## Tuesday, November 21, 2017

### 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

## Wednesday, August 16, 2017

### Laurie Smith, researcher of early building design in England, par excellence

Laurie Smith knows the geometric design systems used in medieval England.
He writes and teaches about geometry.

Here - as a quick introduction to his websites - is the last page of 4 of his diagram showing how to draw a square using a straight edge and a compass.
It is a beautiful drawing, easy to read on his website, hard to reproduce here.
His explanation at the bottom is also beautifully clear.

The websites are here:

http://www.thegeometricaldesignworks.com/

http://historicbuildinggeometry.uk

The masonic guilds of medieval Europe passed down the methods of construction and the geometry used with diagrams and hands-on explanation. They did not use paper - it was barely available - and thus left notations on the buildings as decorative carvings and casual sketches, information we often don't recognize as the language of construction.
Laurie can read and translate the notes. He is one of the people in Europe researching, documenting, and teaching about medieval framing.
I suggest all those who dismiss the idea of Practical Geometry read his websites.
Those who wish to learn how to use Practical Geometry can be inspired by the diagrams as they follow his instructions.

I have attended his lectures. and was fortunate to be able to take a workshop with him at Trillium Dell Timber Frames in Knoxville, Illinois.

We built a timber frame pavilion  from scratch using geometry.

Here is Laurie consulting - in the blue shirt in the middle - as we work around him. Laurie drew, taught and advised.

I wrote about this here:
http://www.jgrarchitect.com/2014/07/geometric-design-intensive-june-2014.html

The photograph shows Laurie's diagrams for the frame posted on the wall as one of us begins the fashioning of joints.

The frame, composed of overlapping squares  was also laid out on the floor with chalk and a compass.

The whole process is described with diagrams and pictures on Laurie's website.*

A view of the mortise I helped cut as part of a 2 woman team. It fit into the frame on the first try.

We finished erecting the frame one evening at dusk.
Of course we all climbed into it to sit for a formal portrait.

* To see the whole project and the finished pavilion look for  "Appleton Octagon Pavilion, Illinois, USA" in Laurie Smith's  Historic Building Geometry website listed above.

### PTN Workshops in Detroit, Sept 8-10

IPTW 2017 - The Preservation Trades Network - will be in Detroit at the Detroit Yacht Club Sept, 8-10.
I will be teaching 2 sessions on how to draw squares with a compass, how to layout frames using geometry as we did 200 yrs ago.
And some history (Vitruvius, Palladio, Serlio, Gibbs, even Isaiah in the Bible! ) on the side.

Of course the use of Practical Geometry didn't stop 200 years ago. The knowledge came with the settlers to the Mid-west. Houses and barns, public structures were laid out and framed using the honored patterns.

I will include examples of mid - 19th century framing and design as well as earlier 18th c. antecedents.

You can come.   http://ptn.org/iptn-2017

## Thursday, July 27, 2017

### East Hoosuck Quaker Meeting House, 1786

Update: 10/25/2017
To check the reliability of the HABS drawings  I measured the Meeting House this month. Yes, the drawings used here are accurate.

This Meeting House for the East Hoosuck Society of Friends (Quakers), built in 1786, is now a museum in Adams, Massachusetts. It sits high on  a hill in its cemetery, looking east over the Hoosic River to the Berkshire mountains. This is its west side.

As I was creating a handout for the guides about the scribe rule markings visible on the frame, I wondered what the geometry might be. Quaker communities existed nearby in New York, Pennsylvania, and New Jersey. We knew Quakers migrated up the Hudson River watershed from Rhode Island and Nantucket after the  Revolution. Would I see similarities to other frames I had measured?
I did see similar ways of laying out a frame. However, without more research I cannot say these layouts were particular to Quakers.

The Friends Meeting would have told the master carpenter how large the building should be,  that windows were needed for light and ventilation, fireplaces for warmth. These Friends knew that the door should face south,  that the wind here came around the mountain from the northwest, that a chimney is best supported by bringing it through the roof at its peak.

The framer would have began with the floor plan; so I did too.  He made the meeting house 28' wide on the west end; the posts set in the corners.

He laid out a square from the inside of the posts and marked locations for  posts on the corners.*

Why would he have begun his layout on the inside edge of the posts?

Perhaps because the trench in which to place the footings for the posts would be outside the line. The ground under the frame would not need to be excavated.

