A Course of Mathematics for the Use of Academies, as Well as Private Tuition
S. Campbell & son, E. Duyckinck, 1822 - Mathematics
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Common terms and phrases
acting altitude axis ball base beam becomes body centre circle consequently Corol Cosine curve denote descending described determine diameter direction distance divided draw earth effect equal equation EXAM example expression fall feet figure fluent fluid fluxion force former given given plane gives gravity greatest half Hence horizontal horizontal plane inches increase length less manner means measured meet motion moving nature nearly parallel passing perpendicular plane position pressure PROBLEM produced projections proportion PROPOSITION quantity radius ratio resistance respectively right angles roots rule side sine solid space spherical square straight line supposed surface tangent theorem tion triangle velocity vertical weight whole
Page 437 - ... is equal to half the weight of a column of the fluid, whose base is equal to the surface pressed, and its altitude the same as that of the surface. Or, by art. 314 of the same, the pressure is equal to the weight of a column of the fluid...
Page 623 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the O's...
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 240 - Then say, As the weight lost in water, Is to the whole weight, So is the specific gravity of water, To the specific gravity of the body.
Page 167 - The screw is a spiral thread or groove cut round a cylinder, and every where making the same angle with the length of it. So that if the surface of the cylinder, with this spiral thread on it, were unfolded and stretched into a plane, the spiral thread would form a straight inclined plane, whose length would be to its height, as the circumference of the cylinder...
Page 155 - A LEVER 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. There are three kinds of levers.
Page 203 - The pressure of the fluid on any horizontal surface or plane, is equal to the weight of a column of the fluid, •whose base is equal to that plane, and altitude is its depth below the upper surface of the fluid.
Page 258 - ... preceding equation is only of the fourth power or degree ; but it is manifest that the above remark applies to equations of higher or lower dimensions : viz. that in general an equation of any degree whatever has as many roots as there are units in the exponent of the highest power of the unknown quantity, and...
Page 451 - ... increasing the charge, the velocity gradually diminishes, till the bore is quite full of powder. That this charge for the greatest velocity is greater as the gun is longer, but yet not greater in so high a proportion as the length of the gun is ; so that the part of the bore filled with powder, bears a less proportion to the whole bore in the long guns, than it does in the shorter ones ; the part which is filled being indeed nearly in the inverse ratio of the square root of the empty part.
Page 40 - In Every Spherical Triangle, the Sines of the Angles are Proportional to the Sines of their Opposite sides. If, from the first of the equations marked 1, the value of cos A be drawn, and substituted for it in the equation sin2 A = 1 — cos2 A, we shall have . , , cos2 a + cos