Archimedes Texts

201
Shast. But from that natural Instinct or Sense
in the Mind by which, as we have already ob
served, we judge of Beauty and Gracefulness,
they found, that one of these was too thick and
the other too slight; for which Reason they
altered them both, rightly supposing that the
Truth must lie in some Medium between these
two vitious Extremes. Accordingly, with the
Help of the Rules of the Arithmeticians, they
joined their two Numbers together, and divid
ed the Total in half, and then they found that
the mean Number between six and ten was
eight: Whereupon they made the Height of
their Column eight Times the Diameter of the
Bottom of the Shaft; and this they called the
Ionic. They also formed their Doric Column,
which is proper for Buildings of greater Solidi
ty, by the same Rules. For Example, they
joined the smaller Number before-mentioned,
which was six, with the Ionic mean, which was
eight, whereof the Total was fourteen; this
Total they divided into two equal Parts, and
this gave them the Number seven, which they
took for their Doric Column, making its Length
seven Times the Diameter of the Bottom of the
Shaft. Lastly, they made their thinnest Order,
which they called the Corinthian, from the Ionic
mean Number joined to the greatest of the for
mer Numbers, and so taking the Half as
before; for the Ionic mean Number was eight,
and the greatest Number was ten, which add
ed together made eighteen, the Half whereof
was nine, whence they made the Height of
their Corinthian Column nine Times the Dia
meter of the Bottom of its Shaft, as they did
the Ionic eight, and the Doric seven: Of which
we need say no more in this Place. We are
now to say something of the Collocation, which
relates to the Situation of the several Parts;
and this is much easier to conceive where it is
ill done, than it is to lay down exact Rules for
the doing it: Because indeed it is chiefly to be
referred to the natural Judgment which we
have formerly observed to be innate in the
Mind of Man, though it may in some Mea
sure be derived from the foregoing Rules for
the Finishing. However, we shall just men
tion a few general Remarks upon this Head.
The very smallest Parts or Members of the
Work, if they are set in their right Places, add
to the Beauty of the whole; if they are placed
in mean or improper Situations, though excel
lent in themselves, they become mean. We
see the very same Thing in the Works of Na
ture: As for Instance, if a Dog had one Ear
like that of an Ass, or if a Man had one Foot
bigger than the other, or one Hand very large,
and the other very small, we should immedi
ately pronounce such a one deformed; or to
see even an Horse with one Eye grey, and the
other black, is very offensive: So agreeable it
is to Nature, that the Members on the right
Side should exactly answer the left: Wherefore
the very first Thing we are to take Care of
must be, that every Part, even the most Incon
siderable, lie duly to the Level and Plum-line,
and be disposed with an exact Correspondence
as to the Number, Form and Appearance; so
that the Right may answer to the Left, the
High to the Low, the Similar to the Similar, so
as to form a correspondent Ornament in that
Body whereof they are Parts. Even Statues,
Pictures, or any other Ornaments of that Sort
with which we embellish our Work, must be so
disposed as to seem to have sprung up naturally
in their properest Places, and to be Twins. The
Ancients were so punctual in this mutual Cor
respondence of the Parts, that even in fixing
up their Scantlings of Marble, they used to
make them answer each other exactly to a
Size, Quality, Angles, Situation and Colour:
And especially in those most beautiful Orna
ments, Statues, wherein the Ancients were such
great Masters, and in which I so much admire
the Excellence of Art, they were careful in fix
ing them up, as well on Pediments of their
Temples, as elsewhere, that those on one Side
should not differ from those on the other, in
the smallest Particular either of Design or Ma
terial. We see Statues of two or four Horses,
and of their Drivers and Lookers on so exact
ly like to each other, that Art in them may be
said to have exceeded Nature, in whose Works
we hardly ever see one Feature so exactly like
the other. Thus we have shewn what is Beauty,
and wherein it consists, and with what Num
bers and Finishing the Ancients used to erect
their Structures.