Geometry in Construction = Practical Geometry

Geometry in construction = practical geometry.

Does that seem strange, a philosophical stretch?  As recently as the 1930's it was widely understood, commonplace.  Since the 1950's, geometry has been taught as precise, logical, beautiful, magical, amazing.  But practical? Barely. Today the idea is usually met with skepticism.

However, you who read my blog know this is what I study: what those builders know about geometry and how did they use it? 

 

Euclid's geometry starts with a Point which has no dimensions.  Two points make a Line - 1 dimension.  3 make a Plane - 2 dimensions.

 

4 points make an object  - 3 dimensions.  

 

How can this geometry be practical? 

A Line laid out between 2 points will always be straight. 

A Line drawn by hand might curve; a Line marked by snapping a length of twine cannot curve. This is the beginning: it will be true.  If the geometry is not accurate it will not be practical.

The Line A-B can become a radius. The radius can draw a circle. 

Whether the circle is drawn with a compass set to the length of the radius. or by hand with a length of twine, it will close if the the work is accurate. If the circle does not close upon itself it is not true.        At every step of the layout if the geometry doesn't hold, the designer will know to stop and correct the drawing.

 

The radius of the circle always divides the circumference of the circle into 6 parts. If the points on the circle, marked by swinging the arc of the radius, are not spaced accurately they will not end exactly where they began. They will not be true. The work cannot proceed. These 6 points on this daisy wheel are not quite accurate.  Note that the daisy petals' shapes are not identical; the points are not equidistant. If I measured the diameters, petal to petal, they would not match. I was not careful enough.        

 

 

 

 The 6 points, joined with lines, can be used in construction.

 

The rectangles that come from the 6 points can be proved by their diagonals. If they match, the rectangle will have 90* corners and be true. If the diagonals do not match the shape is not a  rectangle. 

A building needs to be stable, whatever materials it is made from, whatever form it takes. For simple vernacular housing the circle was the practical geometry needed to erect a stable, sturdy dwelling.  

The layout tools available to the builder of the Lesser Dabney House* in rural Virginia, c. 1740, were twine, some pegs, a straight edge, some chalk or soot so the twine could mark a line, perhaps a scribe, a compass.

The builder could have laid out this house with the first 4. A peg could have served as a scribe to mark a point. Twine with a loose knot around a peg turns as a compass does.

 

 

 

Here is the floor plan as it was recorded by Henry Glassie, c. 1973: 3 rooms with 2 chimneys and a stair to the attic.  3 windows, 4 doors. The door to the left may have gone into another shed.

 

 

The builder stood where he wanted the main wall of the house to be. He pegged the width he chose with twine A-B. That length became his radius. He drew his arcs to find the center of his circle C. Then he drew his circle.  And found it true. The circle's radius steps off 6 times around its circumference. The arc create the 'daisy wheel'.

 

A-B in the diagram above became 1-2,  the width of the house. The arcs 1-3 and 2-6 of that width crossed at the center of the circle with its 6 points: 1,2,3,4,5,6. 

The Lines 1-5 and 2-4 laid out the side walls; 6-3 locate the back wall. Diagonals across the rectangular floor plan proved the layout to be true.

The main block is about 20'x17'. The 2 doors  welcomed cooling through breezes in the summer. The wall room on the right may been a later addition to create a parlor, more private and warmer in winter.

Then the builder added the shed. He made his twine the length of the house, folds it in half and then in half again. He then knew what was 1/4 the length of the house (x). He laid out that length (x) 3 times to get the depth of his shed. He stretched his twine diagonally from one corner to the other. If the twine measured 5(x) his shed walls were a 3/4/5 rectangle; the corners 90*, and  true to the main house. The shed roof framed cleanly against the house and was weather tight.

The circle and the 3/4/5 triangle - Practical Geometry -  were the only measuring systems necessary to construct this house.

 

*The Lesser Dabney House, Fig. 45, Type 3, p, 105; the photograph: p.104. 

Henry Glassie, Folk Housing in Middle Virginia, U Tennessee Press, 1975; plans, drawings and photographs by Henry Glassie.

Henry Glassie recorded floor plans and what history he could find, He photographed. He did not make measured drawings like those in HABS  now in the Library of Congress and available on its website.

 

 

Virginia Folk Housing, Part 2 of an update

 

The Moore House* photographed by Henry Glassie, built before 1750.

