392 PHILOSOPHICAL TRAKSACTIONS. [aNNO 1740. 



Concerning two Species of Lines of the Third Order, not mentioned by Sir Isaac 

 Newton, nor by Mr. Stirling. By Mr. Edmund Stone *, F. R. S. N" 456 

 p. 318. 



Mr. Stone having for some time past been reading and considerirtg the little 

 treatise of Sir Isaac Newton, intitled, Enumeratio Linearum tertii Ordinis, as 

 also the ingenious piece of Mr. Stirling, called, Illustratio Tractatus Domini 

 Newtoni Linearum tertii Ordinis ; he observed, that they have neither of them 

 taken notice of the two following species of lines of the third order; and he 

 ventures to affirm, that the 72 species mentioned by Sir Isaac, with the 4 more 

 of Mr. Stirling, and these 2, making in all 78, is the exact number of the dif- 

 ferent species of the lines of the 3d order, according to what Sir Isaac has 

 thought fit to constitute a different species. 



The 2 species are to be reckoned among the hyperbolo-parabolical curves, 

 having one diameter, and one asymptote, at N° 8 of Newton's Treatise, or 

 p. 104 of Mr. Stirling's ; its equation being xyy = + bx'^ + ex + d; which will 

 give, not 4, as in these authors, but 6 species of these curves : for, 



1. If the equation bx^ + ex -\- d ^ O, has 2 impossible roots, the equation 



* Mr. Edmund Stone was a rennarkable instance of the effect of industry united to good natural 

 talents; having raised liimself to an eminent rank in the mathematical sciences, as well as in the 

 languages, by his own application alone ; all the instructions he ever received, being only to know 

 the 24 letters of the alphabet, which he was taught at 8 years of age, by a servant in the duke of 

 Argyle's family, where young Stone's father was gardener ; with whom, also, at an early age, the 

 son became a servant ; in which situation he spent a considerable part of his life. When about 18 

 years of age, his extraordinary talents were accidentally discovered by the duke, who found him in 

 the garden reading Newton's Principia in the Latin language ; when, on inquiry, the duke learned 

 that by procuring books, he had made himself master of arithmetic, geometry, &c. as well as the 

 Latin and French languages. Delighted with his conduct and conversation, tlie duke drew him from 

 obscurity, and placed him in a situation to pursue his favourite studies. 



The time of Mr. Stone's birth is unknown, though it was probably towards the latter end of the 

 17th century, as the first edition of his Mathematical Dictionary was printed in 1726. After which, 

 several other useful works, both translations, and books of his own composition, follow at certain in- 

 tervals of time. As, 2. — A Treatise on Fluxions, in 1vol. 8vo. 1730; the first part being a trans- 

 lation, from the French, of I'Hopital's Analyse des Infiniments Petits; and the 2d part, or inverse 

 method, being supplied by Stone himself. 



3. The Elements of Euclid, in 2 vols. 8vo. 1731 : being a neat and useful edition of those ele» 

 ments, with an account of the life and writings of Euclid, and a defence of his elements against mo- 

 dern objectors. 



4. Dr. Barrow's Geometrical Lectures, translated from the Latin, in 1 vol. 8vo. 1735. Besides 

 several other smaller works. 



The time of his death is also unknown. 



