How to Layout a Pediment: 350 years of instructions

A short history of classical pediments in the Western world,  c. 1540 to c.1903. 

Vignola's Rule was first laid out by Giacomo (Jacopo) Barozzi da Vignola in his Cannon, published in 1562.

This image was  published in 1903 in William Ware's The American Vignola.* 

 

Was it Vignola's  rule or did he just record it? 

It's possible that the Rule itself was already widely known.  

 

In 1540 Sebastiano Serlio drew this sketch in Book IV of his On Architecture.* 

He wrote, "...
having drawn the cornice, divide the upper line from one side to the other in the middle, between A and B; drop half of this plumb from the middle to make C; then placing one compass point on C and the other on the side of the cornice A, arc to the side B; the highest point of the curved line will mark the required height for the pediment. A curved pediment can also be made with such a rule."*

The diagram shows the actual twine held tight at Points A and B. It is a Line with its ends dangling and curling.

 

Palladio doesn't describe this, but the roofs in his The Four Books of Architecture (1570) use the same pitch. 

 

Vignola's book on architecture was translated, of course.

This image, c. 1600, attributed to Vignola, comes from a book published in Spain.

 

 

 

 

 

 

His 5 Orders of Architecture* were translated into English and published by John Leeke in 1669. Vignola's portrait (Plate I)  is surrounded by a decorative frame topped by an extravagant  pediment.  It does not quite follow Vignola's Rule. Follow the red lines.

 

 

 

 

 

 

John Leeke' book  included 3 pediments attributed to 'Michel Angelo'. This one, the simplest, does seem to use Vignola's formula. The angle is the proper 22.5*. Did Michael Angelo know of Vignola's work?

 

 

 

A complete English translation of Serlio's 5 Books on Architecture, including the sketch of the pediment's layout, was available in the UK about 1720. 

James Gibbs probably had read both Vignola and Serlio.  He uses the geometry in the pediment of a Menagery, in his book, On Architecture*. Perhaps Gibbs includes the knowledge of this diagram when he writes that his 'draughts ... may be executed by  any Workman who understands  Lines'. 

William Salmon's book, Palladio Londinensis*, published in the 1750's, was intended for the London builder. Pediments are included; their proportions are measured in parts. Perhaps Salmon considered the understanding of geometry by London's builders to be scant, or that it was not applicable to London's tightly set row houses.

 

 

The rule for laying out a pediment came to the States with craftsmen as well with their pattern books. The Rockingham Meetinghouse, finished by 1797, is a classic New England meeting house:  plain and unadorned...

 

 

until you look at its doors. The pediments of the classical frontispieces follow Serlio's layout. 

 

I began my diagram here on the lower edge of the pediment's frame. If the layout is moved to the upper edge of that plate, the arc marks the top of the ridge of the pediment roof, rather than at the underside.

 

 

At about the same time William Pain includes the same arcs (lightly dashed here) and describes how to draw them in The Practical House Carpenter,* a pattern book widely available in the States.

Here is Asher Benjamin's simplification of Pain's engraving in The Country Builder's Assistant*, published in 1797.

 

 

 

 

 

 

This door front in Springfield, VT, c. 1800, was probably inspired by Benjamin's illustration.

 

 

 

 

 

The Industrial Revolution brought new tools and materials. Galvanized metal allowed shallow roof pitches which didn't leak.

 

 

 

Here's an example of a shallow roof pitch from Samuel Sloan's pattern book, The Modern Architect*, published in 1852 .

 

 

 

 

Sloan's Plate XXXV shows the steeple structure. The frame spanning the building uses the traditional roof pitch of Serlio's pediment (22*). The pitch of the roof is much shallower (15*)

For the next 50 years architectural style was giddy with the designs made possible by the Industrial Revolution.

 

 By 1900, the design possibilities made possible by 60 years of industrialization were taken for granted. Architects looked to Europe, especially the Ecole des Beaux-Arts in Paris, for inspiration, and perhaps a re-grounding in tradition.

 

William Ware wrote The American Vignola in 1903 as a guide for his students at the Architectural School of Columbia University. 

Here's his Plate XVII with many pediments. The dotted lines compare measured/built pediments in Greece and Rome to Vignola's standard.

