Monday, September 26, 2022

The Geometry of Ionic volutes, as drawn by those who used them


Ionic volutes, those curly ends of Ionic capitals, with these wonderful curves!
How were they drawn? 

This post began as an exploration of the use of practical geometry vs. the use of the golden section in construction.  In all my research I found no references to the golden section as a construction tool.

So, what to do with the images and descriptions I found? Write about them!

Here are the instructions, written by the designers, master builders, architects, and those who used these volutes. 

First, of course, is Vitruvius. He writes, in the 1st c. BCE,  "As for the drawings of volutes so they are properly coiled with the use of a compass, and the way they are drawn, the form and the principal of these will be set down at the end of the book.' * 

Unfortunately, those drawings at the end of his book are lost. 

Beginning about 1540, many architects, builders, historians, professional and amateur, measured the Ionic volutes still extant, those created during the Greek and Roman empires.

Giacomo Barozzi de la Vignola published his engravings in 1562. The illustration  is from the English translation of Vignola by John Leeke in 1669. Vignola begins by noting the reference lines and then the small square in the circle in the upper right corner of the page, 'A'. "Having drawn the Cathetus (the vertical guideline) of this first voluta and the other line S square to it, the said eye is divided in the manner expressed above in the figure A..." 17 lines, total, all quite easy to follow.


Andrea Palladio and Sebastiano Serlio worked at the same time as Vignola and probably knew him. 

 Here is Palladio's drawing in his 4 Books of Architecture, First Book, Plate IXX, 1570. 

Serlio's On Architecture, was written before 1550.  Serlio takes 32 lines to explain how to draw the volute.  He includes, "This matter (as I said) consists more in the practice than in the art because making it diminish both to a greater or lesser extent is dependent on the architect's judgement in placing the point of the compass a little higher or a little lower. The size of the band should not always be all the same."

If you look carefully at Vignola, Palladio and Serlio's drawings, you will see that they do not quite agree about the location of those 2 first lines, the cathetus and its perpendicular. They probably had measured different volutes. Later writers mention which volutes they think to be most perfect.

Serlio's treatise was translated from Italian to Dutch to English in 1611. A complete English translation of Palladio wasn't available until after 1715.


Batty Langely's The Builder's Director or Bench-Mate, was published in 1745, London, a compilation of "all that is useful to Workmen,... and at so easy a Rate, as to be purchased by any common Labourer." He includes variations for Ionic capitals: 'modern' and 'ancient' all of which are explained by 'Minutes and Parts'. This is his first drawing of 6.

Batty Langley's books continued to be published after his death in 1751, and were available in the Colonies.


William Pain published similar 'practical builder' pattern books at about the same time. Here is his Plate XVI from The Practical House Carpenter, or Youth's Instruction, London, 1794, for volutes with parts. He writes that he has included " ... all the measures figured for practice: to draw it, set the compasses at the angle a in the profile..." He rewrites the earlier instructions given by others and reminds the reader again that he has included "the measures all figured for practice."




 Owen Biddle's pattern book, The Young Carpenter's Assistant, 1805, Philadelphia, includes these less flowerly drawings and instructions.




 Asher Benjamin's  American Builder's Companion, originally published in 1804,  includes similar diagrams.




However, his revised 1827 edition includes the drawing above and also this diagram. "Plate F, From the Inside of the Portico  of the Temple of Minerva, at Athens." 

"Fig. 1. Volute of the capital, with the measurements in feet, inches, tenths, hundredths, & etc."

A footnote explains how to read Feet, Inches "and the decimal parts". 


The Architect, or Complete Builder's Guide, written in 1839,  has  this drawing, Plate X.  Asher Benjamin notes, "The  carver will find it to his advantage to imitate these drawings faithfully, and thus escape the censure deservedly cast upon the many clumsy, awkward productions of this capital, which may be seen in both town and country." 

 Benjamin's books were published through the 1850's.


Then there's a break - I've found no English language 'how-to' pattern
book instructions on volutes during the height of the Industrial Revolution.
Ionic volutes were used: here on c.1896 porch columns. Probably these were created by craftsmen for a company which specialized in plaster and wood composites. They are probably available today.



In 1903, in The American Vignola, William Ware describes how to construct a volute, "The vertical line a b, Fig 91, through the center of the eye of the Volute, and the horizontal line c d, will mark in the circumference of the eye the four corners of the square within which a fret whose angles may serves as centers..."* 

6 sentences;  22 lines of instructions. This is a small drawing at the bottom corner of a page.

Architectural Graphic Standards' first edition was published in 1932.  This page in every edition  I own:  2nd -1936, 3rd -1941, 4th -1953,  5th - 1966,  but not the 8th - 1988. 

