Archimedes Texts

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

SIMPL. 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 Gentle
man, that I did not guesse at this solution, nor should I have
thought upon it, without your help, or without long study.

SAGR. The resolutions, which between you two have been
alledged touching this last doubt, hath, to speak the truth, satisfi
ed me also. But at the same time this consideration of the vi
fible 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 middle
most parts, which receive them directly. And its possible, that a
tract or space of v. g. twenty degrees in breadth, and which is to
wards 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 e
qually 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