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 Sphera 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, BIA are together greater than the tri- 
angle AAT (fig. pag. 79, Oxf. ed. fol. 1792). 
Dr. Barrow (in whose edition this is Prop. XII.) says, 
“‘liquet .... quia AB+BI'> AT, et altitudo communis est,” 
which is evidently not true, unless the triangle ABI’ 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, TA common, and the angle TAZ > the angle PAE, 
the triangle TAZ > the triangle TAE. 
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 AAT, and states what he considers to 
be the objection of the Oxford editor, viz., that the triangle 
TAZ will not include the triangle [AE in the case of 
the angle AAB > the angle AAT, and that it cannot, there- 
fore, be inferred generally, that the first of these triangles > 
the second, He then subjoins a different demonstration. 
