Saturday, May 25, 2024

A Daisy wheel is a Module

Andrea Palladio wrote that he chose to use a Module to lay out the columns he drew.*

All the dimensions which he noted were derived from the diameter
 of the column measured at the bottom,  ie: the height of the column, the capital, architrave, frieze and cornice.

He wrote, " the dividing and measuring the said orders, I would not make use of any certain and determinate measure peculiar to any city, as a cubit, foot, or palm, knowing that these several measures differ as much as the cities and countries; but imitating Vitruvius, who divides the Doric order with a measure taken from the thickness or diameter of the columns, common to all, and by him called a module, I shall make use of the same measure in all the orders." 




The cross section, the diameter, of a column is a circle.





A daisy wheel is a circle.

It's easy to draw with a compass or dividers.









It is a module.




This sheathing board leans against my corn crib. It was siding for a timber framed shed, part of a farm complex in Danby, Vermont. The board is 10' tall, angled at the top to fit under the roof eaves. 



Today it folds in 2 places. It fits in my car; it stands on its own at a conference, ready to be seen and examined.



The daisy wheel was cut into the board at a height of 42"  above the floor, a good height for the builder and his crew who would have set their dividers to its width. All of them needed to be using the exact same dimension (their module) as they laid out their work.  


This daisy wheel's diameter is slightly more than 8 inches.

The wheel is just above the center of the photo. In the images below the board has been laid down. 



Dividers set from one petal to the other across from it, the diameter of the daisy wheel.

Note the holes on the circumference and the center left by previous users.




Here the dividers, set open at the same angle, are rotated 60* farther around the circumference. They are at the points of another pair of daisy wheel petals, the circle's diameter. The distance is the same as it was before. 

Note the holes are not quite on the petals tips, rather they are on the circumference of the circle. Many daisy wheels were not precise.  




Here the dividers points have been slipped into the holes drilled by all the previous carpenters' dividers.


My dividers slid right in place, so secure they stood by themselves.

I had never tried this before - I was surprised and awed: my placement was one that many had done before me. 


The black marks on the board above the daisy wheel are the holes left by rusty nails.


* Andrea Palladio, Four Books on Architecture, 1570, Isaac Ware English Translation, 1738, Dover reprint, 1965. Palladio's statement about modules is on page 13, First Book. The image of the Doric Order is Plate XII, First Book. 

Friday, May 3, 2024

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.



Saturday, February 17, 2024

"Keep Within the Compass", Cautionary Prints, c. 1785

Here: a well off and contented woman,  her space defined by the compass which is encompassed by a circle.

The print, dated 1785, is now in the British Museum. Prints like this showing women and men within the circle, scribed by the open compass, with corner vignettes, were common c.1780.

 The woman is sheltered by the compass. She is in a tranquil country setting with her dog and her wealth, her book. Beyond the circle is the vivid story of her possible dissolution: drink and gambling leading her to debtors' prison where she must break hemp. 

The words on the circle are, "keep within the compass and you shall be sure to avoid many troubles which others endure". On the swing arm of the compass is engraved, "Fear God'.

Googling the phrase running around the circle, "Keep within the Compass" brings up this image and a description of Free Masonry, including the idea of the circle as a symbol for God. 

Whoever wrote the entry ignored that well made, shiny compass with a serrated, adjustable swing arm, tapered legs with well defined knobs and sharp points ready to scribe that circle. The commentary only says that it shelters the woman.

Why did the print maker draw a compass so carefully if it wasn't part of the visual message? A shiny shimmering circle would have sufficed. The compass is a tool; here the tool of God, and the tool required to draw the circle.

I think the writer, and we as a culture, have forgotten common skills and so we no longer understand references and images our ancestors took for granted. 

As recently as 1950, compasses were tools, used every day by people who built with their hands: masons, carpenters, as well as crafters in many trades, architects and designers.  This image is an illustration from Basic Technical Drawing, published by The Macmillan Company in 1956 and 1962, written by Henry Cecil Spence. 

70+ years later we have almost no experience of geometry as practical knowledge, of compasses as instruments.**




When the 'Keep within the Compass' print was first made the designs in patterns books included geometry as a matter of course.

Plate XXXVIII in William Pain's pattern book,  The Practical House Carpenter, printed in London in 1794, assumed that his readers used geometry: "...the height of the column... to be divided into 9 equal parts, one of which will be the diameter of the column at bottom..." 

His description for the pediment begins, "to find the pitch of the pediment set the compass at a..." His readers understood the compass cues: the letters and the dashed lines, the notation of lengths on the line along the left side. 




Here is Plate X in Asher Benjamin's  pattern book, The Country Builder's Assistant, printed in Greenfield, MA, in 1797.

His descriptions include 'diameters', 'arch lines' and notes about where to 'set the compass'.  He writes, "Divide the height of the  column into 10 parts, one of which is the diameter of the column."

The compass was used for measuring as well as a layout.






