Spherical triangle with a trefoil

Three swings at one opening, each from a corner through the other two, close a triangle with curved sides. Parker’s Glossary of 1850 calls it a spherical triangle. From the late thirteenth or early fourteenth century it is one of the curved forms common in window tracery: in England through the Decorated style, geometric from 1250 to 1290 and curvilinear from 1290 to 1350, and in some windows of Milan Cathedral. In a church its three corners have been read as a figure of the Trinity. The record gives the window, not its working, so the trefoil here is set out by a construction of our own, and it is exact. Each pair of swings crosses again beyond the third corner, and the lines through those crossings meet at the centre. Each lobe touches its side at the middle and the two lines beside it, so the lobes touch one another on those lines. One lobe is found by equal tangents, and its two openings are carried round to the others.