Plane

“ But imagine a vertical plane from the highest point of which are drawn lines inclined at every angle and extending indefinitely; imagine also that heavy particles descend along these lines each with a naturally accelerated motion and each with a speed appropriate to the inclination of its line. ”

“ And again from the same source:
"But beyond your plane, and beyond mine, are plane after plane, connected with our earth, the splendors of which man cannot conceive. And there are likewise many planes around the other planets of our chain—and there are millions of other worlds—and there are chains of universes just as there are chains of planets—and then greater groups of these chains—and so on greater and grander beyond the power of man to imagine—on and on and on and on—higher and higher—to inconceivable heights. ”

“ The rational horizon is marked by a plane, perpendicular to a plumb-line and passing through the earth’s center; while the sensible horizon is determined by a plane, also perpendicular to the plumb-line, but passing through the eye of the observer. ”

“ All directions in this plane can be considered as compounded of two, from A to B, and from A to C. Out of the infinite variety of such directions there is none which tends in a direction perpendicular to Fig. 2; there is none which tends upwards from the plane of the paper. Conceive a being to exist in the plane, and to move only in it. ”

“ And the parts of the envelops of the rolling plane between these lines, although a continuation of the developable surfaces which have been described, and representing states of the body, of which some at least may be realized, are of minor interest, as they form no part of the surface of dissipated energy on the one hand, nor have the theoretical interest of the primitive surface on the other. ”

“ It must be understood that the matter of each plane or subplane interpenetrates that of the plane or subplane below it, so that here at the surface of the earth all exist together in the same space, although it is true that the higher varieties of matter extend further away from the physical earth than the lower. ”

“ So inclined is the plane on which it rests, that it appears at first sight as if a slight alteration of its position would cause it to slide along the plane into the sea; standing as it does within two or three feet of the edge of the precipice. ”

“ We shall begin with our solar system, in which the earth describes an orbit around the sun. That orbit is contained within a plane, which plane passes through 208the centre of the sun. We may neglect for the present the earth’s occasional slight deviations from this plane which are caused by the attractions of the other planets. ”

“ Let us imagine a vast infinite Gulph, or Medium, every Way extended like a Plane, and inclosed between two Surfaces, nearly even on both Sides, but of such a Depth or Thickness as to occupy a Space equal to the double Radius, or Diameter of the visible Creation, that is to take in one of the smallest Stars each Way, from the middle Station, perpendicular to the Plane's Direction, and, as near as possible, according to our Idea of their true Distance. ”

“ So on the Earth, the summits of a number of mountains close together appear situated in one plane, if the spectator is a long way off and standing at the same elevation. So when the sea is rough, the tops of the waves seem to form one plane, although between the billows there is many a gulf and chasm, so deep that not only the hulls, but even the bulwarks, masts, and sails of stately ships are hidden amongst them. ”

“ In perspective drawings of the sphere, the plane on which the representation is actually made may generally be any plane perpendicular to the line joining the centre of the sphere and the point of vision. ”

“ Inasmuch, then, as any plane which cuts the earth into two parts through its centre of gravity must equally divide the weight of the whole earth, it follows also that the same plane would exactly bisect the great spheroid of the oceans. ”

“ The inequalities or secular variations affect the elements of the orbits, such as the inclination of the plane of the orbit,—the semi-major axis of the ellipse, or the mean distance of the planet from the sun,—the eccentricity of the ellipse, or the relation between the distance which separates the forces from the centre and the semi-major axis assumed to be unity,—and the movements of the perihelions and the nodes. ”

“ Let us now suppose a system of particles moving in space under their mutual actions. The projections of these particles on a plane will move as if they were the particles themselves subjected to the action of forces which are the projections of the actual forces on the same plane, and as the reactions between any two particles are equal and opposite, the projections of 379those reactions on the plane are equal and opposite. ”

“ If a body descends along two inclined planes of different lengths but of the same vertical height, the distance which it will traverse, in the lower part of the longer plane, during a time-interval equal to that of descent over the shorter plane, is equal to the length of the shorter plane plus a portion of it to which the shorter plane bears the same ratio which the longer plane bears to the excess of the longer over the shorter plane. ”

“ However, just as the explorer on the physical plane would probably commence his account of a country by some sort of general description of its scenery and characteristics, so it will be well to begin this slight sketch of the astral plane by endeavouring to give some idea of the scenery which forms the background of its marvellous and ever-changing activities. ”

