## A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |

### From inside the book

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**Logarithms**371 204 Inflexion of Curves - 376 218 Radius of Curvature 378 Involutes and Evolutes 380 232 Centre of Gravity 383 234 Pressure of Earth against Walls 386 Flexibility and Strength of Tim- 235 ber 390 244 247 257 Practical ... Page 18

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**logarithms**, as frequently happens in geodesic opera . tions , tan ( A - B ) may be readily determined without first finding the number corresponding to the logs . of a and b . For if a and b were considered as the sides of a right ... Page 19

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**logarithmic**com- putation , ( however well fitted they are for instruments of in- vestigation ) , another may be deduced thus : In the equation b2 + c2 — a2 for cos . A , ( given equation 11 ) , viz . cos a = if we 26c " substitute ... Page 22

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**logarithms**would be negative . To avoid this , the tables of**logarithmic**sines , cosines , & c . are comput- ed to a radius of 10000000000 , or 10to ; in which case the lo- garithm of the radius is 10 times the log of 10 , that is , it ... Page 24

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**logarithms**of two sides of a triangle are 2-2407293 and 2.5378191 , and the included angle is 37 ° 20 ′ . It is required to determine the other angles , without first find- ing any of the sides ? Ex . 17. The sides of a triangle are to ...### Other editions - View all

### Common terms and phrases

abscissas 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 fluxion given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinates 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 velocity vertex vertical plane vertical projections vibrations weight whole

### Popular passages

Page 467 - 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 393 - 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.