268 



be understood in its details, without the aid of diagrams, as 

 exhibited to the Academy. 



The instrument is designed to register, by itself, for 

 twelve hours at a time, and at such an interval its registra- 

 tions require to be read off and noted. 



Dr. Todd read a letter from C. T. Barnwell, Esq., con- 

 taining some observations on two passages of Archimedes, 

 De Sphcera et Cylindro, where commentators appear to have 

 been strangely misled. 



The first occurs in the Demonstration of Proposition I. of 

 the first book. 



In the demonstration of this proposition it is assumed that 

 the triangles ABA, BFA are together greater than the tri- 

 angle AAr (fig. pag. 79, Oxf. ed. fol. 1792). 



Dr. Barrow (in whose edition this is Prop. XII.) saj'^s, 

 "liquet .... quia AB + Br> AF, et altitude communis est" 

 which is evidently not true, unless the triangle ABP were 

 equilateral. 



In the German edition of J. C. Sturm (where this is 

 Prop. IX.) the following most extraordinary inference is 

 drawn from Euc. I. 24, viz., that, since (fig. in p. 80) 

 AZ > AE, fa common, and the angle FAZ > the angle FA E, 

 the triangle FAZ > the triangle FAE. 



In the Oxford edition, the demonstration of Eutocius is 

 condemned as invalid ; but the editor, without stating the na- 

 ture of his objection, contents himsetf with adding " sed res 

 ipsa satis patet." 



Flauti, of Naples (Corso, vol. I.) observes, and rightly, 

 that the line AZ should have been directed to be drawn in the 

 plane of the triangle AAF, and states what he considers to 

 be the objection of the Oxford editor, viz., that the triangle 

 FAZ will not include the triangle FAE in the case of 

 the angle AAB > the angle AAF, and that it cannot, there- 

 fore, be inferred generally, that the first of these triangles > 

 the second. He then subjoins a different demonstration. 



