The Practical Geometry of the Parson Barnard House: the Floor Plan

The Parson Barnard House, North Andover, Massachusetts, built in 1715. This picture was taken in 2022.

The original house is the front (left) section: 2 rooms up and down, each with a fireplace. The chimney in the middle served all the fireplaces and acted as a radiator.

The saltbox extension was added c.1720. The rear wing dates to the 1950's.

 

 

 

 

 

John Abbott measured and drew the floor plans and elevations of the house for HABS in 1934. At that time it was thought that Simon Bradstreet had lived here. Now we know the families of the Reverend Thomas Barnard and his son, the Reverend John Barnard, were the first residents from 1715  to 1757.
 

 

Here are the tools a  Massachusetts Bay Colony carpenter had in 1715 for planning and laying out buildings*. He used a compass, a square, horizontal and vertical levels, a straight edge marked in regular increments (which might or might not be inches) and a line with a spool on one end and a plumb bob on the other. The builder also had an awl, chalk, charcoal, and an 8 or 10 ft. rod.

His square was small and might not have a true 90* corner. His inch, foot, rod, varied from those of other carpenters. He would have learned his skills as an apprentice to a master carpenter, become a journeyman, then a full-fledged carpenter. His training would have included practical geometry. Tape measures had not been invented, paper was precious. He drew plans on framing floors, on sheathing, on dirt. He did not need to be literate.

Using a compass, a straight edge and a scribe a carpenter could layout the plan on a board, then step off the plan on the site with his rod or his compass, set his lines, and true them. This is the same order in which we layout buildings today; we simply use more modern tools.

This is the floor plan of the original house.
Noted in black are the sills, the posts and beams for the first floor frame . 

 The carpenter knew the first floor would have a Hall - on the right labeled 'living room', and a Parlor - on the left called the 'dining room'. 

 

Between them, in the center of the house would be the chimney stack with a separate flue for each of 4 fireplaces.

Here is the chimney above the roof with articulated flues.  

These spaces add up to a house about 18 ft. wide by 42 ft. long.

 

 

The width and length of the house were stepped off with a compass or marked on a length of twine. The exterior of the house would have been staked.  3 foot units could have been stepped off 6 times for the width and 7 times for the length. Layout with a rod marked in feet would probably have been faster. A chalk line might have been snapped. Lines could have been tied to stakes for the men digging the foundation. Diagonals would have trued the foundation. All of this is similar to how we layout buildings today.

Stone foundations of  pre-1900 houses tend to be vertical on the inside of the wall, the basement side, battened into the soil on the exterior. 2 lines would be required to accurately set the top of the foundation - where the sill would sit, where the outside wall of the house would stand.   

The length of the beams of the frame, approximately 18 ft., probably determined the house width.  

The Hall, the biggest room, was a multi- purpose room, used for cooking, chores, gathering. Often set in the southeast corner of the house, it had sunshine from early morning to late afternoon.  Here the room is square with a beam to support the 2nd floor across its center. The arc of the 18' width locates the posts.

Note that the dimensions appear to begin at the inner side of the right hand posts, indicating that while the exterior of the foundation was laid 18 ft. x 42 ft., the layout for the timber frame appears to have been set from the sill and those first posts. 

Laying out the geometry from the inside of the frame would have been a practical choice. The sills would not cover the line, but located beside it. Truing a rectangle by checking its diagonals to the outside corner of a post would be tricky, especially after the posts were in place. The framing timbers also needed to set to the line. And, the outside of a stone foundation could be irregular - as field stones are - without compromising the bearing of the frame on the foundation. 

This length, this inside dimension, would also have been the one the framers used to lay out the mortise and tenon joints on the beams.

Next to the Hall is the chimney stack. In plan it is a 3/4/5 rectangle often used by masons to keep the bricks plumb and level during construction. The fireplaces fit within, their fires creating a massive heat sink.  

The entry and staircase fit into the leftover space in front of the stack.

 

 

The Parlor, the room to the left, was used for business and formal occasions, to welcome and entertain visitors. Sometimes it was also the master bedroom.

It was smaller than the Hall and also had a centered beam.  The arcs cross at the outside edge of the wall, setting the width of the room. 

The length of that width could easily be measured from the layout of the Hall. Here the arcs cross, giving 2 points for drawing a line which, extended, is the width of the Parlor. Note the black line with arrows.

