Whether a body falling upon the superficies of another body and being reflected from it, do make equal angles at that superficies, it belongs not to this place to dispute, being a knowledge which depends upon the natural causes of reflection; of which hitherto nothing has been said, but shall be spoken of hereafter.
In this place, therefore, let it be supposed that the angle of incidence is equal to the angle of reflection; that our present search may be applied, not to the finding out of the causes, but some consequences of the same.
I call an angle of incidence, that which is made between a strait line and another line, strait or crooked, upon which it falls, and which I call the line reflecting; and an angle of reflection equal to it, that which is made at the same point between the strait line which is reflected and the line reflecting.
If two strait lines falling upon another strait line be parallel, the lines reflected from them shall also be parallel.
1. If two strait lines, which fall upon another strait line, be parallel, their reflected lines shall be also parallel.
Let the two strait lines A B and C D (in [fig. 1]), which fall upon the strait line E F, at the points B and D, be parallel; and let the lines reflected from them be B G and D H. I say, B G and D H are also parallel.
For the angles A B E and C D E are equal by reason of the parallelism of A B and C D; and the angles G B F and H D F are equal to them by supposition; for the lines B G and D H are reflected from the lines A B and C D. Wherefore B G and D H are parallel.
If two strait lines drawn from one point fall upon another strait line, the lines reflected from them, if they be drawn out the other way, will meet in an angle equal to the angle made by the lines of incidence.
2. If two strait lines drawn from the same point fall upon another strait line, the lines reflected from them, if they be drawn out the other way, will meet in an angle equal to the angle of the incident lines.
From the point A (in [fig. 2]) let the two strait lines A B and A D be drawn; and let them fall upon the strait line E K at the points B and D; and let the lines B I and D G be reflected from them. I say, I B and G D do converge, and that if they be produced on the other side of the line E K, they shall meet, as in F; and that the angle B F D shall be equal to the angle B A D.