DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.4423#0182
THE COLUMNS,
139
PLATE VI.
THE METHOD OF DESCRIBING THE SPIRAL LINES OF THE
IONIC VOLUTES.
With regard to these Architectural spiral lines, composed of the arcs of circles, we have
nothing left in the ancient geometry to guide us to a solution of them, as all the Greek works
upon Architecture are lost, and Vitruvius carefully avoids all geometrical explanations in his
work upon the subject; but we possess the original curved lines executed with wonderful
precision in the marble, and with these data we may now proceed inductively to endeavour to
recover the ancient method of describing the spirals of the volutes.
It has been already stated that the designing of the volutes of the Ionic capitals is
divided into two operations. Firstly, to determine the dimensions and the positions of the
parallelograms within which each revolution of the spirals is described, and, secondly, to
describe the curves of the spirals within these given parallelograms, ABDC, A'B'D'C, A//B//D"C//;
and it is the second part of the subject that now remains to be considered.
The following method of describing the spiral lines of the Ionic volutes, when the
dimensions and the positions of the parallelograms are given, was discovered and worked out by
Mr. John Robinson, after several failures on my own part to lay down these curves correctly;
and the curved lines described by it agree so accurately with the tracings of the volutes
obtained from the original marble capitals, that I believe there can be but little doubt of its
having been the ancient method of drawing these spirals, whenever they are composed of the
arcs of circles, as is the case in the Ionic capitals.
To Describe the Spiral Lines.
Fig.l.
Fig. 1. Given the parallelogram ABDC ;
then upon the line, AB, construct the right-
angled isosceles triangle, AEB, and upon the
line, DK, construct the right-angled isosceles
triangle KGD.
The points E and G must always be
in the same perpendicular line, therefore,
ab + dk . ,
—-2----is always equal to the side DB,
for BO = f and OD
—, therefore,
BO + OD = BD = — + ^ = AB + DK
xjxj 2 2 2
139
PLATE VI.
THE METHOD OF DESCRIBING THE SPIRAL LINES OF THE
IONIC VOLUTES.
With regard to these Architectural spiral lines, composed of the arcs of circles, we have
nothing left in the ancient geometry to guide us to a solution of them, as all the Greek works
upon Architecture are lost, and Vitruvius carefully avoids all geometrical explanations in his
work upon the subject; but we possess the original curved lines executed with wonderful
precision in the marble, and with these data we may now proceed inductively to endeavour to
recover the ancient method of describing the spirals of the volutes.
It has been already stated that the designing of the volutes of the Ionic capitals is
divided into two operations. Firstly, to determine the dimensions and the positions of the
parallelograms within which each revolution of the spirals is described, and, secondly, to
describe the curves of the spirals within these given parallelograms, ABDC, A'B'D'C, A//B//D"C//;
and it is the second part of the subject that now remains to be considered.
The following method of describing the spiral lines of the Ionic volutes, when the
dimensions and the positions of the parallelograms are given, was discovered and worked out by
Mr. John Robinson, after several failures on my own part to lay down these curves correctly;
and the curved lines described by it agree so accurately with the tracings of the volutes
obtained from the original marble capitals, that I believe there can be but little doubt of its
having been the ancient method of drawing these spirals, whenever they are composed of the
arcs of circles, as is the case in the Ionic capitals.
To Describe the Spiral Lines.
Fig.l.
Fig. 1. Given the parallelogram ABDC ;
then upon the line, AB, construct the right-
angled isosceles triangle, AEB, and upon the
line, DK, construct the right-angled isosceles
triangle KGD.
The points E and G must always be
in the same perpendicular line, therefore,
ab + dk . ,
—-2----is always equal to the side DB,
for BO = f and OD
—, therefore,
BO + OD = BD = — + ^ = AB + DK
xjxj 2 2 2