Showing posts with label diameter. Show all posts
Showing posts with label diameter. Show all posts

Thursday, July 24, 2025

The geometry of 18th C. furniture design explored by Steve Brown and Will Neptune



 Steve Brown and Will Neptune, are cabinet markers who also teach. 
They wrote  Classic Proportion in Eighteenth Century Furniture Design.*  It is a fascinating exploration of the use of geometry in the design of 18th c. cabinet makers. The illustrations are beautiful.

I first read the article around 2020. Unfortunately, I knew very little about 18th C. cabinetmaking. Visually, the circles overwhelmed me. I just didn't get it. I put the article aside, hoping that maybe later I would understand. 

Last winter  I tried again. The article references James Gibbs' Rules for Drawing the Several Parts of Architecture**, first published in 1722. a book I hadn't read.  I bought a copy. It was a poor reproduction, difficult to read. Then I found a clean, legible copy online. I could enlarge the words and images to easily study them.  This drawing is part of Plate XXXVII.

Gibbs wrote clear and thorough explanations. 

 As I learned, I remembered the tic marks and notations  running up the borders of other pattern books: Wm Pain, A. Benjamin, Owen Biddle.  Now those segmented lines made sense. They are units of measure, a length which determines the other lengths in a specific design, a dimension that can be set with dividers, a compass. Palladio used m for 'module', Gibbs used dia for 'diameter'. Both are names for the same thing, a dimension, a building unit.    

I found that Gibbs' rules for frontispieces were used on this side of the Atlantic. ***  

 

Here is a partial view of Pain's Frontispiece in the Ionic Order, c. 1774.***

The dimensions of the door are noted in diameters as well as in feet and inches. 

 

Asher Benjamin's engraving of a Doric entrance, 1797, lays out the dimensions along the left side, but simply lists them along the bottom. He writes that "the height of the column is 10 parts, one of which is the diameter of the column..."  He uses one diameter for the sub-plinth, two for the entablature.

Yes, Asher Benjamin's first book has poor quality prints.***  

  

 

 

A partial view of an Owen Biddle frontispiece showing  a scale at the bottom, the door width divided into 9 parts, and the height shown as 10 diameters. ***


Finally, I could begin to read 'Classical Proportions'. To encourage you to read the essay, here are 2 diagrams from the article. 

Figure 12, Line drawing of a Chapin high chest of drawers with a modular overlay.

 

 

 

 

 

 

Figure 49 is a detail of the foot and ankle of a leg.


 

 

 

 

 

Figure 50 shows the diagrams for the geometry used to lay out the sizes and curves of the foot, showing, to quote the authors,"the stages of development." As this is quite similar to my understanding of how designs develop I thoroughly enjoyed thinking through the details. 

 



  


  

 


  


  

 


 

 

 

 

 *Classic Proportion in Eighteenth Century Furniture Design is available on line. https://chipstone.org/article.php/787/American-Furniture-2017/Classical-Proportioning-in Eighteenth Century Furniture Design.  

** James Gibbs, Rules for Drawing the Several Parts of Architecture, London, 1722.

*** William Pain, The Practical Builder, published in London, 1774. partial view of PlateXVI.

      Asher Benjamin, The Country Builder's Assistant, published in Greenfield, MA, 1797. partial view of Plate X.

     Owen Biddle, Biddle's Young Carpenter's Assistant, Philadelphia and New York, 1805, partial view of Plate 17. 

My blog posts which explore the use of Gibbs' Rules in the States.  

https://www.jgrarchitect.com/2024/12/james-gibbs-rules-for-drawing-several.html

https://www.jgrarchitect.com/2025/01/james-gibbs-and-rockingham-meeting-house.html 

 

Sunday, May 31, 2020

Owen Biddle's "The Young Carpenter's Assistant"


 Owen Biddle's pattern book The Young Carpenter's Assistant was published  in Philadelphia in 1805.
I am rereading it, looking especially at his use of Practical Geometry.