 

This house has 2 rooms up and down, 2 fire places, 2 chimneys, and a shed on each end. The main block  is double the size of the house I wrote about in Part1: https://www.jgrarchitect.com/2022/11/virginia-folk-housing-update.html

The geometry begins as it did in Part 1, using the width as the circle's  radius.   

 

Here is the floor plan: 2 rooms with fireplaces, and sheds on both ends.

The daisy wheel progression begins with a length A-B which becomes the radius of a circle here lettered C-A.

The daisy wheel for this house begins with the left wall of the main house.

That wall's width  is the radius, 1-6. A is the center of the circle. The daisy wheel lays out the other 4 points, 2, 3, 4, 5.  

 Lines 1-3 and  6-4 are the sides of the house. 2-5, the diameter of the circle, lays out the interior wall.

 

Lines 1-5 and 2-4 can extend forever. Where is the right end wall of the house located? Where is C? 

It's at the end of the circle, but that's only a point, not a line. 2 points are necessary to draw a line to mark the right end of his foundation and the floor of the house.

If the carpenter extends his arcs he can quickly find the missing points. 

Extend the arc centered at 3 (2-A-4) to B.  The arc centered at 4 (5-A-3) crosses the earlier arc at B.   He has 2 points: A and B, And can draw line A-B. 

Now C is fixed at the intersection of A-B. C is the center of a new arc, (7-A-8). The extended arc from 5 (6-A) crosses at 7. The arc 2 (1-A) crosses at 8. 7-C-8 locates the right wall.

C also locates the center of the fireplace and the chimney. 

The daisy wheel is often dismissed as a design tool. It is flexible, quickly drawn, and accurate. 

The geometry comes from the first length - the width chosen by the owner and builder for this house. That width, and the house, could be bigger or smaller to suit the owner's needs and budget, as well as to the lumber available for joists and rafters. 

Once the carpenter decides on a width he uses one compass setting, one radius, for the whole layout. Every point is checked. As the lines are marked, the diagonals can prove the layout to be  true.

If he drew a layout at a smaller scale, he could easily step off to full-sized construction dimensions with his compass. He could also draw the layout on the ground, stake the points and mark the wall locations with twine just as framers and masons do today. 

Consider how the plan would be laid out if the circle is not used. Use a 10' pole - a common tool of the time.  Each corner would need to be figured independently;  every dimension stepped off separately, and with what accuracy? 

The daisy wheel locates all angles and lengths quickly. It has built-in checks from the beginning and as the layout progresses: if the circle doesn't close, the 6 points will be uneven, the arcs won't cross, the diagonals will not match. The layout will not be accurate.

 Both wings are 3/4/5 rectangles. See the left shed. The floor plans of wings were usually 3/4/5 rectangles so that they would sit square to the existing house. All the joists would then be the same length; as would be the rafters.  

 

 

My earlier complex geometry 'works'; the lines are there. But they don't give the basic information the builder needs: the dimensions of the foundation, the floor plan, the size of the house.

 

*The Moore House, Fig. 31, Type 5, p, 77; the photograph: p.76. 

Henry Glassie, Folk Housing in Middle Virginia, U Tennessee Press, 1975; plans, drawings and photographs by Henry Glassie.

Virginia Folk Housing, Part 1, an update

The house recorded by Henry Glassie in Folk Housing in Middle Virginia * were basic shelter for people with few resources. They may have been the first house for someone homesteading, built by a sharecropper or by someone enslaved.   

This is Fig. 35, The Parrish House, a "small mid-eighteenth-century house of sawed logs", p. 84 in Glassie's book.*

 

The geometric diagrams I drew in May 2014,** were accurate but much too complex for these houses. More importantly they didn't begin as a carpenter would: with the size of the foundation and the floor plan.

 

 A carpenter's first question is, " Why?" Then he asks, "How big? How long? How wide?" 

The red line across the bottom of the floor plan is 'how long', about 21 ft. That distance can be the beginning of the layout, the first Line that determines all the others.

 

That Line can be the radius for a circle:

The arcs of the Line A-B cross at C. That's the center of the circle for the layout of this house.

In the diagrams below: 1) B-C is the radius of the circle. 2) Beginning with B on the circumference  the arcs of the daisy wheel are added. The 6 even spaced points around the circle A, B, D, E, F, G  are located.

 

 

 

 

Connect the Lines. A-F and B-E are perpendicular to A-B. G-D is the diameter. They mark the width and length of the rectangle for the house plan.  If there is a question about accuracy, diagonals can be used to true the shape.