 

 

 

 

 

 

 

 The 2 small diagrams on the right side Plate XVII are his codification to Vignola's Rule. 

 

 

 As I compiled these illustrations I found 2 caveats:

Owen Biddle* published his pattern book in 1804. Instead of a general rule for 'a pitch pediment frontispieces', Biddle wrote that the roof angle was 2/9 of the span. He also wrote that for 'the townhouse with a narrow front... the true proportions of the Orders may be dispensed with..." p. 34

William Ware noted that "...if a building is high and narrow, the slope needs to be steeper, and if it is low and wide, flatter." p. 45

And finally, this advice from William Salmon: "...when you begin to draw the Lines,... omit drawing them in Ink, and only draw them with the Point of the Compasses, or Pencil, that they may not be discovered when your Draught is finished..." p. 103.

 

*The books from which I have copied illustrations and quotes for this blog are listed in alphabetical order by author.

Asher Benjamin, The Country Builder's Assistant, Greenfield, MA., 1797, Plate 10. 

Owen Biddle, The Young Carpenter's Assistant, Philadelphia, 1805, Plate 15. 

James Gibbs, On Architecture, London, 1728, introduction and Plate 84.

William Pain,The Practical House Carpenter, fifth edition, London, 1794,  Plate 38.

Sebastiano Serlio, On Architecture, , c. 1545, Book IV, page xxviii.

Samuel Sloan, The Modern Architect, 1852,  Plates XXVII and XXXV.

WilliamWare, The American Vignola, W.W. Norton & Co., NYC, 1903, Plate XVII.

 

 

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: 

https://www.jgrarchitect.com/2019/06/bibliography-includiung-websites.html

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.

Lesson 7, How to layout a frame with Lines

 Lesson 1 is here: https://www.jgrarchitect.com/2020/04/lessons.html

What's a Line?

A Line is a basic tool for layout and design.

Serlio, in 1520, used twine with a plumb bob as his Line. On  the frontispiece of his book, On Architecture, he drew his Line entangled in the metal scrolling. The end for tying is frayed.

 

 

 

 

Even through we now write 'line' without the capital L, we still use lines to keep our construction 'true' - straight, square, and plumb.

 

Patrick Kennedy, in Kentucky in 2020, used his line to keep his new stone wall straight. He tied his line to wood stakes. Rebar is also commonly used today.

photograph courtesy of P. Kennedy. 

Modern examples of using lines to keep construction square and plumb:
Checking a foundation's diagonals will ensure its rectangle is true. A square frame is easier to erect than one which is crooked.

A rectangle will have 4 square - 90* - corners if its diagonals  are equal. Here the far rectangle is not true. The diagonal is too long. It  should meet the corner at the upper spot.

Plumb lines ensure that walls are true or plumb: straight up and down, 

If an existing wall is not true the framer must know in order to compensate for the discrepancy. Here the plumb line with its  bob on the bottom shows that the foundation wall slopes.

How lines were used historically in construction can be seen in the frames of buildings built for utility. No one was showing off - just getting the job done - using what was ordinary.

Tuckahoe Plantation., Virginia

Cabins for enslaved people c. 1750.

 

 

This is minimal housing. We are lucky it survived.

 

 

 

 

 

Its geometry:

1)   A line - a length of twine - could have been used to layout the 2 square units.
Lesson 5 and Owen Biddle's Figure H show the steps. ,

 

The builder could have been laid out the foundation knowing only where to site the cabin and how big it would be. He didn't need drawings. He could set his foundation and lay the floor using only his Line and some pegs.

 

2 - The Lines measured the diagonals: if they matched the 2 squares were true. The diagonals also crossed at the center of each unit, locating the fireplaces, doors and windows.

 

The cabin floor could have became the framing floor. The Lines necessary for framing could be marked with a chalked line. 

Carpenters today build this way: they use the floor of whatever they are building as their framing floor. When the frame is ready it is lifted into place.

The square and its lines determine the wall height (red arrow). The 2nd floor is set at half the square. The roof begins as a square set above the wall. The roof pitch is the diagonals of the 2nd square. The chimney is 1-1/2 squares tall. 