His first drawings, A and B, on Plate 1 are a plan and section of a drafting board. His instructions include how to construct the frame and the panel, and how to locate the small wood buttons which will keep the dampened paper in place while it dries by the fireplace to become "smooth as a drum head" .*
Drawing C is a T Square whose construction is also described.
He lists the tools a student would need; including a small compass, often called a 'bow pen'.

The rest of Plate 1, Plates 2, 3, with Biddle's descriptions explain "the most useful geometric problems every Carpenter ought to be acquainted with."*

I read between the lines: What was common knowledge that did not need explanation?

- 'Carpenter's Assistants' might have been men who needed to learn more about construction but had not had regular apprenticeships. Many apprentices ran away before completing their training; the most famous one is Benjamin Franklin.
 -  The carpenter's assistant had little experience with paper for architectural drawings. He used a convenient board, a compass, a straight edge, and an awl when he needs to work out a design. These designs are often found on boards during renovation.
-  Biddle specified the compass to be small because there are many different sized compasses. The ones shown here are in a cabinet maker's shop. The biggest is about 16" tall
-  Geometry was a practical tool in construction.

Biddle had set up a school to teach 'architecture' to carpenters.  Assistants might not have been trained to draw in their apprenticeships. Those who designed might not trained under a master builder.  Biddle himself was a contractor becoming an architect.





Biddle has  includes 2 drawings of the same construction. Biddle first explains the design, Plate 15. Then he details how to make the construction drawing become an inviting illustration for a potential client, Plate 16.

Here is Plate 15. In his description Biddle says he gives 'the lines of a pitch pediment frontispiece'.  He writes about 'Lines' as Serlio did: the Lines for layout and design. He adds that the  "Column is made 10 diameters in height." The use of diameter of the column as a measurement is discussed by Palladio.


Biddle says for the best appearance "the door should be as wide as  half its height"*. The scale on the right side of the drawing is labeled '10 diameters'. Did the 'door' consisted of just the part that's hinged? No, Biddle's dimensions include the door and its surround. Here is the door with a height of 10 units divided into 2 red squares, each  5 units square.

As I followed Biddle's notes and dimensions on the drawing I learned how he thought about construction and design: his unit is the door and its frame: the 'door'  itself was not the measure; the door frame between the columns is. The column's height includes its base and its capital, but not the lower base  which is noted as 8" high. This allows the base to be adjusted to fit the vagaries of the location.





Of course the fanlight is a semicircle. The frame is half the height of the squares of the door. 
The key stone of the semicircular fanlight was the center of the square, the height of the pediment 3/4 of the square.

The roof pitch falls exactly along the Lines which cross the square and locate its 3/4 mark.

The notes on the right side about the height of the little columns in the architrave and the  return of the eaves reference the span of the door which is derived from the height of the columns.




Biddle notes at the bottom of the actual door its width: 9 parts.  the parts lay out the panels. The panels themselves are 3 parts wide. Their length and spacing is also determined by the 9 parts.
The fan light's rays are also set by the 9 units. . The tic marks for the 9 units extended to the arc of the fan light layout the fins. The rhythm for the main fins is 1,2,3,2,1.  In the center of the 'petals' of the fan lights are more tic marks - the centers of the arcs that create the tracery.

I tried to draw this clearly. What resulted was a jumble of lines. I'll try words:
Biddle began with the diameter of the column. He used 10 diameters to create 2 squares for door and 3/4 of the square for a fanlight and architrave. His 5 unit width is divided into 10 units, 9 of which are the physical door. The Lines inform all his design.
Biddle uses 10 parts because he supposes
"that the door is for a town house with a narrow front..."  The parts will be in proportion to each other, but take up less space.


The  square shown here has already been divided into 4 equal parts. The Lines divide the 4 rectangles into 5 rectangles. The bottom and top lines defining the square are thus divided into 5 equal parts.



Plate 16

Here is the same entrance shaded. He writes " ...the student should make it his business to understand the effects of light and shade..."  He explains how to think about shading in 2 paragraphs, where "the shade should be strong", where the part should be "bright".

Plates 17 and 18  are similar: one drawing setting up the design itself, the next explaining how to shade the design.  