 

 

Here is the plan within its circle, the circle that begins with the carpenter's choice of width, his 'module'.

 

 

The masonry block for the 2 chimneys is square, centered, and 1/3 of the width the house. Glassie's photograph shows a shed sheltering that fireplace.

 

Part 2: https://www.jgrarchitect.com/2022/11/virginia-folk-housing-update-part-2.html

Another introduction to the geometry: https://www.jgrarchitect.com/2023/01/geometry-in-construction-practical.html

 

*Henry Glassie, Folk Housing in Middle Virginia, U Tennessee Press, 1975. The book includes more information, drawings, and a photograph of the house. It no longer exists.

** The original post is here:  https://www.jgrarchitect.com/2014/04/18th-c-virginian-folk-houses.html. Its companion, here: https://www.jgrarchitect.com/2014/05/18th-c-virginian-folk-houses-part-2.html

I considered deleting the 2 posts, but their existence brought a comment and question which prompted this update.

Also:

As I read them I realize how much I have learned about geometry since 2014. I saw it and tried to explain it, just as Henry Glassie did in his Rules, Chapter IV, The Architectural Competence.

When I began to study Practical Geometry there were no books, no one for discussions or critiques. I was teaching myself, reading early pattern books line by line. Laurie Smith was the only person I knew who saw geometry as I did, and he was in the UK. Later that year he came to the States; I took a workshop with him. I was able to work with him until his death last year.  

I don't want this information to be lost again. I want others to find it, question it, reject and/or improve upon my analysis, their own analysis, expand our understanding.

  

 

The Tuckahoe Cabin Geometry

 This is the double slave cabin at Tuckahoe Plantation, Thomas Jefferson's childhood home in Virginia.
I have written about it before:  http://www.jgrarchitect.com/2014/06/cabin-tuckahoe-plantation-goochland.html


The simplicity of the cabin and its HABS drawing make it an easy building to use when I teach hands-on Practical Geometry.




The beautiful hand drawn lines and details of HABS drawings fascinate students. And they get a little history.
Here the elaborate paneled front door for the plantation house, its ceiling pattern, and columns are shown with the little, uncomplicated cabin.
Craft, wealth, slavery c, 1750,  are visible side by side.


Remember that you can click the drawings to enlarge them.

The cabin illustrates the Rule of Thirds.
Students unused to geometry can grasp the basics quickly as they discover the design simplicity of the floor plan.They explore the geometry of the elevations with curiosity, not in trepidation.

For a tutorial on the Rule of Thirds:
http://www.jgrarchitect.com/2016/10/practical-geometry-drawing-diagrams.html




BUT -  This is academic.
How did a carpenter actually use this knowledge?

I wasn't there. So, I am guessing? No.

I've read the written documents, 'read' the drawings that have no words - from that period and the more recent era of HABS. I've measured and documented these buildings, participated in repairing and framing them as well as their deconstruction.
I make connections to the old ways of laying out a frame from the way we lay out today using the same tools our ancestors had - a line, a square, a plumb bob, a pencil - and  a compass.


Here is a construction scenario for this cabin.

The carpenter plans to build a 2 room cabin with a loft, 2 doors, 2 windows, back to back fireplaces on this site.
The size is standard, each room about 16' x 16'. He either builds right here, or he uses a framing floor. In either case it is a flat, level surface. His geometry will establish his points and keep his frame square.
 He measures off 16' with twine, using his own handmade rule. He then stretches out his twine another 16-20 ft, pulls it taut.
He now has a straight Line.
Maybe he has chalk and snaps it, making a line.  Maybe he pegs it.
Modern carpenters snap and set lines regularly. We still call them 'lines'.


1 - On his Line he marks his first point (A).

2 - He chooses a radius and draws 2 arcs, one with its center at (B), one with its center at (C).  He now has 2 points where his arcs cross and can draw a line perpendicular to his Line.

3 - He chooses his dimension -  here, 16 ft -  puts his compass - perhaps a string with a knot at 16' -  at (A) and draws a semi-circle (D-E).
Now he has a new point (F). His cabin is now 32' long; its width is 16' (A-F)

4 - Using (F) as his center he draws another semi-circle.

5 - Then he draws 2 quarter circles using (D) and (E) as his centers. Where the arcs cross (G) and (H) are the upper corners of his cabin.

6 - He swings the other arcs, and now has 4 internal points in each room of the cabin. He marks those points.