 

 

 

 

 

No numbers were needed to lay out this cabin's frame, just practical geometry, some twine and something to mark the important points. The carpenters needed to understand practical geometry but not reading, writing or arithmetic.

 

 

 

 

The front elevation is an after thought. The plan and end elevation have already determined all locations.

 

 

Carpenters use center lines to locate windows and door. They then frame on either side of the opening. 

Masons, however, need to know where to end the row of bricks. The lines for brick or stone construction often end on the side of an opening.

 Owen Biddle's simple town house is a good example. It has 2 rooms up and down, plus a basement and entrance porch.

This layout could be drawn on the first floor just as the cabin could have been. A drawing might have been necessary for the front entrance with its fan light.  I have seen such drawings on wood which - when no longer needed - became roof sheathing.

Biddle's basic Lines locate the window location and height, the entrance size. 

His floor plan uses the Lines to locate walls and the fireplaces.  

The illustration was a guide for the 'carpenter assistant' so it is quite straightforward. It is the proportions that give the house presence.

Still, the house would be bare, spare as farmhouses are, without the details: the fanlight, the porch columns, the fretwork.

Other illustrations in his book use more complex geometries.

 

My introduction to the Tuckahoe Plantation cabin is here.\: https://www.jgrarchitect.com/2014/06/cabin-tuckahoe-plantation-goochland.html

When I teach Practical Geometry, we often lay out the Tuckahoe cabin with a line. The floor plan appears as we swing the arcs and mark the intersections.

Owen Biddle's town house is elegant, and very simple. A step by step analysis of the geometry is here: https://www.jgrarchitect.com/2015/11/owen-biddles-plan-and-elevation-for.html 

 

The previous posts in this series  Lessons 1-6  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

 

 

 

 

Owen Biddle's 'Young Carpenter's Assistant' , Plate I, G

A note on Owen Biddle's Plate I, Diagram G. in his pattern book for beginning carpenters. *

 

I wrote about Diagram G on this post: https://www.jgrarchitect.com/2020/06/practical-geometry-lessons-lesson-5.html

I said that Biddle was not just introducing his 'carpenter assistant' to geometry; in Diagram G Biddle was explaining how to layout a square corner to work out a structural detail, cut a board, or set a frame on site.

Since then I have explored the theoretical geometry of that diagram.

The number of right angles which can be drawn in a circle is infinite. The rule always works. That understanding is part of why geometry is seen as mystical or sacred.

This 'squaring the circle' diagram is from

Robert Lawlor's Sacred Geometry*. (page 77, diagram 7.5)

It uses a geometry similar geometry to Biddle's diagram G: a diameter and an angle. Here the diameters are evenly spaced and the same angle  is used at every point on the circumference. But the angle is not 90*. It is not a 'square angle'.

This is decorative, not structural.

The shapes do not close. The line continues for 5 rotations. It does not create a square, but seeks to define the perimeter of a circle with straight lines. 

,

I am often told that I work with Sacred Geometry, that the geometric patterns I recover are theoretical, mystical, and sacred. I agree they are geometry. No, they are not sacred. They are practical. They are geometry used in construction.

Here is how Biddle's diagram comes about: 

Begin with  a point  - A

Choose a radius - A-B,  and draw a circle. Using the daisy wheel find the diameter - B- A- C, dotted and dashed line.

Pick a point on the circumference of the circle - D.

Here I have chosen 3 different D's  at random.

Connect B-D and D-C.

Each diagram will have a 90* (right) angle at the intersection of  B-D-C.

Wherever the D is placed. the angle will be 90*.

Biddle's Diagram G begins with my line B-D.

It describes how to find my 90* angle of B-D-C. (his a-b-c) The answer is to find the diameter of a circle (a-d-c) that intersects a. That will give c. That will give the 90* the carpenter needs.

 

By Hound and Eye* has a very similar diagram for drawing a right angle .
The book is a  guide to furniture design, full of practical geometry. Each geometric problem is described step by step; practice work sheets are included.

This pattern is the beginning of a handmade try square. 

 

*Owen Biddle's The Young Carpenter's Assistant, 1805, Philadelphia. Dover Publishing  reprint,  See my Bibliography for more information.

*Robert Lawlor, Sacred Geometry, Philosophy and Practice, 1982, Thames and Hudson, London.

