Dr. R. Hey's Propositions; &c. 349 
possibly be brought to co-operate with the theory here given 
or begun, so as that, in conjunction, they may afford consider- 
able advantage to the practice of perspective ; especially where 
a number of circles together are to be represented. 
The same four propositions are built upon the sixth on 
perspective: of which the construction (as given in fig. 5,) 
may be seen in Hamilton's* Stereography. That it was not 
taken from his work, but separately discovered, has no claim 
to the attention of the reader, except in this respect ; that, in 
the solutions of any problem, the more persons there are who 
give independently the same solution, the more likely it is 
(caeteris paribus) to be better than any solution not yet dis- 
covered. The demonstration also has been varied; both of 
this sixth proposition, and of some other things which, though 
not new in substance, it has been judged expedient to insert. 
For the seventh of the propositions on perspective, I am 
also indebted to Mr. Kerrich : though, for the proof here 
given of it, I am responsible. 
The foregoing account appears to be all the previous infor- 
mation necessary to trouble a reader with, who may be going 
to examine the propositions in his closet. But, as mathematical 
demonstrations, accompanied with diagrams, cannot be ac- 
commodated to a public reading, some further particulars are 
therefore here subjoined : which, if the Paper should have the 
honour of being received by the Royal Society, may give a 
better insight into its nature and intent. 
The whole had its origin in the study of that part, of the 
John Farcy junior, obtained the gold medal, in May 1813, from the Society for the 
Encouragement of Arts. For its merits I refer to that Society. 
* B. III. Sect. II. Prob. 1. 
MDCCCXIV. 
Zz 
