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XVIII. Propositions containing some Properties 0/ Tangents to 
Circles; ^ Trapeziums inscribed in Circles^ and non- 
inscribed. Together with Propositions on the Elliptic Represen- 
tations of Circles, upon a plane surface^ by Perspective. 
By Richard Hey, LL. D.; late Fellow of Sidney Sussex and 
Magdalen .Colleges , in the University of Cambridge, Commu- 
nicated by the Rev. Edward Balme, M. A, F, R. S. 
Read March 31, 1814. 
Th E propositions of the first series, and which are termed 
Introductory, had their origin from my attention being directed 
to the perspective representation of a Circle. But they are 
kept separate from the perspective propositions. Comprising 
some things believed to be new, and forming a short system 
in themselves, they may, on these accounts, be acceptable to 
other Readers besides those who study perspective. 
A desideratum, in the science of perspective, had been 
suggested to me by the Reverend Mr. Kerrich, Principal 
Librarian to the University of Cambridge ; namely, of some 
law or laws which the axes, of ellipses representing circles, 
might be found to observe in their directions. An attempt, 
grounded on this suggestion, is contained in the four Propo- 
sitions concluding the second or Perspective series. If these 
be correct, it is hoped that a foundation is laid, for further 
improvement by persons younger than myself and differently 
circunastanced. And some mechanical instrument * may 
* The invention of an Instrument for the ready delineation of Ellipses, by Mr. 
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