# A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes

W. E. Dean, 1831 - Mathematics

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### Contents

 Spherical Trigonometry 26 Resolution of Spherical Triangles 40 Geodesic Operations 60 Problems in Trigonometrical Sur 72 On Algebraical Equations 99 Nature and Properties of Curves 114 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 264 Of the Siphon 273 Of the Baronmeter 279

 Centre of Gravity 172 Equilibrium of Arches 180 Dynamics 189
 Motion of Machines and their 446 Crifices in their Bases 562 Additions to Geodesic Operations 575

### Popular passages

Page 463 - Or, by an. 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 203 - VI, its Corollaries and Scholium, for Constant Forces, are true in the Motions of. Bodies freely descending by their own Gravity ; namely, that the Velocities are as the Times, and the Spaces as the Squares of the Times, or as the Squares of the Velocities. FOR, since the force of gravity is uniform, and constantly the same, at all places near the earth's surface, or at nearly the same distance from the centre of the earth ; and since • this is the force by which bodies descend to the surface ;...
Page 247 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 297 - 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 35 - Two planes are said to have the same or a like inclination to one another which two other planes have, when the said angles of inclination are equal to one another.
Page 83 - Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, on the surface of a sphere whose radius is r ; then...
Page 389 - Multiply the number in the table of multiplicands, by the breadth and square of the depth, both in inches, and divide that product by the length, also, in inches; the quotient will be the weight in Jbs.t Example 1.
Page 252 - 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 148 - Body is either Hard, Soft, or Elastic. A Hard Body is that whose parts do not yield to any stroke or percussion, but retains its figure unaltered. A Soft Body is that whose parts yield^to any stroke or impression, without restoring themselves again ; the figure of the body remaining altered.