Archimedes Texts

321
equilibrated, and in their greatest curvity, one while with
their convexity towards the upper part, and another while
towards the lower part of the Solar Discus. And because
those positions are in continuall alteration, making the in
clinations and incurvations now greater, now lesser, and some
times reduce themselves, the first sort to perfect libration, and
the second to perfect perpendicularity, it is necessary to assert that
the self same Axis of the monethly revolution of the spots hath
a particular revolution of its own, whereby its Poles describe
two circles about the Poles of another Axis, which for that rea
son ought (as I have said) to be assigned to the Sun, the semidi
ameter of which circles answereth to the quantity of the incli
nation of the said Axis. And it is necessary, that the time of its
Period be a year; for that such is the time in which all the ap
pearances and differences in the courses of the spots do return.
And that the revolution of this Axis, is made about the Poles of
the other Axis parallel to that of the Ecliptick, & not about other
points, the greatest inclinations and greatest incurvations, which
are always of the same bigness, do clearly prove. So that finally, to
maintain the Earth fixed in the centre, it will be necessary to as
sign to the Sun, two motions about its own centre, upon two seve
ral Axes, one of which finisheth its conversion in a year, and the
other in lesse than a moneth; which assumption seemeth, to my
understanding, very hard, and almost impossible; and this de
pendeth on the necessity of ascribing to the said Solar body two
other motions about the Earth upon different Axes, describing
with one the Ecliptick in a year, and with the other forming spi
rals, or circles parallel to the Equinoctial one every day:
whereupon that third motion which ought to be assigned to the
Solar Clobe about its own centre (I mean not that almost
monethly, which carrieth the spots about, but I speak of that o
ther which ought to passe thorow the Axis and Poles of this
monethly one) ought not, for any reason that I see, to finish its
Period rather in a year, as depending on the annual motion by
the Ecliptick, than in twenty four hours, as depending on the
diurnal motion upon the Poles of the Equinoctial. I know, that
what I now speak is very obscure, but I shall make it plain unto
you, when we come to speak of the third motion annual, assign
ed by Copernicus, to the Earth. Now if these four motions, so
incongruous with each other, (all which it would be necessary to
assign to the self same body of the Sun) may be reduced to one
sole and simple motion, assigned the Sun upon an Axis that never
changeth position, and that without innovating any thing in the
motions for so many other causes assigned to the Terrestrial
Globe, may so easily salve so many extravagant appearances in