will ''derive many advantages. Especially he will become skilled in making'' correct approximations to the values of quantities, which cannot be found exactly, to any degree of accuracy which may be required.