Pennethorne, John; Robinson, John [Ill.]: The geometry and optics of ancient architecture: illustrated by examples from Thebes, Athens, and Rome (London [u.a.], 1878)

THE COLUMNS.

135

consider whether it is possible from the existing examples in Athens, inductively to recover
the ancient method of proportioning and of tracing the spiral lines of the Ionic volutes.

The idea of the spiral line, as that of other curved lines, is suggested by many forms
that we find in nature : it may also be derived from the cone, by conceiving a continuous
line winding round it from the base to the vertex. In the ancient geometry we have
the spiral of Archimedes, and some of the spiral lines of the Greek ornaments will,
perhaps, be found to be true examples of this form of curve; but in the case of the Ionic
capitals, it is clearly stated by Vitruvius that the spiral lines are composed of the arcs of
circles, and the tracings taken from the existing Greek volutes show clearly that this is
the case.

It is easy also to derive from the marble the fact that each revolution of the spiral
lines is contained within a given parallelogram, the sides of which are in some exact propor-
tion, as 5 : 6, or 6 : 7, etc. Thus, in the volute of the Ionic Column of the Propylaea, taking
as an example the No. 1 spiral line, see Fig. 3, then—

The parallelogram ABDC, containing the first revolution of the

No. 1 spiral line, the ratio of the sides, DB : AB are as 6 : 7

The parallelogram ArBrDlC, containing the second revolution of the

No. 1 spiral line, the ratio of the sides, DB' : AB1 are as 6 : 7

The parallelogram AJ'BVG11, containing the third revolution of the

No. 1 spiral fine, the ratio of the sides, ~D!,B!I : A/rB/; are as 6 : 7

*

These are simply the observed facts, but beyond these observed facts there is still
required some law for fixing in position and in dimension these several parallelograms one
within another, and for this law I am indebted to the careful study of the subject by
Mr. John Robinson, who discovered the relationship between the several rectangular lines con-
taining the No. 1 spiral fine. Thus, in—

Fig. 3. The given proportions of the rectangular lines containing the No. 1 spiral line of the
volute of the Propylsea.

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The parallelogram ABDC is derived from
the general given proportions of the capital,
and it is required to lay down the two inner
parallelograms, AB'D'C and A'BWC''.

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