# A Course of Mathematics: For the Use of Academies as Well as Private Tuition. In Two Volumes, Volume 2

W. E. Dean, 1831
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### Contents

 ANALYTICAL Trigonometry 14 Resolution of Spherical Triangles 40 Geodesic Operations 60 On Algebraical Equations 114 Mechanics Definitions 149 Mechanical Powers 158 Centre of Gravity 189 Collision of Bodies 195
 Measurement of Altitudes by 281 150 301 292 319 Pressure of Earth against Walls 386 Flexibility and Strength of Tim 396 The Motion of Bodies in Fluids 425 Cohesive Force of Substances 439 Motion of Machines and their 446

 Ballistic Pendulum 218 Central Forces 232 Of Hydrostatics 247 Buoyancy of Pontoons 257 Of Pneumatics 264
 281 464 Promiscuous Exercises 476 280 523 Additions to Geodesic Operations 575

### 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...