Sylla then, taking up the discourse, said: There is indeed a great deal of probability in all that you have spoken. But as to the strongest objection that is brought against it, has it, think you, been any way weakened by this discourse? Or has our friend quite passed it over in silence? What opposition do you mean, said Lucius? Is it the difficulty about the moon, when one half of her appears enlightened? The very same, answered Sylla. For there is some reason, seeing that all reflection is made by equal angles, that when the half-moon is in the midst of heaven, the light proceeding from her should not be carried upon the earth, but glance and fall beyond and on one side of it. For the sun, being placed in the horizon, touches the moon with its beams; which, being equally reflected, will therefore necessarily fall on the other bound of the horizon, and not send their light down hither; or else there will be a great distortion and difference of the angle, which is impossible. And yet, by Jupiter, replied Lucius, this has not been forgotten or overpassed, but already spoken to. And casting his eye, as he was discoursing, upon the mathematician Menelaus; I am ashamed, said he, in your presence, dear Menelaus, to attempt the subverting and overthrowing of a mathematical position, which is supposed as a basis and foundation to the doctrine of the catoptrics concerning the causes and reasons of mirrors. And yet of necessity I must. For it neither appears of itself nor is confessed as true, that all reflections are at equal angles; but this position is first checked and contradicted in concave mirrors, when they represent the images of things, appearing at one point of sight, greater than the things themselves. And it is also disproved by double mirrors, which being inclined or turned one towards the other, so that an angle is made within, each of the glasses or plain superficies yields a double resemblance; so that there are four images from the same face, two answerable to the object without on the left side, and two others obscure and not so evident on the right side in the bottom of the mirror. Of which Plato renders the efficient cause; for he says, that a mirror being raised on the one and the other side, the sight varies the reflection, falling from one side to the other. And therefore, since of the views or visions some immediately have recourse to us, and others, sliding to opposite parts of the mirror, do again return upon us from thence, it is not possible that all reflections should be made at equal angles. Though those who closely impugn our opinion contend that, by these reflections of light from the moon upon the earth, the equality of angles is taken away, thinking this to be much more probable than the other. Nevertheless, if we must of necessity yield and grant thus much to our dearly beloved geometry, first, this should in all likelihood befall those mirrors which are perfectly smooth and exquisitely polished; whereas the moon has many inequalities and roughnesses, so that the rays proceeding from a vast body, and carried to mighty altitudes, receive one from another and intercommunicate their lights, which, being sent to and fro and reciprocally distributed, are refracted and interlaced all manner of ways, and the counter-lights meet one another, as if they came to us from several mirrors. And then, though we should suppose these reflections on the superficies of the moon to be made at equal angles, yet it is not impossible that the rays, coming down unto us by so long an interval, may have their flexions, fractions, and delapsions, that the light being compounded may shine the more. Some also there are who prove by lineary demonstration, that many lights send a ray down by a line drawn below the line of reflection; but to make the description and delineation of it publicly, especially where there were many auditors, would not be very easy.