A new treatise on mechanics, by the author of A new introduction to the mathematics

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Whittaker, 1841 - 184 páginas
 

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Página 162 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 24 - In any proportion, the product of the means is equal to the product of the extremes.
Página 180 - ... we substitute the causes which produce them, it may be said that the accelerative force is as the moving force directly, and the quantity of matter moved inversely,
Página 157 - THE WEDGE. The wedge is a double inclined plane, consequently its principles are the same : Hence when two bodies are forced asunder by means of the wedge in a direction parallel to its head, — Multiply the resisting power by half the thickness of the head or back of the wedge, and divide the product by the length of one of its inclined sides ; the quotient is the force equal to the resistance.
Página 33 - ... passed over in the 4th second is seven times that passed over in the 1st ; that the space of the 5th second is nine times that of the first ; and the space of the 6th second eleven times that of the first. Hence, we arrive at the important conclusion that the spaces described in the succeeding seconds increase in the ratio of the odd numbers 1, 3, 5, 7, 9, 1 1, 13, &c. &c. Fig. 9. 15. "We shall now consider the spaces passed over, not in the seconds taken singly, but in any number of them taken...
Página 143 - ... The movable pulley changes its position with that of the weight, and effects a saving equal to half the power. An equilibrium is preserved between the power and weight, when the weight is equal to the product of the power and twice the number of movable pulleys. RULE. Divide the weight to be raised by twice the number of pulleys in the lower block ; the quotient will give the power necessary to raise the weight. EXAMPLE. Required the power to raise 600 Ibs. when the lower block contains six pulleys....
Página v - Motion, or change of motion, is proportional to the force impressed, and is produced in the right line in which that force acts.
Página 130 - So that the length of the winch doubles the power gained by each trundle. As the power gained by any machine, or engine whatever, is in direct proportion as the velocity of the power is to the velocity of the weight ; the powers of this crane are easily estimated, and they are as follows.
Página 1 - FIRST LAW.—A body continues always in a state of rest, or of uniform rectilinear motion, until by some external force, it is made to change its state.—This law contains the doctrine of INERTIA, expressed in four particulars. First, that unless put in motion by some external force, a body always remains at rest; secondly, that when once in motion it continues always in motion, unless stopped by some force; thirdly...
Página ix - ... as the distance between the threads to the circumference of the cylinder in which the spiral moves.

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