The Practical Geometry of Boston's Old North Church

 

The Old North Church, in Boston's North End, was built in 1723.*

The church fathers responsible for its construction had visited England where they had probably seen the churches in London built after the Great Fire in 1669. Those churches were built using the new Classic architectural style which included half circle windows as are in the church instead of pointed ones.

I visit the church when I share/explore Practical Geometry with the North Bennet Street School Preservation Carpentry students. We, along with the instructors, see its construction first hand, from the crypt with its tombs to the timber roof frame in the attic.    

 This year I explored the church's geometry. The Historic Structures Report for the church, written c. 1950, includes floor plans which trace the evolution of the church interior. These are not HABS drawings, not as detailed and possibly not as accurate. This is, therefore, a preliminary exploration.

The exterior is brick. The floors and and roof are timber framed. One of the church fathers seems to have overseen the master mason responsible for the foundation and walls. A master timber framer was responsible for the roof. All of these men would have known Practical Geometry. 

 

 

Drawing #1 shows the church interior layout in 1730. The entrance and apse are extensions of the main space. The pulpit with its curvy stair is drawn to the left of the apse. In later years the pew locations, the stairs and some exterior doors change. 

The geometry of the exterior walls is simple. It is the 3/4/5 rectangle. The 2 3/4/5 triangles and the rectangle are outlined in red.

 

 

 

 

 

In Drawing #2 the black diagonals of the Rule of Thirds cross the interior. Where they cross are the points*** which locate the red vertical lines which divide the space in thirds. These lines layout the inside width of  the apse and the entry.  

The distance of 2 of the columns from the back and/or the front walls is also set: see the dashed red line at the 2/3-1/3 division of the church interior.

The apse plan is a half circle. The entry is square. Both are drawn in red. The  church wall is a little thicker at the entry to support the steeple. 

Drawing #3:  The square laid out by the Rule of Thirds ( in Drawing #2) can also be divided horizontally by the same Rule - see the black lines . The points allow 3 equal divisions across the church - the red lines, labeled A. 

 

 

 

 

   

Drawing #4: By adding  the Rule of Thirds' vertical lines  - again the black lines - the points are found on the red lines (A). These points locate the columns on both sides of the body of the church: the vertical red line which crosses the A lines at B to mark the distance between the 3 columns on each side along the length of the church. The fourth column, located in the space at the bottom of the drawing, uses the same spacing as .the other columns

 I have drawn only the left side. The right side matches the left. Too many lines become visually confusion.

 

Drawing #5: The windows were centered between the columns. 

In a time where candles and  torches were the only artificial lighting available, placing the windows for maximum natural light was essential.   

The arcs in black  on the right side locate the center line (C) of the window. 

The centers of radii for the arcs begin at the columns. IE: place your compass point on the outside edge of the column; swing an arc. Swing a similar arc from the opposite column. The line drawn by the 2 points where the arcs cross will locate the center of a window. 

*The church is best known for its steeple where Paul Revere hug his lanterns on April 15, 1775, warning the citizens of Massachusetts Bay by which route the British soldiers would march to Lexington and Concord.

 **This drawing is by Suzanne Carlson, from  John Fitzhugh Millar's book, The Architects of the American Colonies, Barre Publishers, Barre, MA, 1968. Used with permission from John Fitzhugh Millar.  

*** Remember that in geometry, Practical or otherwise,  a Line cannot be drawn without 2 points. To learn about the Rule of Thirds, see  https://www.jgrarchitect.com/2020/08/lesson-6-rule-of-thirds-part-1_21.html

 

 

 

 

  

The layout of an Italianate window pediment, Part 2

Last September I wrote about duplicating this ogee molding  - the continuous double curved casing above the triple windows in the center  of the photograph. 

 

Here's the link to the post: 

https://www.jgrarchitect.com/2025/09/the-layout-of-italiante-window-pediment.html 

  

 

Nathan Goodwin, the master carpenter for the reproduction, and I worked out the geometry. We didn't quite agree about the steps. That was interesting but not important. He laid out the curves and created the pediment.