The pages are quite yellow - I've toned them down here to make them more legible.



The 8th edition of  Architectural Graphic Standards, 1988, no longer dedicated a page to Ionic details. 

The last 2 pages of the book, titled  Classical Orders at the top and CLASSIC ORDERS at the bottom, are a crowded introduction to centuries of architecture. 

Here's about 2/3 of the second sheet. The architects who complied the page are credited not their sources. 

Do I have a conclusion? Not really. 

I looked for the Golden Section and didn't find it. I read convoluted and simple language as people who knew construction explained with words how to draw something complex.  Many descriptions expected experience using compasses. I appreciated the authors who said, "Practice!" Words help; they are not a substitute for drawing.

Books not listed here are in my bibliography:

Asher Benjamin, Practice of Architecture and The Builder's Guide, new introduction by Thomas Gordon Smith, De Capo Press, New York, 1994.

Batty Langley, The Builder's Director or Bench-Mate, published first in 1754, London, reprint, publisher unlisted.

William Pain,  The Practical House Carpenter, or Youth's Instruction, London, 1794. reprint by Dover Publications.

Ramsey/Sleeper, Architectural Graphic Standards, John Wiley & Sons, Inc., New York

Giacomo Barozzi daVignola, Canon of the Five Orders of Architecture, John Leeke, translator, published by William Sherwin, London, 1669.

Vitruvius, Ten Books on Architecture, edited by Ingrid D. Rowland, Thomas Noble Howe, Cambridge University Press, 1999

*Wm. R. Ware, The American Vignola, 1903, Dover Publications, 1994, p. 30. 

*Book 3, Chapter 5, paragraph 8,  translation by Ingrid D. Rowland; Viruvius, 10 Books on Architecture, Ingrid D. Rowland and Thomas Nobel Howe, Editors, Cambridge University Press, 1999.

Wednesday, July 27, 2022

The Baptist Church of Streetsboro, Ohio, Part 1

This is the Old Baptist Church at Streetsboro, Ohio, built about 1820.

Here are the HABS drawings.

 I wondered about its geometry. What framing traditions had the master builder brought with him to Ohio?
It looked linear, simple, obvious. Was it?

I explored the plan and elevation. While many forms of the Lines created by circles and squares worked pretty well, nothing quite fit.  
I went back to the basics, the construction: What did the carpenter do? In what order?

He was asked to build a church about 'so big'  - here about 36' x 50'. He laid out a rectangle using the 3/4/5 Triangle.  The HABS drawings are blurry and tiny. The dimensions appear to be 38'-4.5" wide by 51' long,  3 units wide by 4 units long. (The length is about an inch too short.)

The triangles are ABC and ADC. They could also be ABD and BCD. The 2 layouts cross in the center.
The carpenter could check his diagonals, just as workers do today. When the diagonals were the same length the floor frame was square.

 The bents for the frame were naturally the same width as the floor. It seemed possible that the framer used the floor of the church for his layout. I had seen this in an upstate NY barn. I wrote about it here:

The elevation of the front of the church appears to be 2 squares wide. But the pediment did not come easily from that form - slightly too big.

However when I laid out the frame based on Lines laid on the inside edge of the sill and posts, everything fit and the peak of the bent, the location of the ridge of the church was the center of the rectangle. So simple, so easy!

How was it to the framer's advantage to lay out the frame from within the frame, not outside?  
He needed at least 3 bents, probably 5 or more. He needed consistent marks for lengths and widths of all members and for each mortise and tenon. The Lines laid inside the frame would not be disturbed while the frame was laid out and marked. The timbers could be moved off the floor to cut the joints; another bent could be laid out.  Or the bents could be stacked on each other.
Modern framers using timber and dimensional lumber stand within their work, measure, mark, and check from inside. Then they cut the lumber someplace else. Why not this earlier framer too?

After the bents and the roof trusses came the walls and the windows.
The spacing of the windows and their width comes from the rectangles that are within the original larger rectangle.
The green lines are 2 of those rectangles, the dashed lines with arrows on the left show the window frame locations.  The green dashed line with an arrow on the right ( top left) is the width. 


The geometry of the bents determined the shape of the facade, the height of the pediment. The front elements of the church - the  pilasters and a grand door -  were designed after the frame. The front windows were in place, therefore the pilasters needed to be equidistant on each side.
The door went in the middle, that's custom. Then there was the left over space in between. (See more about this below.)