This sculpture of James Watt. the Scottish engineer, carved about 1820, during his life time, shows him using a compass to design the steam engine.

The compass was an engineer's design tool.




James Watts' little compass is a measuring and design tool, a tool for thinking carefully, thoughtfully.


Here are 2 more historic prints of people within the compass and pictures in the corners of their desolution if they do not keep within the compass. 

 The gentlewoman is finely dressed with a devoted pup and a chest of jewels and garments beside her, a purse on her arm, a book in her hand. She keeps within the circle drawn by the compass. The sky is a lovely blue.

Clockwise from the upper right: The gentlewoman drinks, does not tend to her baby or her sewing.

She gambles and plays cards. losing her money.

The constable (in blue, an official someone) takes her off to debtors prison

where she must break hemp to help make the ropes for the English navy, and will be flogged if she doesn't.

 And, in case you needed reminding,  "Prudence produceth esteem".

Here is the gentleman, prosperous with land, servants, crops, a mill. He is finely dressed and well fed. 

In the corners are his downfall because he did not "keep within the compass": wine and women, gambling in the upper corners. 

His investments, his goods and ships, are lost at sea so that he too ends up in debtors' prison.


The final words: "Industry produceth wealth"







In case you wondered: God knows about compasses. Here He is creating the world, from the frontispiece of a  German Bible, c. 1250.







My thanks to Patrick Kennedy (of Historicorp and PTN)  who introduced me to these images several years ago.

To see the prints at a bigger scale look for the British Museum website and  'Keep within the Compass' online.


*William Pain, The Practical House Carpenter, 1794, 5th edition, London; Plate 38. Reproduction from British Library by Gale Ecco Print Editions

**The compassess sold as toys lack sharp points. They are useless because they skitter across the paper.  Without a fixed point for a center a compass can not draw a circle.

Tuesday, January 9, 2024

The Practical Geometry of the Parson Barnard House: Addendum


How did the builders of the Parson Barnard House actually use Practical Geometry?
Did they have to draw arcs with twine every time they wanted to measure something? 

Probably not. I think that they knew the geometry so well that they could take short cuts in laying out a house .*

Consider a carpenter's education in 1715, when this house was built.  A boy would have been apprenticed to a carpenter when he was about 11 years old. Along with woodworking skills he would have learned the fundamentals of geometry: how to use a compass and line for measuring lengths, how to lay out basic shapes with a compass and a straight edge. 

After 7 years of training the apprentice became a journeymen. He would have traveled and worked for other carpenters. He would have broaden his understanding of practical geometry and understood how geometry works. He would have been able to skip steps.


The previous posts on the Parson Barnard House** explored the geometry used to lay out the house frame and window locations on the front facade. 



The width chosen for the sill, about 18 feet, was the dimension used for the layout. The room sizes and the overall width and length of the house come from that first length. The bent's rectangle comes from using the sill length as the radius of the daisy wheel by which the framers laid out rectangles.



 The sill length was also the beam length for all the bents.  

The diagonals are the Lines which true the rectangle's corners and mark the location of the 2nd fl. beam. See earlier posts**




The chimney mass is the only part of the house with unrelated dimensions. Built of brick, it used the 3/4/5 rectangle.**


The carpenters would have staked a line at one end of the house for the exterior of the foundation 1-2.
Then they laid out the length, 18ft, and staked it 1-2. They laid out a right angle (here shown as a 3/4/5 triangle), and extended that line 1-3 18 ft. - marking the second side of the square; they didn't need to swing the arc. from 2 to locate 3, marking 3 corners of the square: 1, 2, and 3




The 18 ft. Lines arced from the corners 2 and 3 would cross, locating the 4th point. The carpenters didn't need to draw the arcs, just where they crossed.



Then they would check to be sure it was true, just as builders do today.


Matching diagonals across the square would confirm the carpenters' accuracy.  1-2 = 3-4

The Parson Barnard House geometry uses the length A for its floor plan and its bents. That length comes from the arcs of the length of the bent. It could have been found by 1) folding the Line (about 18 ft long, the length of the bent) in half, marking that point - shown here on the bottom line of the square  - and then 2) marking where the arcs cross (dot).  A length from the base to the arcs' intersection, the dashed line A, could be transferred to the side of the square, giving the width of a room, the height of the bent.  (NB: Geometry requires 2 points in order to draw a straight Line.) 

The carpenters only needed to find this length once. They could have marked it on a plank for reference until the frame was complete, then used the plank as sheathing for the walls or roof. 

Some of these layouts have been found and saved: Eastfield Village in East Nassau, NY, ( has some which they noticed on the roof sheathing when the Inn was dismantled and  moved to the site.  Unfortunately, because we have lost most of our understanding of practical geometry, those doing restoration rarely look for such notations left by earlier craftsmen. 

*NB: When I teach, the students and I swing the twine in arcs to mark the corners of a house foundation. It was easy, fun, and exciting as we see the shape come into being.  

