APPENDIX. 67 



perhaps of fatisfaction to fome, who envied that fcience the 

 certainty of its conclufions. On account of fuch, it muft be 

 obferved, that there are problems fo extremely difficult, that, in 

 the folution of them, it is poflible only to approximate to the 

 truth j and that, as in Arithmetic, we neglect thofe fmall frac- 

 tions, which, though of inconfiderable amount, would exceed- 

 ingly embarrafs our computations ; fo, in Geometry, it is fome- 

 times neceflary to reject thofe fmall quantities, which would 

 add little to the accuracy, and much to the difficulty of the in- 

 veftigation. In both cafes, however, the fame thing may hap- 

 pen j though each quantity thrown out may be inconfiderable in 

 itfelf, yet the amount of them altogether, and their effect on the 

 lad refult, may be greater than is apprehended. This was jufl 

 what had happened in the prefent cafe. The problem to be re- 

 folved is, in its nature, fo complex, and involves the eftimation 

 of fo many caufes, that, to avoid inextricable difficulties, it is 

 neceffary to reject fome quantities, as being fmall in comparifon 

 of the reft, and to reafon as if they had no exiftence. Dr 

 STEWART, too, it muft be confefTed, had an additional motive 

 for wifhing to fimplify his inveftigation. This was, his refolu- 

 tion, to employ in it no other method than the Geometrical, 

 which, however excellent in other refpects, is inferior to Alge- 

 bra, for the conducting of very complicated reafonings. The 

 fkill of this moft profound and experienced Geometer, could 

 not remedy that defect ; and he was reduced to the neceffity of 

 rejecting quantities, which were confiderable enough to have a 

 great effect on the laft refult. An error was thereby introduced, 

 which, had it not been for certain compenfations, would have 

 become immediately obvious, by giving the fun's diftance near 

 three times as great as that which has been mentioned. 



THE Author of the pamphlet, referred to above, was the firft 

 who remarked the dangerous nature of thefe fimplifications, 

 and who attempted to eftimate the error to which they had 



(I 2) given 



