A Course of Mathematics: For the Use of Academies, as Well as Private Tuition, Volume 2

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Contents

 Spherical Trigonometry 26 Geodesic Operations 6 34 Problems in Trigonometrical 72 On Algebraical Equations 99 Nature and Properties of Curves 114 Construction of Equations 137 Mechanics Definitions c 149 Parallel Forces c 158
 Collision of Bodies 195 Laws of Gravity Falling Bodies 218 Central Forces 232 Ballistic Pendulum 244 Buoyancy of Pontoons 257 Of Pneumatics 2 264 Of the Siphon 273 TMetion of Mechines and their 464 Of the Baronmeter 279 Promiscuous Exercises 477

 Centre of Gravity 172 Equilibrium of Arches 180 Dynamics 189
 Of the Thermometer 280 On the Exhaustion of Wessels 562 Resistance of Fluids 283 575

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 465 - Or, by art. 249 of the same, the pressure is equal to the weight of a column of the fluid...
Page 70 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Page 295 - 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 154 - 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 245 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 297 - 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 250 - 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 490 - 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 457 - ... 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...