A Course of Mathematics: For the Use of Academies as Well as Private Tuition, Volume 2
Campbell, 1812 - Mathematics
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acting altitude angle axis ball base beam becomes body centre circle consequently constant Corol cosine curve denote descending described determine diameter direction distance divided draw earth effect elevation equal equation Exam example experiments expression fall feet figure fluent fluid fluxion force former given gives gravity greater greatest half Hence horizontal inches increase latter length less manner means measured motion moving nature nearly parallel pass perpendicular plane positive pressure PROBLEM proportional PROPOSITION quantity radius range ratio resistance respectively roots rule sides sine solid space spherical square strength stroke substituted supposed surface taking tangent theorem third tion triangle velocity vibrations weight whole
Page 435 - Or, by art. 3 14 of the same, the pressure is equal to the weight of a column of the fluid...
Page 11 - 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 153 - 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 239 - 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 238 - As the weight lost in water is to the whole, or absolute weight ; so is the specific gravity of water ' " to "the specific gravity 'of the body . 2.
Page 153 - LBVER is any inflexible rod, bar, or beam, which serves to raise weights, while it is supported at a point by a fulcrum or prop, which is the centre of motion. The lever is supposed to be void of gravity or weight, to render the demonstrations easier and simpler.
Page 449 - It has been found, by these experiments, that no difference is caused in the velocity, or range, by varying the weight of the gun, nor by the use of wads, nor by different degrees of ramming, nor by firing the charge of powder in different parts of it.
Page 80 - The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 302 - ... 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 126 - 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...