The plan could also be trued from the interior edge of the posts much more easily than from the exterior when the posts were in place: the diagonals would be made equal across the rectangle. Contractors today still 'true' foundations by pulling lines.

His center line located the middle posts on the north and south walls as well as the 8 sided posts that are located between the pews.

Using the Rule of Thirds, he laid out the eastern end. The location of the eastern wall posts is 1/3 the width of the main square beyond the square.
I have marked the 1/3 of the square and the extension with arrows in red.

The center line running east west determined the post on the east wall.

His post locations set, the framer laid out the 4 bents. This is the eastern exterior bent.

It uses crossed squares with the side of the square the height of the wall from floor to plate.
Even the braces follow the geometry.

The height of ridge of the roof, and thus the pitch  of the roof, was set by the intersection of the arcs of the height of the wall.

This way of finding a ridge was also used in the Hartford, NY, barn I measured in  2014.    http://www.jgrarchitect.com/2014/12/a-hartford-new-york-barn-was-carefully.html

The window placement was determined by the same crossed squares geometry.
The 4 sides of the windows are determined by the geometry.
I have drawn the lower window only. The upper window requires more lines which are hard to read at this scale.

The south facade of the meeting house is 2 squares wide.

Quakers worshiped together, men and women, and children.

Their  Meetings for Business were held separately: women on the left, men on the right, with a wall between them which could be raised or lowered as needed. Thus the two doors which sit neatly within one quarter of the square.

The window sizes on the south side do not fit the geometry. They were probably enlarged  when the men's stair was added.
Both scribe and square rule framing details as well as joist pockets without joists indicate renovations.

For me it's fun to see how the first floor windows are located at the bottom of the stairs, where light would be needed for safety.

*The hybrid barns  in New Jersey which I looked at earlier were also laid out based on dimensions measured between the posts: http://www.jgrarchitect.com/2017/06/practical-geometry-for-hybrid-dutch.html

For more information about the Meeting House and the Quaker community in Adams please see:

www.adamshistorical.us/collections/quaker_house/index.html

## Tuesday, June 27, 2017

### Practical Geometry for Dutch Hybrid Barns, Part 2

This is the second part of my look at the geometry of the layouts of New York and New Jersey barns built at a time of intermingling of old world building traditions - post 1800.

Huber included 4 hybrid barn floor plans in his introduction to the second edition of John Fitchen's
The New World Dutch Barn.
This is Illus. 7, p. xxxi

As before I redrew the plan based on the given dimensions.

I found again that the framer began his layout after he had decided the size: here about 25 ft x 50 ft. Beginning from the left side, with the corner posts already in mind, he laid out 2 squares.
If I layout the squares from the right side the
geometry does not quite work.
The center of each square is just about the same distance to the right of a beam.

If the framer laid out the squares using the rule explained by Asher Benjamin, Owen Biddle, and Peter Nicholson * he would have swung an arc the width of his proposed barn from the corner of his plan. When he swung an arc from the other corner the 2 arcs crossed. And there - where I have added a circle - he located his beam.
He would have used a cord to mark the distance on each long wall for the location of the posts.

That beam is the center for a circle that determines the locations of the other 2 beams - marked by 2 more circles.
That  first circle is also the center of a square. The framer could have laid out a square, or simply taken half the length of his end wall (already measured by the layout of the squares) and laid that out on either side of his middle posts and beam.

The 4th layout is quite different from the others;
Here are Huber's drawing and notes for Illus. 4, p. xxviii.

and my redrawing, using his dimensions.

I turned it so that the side where the framer began his layout is to the left. Knowing what he wanted to build  he could use the barn location as his framing floor.

I think he laid out a square, 38 ft on each side and placed his corner posts outside the lines.

He had several choices for placing his intermediate posts and beams using geometry.

Here is one:  He located the center of the wall. Using half the length of the square's side he drew an arc on each end. Using the center of his square he drew a circle.
Where the arcs intersected he drew a line and located his posts on the exterior walls.

Using the distance from the exterior square of the barn to the intermediate posts as his radius he drew 2 more half circles. where the radii cross he laid put his bays and set the interior posts at the intersections.

Here are other options:

The framer could have laid out the barn with 4 squares. As each was laid out the arcs would have crossed, just as they did in the barn shown in Illus. 7.
.
He could also have used the circle to find the length and width of his barn. Both of these systems seem to be more complicated than the order I described.

These diagrams may become teaching tools when I give a workshop at the International Preservation Trades Network Workshops in Detroit this September.

