ON A NEW PRINCIPLE OF LE.GENDRE's. g85 



r: 4g'r« f T^ ) = T because d= -^ ) 4gT* X 



4 "" >* — c* 



—^ ^ =r 4g' r — c*. Therefore the velocity acquired in 



descending through d — r'lsvzz \/Agr — c ~36553'3482 

 feet per second ; which, added to the given velocity 2896'9482 

 feet per second, gives 39450*2377 feet, or 7*471768 miles 

 for the velocity of projection to cause a body to move to an 

 infinite distance. 



To be contimied. 



i- Remarks on a neio Principle introduced by Legendre in his 

 Elements of Geometry. In a Letter from Thomas 

 Knight, Esq, 



To Mr. NICHOLSON. 

 SIR, 



R. LEGENDRE in his *' Eltments de Gcom(:lrie' New mode of 

 {p. 311, 3d Ed.) has attempted to demonstrate certain pro- Legendre ^ 

 positions, by a new and very peculiar kind of reasoning ; 

 fonnded on the consideration of functions, and the homo- 

 geneity of quantities. 



The principle, introduced by this eminent geometer, ap- favourib'y re- 



ptars to have been favourably received by his own countrv"^^'^'^ ,, 



' ^ . ' France, and by 



men; but has of late been alternately praised and censured some in Brl- 



by some of our writers : though no very convincing argu- *'""> 



ments have been advance*! on either side of the question. 



If you can afford. me a place in your valuable Journal, I but it isfJla- 



will endeavour to prove the fallacy of i\Ir. Legendre's rea- 



soninm ; first, by showing, that it would lead to the most 



absurd- concl nsions ; and, secondly, by clearly pointing out 



the errour in this mode of investigation. 



Xbe 



