270 



In a modern German edition of the whole of Archi merles, 

 by Nirze (Stralsund, 1824), Hauber's demonstration is adopted, 

 but in a less advantageous form, and with an ernoneous figure. 



The second occurs in the Demonstration of Proposition V. 

 of the second Book. 



At the foot of page 157, Oxford edition, it is said : " Since 

 the ratio of AA to AX is given, as well as that of PA to 

 AX, the ratio of PA to AA is also given." But this is untrue 

 with respect to the first of these ratios, which is not given. 

 Indeed, if it were, the analysis would here be at an end ; for, 

 since (p. 157, lin. penult.) AA: AX :: BZ: ZX, the ratio of 

 BX:ZX would be given, as also ZX (since BZ is given) and 

 the point X. 



But it is remarkable that this corruption is as old as the 

 time of Eutocius ; for he has been led into an error so gross, 

 that it is hardly possible to imagine how so able a commenta- 

 tor could have fallen into it. This error is no less than the as- 

 sertion (page 160, line 25) that BX is given, because its 

 extremities are given ; whereas the whole object of the analy- 

 sis is to find the point X. 



This corruption of the text has been allowed to pass unno- 

 ticed into the Oxford edition, though it had been corrected in 

 the old Latin translation, in the edition of 1544, as well as in 

 the Greek text of that edition, except that in this latter there 

 is an error of AA for PX. 



Sturm, who does not give a regular translation of his au- 

 thor, has avoided the error in the text, biit it is retained in 

 Nizre and Peyrard. 



Hauber has adopted the correction of the old translation, 

 which is, undoubtedly, just; " since the ratio of PX to AX is 

 given, that of PA to AX is also given." 



The President described certain improvements in the 

 construction of the Anemometer, and exhibited to the Aca- 

 demy the improved instrument. 