These ways of designing were carried with those who settled the Midwest. 2 squares side by side (as used in Illus. 7 above) is the beginning plan for the I House, so named because the shape is so common in Indiana, Illinois and Iowa.

How did these hybrid barns looked? How were they used? Unable to connect the geometry of the plan to that of the intent, the structure, the bents, and dimensions,  I might have missed critical information.

These two barns' geometries especially interest me because they use squares in a way quite similar to the barn in Hartford in upstate NY which I documented. The link to it is:
http://blog.greenmountaintimberframes.com/2014/12/04/geometry-in-historical-frames-a-guest-blog/

The posts about Practical Geometry and Asher Benjamin, Owen Biddle, etc. can be read at: http://www.jgrarchitect.com/2016/08/practical-geometry-as-described-by.html

## Friday, June 23, 2017

### Practical Geometry for hybrid Dutch barns

In Dutch Barns in the New World*  Gregory Huber includes 4 measured floor plans (p. xxviii and xxxi).
He describes some of these barns as hybrids, barns where the central aisle was not used for threshing and the doors were on on the long side, not under the gable.

I started with Gregory Huber's drawing and description of a hybrid barn floor plan in Marlboro, Monmouth County, NJ, c. 1810 - Illus. 2, p. xxviii.

The carpenter who laid out this frame seems to have begun with not only the layout in mind but the size: 36 ft x 48 ft.
He would have had a 10 ft rule marked in feet and inches and a folding compass to use to step off 36 ft and 48 ft. He would then have squared the rectangle with twine across the diagonals - just as carpenter do today.

A post went in each corner - easy to do.
I have redrawn Huber's Illustration to scale and labeled the corners A,B,C,D.
Remember  to click the drawings to enlarge them.

I think the builder then laid out a square, with the sides the distance between his posts on one end of the barn.  Here I have shown the arc of  barn width, A-B determining the length of the side B-E The builder would have know how to lay out a square and would have trued his square with diagonals - the square, the arc and the diagonals are shown here in red.
The line E-F determines the location of one side of the barn's nave; in the drawing it is the 'upper side'.

Modern construction drawings usually dimension to the center of an opening or a post. I often find that master builders who used practical geometry ran a line beside the posts, so it could be there for the framers. This makes sense when one is building using drawings made on boards or plaster with one end of a compass, or a 'pricker', or with charcoal or chalk on a framing floor.

The master builder seems to then have laid out a second square starting from the opposite end of the barn, from C-D. The square is C-D-H-G. The 'lower' side of the nave is H-G.
He sets his posts on the same side of his line each time - in the drawing 'below the line', closer to A-C . This makes the 2 side aisles different widths. Perhaps this was on purpose.

Now the only placing left to determine is the interior posts.
The Rule of Thirds  easily divides the squares into 3 equal rectangles. Where the lines cross is the inside face of the posts and the beams above.

The Rule of Thirds was used by Palladio and Serlio. It is not specific to the traditional framing techniques of English carpenters, although it is very often used, with 'crossed squares' as is seen in this barn.

The second barn I looked at was in Millstone, Somerset County, NJ. c. 1800, shown in Gregory Huber's Illus. 6, p. xxxi.

These one aisle barns he says were accessory, or the next barn built on a farm, not the first one.

Here is my drawing based on the dimensions in that illustration.

As with Illus. 2, the master framer laid out the frame from the insides of the corner posts. He probably started from the left end:   A-F. The patterns of the squares do not layout smoothly if reversed; it can be done, but not easily.
I always look for the simplest, easiest way to lay out a frame, knowing that the framer had many more important things to do than play with geometric patterns.
The layout is straightforward  - 2 squares ( A-B-E-F) and a half (B-C-D-E). B-E locates the interior  posts and beam on the right end.

In this case I think the framer used 9 ft as his beginning length. thus the barn width inside to inside would have been 18 ft.   8"x 12" posts would have made the width of the barn 19'- 4". Huber's measurement is 9'-3". Either the posts were not quite 8" wide, or the 9 ft. length was not quite 'true'. There was no need for it to be true as long as the framer used that dimension consistently.  He was using practical geometry.
The drawing - its 2 red squares with their diagonals - makes the 2 middle post and beam locations clear: the double square was divided into 3 equal bays.

Using practical geometry, I drew a diagonal across the rectangle from D to B. It intersects the diagonals of the squares at the interior beams (G and H) determining their locations. The diagonal from A to E would also cross and intersect the diagonals of the  two squares at the intermediate beams.