 Later Nathan found an article, written c. 1850, by the Episcopal Bishop of Vermont for his clergy, recommended the use of this curved pediment for Vermont parish churches. The Bishop included a drawing of the geometry. It seems unlikely that a church man, even one very well educated, would have designed this. Where had he found it?  

Perhaps the Bishop had seen Peter Nicholson's  Carpenter's New Guide, 10th Edition, published in Philadelphia in 1830. 

Peter Nicholson was a British engineer and scientist. He wrote numerous popular books for master carpenters and builders.  To learn more see this post: 

https://www.jgrarchitect.com/2016/08/practical-geometry-as-described-by_16.html 

The frontispiece of the 10th edition says that the New Guide is "a complete book on lines, for carpentry and joinery, treating fully on Practical Geometry".  

Then after 6 lines describing what the book includes, it say,  "THE WHOLE FOUNDED ON TRUE GEOMETRIC PRINCIPLES"  

This page is fascinating in itself. It reads like an advertisement for the book. And there are 11 different fonts in several different sizes.   

 

 

 

Our pediment is on Plate 10, Page 25. The Plate is described as "The Sections of a Globe....also, the section of any figure standing on an irregular base". 

 

Our diagram is part of Figure 6, in the lower right corner, the geometry used 'To find the Ribs of a Gothic Niche, being the Plan, and No. 1, the Front Elevation" (p.27) The elevation (above) and the plan (below) are in the lower  right corner. The 4 diagrams to the left  describe how to layout each rib. 

 

 

  

 

 Here is a larger image of the niche elevation.

 

 

Nathan and I  were only laying out a molding to go over windows, not a niche. But the upper diagram is what we 'discovered'.   

 

 

 

 

 

 

Here's my rough diagram.  

I teach Practical Geometry but I am still an apprentice compared to Nicholson's mastery.

 

Update 2/26: Thanks to 'old pro millwork' on Instagram, we know this geometric layout goes back to before 1758.This diagram is in The Carpenters and Joiners Repository, by William Pain, published in London, in 1758. Pain prints it again in his later pattern books.  

I will add the diagram.

Asher Benjamin's pattern book in Bennington, Vermont

 

In 1838, Judge Luman Norton, his daughter Louise and her husband Christopher Fenton built this 2 family house in Bennington, Vermont. The side entrances are original; their porches, contemporary.* 

Hiram Waters, Master Carpenter in Bennington, probably designed and built the House.  The record shows that he bought a copy of Asher Benjamin's The American Builder's Companion, 6th edition, published in 1827.** 

Based on my research I think he also owned Benjamin's next book, The Architect, or Practical House Carpenter, 1830**.

Waters used Benjamin's molding profiles as well as his drawing for columns for his own house and carpentry shop. He also used them for this house.

 

The porch roofs and columns in front of the side doors  are 1950's +/-additions. Except for the storm doors, the entries are original. 

 

 

 

 

 

 

The pilasters on either sides of the doors match those in Benjamin's  in The American Builder's Companion.  All the parts are there.

 

 

 

 

This is Plate E,  Ionic Columns 

 

 Here is one of the main doors from the inside. 

  The Norton-Fenton House is currently closed to visitors. These interior photographs were taken in 2017 or earlier. 

 

 

 

This is Plate XLVII from Benjamin's The Architect, or Practical House Carpenter .   The lower casing profile matches that of the house.                                                           

 

 

 Here is the  base of the casings around the front door and its sidelights.

 

 

 

 

 

And Plate XLVIII from
The Architect, or Practical House Carpenter.

 

                       

 

 

 

 

 Finally,  one of the two curved staircases in the Norton Fenton House.

Benjamin uses 9 pages in his 1827 pattern book, 11 in his next book, to describe how to layout and finish these stairs.  

 

 

 Here are details on cutting the face moldings for the sides of the planks used to build the stairs. PLATE LVI, The American Builder's Companion. 

