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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Page 150
... or decrease , it is Variable Motion ; and it is called Accelerated Motion in the former case , and Retarded Motion in the latter . Also , when the moving body is considered with respect to some other body at rest , it is 150 MECHANICS .
... or decrease , it is Variable Motion ; and it is called Accelerated Motion in the former case , and Retarded Motion in the latter . Also , when the moving body is considered with respect to some other body at rest , it is 150 MECHANICS .
Page 151
... moving bodies , by which they continually tend from their present places , or with which they strike any obstacle that opposes their motion . 14. Forces are distinguished into Motive , and Accelera- tive or Retarding . A Motive or Moving ...
... moving bodies , by which they continually tend from their present places , or with which they strike any obstacle that opposes their motion . 14. Forces are distinguished into Motive , and Accelera- tive or Retarding . A Motive or Moving ...
Page 165
... moving from his place , and also by permitting a great many persons at once to exert their force on the rope at r , which they could not do to the weight itself ; as is evident in raising the hammer or weight of a pile - driver , as ...
... moving from his place , and also by permitting a great many persons at once to exert their force on the rope at r , which they could not do to the weight itself ; as is evident in raising the hammer or weight of a pile - driver , as ...
Page 168
... moving , the perp . descent of the power P , will be equal to 3 times as much as the perp . ascent of the weight w . For , though the weight w ascends up the direction of the oblique plane , BC , just as fast as the power P descends ...
... moving , the perp . descent of the power P , will be equal to 3 times as much as the perp . ascent of the weight w . For , though the weight w ascends up the direction of the oblique plane , BC , just as fast as the power P descends ...
Page 189
... moving about the angles A , F , k , F ' , A ' , we must , in order to equilibrium , balance the joint action of P and the semi . arch A at the point F , with the horizontal thrust before - men- Thus we shall have tioned , acting at the ...
... moving about the angles A , F , k , F ' , A ' , we must , in order to equilibrium , balance the joint action of P and the semi . arch A at the point F , with the horizontal thrust before - men- Thus we shall have tioned , acting at the ...
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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...