The framers also had to provide support for the steeple. I have only photographs to show where the steeple sits. Was it directly over the front wall? a few feet back?  I would assume a bent supported the front and back walls of the steeple. The diagrams do show how the width of the tower and the size of the clipped corners were determined: the plan is a square with its corners cut off. 

Carpenter squares began to be manufactured in the States - not imported from Britain - around 1820. They had true 90* corners and consistent dimensions. 3/4/5 triangles and rectangles were easy to lay out accurately. An inexperienced carpenter could erect a  simple frame without much worry. A master carpenter working with church members as a volunteer crew could expect his crew to build a reasonably accurate frame.

Part 2,  the design of the exterior of the church is here:


7/27/22: I wrote this post in 2018. When I reviewed it recently, I saw how much needed to be revised, simplified; how much I'd learned about using geometry in construction during the last 4 years.  Understanding Practical Geometry (the name Asher Benjamin and Peter Nicholson used) is an on-going exploration.


Tuesday, July 26, 2022

The Baptist Church of Streetsboro, Ohio, Part 2

The Streetsboro Baptist Church, built c. 1820: the second phase of its construction - its decoration - the front facade and the steeple.



The first post* discussed how the framer used the geometry of the 3/4/5 Triangle to layout the floor, the bents, the walls and  windows, the roof and steeple. After the framers made the building 'tight to the weather',  joiners would often be responsible for the finish work: window sash, doors, molding.  Different trades had different skills and tools.

I think this division of labor happened here.


The church front on a cloudy day in October. It is a handsome building. It is also a box decorated with boards and moldings. That's what I am looking at in this post.

The HABS drawing is below.



The windows had been set by the framer when he laid out the floor plan, the walls, and the roof frame. The black lines show what the front wall would have looked like when the joiner began his work. Holes for windows, a space - perhaps a larger framed opening - for a door, a triangular gable. 

The congregation expected that this box with a roof would become a modern Greek Revival church. 

Of course the joiner was considering the pediment, the frieze, the architrave. the water table. He also needed to lay out a facade which has grace and rhythm as well as symmetry.


Here is the geometry of the facade as the framer knew it: 3 bays with their height from the floor to the roof trusses, their width between the corner posts, and a door, centered but of undetermined dimensions. The windows are centered within the  3/4/5 rectangles of  the frame's rhythm. Their shape is 2- 3/4/5 rectangles.


I think, the joiner chooses to balance the windows first, to set them as supporting wings to the central door. The corner boards grew to become paired columns balanced by 2 more columns on the other side of the windows. Note that the columns are not on the lines of the bays, therefore the center bay is slightly wider than the side bays. The window bays became back drop to the central bay with its  double door and paneled transom.The joiner 'adjusted' the geometry; but the window bays' symmetry is so strong it is hard to catch. The tall, broad main door, recessed  in the main bay, then surrounded by the columns and the frieze, becomes the focus. 

The joiner 'fooled the eye' and created a dynamic facade, much better than 3 equal rectangles would have been.


The framer built the base which supported the steeple. Its dimensions at the roof are based on the 3/4/5 Triangle.


The steeple uses neither the geometry of the frame nor that of the front facade. It is a series of blocks, decreasing in size, with their corners clipped. The design uses the square and the circles that fit within and without it. Was it the work of the same joiner? **

The HABS drawing shows the steeple sections.

Here I have added the circles  - In 'A' the red circle is outside, the green inside. In 'B' that green circle is now outside, a new smaller red circle inside. 'C' continues the progression with the red circle from 'B' now the outside. The green circle of  'C'  is the base of the spire.

 The steeple layout follows the  drawings of James Gibbs in his book "On Architecture", published in England in 1728. Copies were in the Colonies, available to builders.  I have written about Gibbs' steeples here:  

 These  HABS measurements are too simple for an in depth study of the steeple geometry.

The shapes that make up the tower are a series of blocks with related faces all derived from the simple manipulation of the square: a complete square, 2 squares, one square, half a square (the base for the spire).
The spire's height uses the width of the steeple's base as its unit of measure: it is 1.5 times as tall as the base is wide.

The paneling, edge moldings,  and the series of roofs as the tower extends create the steeple.

The  door itself is approximately square, the transom: half a square. They are the same size as the section of the steeple which holds the bell.

The wall of that bay acts as a setting,  a frame for the door.  The columns and architrave are a second frame.


Look again at the photographs.

The church's grace and presence come from simple proportions in the design and the understanding of how light and shadow give life to the parts themselves and thus to the whole building. 

