21 THE FIEST GIVEN PBOPORTIONS.

CHAPTER III.

THE PROJECTIONS.

In the Second Chapter we have obtained from direct observation the first general Pro-
portions of all the Athenian Porticoes; but in each Portico, before we can proceed with any
calculations, the Projections of the Steps, and of the various members of the Entablatures,
as well as the inclinations inwards of the masses of the Columns and of the Entablatures,
must be determined.

Also, in Temples like the Parthenon and the Theseium, the length of the Upper
Step on the return side must be accurately laid down, and the heights of the Pediments
must be ascertained.

The laying down of these several details, with a few general remarks upon the facts
that have been derived from direct observation, will form the subjects of this Third Chapter.

PLATE IV.

THE GIVEN PROJECTIONS IN THE SEVERAL ATHENIAN PORTICOES
OF THE STEPS, AND OF THE DETAILS OF THE ENTABLATURES,
AND THE FIRST INCLINATION INWARDS OF THE MASSES.

In all the vertical dimensions it has been found that certain corrections are required
before we can arrive at the true executed magnitudes of any Portico; but we find from
observation that all the horizontal dimensions are executed exactly as they are first laid down :
Still before the plan of any given design can be traced and prepared for the required calcula-
tions, all the Projections, namely, the width of the Steps, the Projections of the several parts
of the Entablature measured from the face of the frieze, and the first inclination of the
masses, must be arranged.

The Greeks in all their works never lost sight of the principle of dividing everything
into aliquot parts, so that all their designs can be laid down in Proportion, even to the
minutest details in the Columns and Entablatures without any reference to dimension, and
this we find to be the case with regard to the Projections of the several Porticoes.