*Geo.R. Walker & Jim Tolpin, By Hound and Eye, A Plain & Easy Guide to Designing Furniture with No Further Trouble, 2013,  Lost Art Press, Kentucky The diagram shown above is from page 57.

This pattern is 4 overlapping hexagons.

My granddaughter, who is 7, watched me add the images to this post.

She wanted us to 'square the circle'. I did, using right angles where the diameters met the circumference. That produced these overlapping 6 hexagons, not squares.

She watched closely and observed that accurate work was not easy: my lines did not always cross exactly in the center of the circle. When we finished she asked me to erase all the diameters. This is the result. Maybe she will show me later what she added to the copy I printed for her. 

Practical Geometry Lesson 5, Addendum

Why I left out diagram K from Owen Biddle's Plate 1 in his Young Carpenter's Assistant.

Lesson 5 was written for a student today who wants to draw rectangles using practical geometry.
Biddle was writing for the apprentices he worked with in 1805. They needed to know the practical application of geometry for the buildings they worked on - including the curved parts.

This addendum is like one of those long footnotes in an historic report -  a part of the story that's not quite germane to the subject, but ought to be included.


Biddle  identifies each diagram on Plate 1with a letter. There is no diagram for D. However, in his text, between C and E he discusses the mathematical instruments a carpenter should obtain. Perhaps this is D.  I quote him:

- scales of equal parts on the thin ivory or box rule
- a bow pen or compass
- a small piece of gum elastic for rubbing out black lead lines
- a stick of Indian ink
- 2 camel's hair pencils, one large, one small
- a black lead pencil



There is also no J. And there is no text in its place as exists for D. 




Here is K.  

Biddle writes: "Three points (not in a right line) or a small part of a circle being given to find a center which will describe a circle to pass through the points or complete the circle."

                                                     
                                                     Start with a curve a-b .
                                 The curve in Biddle's drawing above is a-b-c.                       










 The curve divided in half:  Swing 2 arcs that are the same length  above above and below the curve: a-c and b-d. Mark where they cross, at f above and below the curve,









Connect  f and f with a line - here dashed. Mark where the line crosses the arc a-b -  I've labeled it g.
This line divides the arc in half. 
If 2 lines were given - here: a-g and g-b , this step would not be necessary. Biddle's diagram  labels his lines a-b and b-c.

Now, the instructions become complex.
Draw it step at a time. And consider that this is only Plate 1 of Biddle's pattern book. He included 43 more Plates for the carpenter's assistant.  

Divide the lines a-g and g-b in half.
This is shown in Biddle's E  and F diagrams. Check Lesson 5. 

Extend the lines which divide  a-g and g-b in half so they intersect at k,
K is the center of the circle which passes the points or completes the circle.

Refer to Biddle's drawing K above for the complete solution, all neatly explained in only one diagram.  



Clearly Biddle thought this information  was essential knowledge for  every carpenter. His next Plates illustrate why. The construction his 'young carpenter's assistant' would be working on involved determining and laying out many curved lines for vaults, arches, windows, stairs and railings.

Plate 2 discusses ellipses: how to draw them using geometry or a trammel, how to find the center and axes of one already drawn.   















Plate 3 is concerned with octagons, arches, groins. the use of trammels, how to divide a line into parts.

I am quite fond of Figure 1, describing " an Octagon within a square." . Simple, quick, even obvious - if you know geometry.

I have seen  painstaking explanations of  how to lay out an octagonal using algebra: quite painful.

Plate 6 reviews raking cornices and "the sweep of a cornice which will bend around a circular wall and stand on a spring."

Plate 31 lays out "the section and elevation of a circular or geometrical stairs". Biddle includes in figure C  "the manner of drawing a bracket for the ends of the circular steps..." and the careful, detailed instructions.




Plates 32-35 - not included here - explain how to layout the newel, the falling moldings, the hand rail for such a stair.






Biddle's Young Carpenter's Assistant, Owen, Biddle, 1805, originally published by Benjamin Johnson, Philadelphia, and Roland and Loudon, New York. Reprint by Dover Publications, Inc. 2006. If you want this book, you can easily order it from them directly. It has an excellent 15 page introduction with bibliography by Bryan Clark Green.

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