7 - Just to be sure, he trues up the space by checking that his diagonals are equal (G-A, D-F etc.).

8 - The interior points give him the centers for the doors, windows, and fireplaces. The plan of the cabin is done.

The end elevation, or  the 3 bents of the frame:
 9 - He sets up the 16' square with its arcs.

10 - The interior points give him the location for the 2nd floor joists.

11 - The points also give him the center of his elevation. He can draw his Lines and use the Rule of Thirds to find the upper third of his square (J-K). 

12 - (J) and (K) mark the eaves for the roof. He extends the sides of the square, draws his arcs to find the upper corners ( L) and (M), adds his diagonals  (J-M) and (L-K). Ahh - there's the roof!







 The window in the eaves is placed and sized:













A carpenter before the Industrial Revolution would not need my description. He would have learned the geometry as an apprentice. If he needed a reminder he would practice a bit with his compass. He probably didn't have a drawing for such a simple cabin.

However, books with instructions to builders (not architects) did exist. Here are 2 examples.





Batty Langley in The Builder's Director, London, 1751, draws moldings "Proportioned by Minutes and by Equal Parts".  He writes that his little book is to be available to "Workmen" and "any common Laborer."

These window and door 'Weatherings' are all composed of squares and arcs of circles. Langely lays out the parts; the Workman can read the rest.





 Asher Benjamin in The Country Builder's Assistant, Greenfield, MA, 1797, says his book "will be particularly useful to Country Workmen in general".
 He assumes the Workman knows geometry.

Plate XXIX  says only
 "C, is a roof; divide the width of the building into 4 parts, one of which will be the perpendicular height. Divide Fig. D, into 7 parts,give 2 to the perpendicular height.
Fig. E, is intended for a roof to a Meetinghouse; divide the width of the building into 9 parts; give 2 to the perpendicular height; the ends of the Beams, a, a, are to be supported by columns."




My first post on Tuckahoe Plantation is here:    http://www.jgrarchitect.com/2014/05/tuchahoe-planatation-richmond-virginia.htm

Cabin, Tuckahoe Plantation Goochland County, Virginia

I came to Tuckahoe Plantation to look at the cabins. Drawings for them are in the HABS archives. They are the size and layout of the houses whose floor plans Henry Glassie recorded and whose geometry I have written about.
 Dr. Glassie's book,  Folk Housing in Middle Virginia, includes photographs of poorly maintained houses, most beyond repair.

I wanted to see what they might have looked like when they were built and how tall they were. Yes, the HABS elevations show how tall they are. However, for me reading a drawing is a beginning, one  part of
understanding. I need to see the building.


It is very simple. in appearance and geometry, and not only because of its shape and lack of anything beyond the essentials.









It is just squares: 2 across the front, 2/3 of a square for the sides, 2 for the floor plan.




The chimneys are centered on the square.




The doors and windows are centered on the plan and on the center of the square for the front elevation.




The  front and side elevations are two thirds of the square.

 The roof pitch is 12/12 - the diagonal of the square - and begins at the 2/3 line of the lower square.


This way of dividing a square and using the diagonals to determine dimensions is called the Rule of Thirds.
To learn how it is drawn please see my blog post:
http://www.jgrarchitect.com/2016/10/practical-geometry-drawing-diagrams.html

The book, The Chesapeake House, reports that the plastered interior walls of the house are original as is the door between the two rooms. This 'cabin' then perhaps was built for the use of an overseer, or craftsman.

As you can see from my photograph, the little house sits on a green lawn with a dirt path, surrounded by towering leafy green trees. Clean white paint, variegated wood shakes on the roof, a neat brick chimney - all in excellent condition - may give too cheerful an interpretation of conditions in 1750, but I am glad it is being preserved.
Studying the adjoining kitchen, office and storehouses, walking down the path, then around behind the cabin across the lawn to the main house, gave me enough understanding so that as I traveled back roads to Madison's Montpelier I easily spotted similar cabins, now out-buildings on farms or wings to later homes. At Montpelier, where timber framed and log cabins are being rebuilt, I was also able to better read what was there. My visit to Tuckahoe was excellent.

The Chesapeake House, architectural investigation by Colonial Williamsburg, edited by Cary Carson and Carl Lounsbury, The colonial Williamsburg Foundation and the UNC Press, Chapel Hill, 2013.


My previous post about the main house at Tuckahoe Plantation is here: http://www.jgrarchitect.com/2014/05/tuchahoe-planatation-richmond-virginia.html

Tuckahoe Plantation, Richmond, Virginia, 1733-50

Update: August, 2023. This post needs revisions. 