* The New World Dutch Barn, 2nd edition, by John Fitchen, edited and with new material by Gregory D. Huber, Syracuse U. Press, 2001.
If you are curious about Dutch type barns built in the New World (the Colonies) or the antecedents to barns built by settlers in the  Appalachian Mountains or the Midwest before 1860, I highly recommend this book.

Here are some references:
The Rule of Thirds   http://www.jgrarchitect.com/2016/10/practical-geometry-drawing-diagrams.html
Practical Geometry   http://www.jgrarchitect.com/2016/08/practical-geometry-as-described-by.html
Serlio        http://www.jgrarchitect.com/2017/04/serlio-writes-about-practical-geometry.html
Palladio    http://www.jgrarchitect.com/2017/04/palladio-discusses-geometry.html

## Friday, June 16, 2017

### Joseph Moxon, Mechanick Exercises, London, 1683

In honor of Abbot Lowell Cummings. 1923 - May, 2017. A beloved and inspiring architectural historian and teacher.

When I heard of his death I opened his book, The Framed Houses of Massachusetts  Bay. 1625 -1725, Harvard U. Press, Cambridge, 1979.

I thought I was making a nostalgic visit. I had often used his book as a resource when I wrote the 'Sunday Drive' columns for the Eagle-Tribune newspaper, and later returned to consider what he had to say about English precedent and framing. I referred to it when I wrote to him about Asher Benjamin and he answered.

On page 45, were Figures 41 and 42: Plates 4 and 8 from Joseph Moxon's Mechanick Exercises, London, 1683 - not a book I knew.
I wondered what Moxon meant by 'mechanical exercises'. Did he include compasses in his engravings of tools?

I was happy to find that Mechanick Exercises is available on-line, digitized by the University of Michigan.
It is a good read.
Here is the first line in his Preface:

I see no more Reason, why the Sordidness of some Workman, should be the cause of contempt upon Manual Operations, than that the excellent Invention of a Mill should be dispis'd, because a blind Horse draws in it.And tho' the Mechanicks be, by some, accounted Ignoble and Scandalous? yet it is very well known, that many Gentlemen in this Nation, of good Rank and high Quality, are conversant in Handy-Works:

Copied exactly, punctuation and capitals - except for the 's's  that look like 'f's  to modern readers.

The whole book is written in this direct, practical voice. I read it with a smile.

About Geometry he writes in the Preface;
That Geometry, Astronomy, Perspective, Musick, Navigation, Architecture, &c. are excellent Sciences, all that know but their very Names will confess: Yet to what purpose would Geometry serve, were it not to contrive Rules for Handi-Works?

Moxon's book is for the Carpenters Trade. He says " Architecture is a Mathematical Science, and therefore different from my present Undertakings, which are (as by my Title) Mechanick Exercises: p. 117.

He describes all the tools illustrated in the plates.

This is a partial view of Plate 5, Page 63
Moxon's description of Compasses, marked E :  Their Office is to describe Circles, and set off Distances from their Rule, or any other Measure, to their Work.

In other places he writes about using compasses in specific measuring situations requiring marking and scribing, holding stiff their Joint.  He refers to Lines as did Serlio and Gibbs.
I had hoped for more:  practical geometric nomenclature and diagrams, much as Peter Nicholson drew and explained 100 years later.

Moxon did however write wonderful descriptions and explanations.

Of the Rule, marked D in Plate 5, he says in part:
...the manual use of it is, either to measure length with it, or to Try the straightness or flatness of their Work with. They Try their Work by applying one of its Edges to the flat of the wrought side of their Work, and bring their Eye as close as they can, to see if they can see light between the edge of the Rule and their Work. If they cannot, they conclude their Work is Try, and well wrought.

I enjoyed the image of 'trying' with one's eye so close to the crack! And thought immediately of a modern Try Square.

Here is what he said about the Glew-pot:

Then he wrote about the Glew:

The clearest, driest, and transparent Glew is the best: When you boil it, break it with your hammer into small pieces, and put it into a clean Skillet, or Pipkin, by no means greasie, for that will spoil the Clamminess of the Glew, put into it so much Water as is convenient to dissolve the Glew, and make it, when it is hot, about the thickness of the White of an Egg:
Grease in the glue is not good...we know he is right; and 'Clamminess' - a great word! -  meaning 'soft and sticky' is in my unabridged dictionary.