 

 

 

I am always impressed that a carpenter could 'read' these drawings and build from them. Hiram Waters was surely a superb Master Builder.   

 

 

 

 

 

*I've written about the design of this house in an earlier post:

https://passingbyjgr.blogspot.com/2017/05/the-4-front-doors-of-norton-fenton-house.html 

 *I've also written about Hiram Waters, 1797-1890:  

https://passingbyjgr.blogspot.com/2020/10/hiram-waters-workshop-monument-avenue.html 

 

** The Bennington Museum's Wallomsack Review has an excellent introduction to Hiram Waters. https://benningtonmuseum.org/wp-content/uploads/Walloomsack-Review-14-Autumn.pdf

 The unabridged 6th edition of The American Builder's Companion and The Architect, or Practical House Carpenter have been republished by Dover Press.

 

The layout of an Italiante window pediment

 

The curvy Italianate molding above that window in the center?  How did they do that? 

How did carpenters in south eastern Massachusetts in c.1850 lay out the picturesque pediment so it could be cut and assembled?  

 

 

This was the question posed to me by Nathan Goodwin of H.I.S. Construction. He was asked to lay out a copy of that molding for installation above two garage doors. 

Nathan and I posted ideas back and forth. Nathan needed to draw and define the curves, especially how the arc over the shuttered windows evolves into the arc which ends in a point above the main window.

While we focused on that curve I wondered how the master builder laid out the whole design. What geometry might he have used so that the pediment complimented/completed the windows? So it is integral, not just stuck on the top?  

 

 

 

 

 

 

The first task was to see the form that was there: 

A center window flanked by 2 skinny windows, now shuttered. Together with their casings they form a rectangle. The 3 windows' tops are half circles. Around and above them is the embracing molding which follows the semi-circles before it swoops up with a reverse curve to meet at the center in a point. The molding seems to be the same width throughout.  

We saw that the pediment was derived from the windows. The windows and their casings were a rectangle, 4 units wide. Note the red  rectangle and lines below the window sill.  

 

The curve for the section of the pediment over the side windows was easy to see and draw. It's the extension of the small windows' half circles. The red dashed line and the dotted lines drawn here radiate from the center of those shuttered windows. I shared this with Nathan. 

 

The pediment's height over the center window was also easy to find - see the dashed red arc on the right. The half circle's radius is half the width of the windows.  Note the black dashed line. It's a reverse curve. Where was its center? How was it generated?

The white-out on the image comes from us exploring and rejecting options.   

Nathan and I shared ideas back and forth. He posted this suggestion: a layout based on the width divided into 4 units.  

 He extended my 4 units into rectangles, divided the rectangles themselves into 4 parts and used 3 units as the radius for the molding hoods over the shuttered windows. 

The sides of the rectangles cross the semi-circle. He added diagonals from that point to the center of the top of the main window. The crossing point became the center of several exploratory circles for the reverse arc curving to the pediment's center.

 

 

Nathan ended up with this diagram. It worked for the width of the garage doors; he could lay out the curves and cut the parts. 

 
 

 

 

 

I wanted to know about the original design - the layout of windows, casings, pediment with moldings. How might the master builder/ joiner/carver (I don't know his title) have laid out the design? 

 Here's what I saw.  Nathan's division of parts works across the width of the window. The whole width is 16 parts/units.The center window is 6 parts wide; the casing on each side is 1 part. The side windows are 3 parts wide; with one part on each side for the casing.  

Nathan's geometry for the reverse arc over the main window also works. The radius of the center window's arched top is 3 parts, with the casing: 4 parts. This doubled is the diameter of the circle which draws the arc of the  pediment.

More or less! The craftsman left us no notes. And: I am analyzing from a photograph of the window, not the real thing.   

 

 

   

   

 

 

 

 

 

 

 

Asher Benjamin explains how to make stucco

 

First, a brief introduction to stucco. 

Are stucco and plaster the same thing? Not now.Today stucco is used outside. Its recipe will be different from plaster used inside. In 1814, the names referred to the same thing.  

