A 



JOURNAL 



OF 



NATURAL PHILOSOPHY, CHEMISTRY, 



AND 



THE ARTS. 



DECEMBER, 1808. 



ARTICLE I. 



Aimcer to Mr. Barlow's Remarks on the Essay on Poly* 

 gonal Numbers. By J. Gough, Esq, 



To Mr. NICHOLSON. 

 SIR, 



.Y answer to Mr. Barlow's criticism on the solution of Answer to Mr. 

 Fermat's theorem was in the possession of that gentleman. Barlow's criti- 

 I believe, prior to the date of his letter inserted in your 

 Journal, Vol. XXI, p. 118. As Mr. Barlow does not think 

 proper to make use of my permission to publish the reply, 

 I am under the necessity of repeating in your present num- 

 ber arguments, which have been already stated in a private 

 correspondence. 



Mr. B. opens bis criticism by admitting the first three 1st objectloii 

 propositions, with their corollaries, to be correct; but he ^^^^^f^*** 

 does not see in what manner they are to be applied to the 

 general demonstration. This objection may be answered 

 thus: If the remaining propositions be derived from these 

 three, or any one of them, the necessity of inserting them 

 all is established, because the third is derived from the se- 

 cond, and the use of the first appears in the course of the 



VoL.X-Xi, No. 94.— Dec. 1&08. R essay. 