Yes, if the line which measured the width of the square of the Hall  had been folded in half and marked, it also would have given the point needed to determine the width of the parlor. In either instance the framer needed to understand the geometry. Geometry was a tool. It was practical. It is also why the proportions of these buildings are graceful; why they speak to us.

 

 

The Parson Barnard House, seem from its front garden in 2022.

 Note that the geometry of the house is so strong that the front door of the house seems to be in the middle of the facade. Actually the right side is wider than the left side. The windows on the left  are closer together than those on the right and the wall spaces between the door and the windows on either side are not equal. 

The geometry of the frame and the elevations will be another post.  

* the image is the frontispiece  for  Giancomo Barozzi Da Vignola, *Canon of the Five Orders  of Architecture, translated by John Leeke, published by William Sherwin, 1669. 

** A square can be laid out by a compass. Square corners can be determined and proved by a daisy wheel. Here is the visual explanation: the width A-B as the radius of the circle and locates the 6 points of the circumference A, B, C, D, E, F, G. Then: Lines A-F and B-E are perpendicular to A-B. Line G-C locates the end (west) wall  of the Parlor.

For more information and a tutorial see: https://www.jgrarchitect.com/2023/01/geometry-in-construction-practical.html

Practical Geometry Lessons, Lesson 5: Rectangles

Today these skills are not required knowledge for builders. We have steel carpenter squares that have true 90* corners, as well as levels and  lasers. 


The carpenter squares shown here are some of the earliest made in the States. They were made in Shaftsbury and N. Bennington, VT, 1825-60. Some are on display at the Bennington Museum; all are available for study.

The 1503 woodcut at the end of this post includes a square being used for a layout. That square might not have matched the square of another builder.

Practical geometry taught how to 'prove' that an angle was 'true'. Carpenters today still make their work 'true'.  

This "Geometric Problem'  and its solution was particularly important when carpenter squares were not necessarily true: the square corner was not always accurate, not dependably 90*.

This is the end of Lesson 5.
The carpenter's assistant who masters these problems is now ready to assist in layout and framing. Maybe he (no recorded 'shes' that I know of) will go on to learn design. 


For more ways to draw a square  see Drawing a Square, Parts 1 and 2.
Part 1: https://www.jgrarchitect.com/2019/12/practical-geometry-drawing-square-with.html
Part 2: https://www.jgrarchitect.com/2020/01/practical-geometry-drawing-square-with.html



 
After-thoughts and questions:

How did carpenters carry a 10' rod?  Did the rod fold, or come in pieces that could be connected with pegs,  perhaps leather sleeves?
I have seen one in a medieval print, part of which is shown here.
The builder on the left uses a square for layout. Below him is an axe, a saw, and a level with a triangular hole and a plumb bob.
The builder in the center holds a 10' rod.   The landscape to his right is the site where he will layout a building, or perhaps land.
 A 'rod' when used in land surveying is 16.5 feet long. It is also called a 'perch' or 'pole'. How did they carry that awkward length? 'Links' and 'chains' are also used in surveying, so perhaps a rod could be a length of chain.

 Woodcut by Gregor Riesch, Margarita Philosophical, published in Baden,1503.

 

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

 

Practical Geometry - Drawing a Square with a Compass, Part 2

 4 more ways to draw a square with a compass.

For Part 1 see: https://www.jgrarchitect.com/2019/12/practical-geometry-drawing-square-with.html


How to draw a square with a compass  #3
Peter Nicholson wrote about Practical Geometry in 1793.  His first plates are introductions to the first rules of geometry: using a compass to bisect a line,

My blog post about him is : https://www.jgrarchitect.com/2016/08/practical-geometry-as-described-by_16.html
It includes images of Plate 2 and Plate 3.

Here I have copied just the image of a square. Nicholson includes instructions for finding the square 'abcd' by dividing the arc a-e (the black spot) in half then adding that half to a-e and b-e find d and c.

Asher Benjamin and Owen Biddle in their pattern books copy Nicholson.
They do change the order of the letters which makes the steps easier to follow: a and b are 2 corners of the square. The arcs of a and b create c. Half of arc a-c is d. Add the length b-c to the arcs of a-c and b-c to find e and f: the square has its 4 corners.




How to draw a square with a compass, #4


A 3/4/5 triangle always has a right angle (90*) where the lengths 3 and 4 meet.
2 3/4/5 triangles are a rectangle which is 3/4 of a square.
I have drawn this on graph paper for clarity.