“ We have supposed a being living in a plane world, that is, a being of a very small thickness in a direction perpendicular to the surface on which he is.
Now, if we are situated analogously with regard to an ampler space, there must be some element in our experience corresponding to each element in the plane-being’s experience. ”

“ The GROUND-PLANE is the plane on which we stand; the base-line is an imaginary line passing through the middle of the feet as we stand square and erect; and the vertical plane is supposed to stand on the base-line and perpendicular to it. ”

“ Plane figure, a figure all of whose points lie in one plane; Plane geometry, the geometry of plane figures; Plane sailing, the calculation of a ship's place in its course, as if the earth were flat instead of spherical: easy work; Plane trigonometry, that branch of trigonometry which treats of triangles described on a plane.—Inclined plane (see Incline) ; Perspective plane (see Perspective) . [Fr.,—L. planus, plain.]
Plane, plān, n. a carpenter's tool for producing a level or smooth surface.—v.t. to make a surface (as of wood) level by means of a plane.—ns. ”

“ That the surface of all water is horizontal, and that, therefore, the Earth cannot possibly be anything other than a Plane. All appearances to the contrary have been shown to be purely optical and adventitious. ”

“ A spectator near N, partaking of the earth's motion, changes his position with reference to this fixed plane: but being unconscious that he is moving himself, he attributes to the fixed plane a motion exactly similar to his own, but in the opposite direction. ”

“ Yet space is ample enough to give all systems variety of place. While each planet moves steadily along on the edge of its plane, the whole solar equipage is going forward to open a new track on the vast highway of the heavens. ”

“ If a limited inclined plane and a limited vertical line are drawn from the same point, and if the time required for a body, starting from rest, to traverse each of these is the same, then a body falling from any higher altitude will traverse the inclined plane in less time than is required for the vertical line. ”

“ By sidereal revolution of a point on the sun we understand the time which elapses between the two moments when a certain star passes, on two consecutive occasions, through the meridian plane of the point—that is to say, through a plane laid through the poles of the sun and the point in question. ”

“ The plane in which A moves depends entirely on the direction in which it was first started. The body will always continue to move in the same plane as that in which its motion originally commenced. This plane is determined by the point S and the straight line in which A was 299originally projected. ”

“ Every survey of this and other countries, whether ordnance or otherwise, is now carried out in connection with a horizontal datum, and therefore, as no other method proves satisfactory, it is virtually an admission by all the most practical scientific men of the day that the Earth cannot be other than a plane! ”

“ Our knowledge of the behaviour of the plane inclined to its direction of motion is in the main confined to the immediate results of experiment, extended it may be by the drawing of smooth curves through the observed points plotted on a co-ordinate chart. ”

“ Fire, air, earth, and water are bodies and therefore solids, and solids are contained in planes, and plane rectilinear figures are made up of triangles. ”

“ Hence we may conclude that every such system as is presented to us in the infinite variety of Nature, must stand in intimate relation to some particular plane, being that which is known as the principal plane of moment of momentum. ”

“ And if, instead of thinking of a plane-being as living on the surface of a table, we suppose his world to be the surface of the sheet of paper touching the Dark-blue square of Cube 1, then we see that a turn round the Orange line, which makes the Brown line go into the plane-being’s unknown direction, brings the Blue line into his downwards direction. ”

“ If a straight line be at right angles to a plane, every plane which passes through it shall be at right angles to that plane.
Prop. 19. If two planes which cut one another be each of them perpendicular to a third plane, their common section shall be perpendicular to the same plane. ”

“ The perspective of a iiorizontal plane from the picture to the line at infinity occupies in the picture the space between the Iine where the plane cuts the picture and the horizon, and this space is the greater the farther the plane is from the eye, that is, the farther its trace on the picture plane lies from the horizon. ”

“ Here the radius, a straight line, is clearly the determining factor.
We now move to the other pole of the primary polarity, that is to the plane, and let the sphere arise by imagining the plane approaching an infinitely distant point evenly from all sides. We view the process realistically only by imagining ourselves in the plane, so that we surround the point from all sides, with the distance between us and
the point diminishing gradually. ”

“ Similarly, taking a plane—this is by definition not curved in any way, known or unknown, and it can only be conceived to be bent by ampler space being conceived, and its being imagined as having force applied to it so as to become a bent thing in this ampler space. ”

“ The planets all revolve around the sun in the same direction, and in nearly the same plane. The sun and all eight planets rotate on their axes in the same direction, the earth’s rotation being accomplished every twenty-four hours. ”