\ 
180 Description of a Burning Mirror. 
be reflected at the point A,,on account of the angle ZBA 
being divided into two equal parts, and the reflection 
‘being made at equal angles, as we have already shown. 
<«¢ We shall reflect in a similar manner in A the ray PA 
in this manner: Draw the straight lines ZA, ZM, BZ. 
It is evident that ZA is equal to 2Z, on account of the 
angle at B being divided equally into two parts. But 242 * 
is equal to BM, “because from the iniddle point = -they are 
directed towards the points Z,M. Thus. Mz 1s equal to 
BA. Cut, therefore, into two equal parts the angle MEA 
by the line =TO, the point O being considered in ‘the mid- 
dle between the parallels MA, INK; and this line secting 
the parallel MA at the point T}.we ‘shall demonstrate by 
the same reasons that MT is equal to TA, and that TA.... 
Ceiera desint.” 
The mirror of Anthemius, like that of Buffon, has all 
the properties, and nothing but the prnper ess ofa parabolic 
mirror composed of plain glasses. Both these mirrors may 
set fire to an obyecty w hatever its position, may be. The 
mirror of Anthemius, which is ee omietrically constructed, is 
a true parabolic mirror; whereas the mirror of Buffon, when 
it is adjusted, is a very imperfect parabolic mirror. The 
focus of the parabolic mirror of Anthemius js invariable; 
whereas the focus of Bufion’s mirror is variable at pleasure. 
But we should be strangely deceived if we thought thar, 
the position of the object being given and the position of 
the mirror being also given, we scout set fire to an object. 
at any hour of the day or any day of the year. These two 
mirrors cannot produce all their effects, except at the very 
moment when the sun is at the same point in the heavens 
at which it was when the mirror of Anthemius was con- 
structed, and when that of Buffon was adjusted. 
It now remains to speak of the burning mirror of Archi- 
medes, with which he is said to bave burned the fleet of 
Marcellus before the walls of Syracuse. 
The ancient authors who speak of this mirror are Lu- 
cian, Galienus, Anthemius of Tralles, Eustathius, Tzetzes 
and Zonaras. } 
Lucian says, in his Hippias, that Archimedes, by a sin- 
gular artifice, reduced’ the ships of the Romans to ashes. 
Galieuus expresses himself in the follawing manner: 
It isin this way, at least [ think so, that Archimedes burnt 
the enemy’s vessels. For, by the help of a burning mirror, 
we may easily set fire to wool, hemp, wood, &c. and, in 
short, to anv thing dry and light ats 
* De Temperamentis, lib, iit. cap. 2 
Anthemius, 
