On some Combinations of Platbia. 209 



Leaving this Platonist*, let us turn to Mr. Leslie's rea- 

 soning, and consider how far he is right, and where he de- 

 viates from the true line of argument. 



This author justly observer, that the same reasoning 

 which proves that there can be no equaiion between c and 

 yi, B, C, would equally prove that there can be no equation 

 between Cand a,lj,c. Mr Leslie might have gone further ; 

 for we mav without hesitation admit, that the reasoning is 

 just in Loth cases (provided that we keep to the strict 

 meaning of the word equatiun), and ye\. proves notldng in 

 either. 



For the argument drawn from the heterojieneity of the 

 quantities no longer applies, when transferred from the 

 angle itself io such functions as the sine, cosine, or arc to 

 a given radius f; these are lines, and of course cap^^ble of a 

 comparison with lines; whilst they can ?wt be compared 

 with the angles themselves of which thev are calk-d the 

 functions. Hence appears the utter uselesfness of Le- 

 gendre's reasoning. It is true, sir, you have shown that 

 there can he no ecjuation between c and A, B, C ; but if 

 a, /3, 7, represent the cosines of A, B, C, to anv given line 

 (r) as radius, 1 do not very clearlv perceive { fnm any 

 thing you have delivered) why there might not be such an 

 equation between the five lines c, a, /3,7, r; as would en- 

 tirely overturn all you mean to establish. There might, 



for example, be the equation c •= — ^ ', whence 7 = 



• — , ; and the angle C would not depend on A and B alone, 



as you think you have demonstrated. 

 Sept. 14, 1812. X. Y. 



P.S. — I must state that I have never seen Mr. Leslie's 

 Geometry, and know notliing more of his argument than 

 is to be gathered from the Edinburgh Review. 



XXXIX. On some Comhinatinvs of Plafina. /?y Edmund 

 Daw, B.sq., of the Royal Institution. Communicated 

 ly the Author. 



liNTUODl CTION. 



X HK properties vvhich characterize platina, and to which 

 it owes its value, offer many difficulties to the complete 



• Vide EiJinburgli Review, October IflOO, p 4. 



+ I.rt it l)e partirularly ob-ierved, ihar I am hero spe-iking peometrir.illy, 

 and do not mean the sine, >ic Io tbe radius rfue: this is a number, and sup- 

 poses a previous clio'oe of some line- for unit. 



Vol. 40. No. 173. 6V/;/. 1812. O develop. 



