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. 18. But in brief, said he, I wonder how they come thus to allege against us the half-moon, there being the same reason when she is gibbous and crescent. For if the sun enlightened the moon, as a mass of ethereal or fiery matter, he would never surely leave one hemisphere, or half of her globe always appearing dark and shadowy to sense, as it is seen to be; but how little soever he touched her superficies, it would be agreeable to reason that it should be wholly replenished and totally changed by that light of his, which by reason of its agility and swiftness so easily spreads and passes through all. For, since wine touching water only in one point, or one drop of blood falling into any liquor, dyes and colors it all with a red or purple color; and since they say, that the very air is altered and changed with light, not by any defluxions or beams intermingled, but by a sudden conversion and change made in one only point; how can they imagine that one star touching another star, and one light another light, should not be immediately mingled, nor make any thorough confusion or change, but only exteriorly illuminate that whose superficies it touches? For that circle which the sun makes by fetching a compass and turning towards the moon,—sometimes falling upon the very line that distinguishes her visible part from her invisible, and sometimes rising up directly, so that it cuts her in two and is reciprocally cut by her, causing in her, by several inclinations and habitudes of the luminous to the dark, those various forms by which she appears gibbous and crescent,—that more than any thing else demonstrates, that all this illumination of the moon is not a mixture, but only a touching; nor a conflux or gathering together of sundry lights, but only an illustration round about.