A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |
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... Curves 364 189 Quadrature of Curves 367 195 Surfaces of Solids 369 Computation of Logarithms 371 204 Inflexion of Curves - 376 218 Radius of Curvature 378 Involutes and Evolutes 380 232 Centre of Gravity $ 83 234 Pressure of Earth ...
... Curves 364 189 Quadrature of Curves 367 195 Surfaces of Solids 369 Computation of Logarithms 371 204 Inflexion of Curves - 376 218 Radius of Curvature 378 Involutes and Evolutes 380 232 Centre of Gravity $ 83 234 Pressure of Earth ...
Page 37
... curve surfaces , such as the angles at the vertices of cones ; they will manifestly be mea- sured by the spheric surfaces cut off by the prolongation of their bounding surfaces , in the same manner as angles deter- mined by planes are ...
... curve surfaces , such as the angles at the vertices of cones ; they will manifestly be mea- sured by the spheric surfaces cut off by the prolongation of their bounding surfaces , in the same manner as angles deter- mined by planes are ...
Page 63
... curve of double curvature ; but if the earth be a solid of revolution , the terrestrial meridian will be a plane curve . 5. If the earth were a sphere , then every point upon a terrestrial meridian would be at an equal distance from the ...
... curve of double curvature ; but if the earth be a solid of revolution , the terrestrial meridian will be a plane curve . 5. If the earth were a sphere , then every point upon a terrestrial meridian would be at an equal distance from the ...
Page 64
... curve differs a little from the terrestrial meridian , when the earth is not a solid of revolution : yet , in the real state of things , the dif- ference between the two curves is so extremely minute , that it may safely be disregarded ...
... curve differs a little from the terrestrial meridian , when the earth is not a solid of revolution : yet , in the real state of things , the dif- ference between the two curves is so extremely minute , that it may safely be disregarded ...
Page 65
... curves are plane and circular . 8. The situation of a place is determined , when we know either the individual perpendicular to the meridian , or the individual parallel to the equator , on which it is found , and its position on such ...
... curves are plane and circular . 8. The situation of a place is determined , when we know either the individual perpendicular to the meridian , or the individual parallel to the equator , on which it is found , and its position on such ...
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Common terms and phrases
absciss altitude axis ball base beam becomes body centre of gravity circle conic surface consequently Corol cosine curve cylinder denote density descending determine diameter direction distance draw earth equa equal equation equilibrio EXAM expression feet find the fluent fluid force given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinate parabola parallel pendulum perpendicular position pressure prob PROBLEM PROP proportional quantity radius ratio rectangle resistance right angles right line roots Scholium side sine solid angle space specific gravity spherical excess spherical triangle square straight line supposed surface tangent theorem theref tion variable velocity vertex vertical plane vertical projections vibrations weight whole
Popular passages
Page 13 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 469 - Or, by art. 249 of the same, the pressure is equal to the weight of a column of the fluid...
Page 74 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Page 299 - The workmen thought that substituting part silver was only a proper <perquisite; which taking air, Archimedes was appointed to examine it ; who, on putting...
Page 158 - MECHANICAL POWERS are certain simple instruments employed in raising greater weights, or overcoming greater resistance than could be effected by the direct application of natural strength. They are usually accounted six in number; viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.
Page 249 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 301 - In the doctrine of fluxions, magnitudes or quantities of all kinds are considered as not made up of a number of small parts, but as generated by continued motion, by means of which they increase or decrease ; as a line by the motion of a point ; a surface by the motion of a line ; and a solid by the motion of a surface.
Page 254 - Weigh the denser body and the compound mass, separately, both in water, and out of it ; then find how much each loses in water, by subtracting its weight in water from its weight in air; and subtract the less of these remainders from the greater. Then...
Page 494 - The reason is, all bodies lose some of their weight in a fluid, and the weight which a body loses in a fluid, is to its whole weight, as the specific gravity of the fluid is to that of the body.
Page 461 - ... horizontal *. 2. The theorems just given may serve to show, in what points of view machines ought to be considered by those who would labour beneficially for their improvement. The first object of the utility of machines consists in furnishing the means of giving to the moving force the most commodious direction ; and, when it can be done, of causing its action to be applied immediately to the body to be moved. These can rarely be united : but the former can be accomplished in most instances...