S. A plane passing through the point of sight parallel to any original plane. is called the parallel plane.
9, A of rays is that which proceeds front alt origi nal line, or from any line of the original object, by rays from all points of that line terminating in the eye. If the line in the original object be straight, the surface of rays is called a plane e/ rugs, oldie risau/p/a/oe.
10. When the rays proceed front one Or more surfaces of an original object, the whole is called a of (Jr Oldie pyramid ; And if t he base be circular, it is called a cone rays, vi.inal cone, or Optic In every kind of projection from a given point, the projee tion of a straight line upon any surface is the interso tion of a plane of rays with the surface from all points of the straight line to the given point. ne•efore, the painwatnie projection of a straight line is the intersection of the cylindric surface and a plane. It' a right cylinder be cut by a plane perpen dicular to its axis, the section is a circle; if cut parallel to the axis, the section is a rectangle ; and if cut obliquely to the axis, the section is an ellipsis. It the surfilee of the cylinder be extended upon a plane with the sections of the cy liudtic surthce, and a plane cut in each of the positions here stated, the section made by the plane perpendicular to the axis will be a straight line ; and the section made by cutting it parallel to the axis will also Is' a straight line; but the section made by cutting it obliquely will be a curve of similar properties with that known to mathematicians by the name of the jiyure of the lines ; theretbre, the projeetion of ea cry straight line in a plane passing through the eye per pendicular to the axis of the cylinder, will also be a straight line on the extended surface; and eery straight line in a plane passing through the axis will also be a straight line on the extended surface, perpendicular to that formed by the plane passing through the eye perpendicular to the axis.
The panoramic projection of any straight line not in a plane passing through the eye perpendicular to the axis, nor a passing through the axis, is in the curve or an ellipsis ; for in this case the optic rays which cut the cylinder will neither be in a plane parallel to the axis, nor in a plane perpendicular to it.
panoramic representation of any straight line in a plane perpendicular to the axis, but not passing through the eve, is in the curve of an ellipsis, and the optic plane will be at right angles to another plane passing through the axis at right angles to the original line.
In the panoramic representation of any series or parallel lines, the optic planes have a common intersection in a straight line passing through the eye, and the common intersection w ill be parallel to each of the original straight lines; there fore, the indefinite representations will pass through the extremities of the common intersection.
In the panoramic representation of any series of parallel lines in a plane perpendicular to the axis, but not passing through the eye, the C0113111011 intersection of the optic planes is parallel to the plane on which the original lines arc situated.
In the indefinite representations of any number of straight lines parallel to the axis. the visual planes will have a com mon intersection in the axis, and will divide the circumfer ence of the cylinder into portions which have the same ratio to each other as the inclination of the visual planes.
If' an original straight line parallel to the axis lie divided into portions, the representations of the portions will have the same ratio to each as the originals.
If in any original p'ane there he a series of straight lines parallel to each other, and also another series of straight lines parallel to each other, mid at any given angle with the former series, the common intersections of the visual planes w ill make the same angle with etch other, which any line of the one series makes with any one of the other series, and the common intersections w ill be in a plane parallel to the original plane ; and, therefore, it' t he original plane be pe•pen diculdr to the axis, the common intersections of the visual planes will also be in a plane perpendicular to the axis, 'Hence the common intersections of visual from any two systems of straight lines, parallel to any two straight lines at a given angle with each tither in a plane perpendi cula• to the axis, arc also in :1 plane perpendicular to the axis. and make the same angle with each other which the two lines in the original plane make, \‘itli each other, 11. The two points where the parallel of an original line inclined to the axis of the cylinder meets the panoramic sur filet., are called the ranishiny points of that original line, 12. The intersection of the parallel of an original plane is called the canishiny lime of that plane.