In the last 9 years I have learned a great deal about practical geometry.  I have also read Material Witnesses, Camille Wells' book, published in 2018 by the University of Virginia Press, about domestic architecture in Early Virginia. She writes about Tuckahoe in great detail. 

I will leave this as I wrote it in 2014 until my new drawings are ready for publication. 

 

I visited Tuckahoe Plantation recently.  I wanted to see more brick work, after studying the walls of Gunston Hall.

The Tuckahoe Plantation Main House has brick end walls on the south wing, c.1733.  HABS has drawings that I could use, even though they are very small: 1/8"= 1'-0"

The  Plantation is on a bluff above the James River.Originally visitors came by boat. I came by car, turning off a narrow road onto a dirt lane lined with trees and pastures for horses and cows. Finally the buildings appeared, and parking for my car.  I liked entering on foot at a slow pace. There are few signs, and no visitors center. I was almost the only person on the grounds and enjoyed it all, even as I was studying the buildings, thinking about them carefully  I hope to go again for a thorough tour of the house (open only by appointment).

The upper photograph is of the south wing facing the James River. The second is the west wall of the south wing.



As the floor plan shows the House has two wings joined by a Great Hall. It is also surrounded by stately trees and shrubbery, therefore hard to photograph as a whole. The end walls of the south wing feel much more hand wrought than do the walls of Gunston Hall. There is also a subtle brick pattern, dark and light. The North Wing end walls are not brick.
The foundation (above grade) for the house is brick, but the north wing, added in 1750's does not seem to have a basement - no windows or doors, only vertical slits in the walls. I wondered if this difference, as well as the change in chimney construction, would also be visible in the geometry, whether it represented a change in how the north wing and possibly the Great Hall were considered, laid out, and built.

Here are the diagrams. The geometry does change.

I have drawn 3 green diamonds on the South Wing (They could be 3 squares, same proportions.) To the center one I have overlaid the red square and added the diagonals of the half squares which cross at the walls of the South Hall. The points of the diagonals also determine the window openings. The rooms are not quite square.

Both of the North Wing rooms are square - noted by green squares with their diagonals. The squares divide in thirds - red lines in upper square. Then  a new square - drawn in red - is extended to determine the width of the North Hall.

The Great Hall is 2 squares crossed. I've drawn one in green, the other in red. The space where they cross is the entry, the crossing determined by the squares divided into thirds.

I wondered if the brick end walls would be 3-4-5 triangles, which would be structurally sound. They appear to be - see the green diagonal on the south end wall. The window and door sizes and placements do not neatly fit the pattern.

The Great Hall elevation is crossed squares - in green, just as its plan is. The edges of  the squares mark the edges of the windows. The diagonals' crossings mark the height of the door, the centers of the door panels.

The North Wing end wall is 2 squares - in green, divided in halves and thirds - in red. This also continues the floor plan geometry. The roof pitch comes from  the frame - not quite a 12/12, determined by the geometry, not by numbers.

The North Elevation can be looked at two ways.
On the right I have drawn the square (the diamond which marks the centers of  the square's sides) beginning at grade, including the foundation. The left edge is at the door frame.
On the left side I have drawn a square with its diagonals. The length of the square is the height of the wood frame of the wall of the wing; it does not include the foundation. That square ends at the edge of the paneling for the entrance, which are noted on the floor plan.

I do not know enough about the framing for this house. In the Northeast I have seen and worked on many buildings from this period and have knowledge of standard framing and regional variations. I can show how the geometry determined the framing and therefore the design. I wonder if Tuckahoe's framing changed between 1733 and 1750.


Part of my reason to visit to Tuckahoe was to see its intact measured one and  two room houses that looked in the HABS drawings very much like the houses Henry Glassie wrote about. I will write about that next.

Gunston Hall, Mason Neck, Virginia

updated 5/14/2014

Gunston Hall was built from 1755 to 1759 by George Mason as a home for his family on Mason Neck, Virginia.

Gunston Hall in February, 2014,  photograph by Justin Wilcox, through Wikipedia.
The drawings are from the HABS collection.

Gunston Hall, Return to Splender, the 50 page booklet published by the Board of Regents in 1991, came to me from a friend who knew I would like the pictures, the excellent recounting of the history of the house and its restorations, and the HABS drawings. She was right.

