Cyclomathesis: Or, An Easy Introduction to the Several Branches of the Mathematics], Volum 7

fold. plates (diagrs.), 1769

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Side 69 - As the distance between the body to be raised, or balanced, and the fulcrum, or prop, is to the distance between the prop and the point where the power is applied, so is the power to the weight...
Side 70 - C (fig. 555.) of the pulley we draw the horizontal diameter AB; then will AB represent a lever of the first kind, its prop being the fixed centre C, from which the points A and B, where the power and weight act, being equally distant, the power P is consequently equal to the weight W. 1317. Hence, if the pulley be put in motion, the power P will descend as fast as the weight W ascends : so that the power is not increased by the use of the fixed pulley, even though the rope go over several of them....
Side 69 - It is a principle in mechanics, that the power is to the weight as the velocity of the weight is to the velocity of the power.
Side 90 - In thofe of the third kind, at the power, and dirninifh proportionally from that point. The axles of wheels and pullies, the teeth of wheels, which bear greater weights, or act with greater force, muft be made ftronger. And thofe lighter, that have light work to do. Ropes muft be fo much ftronger or weaker, as they have more or lefs tenfion. And in general, all the parts of a machine muft have fuch a degree of fircngth as to be able to perform its office, and no more.
Side 77 - ... so that it may revolve freely, carrying round with it the attached wheel. On the axis is coiled a rope which sustains the weight ; and round the periphery of the wheel is coiled another rope, in a contrary direction, to which is suspended the power. Then supposing the machine to be put in motion, the velocity of the power will be to that of the weight, as the circumference of the wheel to that of the axle ; for it will be perceived that the power must sink through a space equal to the circumference...
Side 76 - ... if the power be taken away, the fcrew will retain its pofition, and hinder the weight from defcending again by its friction, without any other power to fuftain it. In the common fcrew, fuch as is here fuppofed ; ' the threads are all one continued fpiral from one end to the other; but where there are two or more fpirals, independent of one...
Side 128 - MISCELLANEOUS PROBLEMS. To find the specific gravity of a body heavier than water. RULE. — Weigh the body in water and out of water, and divide the weight out of water by the difference of the two weights. EXAMPLE. — A piece of metal weighs 10 Ibs. in atmosphere, and but 8i in water ; required its specific gravity.
Side 122 - Now, by prop. 54, the pressure of the fluid against the hole B, by which the • motion is generated, is equal to the weight of the column of fluid above it, that is the column whose height is AB or a, and base the area of the hole B.
Side 137 - Carol. 3. The air is denser near the earth, than in high places ; or denser at the foot of a mountain, than at the top of it.
Side 44 - C, to D and F, for. the circle DF ; and from A, the projecting point, draw AF/, and AD^, then df will be the tranfverfe axis of the ellipfis. But if D fall beyond the line RE, as. at G,. then: draw. a fine from G backward thro' A to D, and then df is the tranfverfe of an hyperbola.

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