  

These cherubs are plaster. They cavort in the dining room of the Canfield Casino of the History Museum in Saratoga Springs, NY.   

 

 

 

 They are forever in motion on the frieze of the entablature, 

 just below the deep cornice, 

a counterpoint to the circular window ringed with energetic vegetation centered under the coffered barrel vault above.  

Lots and lots of white plaster. Made from lots of molds. Mass production allowed this extravagance in 1902.

 

 

 

100 years earlier moldings were made from wood. Plaster sealed the wall. It was held in place by lath.   

Plaster was lime, sand, hair and water, mixed by hand. 

Its keys fit into the spaces between the lath, holding the plaster in place,  allowing the plaster to create a 'wall'. That plaster kept out drafts, reflected light and created a space, a place. It still does.  

 This plaster is applied to lath which was split by hand, thus the uneven shadows.   

 

This image of the back side of lath shows the plaster keys pushing though the spaces between the lath.  This lath is even because it was cut by a circular saw. This plaster wall would be much smoother than the image above. 

 

 

 

Asher Benjamin shared the latest uses of plaster with aspiring Master Builders in his book, The American Builder's Companion. 

It was first published in 1806, then updated in 1814 to include stucco ornaments (Plate 36,  prefaced by 3 pages (74-76) of instructions, titled Plate XXXVI.

 

 

 

 

Benjamin was a Master Builder with apprentices. He also ran a school for carpenters in Boston. He was skilled at describing how to execute the work. 

 

 

 

 

Here is his footnote describing how to make the stucco. He says to  just mix it up, beat it well every day, and let it cure for four or five days on a brick wall.

Not too much a stretch from plastering a wall, but seemingly far removed from the Canfield's yards of dentil and corbel moldings and the carefree cherubs.

 

He describes the best way to make an ornamental stucco ceiling, by hand. 

Then he explains how to do it more quickly, cheaper. What he describes is the beginning of mass production, ie: the Industrial Revolution, starting us on the path to those cherubs.

For the rest of Benjamin's instructions, please read his notes. He wishes "to give the student every information in my power... and be of no injury to those who are well acquainted with the art of stucco working."*  I think he would be pleased that we are reading his instructions 200 years later.

 

In 2009  I wrote 2 posts about  how Asher Benjamin wanted the builders who would read his pattern books to see and enjoy what moldings could create. He clearly loved the "beautiful variety of light and shade". 

I included the portrait of Benjamin in the first post. Historic Deerfield recently cleaned it. To see it please google 'Asher Benjamin'.


http://www.jgrarchitect.com/2009/01/beautiful-variety-of-light-and-shade.html

http://www.jgrarchitect.com/2009/12/strong-mouldings-and-falling-water.html

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 

 

The Carpenter Square and the Compass - The Evolution of Practical Geometry

 

On May 31, 2025, I will present Practical Geometry and Carpenter Squares at the Early American Trades Association (EAIA)* conference in Rochester, New York. I expect I will be introducing Practical Geometry and then explore how the use of a carpenter square began to change the visual character of our architecture. I hope to see tool collections and hear other members' thoughts.

 What happened after 1820 when the carpenter square became a reliable drafting tool? When the compass, line, and scribe were joined by an L shaped piece of steel with a dependable, true 90* corner?

The squares shown here were made in southwestern Vermont c. 1830-50. They now live at the Bennington Museum, Bennington Vermont, and can be seen by appointment.

 

 

 

 

Here you can see the hand stamped numbers on the earliest squares as well as carefully drawn scales. Were the scales as important to the builder as the true 90*angle?

?

    

The square made design and layout accurate in fewer steps. Units (inches and feet) were uniform, corners were square, always 90*.  A job could be drawn, measured, and laid out more quickly and accurately. However, loosing those steps also changed the proportions. I have written about how this can see seen in vernacular housing design.**** I wanted to learn how an architect might have used the carpenter square. Robert Shaw was a good choice  because he wrote a book.