The booklet relates how George Mason began the building himself and then had his brother find and send  William Buckland from England to help him finish the work.

I was intrigued by the fact that George Mason, a very well educated man, realized that he needed help. I wondered if I could see why by looking at the drawings. He knew enough about construction to begin. What happened? Would the expertise William Buckland brought to the work be visible?



George Mason knew about what kind of  plan would fit his family and their life. He knew how to build with stone and brick, how to set a foundation, cap a window, taper a gable, frame a roof. He knew enough geometry to use 3-4-5 triangles and their permutations.

Remember that the diagrams can be enlarged by clicking on them.

The plan  is 4 triangles, or 2 rectangles with 2 sides 3 units long, 2 sides 4 units long. On the right side he has divided the rectangle in half to make his two formal rooms. He has laid out the diagonals of both smaller rectangles. Where they cross he has placed the wall at the edge of the hall.

Note that the rectangles do not meet at the center of the main doors, but to the right side.

The left side of the house was the family dining room and the Masons' own room which Ann Mason also used as office as she managed much of the plantation.

Here a hall separates the rooms.To determine the width George Mason divided the rectangle in half lengthwise and then added the diagonals. The center point is the location of the inside of the wall to the hall. Where the  diagonals cross to the other side of the brick wall, the corridor walls begin. Note that the stair width is also determined by another division of the rectangle and its subsequent diagonals.

On the right side the inside space is divided - it would be smaller than the outside space - into thirds to place the fireplaces in the center of the rooms. I think it is possible that this is one of the changes Buckland made.
Understanding that wall thickness can throw off symmetry comes from experience. Buckland had training as a finish carpenter (a joiner), but he was young, just 22. Mason was 30; he knew brick and mortar, not perhaps not the finer points of symmetry. Proving this supposition would only be possible if the chimney stack was opened and taken apart - not very likely! So this is truly conjecture on my part.



The end elevations continue to use the 3-4-5 triangle for its proportions.
The door is centered. The top of the brick walls is the top of the rectangle.  The gable repeats the triangles. The bricks end on the upper edge. The shape is square and sound, made possible by the 3-4-5 90* triangle which is always true.
I have noted with a strong dot on the upper diagonals how the window height and location are also determined by the diagonal intersections.

Note that the depths of the porches are also 3-4-5 triangles -  drawn in green.

So then to the main elevations, one facing the water, the other the road.

 We already know that the left and right sides of the house are not equal as George Mason wanted larger formal rooms on the right side.

 Here is where I think he got himself in trouble: the left side is truly not as long as the right - see the dotted red line. Look carefully and the dormers: they are balanced but not symmetrical, nor evenly spaced.

 Perhaps Buckland stepped in here, adding the windows on either side of the front door.
What he really did was divert the eye - he added the Gothic porch to the river front: inviting, decorative. with half circles and Gothic curves. We are drawn to the porch and ignore the symmetry.

March 18, 2023: I wrote this almost 9 years ago.  I now know a lot more about Practical Geometry. Please also see my most recent  post about the porch: 

https://www.jgrarchitect.com/2021/07/the-geometry-of-gunston-halls-north.html

I will not delete the following discussion of the porch design. I want a potential geometer to see that as we recover a lost skill we make assumptions and therefore mistakes. That's ok. It's part of the work..

 

Here and in the house his knowledge of Palladio and what was fashionable in England is obvious. William Buckland knew the classic vocabulary. The booklet shows how plain the walls were without his embellishments. His  use of geometry was also much more sophisticated than George Mason's.

The road front porch which we see today came later, after the Revolution. As roads and bridges improved visitors arrived by carriage, as well as by boat.
The center arch within the pediment, flanked by openings marked by classic columns and lintels, comes right out of Palladio's Books.
And it creates an inviting porch. It is scaled to people - we would like to standing there, hand on the railing, welcoming a guest coming down the drive.
 This layout that we now call  'Palladian' was already widely used in Virginia churches where it was referred to a 'Venetian Window'.

I have drawn the first square - set on the diagonal -  that comes from the height. From that comes the outside dimensions, the outside square, and the square turned 45*. The lines regulate the roof pitch, the floor, the line for the lintels. No doubt he adjusted the size of the square to fit the space.


Then the squares are divided in half and the diagonals added. Now the placement and the width of the columns is determined.

I add this diagram to show how the semi-circular arch in the pediment unfolds down the center of the porch to mark the top of the columns, height of the railing and lands on the first step above the foundation.