14 Mr. Reinagle on Oval and Elliptic Curves. 



have the oval shape more than any other ; the bend of the 

 branches, and the whole external form of many trees is oval. 



There is no form of created things which may not be found 

 to correspond in all its dependent shapes to ovals and ellipses 

 of various disks, even objects which at first sight seem to con- 

 tradict the possibility of meeting this system. 



The lecture was closed by some extracts and quotations from 

 Lomazzo, Dryden, Hogarth, Du Fresnoy, and the Abbe du 

 Bos ; the tendency of which was to show that lines had been 

 mentioned, and had been written upon without any explanation 

 given that could lead to certain conclusions. That all these 

 authors attributed to supreme genius alone, and something of 

 the divinely inspired character in artists, the power to produce 

 those indescribable lines that affect the human eye so strongly. 

 These lines I described as belonging to the oval and the ellipsis, 

 and the confluent lines by conjunction and combination ; that 

 these indescribable lines, which from Plato to Dryden had 

 never been detected or obtained a name ; that puzzled all 

 equally alike, are those alone I attempted, and I believe 

 proved in this lecture, to be the elliptic combinations. 



I stated that the great Greek artists confined themselves to 

 certain rules and principles of unerring consequences in the 

 production of beauty, grace, or grandeur in their figures ; that 

 all their compositions depended upon the same species of rule 

 and order. I pointed out, that fashion is in all countries the 

 destroyer of taste, that it unfits the mind for fixed principles ; 

 that where it dominates, there taste will be always fluttering 

 and never settle, nor have a sure dominion. The Greeks, 

 having no such vile tormentor to divert them from a pure course 

 in their progress, arrived at the summit of perfection in every 

 scientific pursuit, by following sure principles as their guides, 

 and by never abandoning a path traced by nature, and matured 

 by the most sublime philosophy. 



