Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/92

 go accompanied with those illuminating beams of the Sun.

This is true, without any contradiction.

But when the Moon is opposite to the Sun, what difference is there between the tract of the rayes of your sight, and that motion which the Suns rayes make?

Now I understand you; for you would say, that the rayes of the sight and those of the Sun, moving by the same lines, we cannot perceive any of the obscure valleys of the Moon. Be pleased to change this your opinion, that I have either simulation or dissimulation in me; for I protest unto you, as I am a Gentleman, that I did not guesse at this solution, nor should I have thought upon it, without your help, or without long study.

The resolutions, which between you two have been alledged touching this last doubt, hath, to speak the truth, satisfied me also. But at the same time this consideration of the visible rayes accompanying the rayes of the Sun, hath begotten in me another scruple, about the other part, but I know not whether I can expresse it right, or no: for it but just now comming into my mind, I have not yet methodized it to my mind: but let us see if we can, all together, make it intelligible. There is no question, but that the parts towards the circumference of that polish't, but not burnish't Hemisphere, which is illuminated by the Sun, receiving the rayes obliquely, receive much fewer thereof, than the middlemost parts, which receive them directly. And its possible, that a tract or space of v. g. twenty degrees in breadth, and which is towards the extremity of the Hemisphere, may not receive more rays than another towards the middle parts, of but four degree broad: so that that doubtless will be much more obscure than this; and such it will appear to whoever shall behold them both in the face, or (as I may say) in their full magnitude. But if the eye of the beholder were constituted in such a place, that the breadth of the twenty degrees of the obscure space, appeared not to it longer than one of four degrees, placed in the midst of the Hemisphere, I hold it not impossible for it to appear to the said beholder equally clear and lucid with the other; because, finally, between two equal angles, to wit, of four degrees apiece, there come to the eye the reflections of two equal numbers of rayes: namely, those which are reflected from the middlemost space, four degrees in breadth, and those reflected from the other of twenty degrees, but seen by compression, under the quantity of four degrees: and such a situation shall the eye obtain, when it is placed between the said Hemisphere, and the body which illuminates it; for then the sight and rayes move in the same lines. It seemeth not impossible therefore, but that the Moon may be of a very equal superficies; and that neverthelesse, it may appear when it is at the full, no less