Archimedes Texts

419
be perpendicular to the same D E, by reason that the Colure is
erect upon the grand Orb; and therefore the said D E,
shall be the Tangent of the grand Orb in the point A.
So that in this Position the motion of the Centre by the arch
A E; that is, of one degree every day differeth very little; yea,
is as if it were made by the Tangent D A E. And because by
means of the diurnal motion the point D, carried about by G,
unto E, encreaseth the motion of the Centre moved almost in the
same line D E, as much as the whole diameter D E amounts
unto; and on the other side diminisheth as much, moving about
the other semicircle E F D. The additions and subductions
in this place therefore, that is in the time of the solstice, shall be
measured by the whole diameter D E.

Let us in the next place enquire, Whether they be of the same
bigness in the times of the Equinoxes; and transporting the
Centre of the Earth to the point I, distant a Quadrant of a
Circle from the point A. Let us suppose the said Equinoctial
to be G E F D, its common section with the grand Orb D E, the
Axis with the same inclination C B; but the Tangent of the grand
Orb in the point I shall be no longer D E, but another which
shall cut that at right Angles; and let it be this marked H I L,
according to which the motion of the Centre I, shall make its pro
gress, proceeding along the circumference of this grand Orb.
Now in this state the Additions and Substractions are no longer
measured by the diameter D E, as before was done; because that
diameter not distending it self according to the line of the annual
motion H L, rather cutting it at right angles, those terms D E, do
neither add nor substract any thing; but the Additions and
Substractons are to be taken from that diameter that falleth
in the plane that is errect upon the plane of the grand Orb, and
that intersects it according to the line H L; which diameter in this
case shall be this G F and the Adjective, if I may so say, shall
be that made by the point G, about the semicircle G E F, and the
Ablative shall be the rest made by the other semicircle F D G.
Now this diameter, as not being in the same line H L of the
annual motion, but rather cutting it, as we see in the point I, the
term G being elevated above, and E depressed below the plane
of the grand Orb, doth not determine the Additions and Sub
stractions according to its whole length, but the quantity of those
first ought to be taken from the part of the line H L, that is in
tercepted between the perpendiculars drawn upon it from the
terms G F; namely, these two G S, and F V: So that the mea
sure of the additions is the line S V lesser then G F, or then D E;
which was the measure of the additions in the Solstice A. And
so successively, according as the centre of the Earth shall be con