After 300 pages of Smithing, Joinery, Carpentry, Turning, and Bricklaying, the last 50 pages are devoted to thorough instructions for laying out sun dials  - with annotated diagrams.

Joseph Moxon (1627-1691) was an English printer who specialized in mathematical books and maps. He made globes and mathematical instruments. As well as this book I have quoted from he wrote a book about printing, the first written codification of knowledge which had been passed down orally.  He was the first tradesman to become a Fellow of the Royal Society (look it up!).

In the book on printing he described how to draw the letters of the alphabet using a straight edge and a compass.
Page 257,  Architectural Graphic Standards, 2nd edition, C G Ramsey and H R Sleeper, published by John Wiley & Sons , 1936.  (250 years after Moxon,)  shows the same thing. Note how radii are indicated for arcs - especially clear in the letters O and Q.
I am glad to have met Joseph Moxon. Thank you, Abbot Lowell Cummings.

One of the columns written for my 'Sunday Drive' can be found at http://sundaydrivemerrimackvalley.blogspot.com/2008/04/47-manning-house-37-porter-road-andover.html

## Wednesday, May 10, 2017

### Bibliography for Practical Geometry

Tonight I will talk about Practical Geometry.
I will quickly review the documented - in writing - use of geometry from its mention in Isaiah to James Gibbs ' note in his Book on Architecture.
I will not have time to discuss the implications, nor even the reasons there are so few written notations. Curious people can read my blog and refer to this list.

I should have included: The Bible, Isaiah, 44, 13.

PRACTICAL GEOMETRY                 lecture for SAH Latrobe, Washington, DC, May 2017
IPTNWorkshop, Detroit, Michigan, Sept., 2017                                                                                        Hale Village and Farm Museum Ohio, June 2018
Bennington, VT, Historical Society, Sept., 2018

BIBLIOGRAPHY

Benjamin, Asher. The Country Builder's Assistant,  Greenfield, MA: Thomas Dickman, 1797; reprint: Applewood Books, Bedford, MA, 1992.

The American Builder’s Companion, 6th edition, R. P. & C. Williams, Boston, 1827
*Biddle, Owen. Young Carpenter’s Assistant, published by Benjamin Johnson, Philadelphia, 1805.
*Gibbs, James. Book on Architecture, London, 1728
Rules for Drawing the Several Parts of Architecture, printed by W. Bower for the author, London, 1732, ECCO print edition
Green, Bryan Clark. In Jefferson’s Shadow, the Architecture of Thomas R. Blackburn, Princeton University Press, NY, 2006
Harris, Leslie.  Robert Adam and Kedleston, The National Trust, London, 1987.
Knight, Edward H.  American Mechanical Dictionary, Vol I, II, III; J.B. Ford & Co. NY, 1874.
Nicholson, Peter.  The Carpenter’s New Guide, 1793, London; 10th ed., Philadelphia, 1830.
The New and Improved Practical  Builder, London, Thomas Kelly, 1837
*Palladio, Andreas. The 4 Books of Architecture, 1570, translated and published by Isaac Ware, London, 1738.
Serlio, Sebastian.  On Architecture, Lyon, France 1530, translated into English, 1611, available on-line
* Shaw, Edward.  The Modern Architect, Dayton & Wentworth, Boston, 1854
* Vitruvius, Marcus. The Ten Books on Architecture, c. 10 BCE, translated by Morris Hicky Morgan, Harvard University Press, 1914.
also edited by Ingrid D. Rowland and Thomas Noble Howe, Cambridge University Press, 1999.

*Reprinted by Dover Publications, Inc., Mineola, NY

Drawings:
HABS drawings, Library of Congress, Washington, DC
Denison Bingham Hull, Old First Church, Bennington, Vermont, c. 1935.
James Platteter, barn frame for Green Mountain Timber Frames, 2014
All others: Jane Griswold Radocchia

Web sites:
for Jane Griswold Radocchia: www.jgrarchitect.com   and   www.janegriswoldradocchia.com
for Laurie Smith: http://historicbuildinggeometry.uk/ and http://www.thegeometricaldesignworks.com/

## Thursday, April 20, 2017

### Palladio Discusses Geometry

This is part of Plate 1, The Second Book of Andrea Palladio's ARCHITECTURE.

