269 
Hauber, in his excellent edition of this treatise (Tubin- 
gen, 1798), appears also to admit the objection; for he gives 
another demonstration of the assumption in question, which 
is, perhaps, preferable to Flauti’s. Peyrard does not attempt 
any explanation or demonstration. 
It is, however, very remarkable, that not one of the edi- 
tors seems to have observed that, in the subsequent applica- 
tion of Prop. X. (see the Corollaries at the end of Prop. XIII. 
p. 86) the triangle AAT is composed with the lesser of the 
two conical surfaces intercepted between the lines AA, AT; 
and consequently, that the lesser of the two segments, into 
which the circle is divided by the line AT’, is the one which 
should have been bisected in B. 
The figure in p. 80, when corrected accordingly, will be 
this : 
where, since the angle TAZ (=the angle TAB) is > AE, 
and < T'AA (since PB< IA), the triangle PAZ will evidently 
include the triangle. AE, and the demonstration given by 
Eutocius will be valid. The only objection now to be made 
to it is, that it is unnecessary ; for, since "B+BA > TA, and 
the perpendicular on 'B or BA is also > that on TA, it at 
once follows that the triangle TAB + the triangle BAA > 
triangle TAA. 
In every edition, the point Z appears to be in the circum- 
ference of the circle "BA, which seems to have misled Sturm 
and, perhaps, the Oxford editor also. 
