Jane Griswold Radocchia

Tuesday, November 16, 2021

Bibliography for Practical Geometry, aka Architectural Geometry

A list of books by and about builders and architects who used Practical Geometry; many are primary sources.
At the end are other sources, websites, and credits.
It does not include books I refer to in a specific post. For example: Audel's Carpenters and Builders Guide, Theo Audel & Co. Publisher, NYC, 1923, is footnoted at the end of that post: https://www.jgrarchitect.com/2018/11/lines-in-historic-and-modern.html.

A few are books on architectural history and technology which I reference regularly: Bannister Fletcher's History and Knight's American Mechanical Dictionary.

PRACTICAL GEOMETRY aka ARCHITECTURAL GEOMETRY

BIBLIOGRAPHY

Benjamin, Asher. The Country Builder’s Assistant, 1797, Dickman, printer, Greenfield, MA –

reprint by Applewood Books, Bedford, MA.

*The American Builder’s Companion, 6^th edition, RP &C Williams, Boston, 1827

Biddle, Owen. *Young Carpenter’s Assistant, published by Benjamin Johnson, Philadelphia,

1805.

Charles, FWB. The Great Barn of Bredon, Its Fire and Reconstruction, Oxbow Monograph 76,

1997, Oxford Books, Oxford, UK.

Colvin, H.M., A Biographical Dictionary of British Architects,1600-1840, Harvard U. Press, Cambridge, 1954.

Fletcher, Bannister. A History of Architecture on the Comparative Method, Charles Scribner’s

Sons, NY, 17^th Ed. 1967.

Gibbs, James. *Book on Architecture, London, 1728

Rules for Drawing the Several Parts of Architecture, printed by W. Bower for the

author, London, 1732, ECCO print edition

Glassie, Henry. Folk Housing in Middle Virginia, U of Tennessee Press: Knoxville, 1979

Green, Bryan Clark. In Jefferson’s Shadow, the Architecture of Thomas R. Blackburn, Princeton

University Press, NY, 2006

Harris, Eileen. British Architectural Books and Writers, 1556-1785, Cambridge U. Press, Cambridge, 1990

Harris, Leslie. Robert Adam and Kedleston, The National Trust, London, 1987.

Knight, Edward H. American Mechanical Dictionary, Vol I, II, III; J.B. Ford & Co. NY, 1874.

Macaulay, David. Mosque, 2003, Houghton Mifflin co., Boston. His many books are excellent references.

Nicholson, Peter. The Carpenter’s New Guide, 1793, London; 10^th ed., Philadelphia, 1830.

Palladio, Andreas. *The 4 Books of Architecture, 1570, translated and published by Isaac Ware,

London, 1738.

Serlio, Sebastian. On Architecture, Lyon, France 1530, translated in1611, available on-line.

Translated by Vaughan Hart and Peter Hicks, 1996, Yale University Press, New Haven

Shaw, Edward. *The Modern Architect, Dayton & Wentworth, Boston, 1854

Smith, Laurie, The Geometrical Design of St. David’s Cathedral Nave Ceiling, A Geometer’s

Perspective, The Geometrical Design Works, 2017, printed Exeter, UK. and others.

Vitruvius, Marcus. *The Ten Books on Architecture, c. 10 BCE, translated by Morris Hicky

Morgan, Harvard University Press, 1914.

Ware, William R.. The American Vignola, * of the first edition published by WW Norton& Co. NY, 1977 ( original edition, 1903)

*Reprinted by Dover Publications, Inc., Mineola, NY

Drawings:

HABS drawings, Library of Congress, Washington, DC

Denison Bingham Hull, Old First Church, Bennington, Vermont, c. 1935.

James Platteter, barn frame for Green Mountain Timber Frames, 2014

All others: Jane Griswold Radocchia

Web sites:

www.jgrarchitect.com (you are here!) and www.janegriswoldradocchia.com

for Laurie Smith:

http://historicbuildinggeometry.uk/ and http://www.thegeometricaldesignworks.com/

Monday, October 18, 2021

Geometry of the Old First Church Fanlight - an Addendum

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 first circle crosses the pencil lines and marks the center of the next circles.

