A NEW AND EASY SYSTEM OF LINES, FOUNDED ON GEOMETRICAL TO WHICH IS ADDED A COMPLETE TREATISE ON MATHEMATICAL INSTRUMENTS. ALSO, MENSURATION, TABLES OF THE WEIGHTS AND COHESIVE STRENGTH OF THE SEVERAL MATERIALS USED IN THE CONSTRUCTION OF BUILDINGS, &C. BY LUCIUS D. GOULD, ARCHITECT. NEW-YORK: PUBLISHED BY DANIEL BURGESS & CO., 60 JOHN-STREET. 1853. Ena 688.53 F Eng HARVARD UNIVERSITY AOL OF ENGINEERIN JUN 20 1917 TRANSFERRED TO ENTERED according to Act of Congress, in the year one thousand eight hundred and fifty-three BY LUCIUS D. GOULD, In the Clerk's Office of the District Court of the United States for the District of New Jersey. J. P. JONES & CO., STEREOTYPERS, 183 William-st., N. Y. C. A. ALVORD, PRINTER, 38-257 13 PREFACE. THE object of this work is to furnish House Carpenters with the practical directions necessary to find the lines for cutting every description of joint, as well as for framing the most difficult roofs, according to a new and easy system, founded on accurate geometrical principles. For more than twenty years, the author has applied the rules here laid down, to the framing and connecting of timbers; to the framing and constructing of roofs; to the mitering of planes and irregular surfaces at any angle; to the mitering of circles, and to finding the joints in every variety of splayed work; also to the elevations of the frame work of roofs, and to ascertaining the relative sizes required to support a given weight. Together with these rules, the author also presents tables of the weight and cohesive strength of the different materials used in the construction of buildings, as well as the weight required to crush said materials. And to all this is added a complete treatise on mathematical instruments. There can be little doubt that a work of this kind is very much needed by carpenters and builders, especially by those who are inexperienced in the different kinds of labor which they are liable to be called upon to perform. Many a journeyman carpenter has found himself suddenly thrown out of employment, simply because he was ignorant of the rules by which he should perform some required task. It is rather for the benefit of such, than for the experienced workman, that this volume is designed; and should it be the means of promoting their interest, or inciting them to a study of the noble science upon which these arts are founded, the author will feel well compensated for his labor. It is but due to acknowledge, that the valuable works of Mr. PETER NICHOLSON and THOMAS TREDGOLD, have been freely consulted in the preparation of this volume. NEWARK, N. J., May, 1853. GEOMETRICAL DEFINITIONS. PLATE I. 1. A point is that which has position, but not magnitude. 2. A line, Fig. 1, is length without breadth. 3. A surface, Fig. 2, or superfices, is that which has length and breadth, but not thickness. 4. A body, Fig. 3, or solid, is that which has length, breadth and thickness. 5. Lines are either right or curved, Figs. 7 and 8. 6. A right line, or straight line, lies all in the same direction between its extremities, and is the shortest distance between two points, Fig. 1. 7. A curve continually changes its direction between its extreme points, Fig. 7. 8. Lines are either parallel, oblique, perpendicular, or tangential. 9. Parallel lines, Figs. 7 and 8, are always at the same perpendicular distance, and, if produced, would never meet. 10. Oblique lines, Fig. 9, change their distance, and would meet, if produced, on the side of the least distance. 11. One line is perpendicular to another when it inclines not more on the one side than the other, or when the angles on both sides of it are equal, Fig. 11. 12. A line or circle is tangential, Fig. 10, or a tangent to a circle or other curve, when it touches it without cutting, if both are produced. 13. An angle is the opening between two lines having different directions and meeting at the same point, Fig. 9. |