Palladio's 4 books of Architecture were published in`1570 in Venice.  They were meant for Italians. He wrote in terms of the local climate, and materials he used in and around Venice. He also shares ways of  working that  today we would agree are 'best practice".
Here is a small example.
He explains in Book I, Chap. II, On Timber
that timber should be felled in autumn or winter, "in the wane of the moon". This may be because of the gravitational pull of the full moon on sap.
Palladio adds that the timber must be "laid in a proper place,.. shelter'd from the south sun, high winds, and rain."
This final sentence would delight all modern contractors: "Those therefore who are about to build, ought to be inform'd from men thoroughly acquainted with the nature of timber, that they may know which is fit for such and such uses, and which not."

Many Northern Europeans traveled to Italy as part of their education. The 4 Books were admired and translated. Inigo Jones, English Master Builder, brought his own copy back when he returned from Italy in 1614. He marked it up. He used it. Today his copy is kept at Worcester College, Oxford.

The first Book is about construction and materials and the all important Roman columns; the second Book discusses houses; the third Book reviews public places and spaces; the fourth Book concludes with Roman temples.
Note: the word 'fabric" means something fabricated, constructed, a building.

He starts Book I, Chapter I :  "...three things, according to Vitruvius, ought to be considered in every fabric*...and these are utility, or convenience, duration, and beauty."...
"Beauty will result from the form and correspondence of the whole, with respect to the several parts, of the parts with regard to each other, and of these again to the whole; that the structure may appear an entire and complete body, wherein each member agrees with the other, and all necessary to compose what you intend to form."
This is what  we called Practical Geometry 200 years later.

Book I has beautiful drawings of the five orders - the proper proportions and ornaments for columns.
In the introduction, Chapter VIII, Palladio writes:
"... in the dividing and measuring of the said orders, I would not make use of any certain or determinate measure particular to any city, as a cubit, foot, or palm knowing that these several members differ as much as the cities and countries; but imitating Vitruvius, who divides the Dorick order with a measure taken from the thickness or diameter of the columns, common to all, and by him called a module. I shall therefore make use of the same measure in all the orders."

Here is Plate XII, Book I. The Dorick Order

Note that he has given dimensions: the column width is 2 modules ( MO.2). the space between the columns is MO. 5 .1/2. tThe  height of the columns is MO. 15.

Palladio includes half of his  'Venetian foot' in his 4 Books. explaining that he divides his whole foot into 12 inches and then each inch into 4 minutes.  He notes that the numbers on his fabrics are dimensions based on this particular foot.

First Book, Chapter XXI, Of the loggias, entries, halls, rooms and of their form

The last paragraph:
The most beautiful and proportionable manners of rooms, and which succeed best, are seven, because they are either made round (tho' but seldom) or square, or their length will be the diagonal of the square, or of a square and a third, or of one square and a half, or of 1 square and two thirds, or of 2 squares.

Here are the diagram for the floor plan house above based on Palladio's list of beautiful proportions.

I have copied from the book. It is not quite square. Therefore my analysis is general.

I have used the division of the square into halves and quarters, and the division of the square into thirds, both ways of lay out that could have been drawn on a board or on plaster and laid out with a rope.

The plan is a square. The square divided into 4 equal rectangles marks the position of the interior walls from top to bottom. They are thicker than the other interior walls, so probably structural.  The line established is on the outside of the walls which would be appropriate for building a wall which would sit on a foundation and support the building.
Palladio may be showing off what a good designer he is, but his drawings are also construction drawings meant to convey to his workmen where to build the walls and the columns.

When the diagonals of the square are added, corner to corner, the interior walls (left to right) at the edge of the stairs are determined.

The placement of the columns in the grand hall are also noted.

Both points divide the square into thirds.

The loggia is 2 squares - one of Palladio's 7 favorite room shapes.

The side rooms are also his "beautiful proportions". Upper right: the square with its width the diagonal of the square. Middle right: the square and a half. Lower right: a square and two thirds.

The main hall is different, not only grand with columns, but centered on the whole house
The upper columns' location comes from the lines. They are at one of the thirds of the square floor plan. The lower columns are then placed the same distance from the wall for symmetry. The diagonals on each side position the columns more directly.
The squares overlap - not in a proportion that Palladio admired. However the overlap is the width of the doors which run from one end of the house to the other.

* fabric is an archaic word for a building, My copy of Palladio was translated into English around 1738.

Andrea Palladio, The Four Books of Architecture, published by Isaac Ware, London, 1738, reprinted by Dover Publications, Inc. NY, 1965.

I will add the practical geometry of the facade next.