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acting action angle axes axis base becomes body called centre of gravity circle common consequently considered constant contained coordinates curve DEFINITION demonstration density described determined difference direction distance divided effect equal equation equilibrium expressed figure fixed fluent fluid fluxion force given greater half height Hence increments length less manner mass means motion moving multiplied nature obtain obvious origin parallel particles passing perpendicular plane portion position pressure principal proportional proposition quantity radius ratio relation remain represent respect rest result right line rotatory SCHOLIUM shown sides similar sin cos sine solid space square straight substituting supposed surface taking THEOREM tion triangles vanish variation vary velocity vertical vibration whence whole
Page 16 - In any right-angled triangle, the square described on the hypotenuse is equal to the sum of the squares described upon the other two sides.
Page 23 - CD be each of them perpendicular to the same plane MN ; then will AB be parallel to CD. In the plane MN, draw the straight line BD, joining the points B and D. Through the lines AB, BD pass the plane EF ; it will be perpendicular to the plane MN (Pr.
Page iii - NB When four magnitudes are propor'tionals, it is usually expressed by saying, the first is ' to the second, as the third to the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second...
Page 155 - To every action there is always an equal and contrary reaction : or the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.
Page 47 - ... cha.nge of rectilinear distance between, two points. Allowing the accuracy of this definition, it appears that two points are necessary to constitute motion; that in all cases, when we are inquiring whether or no any body or point is in motion, we must recur to some other point which we can compare with it; and that if a single atom existed alone in the universe, it could neither be said to be in motion nor at rest.
Page 20 - Let the arc of a semicircle on the diameter AB be trisected in the points D, E ; C being the center ; join AD, AE, CD, CE ; then the difference of the segments on AD and AE, may be proved to be equal to the sector ACD or DCE.
Page 127 - The force that accelerates the motion of a body down an inclined plane is to the force of gravity as the height of the plane is to its length, or as the sine of the angle of the plane's inclination to radius.
Page 138 - Two balls are fixed to the ends of rods, in continual revolution, and as soon as the motion becomes a little too rapid, the balls rise considerably," and, by the intervention of a lever, act upon a throttle-valve*, which diminishes the quantity of steam admitted, and of course serves to make the motion less rapid.