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 AAF 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 AF, 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 FAZ ( = the angle FAB) is >FAE, 

 and < FAA (since FB < FA), the triangle FAZ will evidently 

 include the triangle FAE, 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 FB + BA > FA, and 

 the perpendicular on FB or BA is also > that on FA, it at 

 once follows that the triangle FAB + the triangle BAA > 

 triangle FAA. 



In every edition, the point Z appears to be in the circum- 

 ference of the circle FBA, which seems to have misled Sturm 

 and, perhaps, the Oxford editor also. 



