Chap. XXXI.

PRINCIPLES OF PROPORTION.

1609

In one of the tracery heads ofthe windows in the cloister at West-minster, the date of which is about1348, we have two figures that re-semble the plans given to clusteredpillars, indicating at once that thesame principles were applied tothe setting out of both windowsand points of support. Whenthe circumference of a circle isdivided into twelve equal parts,the points which divide them formthe termination of four equilateraltriangles, and we have at theirintersections, not only the centresof the circles that constitute thefilling in, but also the severalmitres and other portions of thefigure.

These rules were evidently ap-plied to windows, and to tracery ofevery description, executed atthe end of the thirteenth andcommencement of the fourteenthcenturies ; also to the plans of themain cluster of pillars in manycathedrals and churches. Fornearly a century, circles and theirintersections formed the ornamen-tal portions of every kind of paneland window head; they wereafterwards blended into otherfigures, and apparently set outupon different principles; but thehexagon and equilateral triangleswere necessary to produce the flow-ing lines which succeeded. Thechange which took place in designno doubt arose from the facilitywhich had been attained by thepractice of this method, and if itwere possible to exhibit eachvariety in England alone, therewould be ample evidence of theinventive power of the freemasons,and the progressive improvementin their school for depicting form.

The quatrefoil in fig. 3011. is metwith in the panels of several altartombs, in the spandrills of the arches of door-ways, and it is worthy of observation thatall the mitres, where the figures change theirform, are perfect for each: had these con-siderations been neglected, we should nothave had the graceful flowing lines foundin these designs : no other triangles crossingare so universally applicable, or require lessskill in their adoption. The student of thepresent day might occupy a life in the col-lection of these subjects, and they are mostexcellent models for the application of therules of theoretical geometry to practice.

Windows of three Days or Divisions aremet with, having heads of singular beauty,inclosed within an equilateral triangle, andso numerous are the designs, that it israre to meet with two exactly similar. In

Fig. 3011

CLOISTERS AT WESTMINSTER ABBEY

Fig. 3012.

CLOISTERS AT WESTMINSTER ABBEY

Fig. 3013.