The first post about the design of the fanlight is here: https://www.jgrarchitect.com/2012/12/old-first-church-bennington-part-2.html

Considering the 'leaves' of the fanlight, those 3 curved petals that fan out from the base of the light: how did Lavius Fillmore, the master builder, and his crew, especially Asa Hyde, the joiner, derive the pattern?

The layout that I drew of the leaves in the last post is too complex.

The church is graceful and direct.

The derivation in the previous post of the leaf pattern is not direct.

The geometry of the church is straight forward. The use of the circle to layout the framing, the design, would have been clear to other people in construction and to the church's congregation, as well as to anyone in that time who was educated beyond grammar school.

And then there's this diagram in my last post:

I drew the way the scallops on the curve of the light can overlap simply by rotating the circles one half a petal's width around the circumference, or 15*.

It is also the pattern of the leaves, just at a scale too big for the fanlight.

Drawn smaller, the pattern has 3 overlapping circles at its center, across what would be the sill of the fanlight. Here the circles come first; the leaves come from the pattern; the fanlight, its size and placement, come from the width of those combined circles.

However, the pattern in the The Old First Church fanlight was laid out knowing the dimensions for the fanlight. The door and its surround, the placement and size of the door in the main elevation, the width and height of the fanlight were determined by the geometry of the building. They were fixed.

So: given the width and height (about 60"w x 30"h) how were the leaves' sizes determined?

The 3 circles across the sill were overlapped. If they were 3 in a row the proportions would be 1/1/1. Then the width could be divided into 3 equal parts. Instead the proportions of the circles are 8/6/8, or 22 equal parts. Dividing a line into 22 segments with a compass and straight edge is complex.

The center lines (faint pencil lines here) of one set of the fanlight's scallops meet at the center of the fanlight These are the scallops that the leaves point to.

The distance between the scallops and the center of the fanlight is the diameter of the circles that will make the leaves.

The red spots are the centers of the circles.

The first 3 circles: where they cross each other and the sill they mark the centers of the next circles.

The 4 outer circles. *The ones that continue below the sill are not completely drawn.* Note that even though the center circle begins the design it was not needed here. It was understood implicitly by the joiner laying out the pattern.

Below is the layout of the leaves with all the circles included.