Here's the link to the post:
https://www.jgrarchitect.com/2025/09/the-layout-of-italiante-window-pediment.html
Nathan Goodwin, the master carpenter for the reproduction, and I worked out the geometry. We didn't quite agree about the steps. That was interesting but not important. He laid out the curves and created the pediment.
Later Nathan found an article, written c. 1850, by the Episcopal Bishop of Vermont for his clergy, recommended the use of this curved pediment for Vermont parish churches. The Bishop included a drawing of the geometry. It seems unlikely that a church man, even one very well educated, would have designed this. Where had he found it?

Perhaps the Bishop had seen Peter Nicholson's Carpenter's New Guide, 10th Edition, published in Philadelphia in 1830.
Peter Nicholson was a British engineer and scientist. He wrote numerous popular books for master carpenters and builders. To learn more see this post:
https://www.jgrarchitect.com/2016/08/practical-geometry-as-described-by_16.html
The frontispiece of the 10th edition says that the New Guide is "a complete book on lines, for carpentry and joinery, treating fully on Practical Geometry".
Then after 6 lines describing what the book includes, it say, "THE WHOLE FOUNDED ON TRUE GEOMETRIC PRINCIPLES"
This page is fascinating in itself. It reads like an advertisement for the book. And there are 11 different fonts in several different sizes.
Our pediment is on Plate 10, Page 25. The Plate is described as "The Sections of a Globe....also, the section of any figure standing on an irregular base".
Our diagram is part of Figure 6, in the lower right corner, the geometry used 'To find the Ribs of a Gothic Niche, being the Plan, and No. 1, the Front Elevation" (p.27) The elevation (above) and the plan (below) are in the lower right corner. The 4 diagrams to the left describe how to layout each rib.
Here is a larger image of the niche elevation.
Nathan and I were only laying out a molding to go over windows, not a niche. But the upper diagram is what we 'discovered'.
Here's my rough diagram.
I teach Practical Geometry but I am still an apprentice compared to Nicholson's mastery.


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