Archimedes Texts

420
stituted in other points of the Quadrant A I, drawing the Tan
gents in the said points, and the perpndiculars upon the same fal
ling from the terms of the diameters of the Equinoctial drawn
from the errect planes by the said Tangents to the plane of the
grand Orb; the parts of the said Tangents (which shall conti
nually be lesser towards the Equinoctials, and greater towards the
Solstices) shall give us the quantities of the additions and substra
ctions. How much in the next place the least additions differ from
the greatest, is easie to be known, because there is the same dif
ference betwixt them, as between the whole Axis or Diameter of
the Sphere, and the part thereof that lyeth between the Polar
Circles; the which is less than the whole diameter by very near a
twelfth part, supposing yet that we speak of the additions and
substractions made in the Equinoctial; but in the other Paral
lels they are lesser, according as their diameters do diminish.

This is all that I have to say upon this Argument, and all perhaps
that can fall under the comprehension of our knowledge, which,
as you well know, may not entertain any conclusions, save onely
those that are firm and constant, such as are the three kinds of Pe
riods of the ebbings and flowings; for that they depend on causes
that are invariable, simple, and eternal. But because that se
condary and particular causes, able to make many alterations, in
termix with these that are the primary and universal; and these
secondary causes being part of them inconstant, and not to be
observed; as for example, The alteration of Winds, and part
(though terminate and fixed) unobserved for their multiplicity,
as are the lengths of the Straights, their various inclinations to
wards this or that part, the so many and so different depths of the
Waters, who shall be able, unless after very long observations, and
very certain relations, to frame so expeditious Histories thereof, as
that they may serve for Hypoth eses, and certain suppositions to
such as will by their combinations give adequate reasons of all the
appearances, and as I may say, Anomalie, and particular irregula
rities that may be discovered in the motions of the Waters? I
will content my self with advertising you, that the accidental
causes are in nature, and are able to produce many alterations;
for the more minute observations, I remit them to be made by
those that frequent several Seas: and onely by way of a conclu
sion to this our conference, I will propose to be considered, how
that the precise times of the fluxes and refluxes do not onely hap
pen to be altered by the length of Straights, and by the diffe
rence of depths; but I believe that a notable alteration may also
proceed from the comparing together of sundry tarcts of Sea,
different in greatness; and in position, or, if you will, inclina
tion; which difference happeneth exactly here in the Adriatick