When carpenter squares became widely available and accurate, the square corners were easy to establish. The compass was only needed to lay out the length.

Before that - before about 1830 - the carpenter could have laid out his square like this:

His length is laid out in 4 units.
He knows approximately where the 2 sides will be. He does not know if his angle is 90*.

Here I have drawn the arc of the length of 4 units - on the right side. Then the arc of 5 units with its center at 3 units  on the left side. where they meet will be the 3/4/5 triangle.











The carpenter did not need to layout the full arcs as I have drawn them.
If he held his Line at the right lengths he could have marked a bit of both arcs where he thought they cross, and then placed a peg where they did cross. He would have checked his square by matching diagonals.

The relationship between the 3/4/5 triangle and the square is good to recognize. However, the 3/4/5 triangle is usually the only geometry. Layout by a carpenter square, widely available in the 1840's, was simpler and took less training than using a compass.





This small, simple house, built c. 1840 for a cobbler, was probably laid out using a carpenter square. I've tried other geometries which almost fit. The 3/4/5 triangle does.


I wrote the original post in 2014. It's time to revisit and review.
Here's the link to the post:
  https://www.jgrarchitect.com/2014/10/the-cobblers-house-c-1840.html



How to draw a square with a compass, #5

 Lay out a perpendicular through a line. Draw a circle with its center where the lines cross.
Draw lines - here dash/dot lines - between the points where the circle crosses the lines.

This square, as a diamond, was often used by finish carpenters because it easily evolves into more complex layouts. 

Below is the entrance porch for Gunston Hall, designed by William Buckland, c. 1761. The rotated squares determine the size of the porch. They also locate the floor, the pediment, the roof pitch, the size of the arch, the height of the rail.
 My post on Gunston Hall is: https://www.jgrarchitect.com/2014/05/gunston-hall-ason-neck-virginia.html

Here the glass facade of
 the Mass. Ave. entrance to MIT. For more, see:











https://www.jgrarchitect.com/2018/04/a-little-bit-of-geometry-of-mit.html



 How to draw a square with a compass, #6

 On a line select a length - see the dots .
Using the length as the radius draw a circle using one dot as the center.
Now there are 3 dots. Draw 3 circles using all 3 dots as centers.
Drop a perpendicular line at the first circle's center.
Now there are 2 new dots for centers of more circles.
Connect the petals where the 4 circles cross.
A square.




This modest farm house, c. 1840, used the square crossed as the squares above are for the Gunston Hall porch.

https://www.jgrarchitect.com/2014/09/how-to-construct-square.html

One last note: the circle to square diagram #6 can also become the diagram for #5. 

Each master builder probably had his preferred way of using his compass, even when he practiced within a tradition.
Still, just as a 3/4/5 triangle is part of a square, these diagrams are also simply different choices, different perceptions of the same geometry.

  

Practical Geometry - Drawing a Square with a Compass, Part 1

Draw a square with a compass? !
Yes.
Here are 2 ways. There are several more.

Compasses make circles. Straight edges make straight lines. Together they can lay out whatever you can imagine.
 
How to Draw a Square with a Compass #1

1)   Choose a length: A-B.  It is also the radius: dashed black line A-B,  for drawing a circle with a compass.
2)   Draw the circle.

I have drawn these diagrams on graph paper, a reference to help show how the square grows.

3)  Switch ends. Hold the compass on B. Swing the arc from one side of the circle to the other: G-A-C.
Hold the compass on C. Swing the arc to find D.
Use D to find E; E to find F. along the circumference of the circle.


The circumference of every circle will always be divided into 6 equal parts by the radius of that circle. The length between each 2 points around the circumference will always equal the radius.

It's easy to draw a daisy wheel. 

However, to construct a square the petals are not needed, only the 6 points on the circumference.

4 )  F-G is the line. It is the same length as the one chosen at the beginning, just in a different location.

G and C are 2 points. that can be connected by a line.
So are F and D. 
They are the same distance apart so they are parallel.

A square has 4 equal sides.  (Just a reminder)
5)  An arc the length of  F-G swung from either F or G will mark  G-H and F-I the same length as F-G.  This is the same length as the chosen line A


 







A square drawn using Practical Geometry, using a compass.  
To check: lay out the diagonals. If their lengths are equal the square is true.   