Here is what Asher Benjamin wanted the joiner - and by extension, we who see the church - to understand about moldings :  

"...the bending, or turning inward, of the upper edge of the Grecian, or quirk ovolo, when the sun shines on the surface [and] causes a beautiful variety of light and shade, which greatly relieves it from plane surfaces, and if it is entirely in shadow, but receives a reflected light, the bending or turning inward, at the top, will cause it to contain a greater quality of shade in that place, but softened downward around the moulding to the upper edge."   ***


* Part 1:

** The Sandown, NH, Meeting House and Gunston Hall in Virginia are good examples of this separation of craft. At Sandown a skilled joiner built the main door and the pulpit, perhaps the wainscotting and box pews. George Mason of Gunston Hall brought William Buckland from England to create the porches and interiors for his new brick house.

**Asher Benjamin, The American Builder's Companion, 6th edition, 1827, R.P. & C. Williams, Dover Publications reprint, Plate IX, Names of Mouldings.


Sunday, June 19, 2022

James Gibbs' Of Architecture, Draughts for a Menagery, Part 2 of 2


The  second menagery in James Gibbs' On Architecture* was never built.  In Part 1 of 2,  I wrote about the first one which was built at Hackwood Park, an estate near London. It is still standing.

Here is Gibbs' portrait with his compass, the mark of his profession. 

Gibbs' expected "any Workman who understands Lines" to be able to execute his designs. What would a workman have seen in Gibbs' drawings? What could I see? Did I understand Lines?

The first option was so simple. I was looking for an equally direct layout for this second design. I could find only complex solutions. They worked, but they were not direct. For 3 months the obvious design  was right there and I couldn't see it. I put the puzzle aside several times.  

This 'menagery' was to be a welcome destination for those strolling through the Hackwood Park estate grounds. Built of stone, the menagery would not have been as dark as this image.The 'draught' elevation accentuates the quoins and articulated arches, to give the workmen the necessary information. 

Like the design which was built, the pavilion required a gracious porch with a room on each side: one for serving and drinking tea, one for the quiet perusal of books about nature, especially birds. The living quarters for the staff who took care of the estate's pheasants were around the back. 

Today a plan usually lays out the exterior dimensions. Here the exterior is to be stone, perhaps ashlar or split, with rusticated, oversized  arches and  quoins (the corner blocks). Using inside dimensions to layout the plan allowed the exterior dimensions to vary.  

Note that Gibbs' drawing of the exterior stone facade is structural. The blocks interlock on the corners; the arches and key stones interlock with the wall. 


The floor plan begins with the central form: the porch and caretaker's quarters. Its size is determined by 2  3/4/5 rectangles overlapped at their mid-points. 

Gibbs assumes the workmen who might copy his 'draught' know how to build walls; he is not providing a construction document.

The wall between the porch and the living quarters is set beside the center of the rectangle found by drawing the diagonals of the main pavilion. This makes the porch large and gracious. It is also the way a mason sets lines today, building beside his lines. 

A workman could true his rectangle to center the doors on the walls.  Note the red line.




 The lines from the corners to the center locate the center lines for the arched columns. 

I have left out many lines here for clarity. They could be added to check the work.

 I call this 'The rule of Thirds' because artists who use these lines as a design tool call it by that name.  It's the 3x3 pattern that appears when we edit cellphone pictures. **


The wings of the menagery are set back 1/4 of the depth of the main block in the front and the back - note the red line with arrows As the geometry here is the 3/4/5 rcctangle it is fitting that the wings' length is proportional to the main pavilion's length: 6/8 or 3/4. 

 The wings are themselves both 3/4/5 rectangles.


The 3/4/5 rectangIe was a common way to add a wing to an existing building. If the mason set his length against the central form at 4 units and his width at 3 units, his wing would be square against the main block. His stone work would be true.  I have drawn the 3 x 4 units here. I have also left my pencil marks for further information (enlarge the drawing!) 

 While this menagery design is more complex to write about than Gibbs' other design*, it is quite easy to lay out with a compass and straight edge. A trained workman would have known the steps. The 3/4/5 rectangle and the Pythagoras Theorem are used today.

 The elevation? It's 4 squares and the same pediment layout that  Gibbs used on the menagery design which was built. The inside dimensions govern. The red arcs drawn show the floor width of the rooms are also the height of the elevations.    

A note: the windows are centered on the rooms' inside wall, but not on the exterior width of the wing.  The quoins are such a strong visual vertical that they appear as an anchor. The windows were centered on the rest of the wall.

The pediment is drawn  following the rules described by Serlio. For step by step instructions, refer to Part 1 of 2 of this post of the draughts for the Menagery.*

 * Gibbs' book On Architecture, published in 1728, includes 150 plates: plans, elevations, sections and perspectives of buildings Gibbs had designed and built. The quote is from his introduction, page i. A reprint is available from Dover Publications.

