Archimedes Texts

317
[as in Fig. 5.] and the Axis, as before A C, by which the plane
of our Meridian would passe, in which plane should also be the
Axis of the Suns revolution, with its Poles, one towards us, that
is, in the apparent Hemisphere, which Pole we will represent by
the point E, and the other shall fall in the occult Hemisphere,
and I mark it I. Inclining therefore the Axis E I, with the supe
riour part E, towards us, the great circle described by the Suns
conversion, shall be this B F D G, whose half by us seen, name
ly B F D, shall no longer seem unto us a right line, by reason the
Poles E I are not in the circumference A B C D, but shall appear
incurvated, and with its convexity towards the inferiour part C.
And it is manifest, that the same will appear in all the lesser cir
cles parallel to the same B F D. It is to be understood also, that
when the Earth shall be diametrically opposite to this state, so
that it seeth the other Hemisphere of the Sun, which now is hid,
it shall of the said great circle behold the part D G B incurved,
with its convexity towards the superiour part A; and the cour
ses of the spots in these constitutions shall be first, by the arch
B F D, and afterwards by the other D G B, and the first appari
tions and ultimate occultations made about the points B and D,
shall be equilibrated, and not those that are more or lesse eleva
ted than these. But if we constitute the Earth in such a place
of the Ecliptick, that neither the boundary A B C D, nor the
Meridian A C, passeth by the Poles of the Axis E I, as I will shew
you anon, drawing this other Figure [viz. Fig. 6.] wherein the
apparent or visible Pole E falleth between the arch of the termi
nator A B, and the section of the Meridian A C; the diameter
of the great circle shall be F O G, and the apparent semicircle
F N G, and the occult semicircle G S F, the one incurvated with
its convexity N towards the inferiour part, and the other also
bending with its convexity S towards the upper part of the Sun.
The ingressions and exitions of the spots, that is, the termes F
and G shall not be librated, as the two others B and D; but F
shall be lower, and G higher: but yet with lesser difference
than in the first Figure. The arch also F N G shall be incurva
ted, but not so much as the precedent B F D; so that in this po
sition the passages or motions of the spots shall be ascendent
from the left side F, towards the right G, and shall be made by
curved lines. And imagining the Earth to be constituted in the
position diametrically opposite; so that the Hemisphere of the
Sun, which was before the occult, may be the apparent, and ter
minated by the same boundary A B C D, it will be manifestly
discerned, that the course of the spots shall be by the arch G S F,
beginning from the upper point G, which shall then be likewise
from the left hand of the beholder, and going to determine, des