350 Dr. R. Hey*s Propositions containing 
science of perspective, which relates to the representation of a 
circle. And the principal result (so far as immediately 
respects that science) is contained in the four propositions 
which conclude the paper, together with the lemma which 
precedes them. This is called a lemma rather than a propo- 
sition, because it does not necessarily involve the consideration 
of a circle. 
That the perspective representation of an entire circle is 
an ellipse or circle, is simply a part of the doctrine of conic 
sections. To that doctrine therefore it is referred, in the first 
of the perspective propositions. An entire circle, supposed 
to be view'ed by the eye through the plane of the picture, 
excludes ( by the hypothesis ) the two cases in which the 
circle touches and cuts the plane, passing through the eye, 
parallel to the picture.*' In which two cases, the representation 
is a parabola and hyperbola respectively. Not having any 
thing new to offer upon these representations, or not any 
thing appearing likely to improve the practice of perspective, 
I have omitted the two cases entirely ; and confined myself to 
the elliptic representations, the circular included. 
The principal inquiry has been, whether, in any instances 
of a number of circles, lying in one plane and having their 
centres in one right line, any lavo or laws could be discovered 
to be observed by the major or minor axes of the represent- 
ing ellipses, in their directions or positions. If it could have 
been proved that the axes converged to a know'n or easily 
discoverable point, this would have been a great acquisition to 
the science of perspective, and have given a direct facility to 
the practice. But, if indeed they do not so converge, it is 
natural to wish that this should be demonstrated. Such a 
