114 Of the Figure of the Earth* 



viousy are not less certain than any other mathematical 

 truths, and were never, I believe, called in question till 

 lately ; when some philosophers apparently ignorant of 

 the mathematics, from a very partial and superficial view 

 of this subject, have attempted to derive conclusions di- 

 rectly contrary to the foregoing. They have undoubt- 

 edly fallen into this mistake from the analogy which sub- 

 sists between the problem which relates to the figure of 

 the earth, and that of its magnitude,^ on the supposition 

 of a globular form. For as in two globes, that which 

 has a degree of a great circle the largest, is of the great- 

 est diameter or radius ; so likewise they imagine, in a 

 body bounded by any curvilinear superficies, that the 

 degree of the curve is the largest, where the superficies 

 is most remote from the center of thcbody^ It is easy 

 to demonstrate that nothing can be more erroneous than 

 this assumption, and that in attributing false conclusions 

 to mathematicians, they have overlooked the futility of 

 their own premises^ which, in fact, have no relation ta 

 the subject, nor any foundation on the principles of sci- 

 ence. 



They take for granted, that the measure of a degree, 

 on the superficies of the earth, is the measure of the 

 same portion of a circle, whose center coincides with 

 the center of the earth, even while they suppose its 

 form to be spheroidical. From which it would appear, 

 that they had not extended their ideas of the nature, and 

 properties of curve lines, beyond their first and most 

 ©bvious principles. 



In a circle, the measure of a degree of the circumfe- 

 rence, is the same as that portion of it, which is inter- 

 cepted by lines forming an angle of a degree at the cen- 

 ter of the circle ; and this is the very essential property 

 of a circle, that its circumference be the equable mea- 

 sure of angles at its center. In the ellipsis, and other 

 curves returning into themselvesy^ the measure of a de- 

 cree of their circumference ^ or of the osculatory circle, 

 in no instance is the same, as that portion of it which is 

 determined by the measure of a degree from the center 

 of the figure. In proportion as the radius of curva- 

 ture approaches to the position, and length of a line 

 dravm from the cehter of the figure^ to a point in the cir- 