* Plates 1, 2, 3, 15, and 16, and their descriptions
Owen Biddle, The Young Carpenter's Assistant; or, A System of Architecture Adapted to the Style of Building in the United States, 1805, Benjamin Johnson, Philadelphia, and Ronalds & London, New York. Reprint 2006, Dover Publications, Inc.

2 good biographies of  Biddle: 1) the introduction to the Dover Edition of Biddle book by Bryan Clark Green. 2) an article by Micheal J. Lewis in  American Architects and Their Books to 1848, edited by Hafertepe and O'Gorman, 2001, U.Mass Press.







Friday, April 10, 2020

PRACTICAL GEOMETRY - Lesson 3








The drawing of 'stepping off' is from Audels Carpenters and Builders Guide, NYC, 1923, p.640.

The holes in the daisy wheel are lower left, center, upper right.  There are others which do not photograph as well. This sheathing board was given to me by the crew that deconstructed the barns. It travels with me when I present on Practical Geometry.

 

The posts in this series  Lessons 1-7  are :

 https://www.jgrarchitect.com/2020/04/lessons.html

 https://www.jgrarchitect.com/2020/04/practical-geometry-lessons-2.html

 https://www.jgrarchitect.com/2020/04/practical-geometry-lesson-3.html

 https://www.jgrarchitect.com/2020/04/practical-geometry-lesson-4.html

https://www.jgrarchitect.com/2020/04/practical-geometry-lesson-4b-old-first.html

https://www.jgrarchitect.com/2020/06/practical-geometry-lessons-lesson-5.html

https://www.jgrarchitect.com/2020/06/practical-geometry-lesson-5-addendum.html

https://www.jgrarchitect.com/2020/08/lesson-6-rule-of-thirds-part-1_21.html

https://www.jgrarchitect.com/2020/08/lesson-6-rule-of-thirds-part-2-serlio.html
 
https://www.jgrarchitect.com/2020/09/lesson-7-how-to-layout-frame-with-lines.html

 

Sunday, December 2, 2018

The Daisy Wheel - a Module, a Diameter, a Part



This post follows my post on Lines: how we designed and framed using compasses and twine.   https://www.jgrarchitect.com/2018/11/lines-in-historic-and-modern.html

I used the Tuckahoe Plantation cabin as a my example.
Its floor plan is composed of 2 squares. Its elevations come from the division of the square into thirds, easily done on a framing floor with cords anchored in place on each end.









As long as the original length, here A-B, was on site to use as a reference, the cabin frame would fit neatly together.



The windows however might be made by a joiner, off site. He could take a length of twine with him that matched A-B. But his windows would be smaller. How does he figure out the needed window size?

He would refer to a daisy wheel drawn by the master carpenter.

The diameter of the circle is a fixed length; the daisy wheel shows the craftsman where that diameter is. It is the Module, the Diameter, the Part described by Vitruvius and Palladio, referenced by the pattern book writers.
'P' on a drawing can also refer to the Latin 'pes' or the Italian 'piede', meaning 'foot'. 


Vitruvius, (Book I, Chapter II, Symmetry,) says. "Symmetry is a proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme, in accordance to a certain part selected as a standard. ... In the case of temples symmetry may be calculated from the thickness of a column, from a triglyph or even from a module."



 
Asher Benjamin divides the lower chord in his truss diagrams into 4, 7, and 9 Parts. 
The Country Builder's Assistant, Greenfield, MA, 1797, half of Plate 29.









Owen Biddle adds a line below his fireplace mantle which divides the width into 5 Parts; and one of those  parts into 4 smaller parts.
Owen Biddle, Biddle's Young Carpenter's Assistant, Philadelphia, 1805, half of Plate 21





The master carpenter chose his circle diameter - often a hand's breath, about 8", or  from thumb to first finger, about 6".
He drew his circle on a board and stepped the radius around the circle 6 times, swinging an arc each time. The pattern is a daisy wheel.
Always, in every circle, the tips of the petals mark the diameter of that circle.  The other carpenters could measure the diameter with a compass whenever they needed.

