22 



GEOMETRICAL PROPOSITIONS, 



His methods 

 were ftated as 

 ■nearly approach' 

 itig the truti* 



Kone of the 

 quadratures of 

 the circle arc 

 more than ap- 

 proximations. 



I know not. Sir, how I could have written in any way 

 farther from " announcing my difcovery with confidence" 

 than the above, or indeed with more diffidence. 



n the firft place, I ftate it only as a near apjyroach to tiie 

 exadi truth, which both your and his criticifras have fully 

 proved it to be : In the next place, I exprefs my doubt of 

 its being even fo cxaSi as it appears to me : And thirdly, I 

 have left its publication to depend on your approbation. 



If thii is not enough to remove all fufpicion of confidence, 

 I have to add, that the fentence which concludes that fubjefl 

 in the paper, ftates, that an unpcrceived error might arife 

 from the fmallnefs of the circles which I ufed; and befide$ 

 this you can teftify for me, that I wifhed the paper to be fup- 

 prelTed altogether before publication, when you (hewed me 

 that it even wanted an hundredth part of being exa6t, though 

 with a much greater inaccuracy the matter contained in it 

 would be ufeful for the purpofes to which I fialed it might 

 be applied. 



As to the proof o^ the fccond faB, it was not from the 

 " convi6tion of its obvious accuracy not requiring prooP* 

 that I did not infert any, but becaufe I concluded it muft be 

 fufficiently obvious after what I had ftated of the firft, (hat it 

 was the fame fort of exptrimental proof I had ufed for both : 

 And if any gentleman will try the experiment as I did, he 

 will find I have not mistiated the matter. 



There may indeed be fome little impropriety in ufing the 

 word fact in a popular fenfe, in any thing like a mathema- 

 tical ftatement; but to notice fuch a trifle with inverted 

 commas, only appears to indicate a fpirit of cavilling on the 

 part of your Old Correfpondent. 



But with all his precifion he has forgot one fact, that puts 

 his computations more on a level with my experiments, which 

 is, that no method has ever yet been difcovered of computing 

 with perfe6t exadtnefs the relative proportions of the circum- 

 ference to the diameter, and of courfe to the other hnes he, 

 mentions ; and that it is only a far-laboured approximation to 

 the truth that has been inferted in the work from whence he 

 has extra6ted the proportions which he has ufed; and that 

 therefore what he has "announced with fo much confix 

 '* dcnce," (to ufe his own words) is not precifely demonftra^ 

 live truth, but only an approach to it. 



