## Elementary Illustrations of the Celestial Mechanics of Laplace: Part the First, Comprehending the First Book |

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absciss action becomes called centre of gravity centrifugal force chord circle coefficients consequently considered coordinates COROLLARY cosine curvature curve cycloid d'u d'u d'y d'z DEFINITION density determined difference direction distance dt dt dx dy dy dz ellipsis equal equation equilibrium evanescent expressed finite fluent fluid fluxion forces acting given point height increments inversely LEMMA magnitude manner motion multiplied obtain ordinate parallel parallelepiped parallelogram particles pendulum perpendicular plane principal axes proportional proposition radius radius of curvature ratio respect right angles right line rotation rotatory inertia rotatory pressures SCHOLIUM sides similar similar triangles sin sin sin sine solid space described square straight line substituting supposed surface system of bodies tangent THEOREM tion triangles vanish variation velocity vertical vibration whence whole Ση

### Popular passages

Page 3 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

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 xv - NB When four magnitudes are proportionals, 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 161 - 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 135 - ... time. Or it may be enunciated in the following terms, the times of descent down all the cords drawn from the same point or circumference of a circle will be the same. This will be made evident by supposing the above figure inverted, D being made the upper point and the balls allowed to fall from...

Page 46 - ... 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 9 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 144 - 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.

Page 265 - ... h the distance of the C'entre of gravity from the axis of .;. The forces, then, which act upon tlie hody at the instant of impact are //

Page 133 - 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.