Part 1 of 2, the post for Gibb's design of the Menagery which was built is here:

** I've posted about The Rule of Thirds in more detail here: 

Thursday, April 21, 2022

The Parson Capen House, 1683, Topsfield, MA

This post, first published in 2014, has been revised based on a better understanding of the geometry. 











Parson Joseph Capen built this house in 1683 in Topsfield, Massachusetts.  He ministered to the town from 1682 until his death in 1726.

The story about this house:  It is still here because it was owned by an old Boston family with extensive land holdings.Their herdsmen drove cattle to market in Boston along Rte 1 (which is practically next door to this house) and  used the house as a way station on their trips into the city. So it wasn't torn down, updated, or abandoned. We are lucky.

The pictures are from the LOC HABS archive. Note the drops and brackets. The windows are casements; in the picture they have been swung open.
For more information and photographs in color see

The geometry for the house is based on the square.  

Here is how a square is derived using a compass, a straightedge and a scribe. 



 Once a carpenter knew his geometry he could layout a square in fewer steps.

The square with its arcs gives the carpenter 4 points - where the arcs cross each other - for dividing his square in half horizontally or vertically. This could have been used for the hall and the second floor beams.     


The chimney and fireplaces were to be in the middle of the house. So the builder laid out the house foundation from the chimney block. The diagram shows in the center the brick which would have formed the back wall of the 4 fireplaces  with 2 square spaces on either side: the parlor and the hall.



Next comes the fireplaces themselves, on both floors, and the flues. On the first floor the main masonry block is a square in plan, the oven needed half a square. Its flue joins the hall chimney.

 On the second floor the chimney mass is square.  


The house has 4 bents, one on each end and one on either side of the chimney mass.  The  fireplaces depths on the second floor determine where the 2 interior bents are placed. It's possible there are bents across the rooms as well. However, since the  summer beams on the first floor appear to be located over windows and the second floor beams do not match the first floor beams, I think not.
The Rule of Thirds was used to lay out the bents. It determined the heights of the floors and the placement of the windows. (The red arrows indicate ceiling heights.)

See this description for how the Rule of Thirds works: 

The cantilevered end beams for the second floor have drops below them. The beams for the interior bents have corbels. These are quite visible in the HABS photographs. The cantilevers for the roof also have drops, as well as corbels in the middle of the roof overhangs on the end elevations.


The second floor overhangs the first floor by about a foot on the south/front side. This was popular in England as a way to protect the daub and wattle walls from rain and wind. Here weather boards - known today as clapboards - covered the frame, but the tradition continued. The attic extends out over the second floor on the sides of the house for the same reason.

These HABS photographs are beautiful and clear. Click the images to enlarge them.

The roof pitch  and the placement of the ridge pole might have been laid out from the second floor.  I have seen this proportion - the crossed arcs of the side of the square - in other First Period houses, It may have been  used here.

Note the corbel beside the 2nd floor window which supports the roof overhang.

Here is the front elevation with the drops and corbels noted. They accent the ends of the cantilevered beams which are the top plates of the bents.



The beams:
In the hall the beam which supports the second floor joists was set in the center.
The parlor, the room to the left, is larger. It needed 2 beams. So the space is divided into thirds. These beams are joined to the beam that runs between the 2 bents on this side. The windows were placed where a post would be located under those beams if they were part of bents.

On the second floor  the ceiling beam are centered. All the beams appear to be set to the side of the lines, not on the line.

This drawing may be an accurate depiction of the front elevation. However, the plans are not quite consistent with this layout.  The windows might be set equidistant from the corners of the house, or not.  They may be centered on the second floor rooms, but not on those on the first floor.

Both sets are grouped together in the same geometry. The casement windows are all the same size.


The measured drawings for the Historic American Building Survey, HABS, were done at 1/8"= 1'-0", a scale which is fine for concept, but not good enough for serious consideration of  construction details.  They have very few dimensions. The drawings from 1916 do not quite agree with HABS.
Some observations:
* The Golden Section is not used here. I find that the Golden Section is about growth; houses are about stability.
* The front door is not centered on the facade; if it were the door could not be opened back against the front wall. The brackets sit under the 2nd floor beams extended to support the cantilever.

4/21/22: I wrote much of this 8 years ago. The layout of the foundation based on the location and size of the chimney back still makes sense. I revisited the framing and the elevations, understanding that the layout begins with the framer who must decide where the bents will be; how tall;  where the marks for the mortises and tenons will be. And how will the second floor and roof cantilevers be supported? I explored how a daisy wheel might have determined the layout. The results were messy. The points were not useful markers for building this frame.