374 
Dr. R* Hey's Propositions concerning 
of any conceived trapezium, whose diagonals produced cut the 
base in I between L and R, and in K beyond R, and if, on the 
diameters LR and IK, be described the semicircles LNR and 
ITK, and if IN and RT be perpendicular to LR ; KN and LT, 
being drawn, are tangents.^ 
Cor. 8. Fig. 12 or 13. If the diagonals of a non-inscribed 
polygon, having an even number of sides, meet in one point; 
the opposite sides will respectively meet, if at all, in the base 
to which that point is vertex in two or more circles. For the 
proof applied -f to the inscribed polygon may, now, be ex- 
tended to the non-inscribed. If two opposite sides be parallel, 
the base is J parallel to them. 
Dnd of the Introductory Propositions. 
On the Elliptic Representation of a Circle, upon a plane surface, 
by Perspective. 
Definitions. 
Although the reader is presumed to be acquainted with the 
principles of perspective; yet the definitions in that science 
have varied so much, that it may be right to prefix a few here. 
Some new terms are also introduced. 
Def. 1. The centre of the picture is that point, in the indefi- 
nite plane of the picture, in which it is cut by a perpendicular 
from the eye. 
Def. 2. The directing plane is a plane through the eye, pa- 
rallel to the picture. 
Def. 3. The intersecting line and directing line, of an objec- 
• Cor. 3 to prop. VI. f Cor. 6 to prop. X. J Cor. i to this prop. 
