A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |
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... 258 Of Pneumatics Of the Siphon Of the Common Pump Of the Air - Pump Of the Barometer Of the Thermometer Diving Bell and Condenser Measurement of Altitudes by the Barometer and Thermometer Resistance of Fluids sin . A = sin . B. cos . c.
... 258 Of Pneumatics Of the Siphon Of the Common Pump Of the Air - Pump Of the Barometer Of the Thermometer Diving Bell and Condenser Measurement of Altitudes by the Barometer and Thermometer Resistance of Fluids sin . A = sin . B. cos . c.
Page 2
... measures of plane angles , ( the ratio of any two plane angles being constantly equal to the ratio of the two arcs of any circle whose centre is the angular point , and which are intercepted by the lines whose inclinations form the ...
... measures of plane angles , ( the ratio of any two plane angles being constantly equal to the ratio of the two arcs of any circle whose centre is the angular point , and which are intercepted by the lines whose inclinations form the ...
Page 6
... measure those angles , the results would evidently be similar : they may therefore be expressed generally by the two following equa- tions , for the sines and cosines of the sums or differences of any two arcs or angles . . sin . ( A ...
... measure those angles , the results would evidently be similar : they may therefore be expressed generally by the two following equa- tions , for the sines and cosines of the sums or differences of any two arcs or angles . . sin . ( A ...
Page 7
... ( measured by an arc greater than a quadrant ) has the same sine and cosine as its supplement ; the cosine , however , being reckoned sub- tractive or negative , because it is situated contrariwise with regard to the centre c . When the ...
... ( measured by an arc greater than a quadrant ) has the same sine and cosine as its supplement ; the cosine , however , being reckoned sub- tractive or negative , because it is situated contrariwise with regard to the centre c . When the ...
Page 18
... measured by arcs constituting a semicircle . So that , if radius be considered as unity , we shall find , that the sum of the tangents of the three angles of any plane triangle , is equal to the continued product of those tangents ...
... measured by arcs constituting a semicircle . So that , if radius be considered as unity , we shall find , that the sum of the tangents of the three angles of any plane triangle , is equal to the continued product of those tangents ...
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Common terms and phrases
absciss 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 plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinate 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 variable velocity vertex vertical plane vertical projections vibrations weight whole
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 469 - Or, by art. 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 299 - 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 158 - 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 249 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 301 - 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 254 - 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 494 - 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 461 - ... 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...