102 Mr. A. H. Haworth's Description of Chloraster, 



stituting for the angles ABC their relations to the right an- 

 gle, the equation C = S(ABc) is an equation entirely between 

 numbers, and consequently the number c cannot be excluded. 



2dly. If the side c is excluded from the equation C = Q ( ABc), 

 then in this equation we have c = 0; but when c=0, then A = 0, 

 B = 0, C = 0, then = fl (0,0 ■ 0). Here the reasoning fails al- 

 together. 



Finally : M. Legendre asserts that the side c is of a nature 

 heterogeneous to the angles A and B. Now the number of 

 degrees in the angles of any plane triangle is determined by 

 the circumferences of the circles of which the angular points 



N 

 are the centres. I have demonstrated elsewhere, that — h 



y 

 = T is the equation ol the tangent straight line to any curve; 



N being the normal, y the ordinate, and h any arbitrary in- 

 crease or decrease of the abscissa ; and that it is homogene- 

 ous to the equation which determines the length of the arc. 

 Therefore the circumference of a circle and the side of a plane 

 triangle are homogeneous quantities. 



When we have to demonstrate a general property which 

 necessarily involves in it notions of infinity, we must rest the 

 demonstration as a postulate which must involve notions of 

 infinity. The difficulty encountered in this theory of parallel 

 straight lines, arises therefore from the constitution of the hu- 

 man mind, and cannot be overcome. 



" Men learn the elements of science from others : and every 

 learner hath a deference more or less to authority, especially 

 the young learners, few of that kind caring to dwell long upon 

 principles, but inclined rather to take them upon trust. And 

 things early admitted by repetition become familiar. And this 

 familiarity at length passeth for evidence. Now to me it seems 

 there are ceilain points tacitly admitted by mathematicians, 

 which are neither evident nor true. And such points or prin- 

 ciples ever mixing with their reasonings, do lead them into pa- 

 radoxes and perplexities." — [Berkeley, Defence of Free Thinking 



in Mathematics, sec. 21.) T „, 



' John Walsh. 



XX. A technical Description of Chloraster, a new Genus of 

 Narcisseae. By A. H. Ha worth, Esq. F.L.S. Sfc. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



\ LLOW me tc reply to E. E. in page 7 of your Miscellany 

 ^*- for January last, and to say that the account of the two 

 Narcisseae there mentioned was published in the Botanical 



Register 



