Archimedes Texts

345
ficies of an oblique Cylinder, which hath for one of its bases
the said annual circle, and for the other a like circle imagina
rily described by its extremity, or, (if you will) Pole, amongst
the fixed stars. And this same cylinder is oblique to the Plane of
the Ecliptick, according to the inclination of the Axis that de
scribeth it, which we have said to be 23 degrees and an half,
the which continuing perpetually the same (save onely, that in
many thousands of years it maketh some very small mutation,
which nothing importeth in our present businesse) causeth that

the Terrestrial Globe doth never more incline or elevate, but
still conserveth the same state without mutation. From whence
ensueth, that as to what pertaineth to the mutations to be ob
served in the fixed stars dependant on the sole annual motion,
the same shall happen to any point whatsoever of the Earths
surface, as befalleth unto the centre of the Earth it self; and
therefore in the present explanations we will make use of the
centre, as if it were any whatsoever point of the superficies.
And for a more facile understanding of the whole, let us design

the same in lineal figures: And first of all let us describe in the
Plane of the Ecliptick the circle A N B O [in Fig. 7.] and let
us understand the points A and B, to be the extreams towards
the North and South; that is, the beginning of [or entrance into]
Cancer or Capricorn, and let us prolong the Diameter A B, in
determinately by D and C towards the Starry Sphere. I say
now in the first place, that none of the fixed stars placed in the
Ecliptick, shall ever vary elevation, by reason of any whatso
ever mutation made by the Earth along the said Plane of the
Ecliptick, but shall alwayes appear in the same superficies, al
though the Earth shall approach and recede as great a space as is
that of the diameter of the Grand Orb, as may plainly be
seen in the said figure. For whether the Earth be in the point
A or in B, the star C alwayes appeareth in the same line A B C;
although the distance B C, be lesse than A C, by the whole
diameter A B. The most therefore that can be discovered in the
star C, and in any other placed in the Ecliptick, is the aug
mented or diminished apparent magnitude, by reason of the ap
proximation or recession of the Earth.

The annual mo
tion made by the
centre of the Earth
under the Eclip
tick and the diur
nal motion made
by the Earth about
its own centre.

The axis of the
Earth continueth
alwayes parallel to
it self, and descri
beth a Cylindrai
cal superficies, in
clining to the
grand Orb.

The fixed stars
placed in the E
cliptick never ele
vate nor descend,
on account of the
annual motion, but
yet approach and
recede.

SAGR. Stay a while I pray you, for I meet with a certain
scruple, which much troubleth me, and it is this: That the star
C may be seen by the same line A B C, as wel when the Earth
is in A, as when it is in B, I understand very well, as also fur
thermore I apprehend that the same would happen in all the

points of the line A B, so long as the Earth should passe from A
to B by the said line; but it passing thither, as is to be supposed,
by the arch A N B, it is manifest that when it shall be in the