Description of a Burning Mirror. 17S 
rors, and even seven, and if they are all at the same di- 
stance from the substance to be burnt, so as that the rays 
which issue from them, mutually intersecting, may render 
the inflammation more considerable. For if the mirrors 
are all in one place} the rays reflected will intersect at very 
acute angles; so that all the place around the axis being 
heated, the inflammation will not take place at the single 
point given. We may also, by means of the construction 
of these same plain mirrors, dazzle the eyes of the enemy’s 
forces, who, not perceiving those who carry them on their 
shields, or above their heads, will fall into confusion. 
“ It is therefore possible, by means of the burning mirrors 
just mentioned, to carry inflammation to a given distance. 
Those who have made mention of the mirrors constructed 
by the divine Archimedes have not said that he made use 
of a single burning mirror, but of several; and I am of 
opinion that there is no other way of carrying inflamma- 
tion to any-distance. . 
But as the ancients, in treating ef common burning 
mirrors, have not explained in what manner the embola 
must be traced except by an organic process, without pre- 
senting on this head any geometrical demonstration, without 
even saying that they were conic sections, nor of what 
kind, nor how they were formed, we shall attempt to give 
some descriptions of similar embola, not without demon- 
stration, but by geometrical processes. 
“Let AB therefore (fig. 7) be the diameter of the burning 
mirror which we wish to construct, or upon which we wish 
to operate, and upon the line PEA, which cuts perpendi- 
cularly the line AB into two equal parts, let A be the point 
where we wish the reflection to be made; the point E be- 
ing the middle of the line AB. Join B, 4, and by B let 
there be drawn to AED the parallel BZ equal to BA; by 
the point Z, the line ZI parallel to BA, cutting at the 
point P the Jine AET. Cut by the middle PA to the point 
©, and @E will be the height of the embola relative to the 
diameter AB, as we shall presently see. Divide into as 
many equal parts as you please the straight line BE; into 
three, for instance, as in the figure subjoined: viz. EK, KA, 
and AB, and by the points K, A, draw at BZ, ET, the 
parallels AM, KN. Afterwards divide into two equal parts 
the angle ZBA, by the straight line BR, the point & bein 
considered as in the middle between the parallels BZ, AM. 
Prolong all these parallels from the side of A towards the 
points 11, P, =, I say that the ray parallel to the axis, 2. e. 
tu Ed, and falling by =B on the mirror at the point B, will 
M 2 be 
