270 
In a modern German edition of the whole of Archimedes, 
by Nirze (Stralsund, 1824), Hauber’s demonstration is adopted, 
but in a less advantageous form, and with an erroneous 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 tts 
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, but 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. 
