DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.4423#0066
THE FIRST GIVEN PROPORTIONS, 41
and Proportion according to the definitions of perfect Proportion previously agreed upon—that
is all the apparent magnitudes must be made to appear commensurable one with another, and
any apparent defects in the appearance of the horizontal hues (that is, if they should have a
concave appearance as mentioned by Vitruvius) must be rectified.
It is of the utmost consequence in each design to determine with accuracy this point,
as it is impossible to re-calculate any work of Greek Architecture and to arrive at the same
dimensions until it is fixed with precision. But as we have seen, there is sufficient data
remaining in the Acropolis of Athens to enable us, in every case, accurately to assume the
original position of the eye with regard to each design, and it must then be proved by the
calculated dimensions agreeing in mathematical accuracy with those that are executed.
The results obtained by theory must in every example agree with those derived from
observation, not approximately, but positively.
It being evidently intended that the several designs should be seen from angular points
of view, we may in every example—
1st. Assume the greatest diagonal line in the plan of the design as the base of a triangle whose
angle at the vertex shall always be equal to 45°, which may be considered as the visual
angle of distinct vision. The vertex of this angle determined on the horizontal plane
will be found to be the fixed designing point.
2nd. The distance of the Upper Step of the design above or below the eye of the spectator
(i.e, above or below the horizontal plane) must also be made a given quantity.
3rd. The centre of the given road of approach is generally the point selected for the position
of the observer.
We have now derived from observation all the given quantities that are required to be
ascertained before we proceed to the second part of the theory of Proportion, namely, the
determination of the apparent magnitudes.
These given quantities are the first Proportions of these several Porticoes; the true
projections of the Steps, Cornices, and other members of the Entablatures; the length of the
return sides; the inclination inwards of the masses of the Columns and Entablatures; the
given length in feet of the Upper Step, which regulates all the other dimensions ; the position
of each design upon its artificial platform; the true height of the Upper Step in each design,
either above or below the level of the eye; and the true position of the eye with regard to the
whole design, which design has now simply to be corrected by trigonometrical calculations to
determine, firstly, the true executed heights of the Steps, the Columns, and the Entablature,
with its subdivisions into Architrave, Frieze, and Cornice, and the several members of the
Cornice, and lastly, the height of the Pediment.
and Proportion according to the definitions of perfect Proportion previously agreed upon—that
is all the apparent magnitudes must be made to appear commensurable one with another, and
any apparent defects in the appearance of the horizontal hues (that is, if they should have a
concave appearance as mentioned by Vitruvius) must be rectified.
It is of the utmost consequence in each design to determine with accuracy this point,
as it is impossible to re-calculate any work of Greek Architecture and to arrive at the same
dimensions until it is fixed with precision. But as we have seen, there is sufficient data
remaining in the Acropolis of Athens to enable us, in every case, accurately to assume the
original position of the eye with regard to each design, and it must then be proved by the
calculated dimensions agreeing in mathematical accuracy with those that are executed.
The results obtained by theory must in every example agree with those derived from
observation, not approximately, but positively.
It being evidently intended that the several designs should be seen from angular points
of view, we may in every example—
1st. Assume the greatest diagonal line in the plan of the design as the base of a triangle whose
angle at the vertex shall always be equal to 45°, which may be considered as the visual
angle of distinct vision. The vertex of this angle determined on the horizontal plane
will be found to be the fixed designing point.
2nd. The distance of the Upper Step of the design above or below the eye of the spectator
(i.e, above or below the horizontal plane) must also be made a given quantity.
3rd. The centre of the given road of approach is generally the point selected for the position
of the observer.
We have now derived from observation all the given quantities that are required to be
ascertained before we proceed to the second part of the theory of Proportion, namely, the
determination of the apparent magnitudes.
These given quantities are the first Proportions of these several Porticoes; the true
projections of the Steps, Cornices, and other members of the Entablatures; the length of the
return sides; the inclination inwards of the masses of the Columns and Entablatures; the
given length in feet of the Upper Step, which regulates all the other dimensions ; the position
of each design upon its artificial platform; the true height of the Upper Step in each design,
either above or below the level of the eye; and the true position of the eye with regard to the
whole design, which design has now simply to be corrected by trigonometrical calculations to
determine, firstly, the true executed heights of the Steps, the Columns, and the Entablature,
with its subdivisions into Architrave, Frieze, and Cornice, and the several members of the
Cornice, and lastly, the height of the Pediment.