QA 529 S37 pt.3 Entered according to Act of Congress, in the year 1845, by NATHAN SCHOLFIELD, In the Clerk's Office of the District Court of Connecticut. G. W. WOOD, PRINTER, 29 GOLD ST., NEW YORK. Peszerela 10-9=41 44074 PREFACE. THIS part of the series consists of spherical geometry, taken mostly from Brewster's translation of Legendre's work. Analytical plane and spherical trigonometry, based on the subject, as found in Rutherford's edition of Hutton's Mathematics, being originally abridged from the larger works of Cagnoli, and others; but, in this work, much improved and enlarged. To which are added many practical exercises on the subject, by way of application. In this treatise will be found many curious and highly useful problems in trigonometrical surveying, and topographical operations, not before published. The properties of the circle are introduced advantageously into trigonometrical problems-hence we are enabled, by geometrical construction, and trigonometrical analysis, to determine many otherwise extremely difficult problems, in a manner at once simple, elegant, and satisfactory. The application of algebra to geometry, is discussed in such manner as to combine the principles of the two sciences. The properties of the parabolic, elliptical, and hyperbolic curves, being such as are formed by the sections of a cone, and hence are usually denominated conic sections, are also discussed. This subject is, with some alterations and additions, taken from Rutherford's edition of Hutton's Mathematics. It is the design of the author, to preserve an unbroken connection from pure elementary to the higher Geometry and mensuration; and with this object in view the present volume, being the third part of the series, is prepared. The well established reputation and the high respectability of the authors from whom our selections have been made, renders it unnecessary for us to discuss their merits in order to secure a favorable reception of this. It will only be necessary for us, in the following pages, to preserve the same degree of accuracy and perspicuity in our digressions as characterise those works, and we shall have nothing to fear from the criticisms of scientific amateurs and mathematicians. |