APPLIED TO THE MENSURATION OP LINES, SURFACES, SOLIDS, HEIGHTS AND DISTANCES. BY B. FRANKLIN CALLENDER, Late Master of the Mathematical Department, Wells School, Boston. "In His hand, He took the golden compasses, One foot he centred, and the other turn'd And said, 'Thus far extend, thus far thy bounds, NEW-YORK: CHARLES S. FRANCIS-252 Broadway. 1.3459 1886, Mar.19. Gift of Dr. S. B. Green, Entered according to Act of Congress, in the year 1836, by In the Clerk's office of the District Court of Massachusetts. PREFACE. ! A FEW years ago, the author of the following work instructed a class of young men in Geometry and Mensuration. At that time, no suitable text book could be found of a sufficiently practical character to meet the wants of either the instructer or pupils in this branch of mathematics; and the only alternative was to use the best which could be procured, and supply the deficiency by preparing a written manuscript. That manuscript forms the foundation of the present treatise. Contributions have, from time to time, been made to the work, till the last year, during which it has received the almost exclusive attention of its author. At the urgent solicitation of several gentlemen who have examined the work, it is now presented to the public, with the belief that it will supply a want which has long been experienced; the want of a work containing a familiar illustration of the principles of Geometry, with a practical application of them to the Mensuration of lines, surfaces, and solids; and the general adaptation of the whole to the common purposes and business of life. Such has been the design of the author in the following work. How far that object has been accomplished, those for whom it has been prepared must decide. Simplicity in arrangement, perspicuity in illustration, and familiarity in the use of terms, are points which have been kept constantly in view. In the following treatise, the principles are presented in an improved and intelligible form; and some of them have never before appeared in any similar work. The Rules for finding the sum, the difference, and the product of the squares of numbers, without finding their squares - The Rule for finding the solidity of a wedge - The Rules for finding the chord of an arc of a circle, and for the construction of an ellipsis, are among the latter. The Rule for the Mensuration of loads of wood for fuel, is brief, simple, and easily applied. In Duodecimals, or multiplication of feet, inches, and parts, it is believed that an essential improvement has been made; rendering that difficult, and, to some, almost inexplicable operation, plain and intelligible. In Common and Decimal Fractions the operations are clear and perspicuous, and may be understood and applied as easily as similar operations upon whole numbers. These, with the Extraction of the Square and Cube Roots, form an important and indispensable introduction to Mensuration, Surveying, Navigation, and other practical branches of mathematics, and are recommended to the attentive examination of the student. There are upwards of seven hundred practical questions and illustrations, relating to the business of the Architect Surveyor, Carpenter, Mason, Painter, Glazier, and other branches of mechanical operation. To the Agricultural, Mercantile, and Commercial community, this work will afford much useful information, applicable to their respective branches of labor and enterprise. The sublime truths of mathematics, emanating, as they do, immediately from the "Great Geometer" of the Universe, and incapable either of improvement or alteration by any human mind, should not be concealed within literary palaces, nor obscured by the mist of technical phraseology when permitted to go out. They are the common property of all, and should be diffused as freely as the vital air, and the light of heaven; that all may comprehend, admire, and enjoy them. In a society, such as the American public, distinguished for the general diffusion of knowledge, every attempt to radiate and extend the light of science will be duly appreciated; and he who dispels the darkness of ignorance from a single human mind, and supplies it with the light of truth, will not be unrewarded. JULY 1, 1836. B. F. C. |