mated by the visual angle; and the visual angle of any object AB increases or dimiħishes reciprocally as the eye O [21. 1. & 4. 6.].

diftance from the

Thus, if EF be

equal and parallel to BA, but nearer the eye, its apparent magnitude is greater than that of BA, in the ratio of the angle EOF to the angle BOA: for if EF meet OA in G, EG fubtends the fame visual angle with BA; therefore the apparent magnitude of an object is reciprocally proportional to its distance from the eye.

4. The plane that paffes through the vifual rays AO, BO, may be called the viJual plane of the object or line AB, which [2. 11.] is in the fame plane; and the planes in which are the triangles ACO, BCO, are the visual planes of AC, BC.

If the object viewed by the eye O, be any rectilineal figure ABC, the folid figure contained by the visual planes, viz. AOC, COB, AOB, and by the object ABC, shall be [def. 12. 11.] a pyramid whofe vertex is O, and whose base is the object ABC; and this pyramid is called the optical, or visual pyramid of the object ABC. If the object be a circle, the rays that proceed from each point of the circumference to the eye are in

the

the fuperficies of a cone, whofe vertex is in the eye, and whose base is the circle, which is the object.

6. If a plane DABE given in position, fig. 3. be erected between the eye O, and the point to be put in perspective H, and if the point G, where the visual ray HO meets the plane DABE, be found, this point shall be the perspective or reprefentation of the original point H. It is in this way that objects are put in perspective, namely, by finding the point where each optical ray meets the faid plane; and if the line or lines made in the fuperficies of the optical cone or pyramid by this plane be thus found, they shall be the perfpective of the object, whether the object be a plane figure or a folid. Hence, the perfpective of a ftraight line paffing through the eye is a point, and the perspective of a plane passing through the eye is a straight line, viz. the common section of that plane with the one that is erected [3. 11.].

7. If the object be a plane figure, whether rectilineal or curvilineal, and if the plane erected between the eye and the object be parallel to the plane in which the

object

object is, the perspective [16. & 10. I I. 4. 1. Appoll. con. or 23. 1. Simf.] (hall be fimilar to the object : also, if the plane erected cut the optical pýramid or cone fubcontrarily, that is, fo that the part cut off from a fcalene pyramid or cone towards the eye, be fimilar to the whole pyramid or cone, the perspective shall be fimilar to the object: See 5. 1. Appoll. con. or 24. 1. Simf. The reafon of this laft appears from what has been already faid: for, because [art. 3.] the apparent magnitude of an object is reciprocally proportional to its diftance from the eye, it is manifeft, that the optical pyramid or cone may be fo cut by a plane, that unequal lines thall fubtend equal vifual angles: and this happens when the part cut off from a scalene pyramid or cone towards the eye is fimilar to the whole pyramid or cone.

1

The perspective of a plane figure is not fimilar to that figure in any other cafe;' and it is manifeft, that the perfpective of a solid, taken upon any one plane, cannot be fimilar to the folid whose perspective it is.

De