** see: 

 *** Brick walls are built row by row. 2 Lines and the 3/4/5  keep them true vertically and horizontally.

Tuesday, December 12, 2023

The Practical Geometry of the Parson Barnard House: Its Assymmetry

The Parson Barnard House, Part 3.*

The front  elevation is asymmetrical.  Did you notice?

The door at the Parson Barnard House is not in the center of the front of the house. But, yes - it's the focal point. The pediment, the surround, the red paint, the chimney above reinforce its importance. The paired windows on each side create a space between them where  the door belongs.  





The paired windows are not equally spaced from the door, see A and A. The spaces between each set of windows are also unequal, see B and B, nor are the distances from the corners equal. see C and C. * *




The frame, the posts and beams, with the door and second floor window centered under the chimney, more or less.** 

The post and beam frame is structure here; it is not the design.





The windows could have been centered in each bay and the house would look like this: simple, direct, and a little crooked, boring.

Note: this looks very much like today's subdivision Colonials with the obligatory 2 windows on  either side of a door. It's acceptable, but that's all.



Instead, the carpenter built this. He gave us balance and grace, a lively facade.

This image is from 2021. The first floor windows in the HABS drawing have been replaced with windows with panes which match the early second floor windows.  


What did the carpenter consider?  

First: the Hall was the larger room; the Parlor, smaller. The front door could not be not centered on the front wall. 

Second: the door needed to swing so that people could go directly into the Hall to the right, the main room of the house. The door must also swing back, fully open, for easy access to parlor.

The drawing shows the door swing with black arrows, The vertical red line is the center of the entry hall, but not the center of the front facade, nor the center of the space between the windows on either side.

The porch is no longer there. It did not date to the early construction.

Third: the 2 main rooms of the house, the Hall and the Parlor, face south. That orientation allowed for maximum sunshine which gave (and still gives) both light and warmth to the interior. Placing two windows on the south wall in each room (and at least one on the east and west walls) was essential. 

Fourth: the parlor was the formal room. It was the parson's study/office; he was the most important person in the town. It required a pair of balanced windows, gracefully placed.

Fifth:The carpenter was using simple geometries: the square derived from a circle. He knew how to use diagonals to divide lines in half. He used the arcs of the square to set a smaller distance as shown here.***

We see today that he had a sense of design, a 'good eye'. Unfortunately, we don't know who he was.    


The window placement came from that geometry and the carpenter's visual understanding of the house: how that facade would 'speak' to those coming as well as to those already in the house. 

Bents were raised one after another, set into the sill below; the plates added above. The carpenter would have laid out the bents  along the sill and the plate on the framing floor before the raising. He would have cut the stud pockets along with those for the posts. The window frames were probably added later as they were hung from the beams at the ceilings, but he would have known the sizes of the windows he planned to install.

The geometry  of the window spacing  in the Hall used the distance from the exterior bent to the center bent in the Hall as a radius. The arcs of the semicircle and its reverse cross at 2 points, once on each side.The secondary arcs cross the semicircles 4 times at their 1/4 points. 2 straight lines with dots on their ends position the outer sides of the windows. 

This layout is 2 4 arc stars side by side.***

The placement of the Parlor windows follows the same geometry. 

I have drawn an alternate way to layout those locations. To read a simpler solution skip to the last paragraph!

Just as in the Hall the length of the arcs chosen is the distance from the right side of the post at the right of the parlor to the right side of the center post. Those 4 arcs cross top and bottom. The line with a dot at each end comes from the 2 points where the arcs cross. It locates the right side of the right window.  

The 4 arc star has 4 points. Those points allow the original square to be divided into 4 equal smaller squares. They also give the length between the window and the right post. That length, drawn here with arrows, gives the distance from the left window to the exterior wall, also a black line with arrows.

Or consider this: the carpenter knotted his twine (his Line) to mark the width of the parlor, outside of the corner post to the inside of the 3rd post. He folded the Line in half, and then again. He now had 4 equal lengths  which he could have marked on the sill and the beams.The outside lengths located the left and right edges of the windows. He folded a shorter Line to locate the windows in the Parlor.**** He would have known his geometry so well he could use short cuts. I write about this is my next post: 

* the link to my posts on the House for the practical geometry of the frame    

http: s:// and 

**The HABS drawing, c. 1934, shows a larger surround and pediment. These were updates to the house, removed to reveal the original 1715 doorway.

 *** I often find this '4 arc star' when I explore Practical Geometry. It follows naturally from the square derived from a radius. The radius is often the width of a room, the length of a beam. It easily provided 2 points for dividing a space in half either way. It is often the width of a room, as it is in this house. I have found no name for this geometry so I am naming it here: the 4 arc star .   

**** He could also have transferred his dimensions to a pole. Carpenters today use a 'pole' to make sure  clapboards and window casings line up around a house. It is a thin board, a piece of scrap, that can be propped up against the house wall and easily moved from location to location,