In architecture, this trinity of vertical, horizontal and curved lines finds admirable illustration in the application of columns and entablature to an arch and impost construction, so common in Roman and Renaissance work.  This is a redundancy, and finds no justification in reason, because the weight is sustained by the arch, and the “order” is an appendage merely; yet the combination, illogical as it is, satisfies the sense of beauty because the arch effects a transition between the columns and the entablature, and completes the trinity of vertical, horizontal and curved lines (Illustration 21).  In the entrances to many of the Gothic cathedrals and churches the same elements are better because more logically disposed.  Here the horizontal lintel and its vertical supports are not decorative merely, but really perform their proper functions, while the arch, too, has a raison d’etre in that it serves to relieve the lintel of the superincumbent weight of masonry.  The same arrangement sometimes occurs in classic architecture also, as when an opening spanned by a single arch is subdivided by means of an order (Illustration 22).

Three is pre-eminently the number of architecture, because it is the number of space, which for us is three-dimensional, and of all the arts architecture is most concerned with the expression of spatial relations.  The division of a composition into three related parts is so universal that it would seem to be the result of an instinctive action of the human mind.  The twin pylons of an Egyptian temple with its entrance between, for a third division, has its correspondence in the two towers of a Gothic cathedral and the intervening screen wall of the nave.  In the palaces of the Renaissance a threefold division—­vertically by means of quoins or pilasters, and horizontally by means of cornices or string courses—­was common, as was also the division into a principal and two subordinate masses (Illustration 23).

[Illustration 22:  THE LAW OF TRINITY.  THE TRINITY OF HORIZONTAL VERTICAL AND CURVED LINES.]

The architectural “orders” are divided threefold into pedestal or stylobate, column and entablature; and each of these is again divided threefold:  the first into plinth, die and cornice; the second into base, shaft and capital; the third into architrave, frieze and cornice.  In many cases these again lend themselves to a threefold subdivision.  A more detailed analysis of the capitals already shown to be twofold reveals a third member:  in the Greek Doric this consists of the annulets immediately below the abacus; in the other orders, the necking which divides the shaft from the cap.

CONSONANCE