A Treatise on the Equilibrium of Arches: In which the Theory is Demonstrated Upon Familiar Mathematical PrinciplesPriestley and Weale, 1826 - 104 pages |
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Common terms and phrases
A B C D abutment angle B C architects axis bisected BO³ body bridge catenarian catenary centre of gravity circle Conic Sections consequently crown multiplied cube curve cycloid determine the height diagonal diameter of curvature dome Draw the tangent ellipse equal equi equilibration extrados Fluxions forces acting given horizontal course horizontal thrust indefinitely intrados joints lateral thrust length loading middle arch motion ordinate Palladio parabola parallel parallelogram perpendicular pier Plate polygon pressure produced proportional PROPOSITION quantity and direction radii radius of curvature represent the force represent the weight right angles roadway secant Sect semi-arch sides sine span stones supposed tangent CT tension thickness three forces tical tion TREATISE triangle trigonometry velocity vertex vertical direction vertical line voussoirs Westminster bridge Whence
Popular passages
Page 43 - ... the practical architect to adopt his visions, raised another system, which is said to secure a perfectly equilibrated structure, by making an equality at every point of the curve. The deduction from this theory consists in making the height of the wall incumbent on any point of the intrados, directly as the cube of the secant of the curve's inclination to the horizon at that point, or inversely as the radius of curvature there. It must be added, that this theory expects the joints of the voissoirs...
Page iii - Plates. A new Edition, with a Portrait and Life of the Author. 8vo. 14s. boards. A Treatise on the Equilibrium of Arches, in which the Theory is demonstrated upon familiar and mathematical Principles. Also the method of finding the drift or snoot of an Arch ; interspersed with practical Observations, illustrated by numerous Figures and three Plates.
Page 90 - A body immersed in a fluid, which is specifically lighter than itself, loses so much of its weight as is equal to the weight of a quantity of the fluid of the same bulk with itself.
Page 12 - The law of sines states that the sides of a triangle are proportional to the sines of their opposite angles. This law can be proved by applying the elementary formula for the area of a triangle ( 34 x base x altitude ) to triangle ABC in Fig.
Page 6 - ... would have sent it to A, or the force Y to D. " I will endeavour to prove this fact beyond all doubt. It is, I think, evident, that the force which acts in the direction BA can neither accelerate nor retard the approach of the body to the line D c, which is parallel to it; hence it will arrive at c in the same time that it would have done had no motion been communicated to it in the direction B A. In like manner, the motion in the direction BD can neither make the body approach to nor recede...
Page 3 - All motion or change of motion in a body is proportional to the force impressed and in the direction of that force.
Page 88 - consider the thrust to be resisted by the friction, which the stones, composing the pier, experience, sliding on each other. From experiments, it has been found that in some kind of stone the friction of one block moving horizontally on another = ¡ of the weight of the moving block.
Page x - to a young artist, might have been ruinous and it was fortunate for the author that his dependence was not on such patrons. The sapient body in question, have, however, been since that time sufficiently chastised for their mismanagement, by a committee of the House of Commons, which wisely took from them all controul over the rebuilding of the bridge, and placed it in more independent hands.
Page x - to a young artist, might have been ruinous, and it was fortunate for the author that his dependence was not on such patrons. The sapient body in question, have, however, been since that time sufficiently chastised for their mismanagement, by a committee of the House of Commons, which wisely took from them all controul over the rebuilding of the bridge, and placed it in more independent hands.
Page 78 - And there should not be a single stone in the arch but what is in thickness at least one tenth part of the chord of that arch; nor should the chord itself be longer than six times the thickness of the pier, nor shorter than four times.