Cyclomathesis: Or, An Easy Introduction to the Several Branches of the Mathematics]., Volume 71769 - Mathematics |
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Cyclomathesis: Or, an Easy Introduction to the Several Branches of ..., Volume 6 William Emerson No preview available - 2016 |
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againſt alfo alſo angle arch axis axle bafe beam becauſe body revolves center of gravity centrifugal force centripetal force circle cofine confequently curve defcending thro defcribed denfity diameter direction diſtance draw ecliptic ellipfis equal equilibrio falling thro fecond femi-tangent feveral fide fimilar fince fluid fmall fome fpace fquare roots friction ftrefs ftrength fuch fufpended fuftained fun's fuppofe fupport furface given Hence hight horizon hyperbola inclined plane increaſed interfection leffer length lever likewife line of meaſures meaſure motion move muſt oppofite orbit paffing thro parallel pendulum perp perpendicular plane of projection pofition pole of projection preffure primitive Prob projecting point Prop pulley quantity of matter radii radius raiſed reciprocally refiftance reft reprefent right line rope SCHOLIUM ſmall ſpace Sphere ſtreſs tangent thefe theſe tion triangles velocity vibration weight wheel whence whofe
Popular passages
Page 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...
Page 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....
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.
Page 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.
Page 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.
Page 42 - 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.