Archimedes Texts

316
circle, either bigger or lesser, according as it is more or lesse re
mote from the said Poles, let us take the point F, equally distant
from them, and draw the diameter F O G, which shall be perpen
dicular to the Axis E I, and shall be the diameter of the grand
circle described about the Poles E I. Supposing not that the
Earth, and we with her be in such a place of the Ecliptick, that
the Hemisphere of the Sun to us apparent is determin'd or bound
ed by the circle A B C D, which passing (as it alwayes doth) by
the Poles A C, passeth also by E I. It is manifest, that the grand
circle, whose diameter is FG, shall be erect to the circle A B C D,
to which the ray that from our eye falleth upon the centre O, is
perpendicular; so that the said ray falleth upon the plane of
the circle, whose diameter is F G, and therefore its circumference
will appear to us a right line, and the self same with F G, where
upon if there should be in the point F, a spot, it comming after
wards to be carried about by the Solar conversion, would, upon
the surface of the Sun, trace out the circumference of that cir
cle, which seems to us a right line. Its course or passage will
therefore seem straight. And straight also will the motion of the
other spots appear, which in the said revolution shall describe les
ser circles, as being all parallel to the greater, and to our eye
placed at an immense distance from them. Now, if you do but
consider, how that after the Earth shall in six moneths have run
thorow half the grand Orb, and shall be situate opposite to that
Hemisphere of the Sun, which is now occult unto us, so as that
the boundary of the part that then shall be seen, may be the self
same A B C D, which also shall passe by the Poles E I; you
shall understand that the same will evene in the courses of the
spots, as before, to wit, that all will appear to be made by right
lines. But because that that accident takes not place, save one
ly when the terminator or boundary passeth by the Poles E I,
and the said terminator from moment to moment, by meanes of
the Earths annual motion, continually altereth, therefore its pas
sage by the fixed Poles E I, shall be momentary, and consequent
ly momentary shall be the time, in which the motions of those
spots shall appear straight. From what hath been hitherto spoken
one may comprehend also how that the apparition and beginning
of the motion of the spots from the part F, proceeding towards
G, their passages or courses are from the left hand, ascending to
wards the right; but the Earth being placed in the part diame
trically opposite the appearance of the spots about G, shall still
be to the left hand of the beholder, but the passage shall be des
cending towards the right hand F. Let us now describe the Earth
te be situate one fourth part farther distant from its present state,
and let us draw, as in the other figure, the terminator A B C D,