CONTAINING MANY VALUABLE DISCOVERIES AND IMPROVEMENTS IN MATHEMATICAL COMPENDIUM OF MENSURATION. BY NATHAN SCHOLFIELD. NEW YORK: PUBLISHED BY COLLINS, BROTHER & CO. No. 254 Pearl Street. Entered according to Act of Congress, in the year 1845, by NATHAN SCHOLFIELD, G. W. WOOD, PRINTER, 29 GOLD ST., NEW YORK. PREFAOE. 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 properțies of the parabolic, elliptical, and hyperbolic curves, being such as are formed by the sections of a cone, and hence are usually de. nominated 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. |