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. But forasmuch as she is not only enlightened herself, but also sends back hither the image of her illumination, this confirms us yet further in what we say touching her substance. For reflections and reverberations are not made upon any thing which is rare, and of thin and subtile parts; nor is it easily to be imagined how light can rebound from light, or one fire from another. But that which is to make the reverberation or reflection must be solid and firm, that a blow may be given against it and a rebounding made from it. As a proof of this, we see that the air transmits the sun, and gives him a way to pierce quite through it, not obstructing or driving back his rays; but on the contrary from wood, stones, or clothes put in the sun, there are made many reflections of light and many illuminations round about. So we see that the earth is illuminated by him, not to the very bottom, as the water, nor thoroughly and all over, as the air, through which the beams of the sun have a clear passage; but just such a circle as surrounds the moon surrounds also the earth; and as much of the earth as this circle includes, so much does the sun enlighten, the rest being left without light; for what is illuminated both in the one and in the other is little more than an hemisphere. Permit me therefore now to conclude after the manner of geometricians by proportions. If there are three things which the light of the sun approaches, the air, the moon, and the earth, and if we see that the moon is enlightened by him, not as the air, but as the earth, it is of necessity that those two things must have one and the same nature, which of one and the same cause suffer the same effects.