3J?0 Mr. J. Snart on the Qiiadratine of the Circle. 



effect. Consequently they can know nothing (until qualified) 

 about bent, circular, or ctirved lines, superficies nor convex 

 solids, such as the perimeters, surfaces and cubic contents of 

 spherical bodies. 



And as this matter seems heretofore either to have been 

 totally unnoticed or forgotten, perhaps the reader will pardon 

 even a mechanical demonstration of this si7ie qua Jio?i, which may 

 be given by placing any number of slender rods of known 

 and uniform dimensions endwise in a rcw; letting each be 

 an inch, a foot, &c. long. Suppose, for example, nine such 

 of a foot long were to be taken ; it is very evident that, if 

 placed in a straight line, they would extend nine feet, as 

 indicated by the Jirst power of figures ; but should any bend, 

 curve, or angular deflection arise in placing them, it is equally 

 plain that they would fall short of their proper extension, and 

 that the said discrepancy must be proportioned to their aber- 

 ration from the right line. And if numbers were aUke sub- 

 ject to these tortuosities, their conclusions would be equally 

 indefinite and f/^ec^/re; i.e. unless their indications have a 

 plenary effect, by operating in straight lines, their assump- 

 tions cannot be true ! But it is very obvious that figures, as 

 spnbols, of whatever they be made the representatives, must 

 be true; indeed they are the very and ultimate tests of, tnith 

 itself! And in this case they would be considered as unities 

 of length, or lineal measure, and therefore the measured nine 

 feet must accord with the numeral nine feet, or concede the 

 point of infallibility to figures, whose first power it is pre- 

 sumed is herein satisfactorily identified and demonstrated. 



And with this rectilineal ^ -.^,^^ "^ 



power, it is that the men- 

 suration of the perimeter 

 of the circle has had to 

 do ; a power which is to- 

 tally incompetent to take 

 cognisance of bent or 

 curved lines, which the 

 segment S of the circle 

 "wotdd be if the chords 

 thereof were extended to 

 a thouscmd millions! (see 

 fig. 1.) and as we have just 

 seen that figures can 

 know nothing but straight 

 lines ; these mathematicians measured only the polygon, but 

 not the circle! 



The second power of figures, which must also be justified 



by 