 

Robert Shaw's The Modern Architect was published in Boston in 1854.** 

 

 The pattern book's frontispiece shows the tools of the builder and the architect. The original drawing is an engraving which is quite dark. The color was added when the book was republished in 1995.

 

In the foreground is a large compass, probably used for stepping off. The architect holds a little one. The architect and builders are shown conferring, syncing the construction dimensions with the drawings .

 

 

Here is Plate 4, a 'Grecian  Frontispiece'

Where did Shaw begin his design?  Conceptually the design surrounds the door, giving it emphasis. So I began there.

Shaw himself stated that the door's height should be "...over twice the breadth of its height as three and seven feet."*** 

I have added the scale below the door: 3 units for the door's width. Then a half unit for the columns on each side and a full  unit for the width of the sidelights. 

These proportions follow those recommended by James Gibbs in 1732. ****

 

 

 

Was Shaw using 'circle geometry' for his layout? I don't think so. The circles don't offer much information. 

While the layout is 2 circles tall, the 12 points around the circumference of the circles give only the height, the width of the entry including the side lights, maybe the location of the transom. Note the arrows.

 

 

I think Shaw used a  simple geometric pattern that is derived from the circle, but which doesn't need to start with a length - a radius - and compass. It starts with the square which is easily laid out by the carpenter square. 

The width of the door and its sidelights was the dimension for a square. That shape was easy to lay out and make true with a carpenter square. Beginning with a length, he set up the corners with the square, added the lines for the 4 sides,  trued the box with diagonals. The diagonals used to find the additional height comes directly from the square. Done.        Note the arrows.  

Was there a name for it? Not one I've found.  It's basically a 'square and diagonal geometry'.

 

 The door, its transom, sidelights, and columns are also a square.

Here the quarter circle arcs, based on the width, cross at the top of the door frame, just below the transom. This layout, creating a slightly smaller rectangle within the square, was often used in layout and design. ****  I think here it is incidental.

I've extended the scale across the bottom and up the right side. It confirms the geometry.

The whole frontispiece is 8-1/2 units wide and 10-3/4 units tall. The door, the pilasters and the sidelights are 6 units wide; the columns are 1-1/4 units each. The columns' capitals are a half unit tall. The entablature is 2 units; the pediment, 3/4 of a unit tall.

Each unit and its parts could be stepped off with a compass. In 1854 the length could also have been stepped off in 12 inches intervals as marked on the carpenter square. As shown in Shaw's frontispiece in his book, it seems the builders used both.

 

The geometry used for the door and its parts is also used for the overall size: the height of the frontispiece is equal to the diagonal of the square.

The lightly drawn dashed line is the arc of the width of the door, showing how it lays out the square. This geometric proportion is also used for the sidelight glass panes (see the image above), but not those in the transom.

 

 

When we architects, restoration trades people, and historians note from visual observation that a particular building is Greek Revival, not Late Georgian, we are seeing geometry. I think we are recognizing, even if subconsciously,  that the rhythms, the proportions of  Federal architecture are different from the Greek Revival proportions shown here.   

 

* EAIA, Early American Trades Association https://www.eaia.us/

https://www.eaia.us/2025-rochester-ny

** Robert Shaw, The Modern Architect, Boston, 1854, originally published by Dayton and Wentworth, republished  (unabridged) by Dover Publications in 1996.

*** Shaw, The Modern Architect, page 63. 

****    For more information about James Gibbs' use of the door width as a unit of measure see: https://www.jgrarchitect.com/2025/01/james-gibbs-and-rockingham-meeting-house.html

            For more information about the square and its rectangle see:                                          https://www.jgrarchitect.com/2023/11/the-practical-geometry-of-parson_20.html

           For information about buildings using the 3/4/5 triangle for layout:

  https://www.jgrarchitect.com/2014/03/railroad-warehouse-frame-c-1850.html  

https://www.jgrarchitect.com/2014/10/the-cobblers-house-c-1840.html  

https://www.jgrarchitect.com/2013/10/1820s-farmhouse-north-of-boston.html