The red spots are the centers of the circles.

The first 3 inner 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.

Sunday, October 3, 2021

Geometry of the Old First Church Fanlight

This is the fanlight over the main door to the Old First Church, built in 1803-5 in Bennington, Vermont. Lavius Fillmore was the Master Builder; Oliver Abel, his Master Carpenter, and Asa Hyde, the Joiner and carver.

The fanlight design consists of 2 parts: the 'scallops' around the curve and the 'leaves' coming up from the base. It is simple, graceful.

How was it laid out? In 2012 - when I first wrote about this fanlight - I knew the geometry for the scallops around the curve - expanded daisy wheels on the horizontal and the vertical axis.

The 3 leaves below the scallops? I was lost.

Laurie Smith - English timber framer, historian, geometer, the most knowledgeable person I know about the use of circle geometry in medieval design and construction - provided an answer.
Here was our geometry for the fan light in 2012. Now, in 2021, I think it is probably not how Lavius Fillmore laid out the pattern.

I post it because we are teaching ourselves. We are constantly learning more about how to use Practical Geometry (or 'Architectural Geometry'). One solution is not the only one.

A square can be derived from a circle in many ways - as can a 3/4/5 rectangle - both done using only a compass, straightedge and a marking tool. To see how the geometry can be followed and bring different designers seeing different paths, arriving at the same solution, is valuable.

The circle, its 6 points around the circumference laid out by the radius of the circle, is set on a line which defines the shape of the fan light.

The circle is surrounded by 6 circles which have their centers on the 6 points. The center pattern is a daisy wheel with 'petals'.

The circles expanded.

This set of circles around the original circle adds petals
to the exterior of the first circle. Add the fanlight shape and the petals become scallops around the arc of the fanlight.

Rotate the circles 15* - or 1/2 a petal - and the fanlight's scallops' locations change.

Overlapped, the daisy petals create the double scallops around the Old First Church fanlight. See the photograph above.

The overlapped petals are also the pattern of the 'leaves' in the fanlight: too big, not in the right location, but crossed as are the leaves.

This pattern is much easier to layout than the geometry in the next 5 drawings. I include those drawings to show another way which is equally valid but more complex.

However, as I have explored the Old First Church geometry over the past 10 years, I have gained a sense of how Lavius Fillmore designed. I do not think he used the sequences laid out here. He understood what the simple act of turning an expanded circle on its axis could create.

The simple solution is here :

https://www.jgrarchitect.com/2021/10/geometry-of-old-first-church-fanlight.html

Here is how the leaves could have been added. These steps are our 2012 solution.

Add regulating lines from the center of the circles to the second ring of circles and center lines in the petals.

Connect the center points of the scallops to each other. Where they cross the petals is the center of the small circles which form the leaves.

The radius of the circles is the distance from the center of the petal to the scallop.

I've drawn it in red to make it more visible. It is a complex layout for a seemly quiet, unassuming design.

This pattern was drawn at about 3/8" = 1'-0". A scale of 1"=1'0" might have been easier. However it would still be tiny here on the page. For clarity I left out the overlapping scallops.

my drawing in 2012:

The real fanlight was laid out full scale - 5+ feet across - on a framing table or floor. The proposed design sketch would have been studied, the arcs drawn with a compass using chalk or charcoal, the lines checked, redrawn, the points pinned. Finally, when the regulating lines were erased, the simple, clean design was visible.

I would like to have been there, listening, watching. as the men drew this. I think they were pleased as they derived the pattern and settled on a design. It's not structural at all. It's one of the first things you see, an introduction to the church. It's also their signature.

Then - I realized that this derivation is not simple enough.

My Addendum, my next post, is my current solution, my current understanding of how Lavius Fillmore, Oliver Abel, and Asa Hyde designed the fanlight.