The cabin width might be the daisy wheel stepped off 3 times, then that length stepped off 10 times. If the daisy wheel was about 8", the width would have been about 20 ft, a common size for small houses before 1850. Or perhaps and I house: 2 rooms 16 ft square and a center hall 8 ft wide, all laid out by stepping off.
The windows might be 3 daisy wheels wide. The joiner fashioning windows needed only take the daisy wheel's diameter with his compass and transfer that length to his work to make the window fit the cabin.

*   *   *           *           *           *            *           *           *            *           *           *           *           *

Here - the asterisks in red - I have counted off 3 units, then used that dimension to count off 10 lengths.

Other daisy wheels have been found on roof and wall sheathing boards. After a building was framed the daisy wheel was no longer needed but the board still was.

Daisy wheels drawn for practice or perhaps to alleviate boredom also exist.

This pattern is on a bedroom wall where it is known that someone was confined due to illness for a long time. It shows no signs of being used as a reference.







The daisy wheel at the beginning of this post is on this board leaning against my breezeway wall. The 9 ft. tall sheathing board was part of an 1780 Vermont barn. The wheel was about 4 ft off the floor - easily accessible. It was drawn by compass; the center and the tips of the daisy's petals were regularly pricked. The radius and the diameter were used as dimensions. As it was in a protected and easily seen location it was probably also used for other buildings nearby.
Its owner gave it to me.

Vitruvius', Asher Benjamin's, and Owen Biddle's books are listed in my post of my bibliography.

If you do not know how to draw a daisy wheel, the steps are shown here.

#1 Draw a circle
#2  using the same radius, place your compass on the circumference - the line of the circle - and draw an arc.
  #3 Where your arc crosses the circle's circumference, place your compass and draw an arc. Do this a total of 6 times.

 #4 When you get all the way around the circumference you have made a daisy wheel.













Monday, April 9, 2018

Practical Geometry at MIT





 This is the curtain wall of the Mass Ave entrance at MIT,  the Massachusetts Institute of Technology, Cambridge, Mass.
The picture arrived in my mail box last week.



Immediately I saw the geometry. I knew what geometry the designer used and how it was manipulated.





I was writing posts for this blog and my local blog. None quite came together. Each had parts which require more drawing, thinking, and better choice of words.
Frustrating.
Then the latest MIT mailing to alumni/ae showed up with this picture.
I laughed. I walked beneath that wall of glass and columns for 4 years. In that time I paid a lot of attention to how we used the space it sheltered, how the shape and size of that 'entrance' directed what we did. The curtain wall was not part of my thinking, although the light it allowed into the rotunda was.
The wall's pattern, rhythm, proportions - or even the idea that it was geometry - was not part of my analysis, nor was it ever alluded to by others. 


Here is the pattern.
Upper left : A square and its diagonals.
Upper middle: The circle that comes from using the diagonal of the square as the circle's diameter.
Upper right: The square that fits around the circle.

How the pattern grows:
Top row: Overlap a circle of the same size, so that the perimeter of each circle touches the square inside the other.
Second row: This pattern can grow sideways as well as up and down.
4 squares on the right: Once established leave out the circle, continue the squares, add the diagonal, horizontal, and vertical lines.


The pattern could have started with the circle and the 2 squares fitted around it.
Using the circle as the unit  - the 'module' or 'diameter' in classical terms - is the traditional way to begin a design. (See Palladio through Asher Benjamin.)

From a photograph I cannot judge the diameter of the column.  Does it taper? have entasis? The pilaster in the corner on the right appears to be the same width as the unit I chose: the original square.
If instead the column is the unit, the module,  the circles of the curtain wall might be 3/4 or 2/3 of the module.

I have been told that the main buildings at MIT - dedicated in 1916, designed by William Wells Bosworth -  were designed using geometry. The drawings of those buildings would be well worth studying.

Practical Geometry has become an integral part of how I see buildings.  I was surprised to find that it has become a design tool for me as it was for those who used it for construction.

Meanwhile, this little bit of geometry was just plain fun.