This upstate NY barn was dismantled for reuse by Green Mountain Timber. It had a daisy wheel scribed on one wall.  The  barn laid out using the 6 points of the circle. The frame of the east elevation is drawn below.

The square frame for the door is in the center. Either side completes the rectangle of the circle.

My post describing this barn:

https://www.jgrarchitect.com/2020/03/a-barn-and-its-daisy-wheel.html




How to Draw a Square  with a Compass, #2

Draw a line.  Mark 2 points on the line.
Open the compass wider than the distance between the  points. Swing an arc across the line, below and above it from each point.
The arcs will cross at 2 points. Draw a line between those points. The new line will be perpendicular to the first line.

Then choose the length of the side of the square A-B. Mark it off on both lines.See the arc B-B.
Swing new arcs the same length (A-B)  from both B's.  See the dashed and dash/dotted lines. They cross at both A's.
All the sides are equal: a square.

St. Jerome's Catholic Church, East Dorset, VT, 1873, was laid out using that simple square  - including how the arcs cross each other. 

My post about it is here:
https://www.jgrarchitect.com/2016/12/st-jerome-catholic-church-east-dorset.html

Part 2 is here:  https://www.jgrarchitect.com/2020/01/practical-geometry-drawing-square-with.html

I explain these ways of using a compass,a straight edge, and a marker to lay out squares and rectangles when I give presentations. I add them here because such information should be readily available on line.

The Compass in Construction

Compasses are regularly portrayed in construction images, and are also regularly ignored.

In October, 2018, the Preservation Trades Network (PTN) met at the National Park Service Historic Preservation Training Center in Frederick, Maryland, for its annual workshops.

I gave 2 presentations on the use of compasses in historic layout and design. More than 30 participants practiced their geometry - with enthusiasm. They asked good questions.

PTN workshops were held in the shops, the yard and storage bays, and an office of the Training Center. Around us were the HPTC logos.
They all included a trowel, a plane, and a compass.

As posted here: 
top: on a brochure
middle: real tools mounted on a board hung on a wall
bottom: an image posted on a bulletin board



I asked the staff who came to my presentation what they knew about using a compass. They told me: not very much.

The image of  a compass is there, along with a trowel for plaster, masonry, and stone work and plane for wood working. The compass as an equally important tool for layout and design. The understanding of how and why to use one has been lost.



 In September, 2019,  PTN joined with Historic Environment Scotland to hold the International Preservation Trades Workshops (IPTW) at the Engine Shed, Stirling Scotland. I gave 3 presentations with slides and hands-on practice drawing layouts and elevations without numbers,  using only a compass, a straight edge, and a pencil.

Our final evening we dined in the Banquet Hall of Stirling Castle, historic home of Scottish kings, including Mary, Queen of Scots, and James VI who became James I of the United Kingdom.  (No, the roof trusses were not this pink! just what my camera saw!)






 Before dinner we toured the castle which is set high above the land and the river.

It is beautifully cared for; the rooms used by the royal family furnished with fascinating furniture and tapestries depicting the time when Mary Queen of Scots and James VI lived there. The signage is excellent: clear, colorful,  with historically accurate graphics and information.

 Even jokes were in period dress: These plaques were beside the  restroom doors; a medieval beast which might be a griffin was watching from the newel post.

This poster was in the courtyard. I liked the images:  the tools in use, the appropriate clothing, and surroundings. visually interesting and easy to understand.






The text explains the work. Except for that compass the master mason holds under his arm.  It is perhaps 24 inches long, with brass fittings and an armature to set the span. This is a serious instrument.
No explanation is given for its use.





I think people simply don't understand how a compass was used. No one  asks how the project was organized, how it was planned and set down so that all the craftsmen  could reference what was to be built.

How did they share their understanding of the scope and detail? The master craftsman laid out the design of the work.
He used his compass to accurately draw and explain his plan to  the other workmen.

 I looked on the internet for the proper name of the 'armature' on a compass used in construction. 'Hinge' is sometimes used but that refers to the part where the legs join.  In the 1920's the 'arm' had become a bar with an adjusting screw; the compass called a 'spring bow".  
Because there is so little written about compasses used in construction I may need to revise this post as I learn more. 
 

Bow compasses

Page 614, Audels Carpenters and Builders Guide #2, Theo. Audel & Co., Publishers, NY, NY, 1923