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.

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 Lower right room might be a square and three quarters.

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.

Sunday, April 16, 2017

Serlio writes about Practical Geometry

The  hypothetical church facade - below -  drawn by Sebastiano Serlio, 1475-1554, was one of the illustrations in his  'Architettura', published in 5 volumes, beginning in 1537. It was translated from Italian into Dutch, then into English in 1611. Christopher Wren and Inigo Jones both had copies.
In 1996 it was translated again by Vaughan Hart and Peter Hicks.

For me a drawing of a building is as good evidence of someone's thinking as his/her words in a book. Here I have both.

This image is informed by geometry.
The extravagance of details - plinth blocks, double columns, not one but three oriel window, stone worked in patterns, is startling. Nothing here is backdrop; all is to be seen. Serlio holds it all together with geometry.

I've put the diagrams for the image at the end of this post because I want to first show a few explanations he gave about the use of geometry.

Serlio's Book I, On Geometry, is not very long, 13 pages.

Here are 2 illustrations.

He presents a problem to the reader on the last page: how to design a door for an existing church.
The answer is, if the church has pillars to take the width between the columns as the dimension of a square, "as high as broad," adding
"the diagonal lines,and the other two cross  cutting lines" will not only give you "the width of the door but also the places and points of the ornaments of the same door as you may see here in this figure."  

The diagram is part of what today we call The Rule of Thirds.  It can regularly be seen in  pre-WWI American construction in layout and design.

Serlio also shows 3 ways to lay out an ellipse. Here are two.

Draw a circle and add one on each side. The left and right sides of the outside circles are the ends of the ellipse.
He does not comment about the need to set the circles on a line - which will establish the point on the circumference where the next circle is added, nor that a line perpendicular to the first line is also necessary to find the points T and K. These are details an experienced mason or carpenter would have known. The
T and K become the centers for radii to draw arcs of the upper and lower sections of the ellipse. "Then placing one point of the compass at K you must " draw "a line with the other point from the figure of 1 to 2.... This figure is very like the form of an Egge."    

The second example begins with 2 squares and their diagonals. The radius for the ends of the ellipse is half the diagonal, g to 1 for example. The radius for the top and bottom of the ellipse is the whole diagonal, f to 2.

Here is the diagram  Owen Biddle of Philadelphia added to his instructions for drawing an ellipse in his pattern book published in 1805.

He did not seem to know of Serlio's layout which looks to be simpler.

Practical Geometry:
The main floor is made up of 2 squares, or perhaps 1 square in the middle and a half square on each side.
The upper floor is also 2 squares if its arcs are included.
I drew in red the diagonals of the squares on the right side. I also extended the main floor diagonal with a dotted line on the upper floor to show how one part is an extension of the other.

On the left side I drew the diagram shown above that Serlio drew for finding a door. Here it indicates the location of the oriel window and the edges of the rounded pediment over the window.

This engraving's  proportions are a little off. Is it because it's just hypothetical, or because it has been reprinted so many times?

Footnotes: I am reading Serlio's  Architettura, Book I, 1611, English translation,  on-line, printing parts of it and then enlarging the page. The English is archaic. So is the spelling. The printing blurred. If I read it out loud it is easier, much like reading hand written property deeds from the 1830's and '40's. The diagrams are clear!

2 books on early American libraries do not mention Serlio.
American Architects and Their Books to 1848, edited by Kenneth Hafertepe and James F. O'Gorman, 2001, U. Mass. Press, Amherst. MA.
Architectural Books in Early America, Janice G. Schimmelman, 1999, Oak Knoll Press, New Castle, DE.

Wednesday, April 12, 2017

The Bible and Vitruvius knew about Practical Geometry; Plato did too.

Practical Geometry  -  A lecture for SAH, Latrobe Chapter , May 9, 2017
I will be in Washington, DC, speaking to architectural historians

The lecture will be copiously illustrated, but not hands-on. Unlike the IPTN Workshops no one will learn to use a compass.

Preparing a talk always requires that I do more research, more than I can share in one talk. So here is some of what I will paraphrase, starting with what was written at least 2600 years ago.

Compasses,  basic tools in geometry, have been standard equipment for builders since early times.In the Bible, the 6th c, BCE, the prophet Isaiah describes the work of woodsmen, blacksmiths, and carpenters as he deplores the creation of graven images:
Isaiah 44: The carpenter stretches out his rule: he marks it out with a line; he fits it with planes, and he marks it out with the compass.

  Vitruvius,1st. c. BCE, does not write easily. He works hard to find the right phrase. However, he is so present, so involved, that I enjoy his work. I feel as if  he is here, intently explaining an idea. I wish I could have discussed Vitruvius with the translator of my edition, Morris Hickey Morgan,

Vitruvius,  The Ten Books of Architecture,
Book I, Chapter I, The Education of the Architect

1: Theory ... is the ability to demonstrate and explain ... the principals of proportion.

3:  Neither natural ability without instruction nor instruction without natural ability can make the perfect artist. Let him be educated, skillful with the pencil, instructed in geometry,know much history,  have followed the philosophers with attention, understand music...  

He then elaborates (I have left some of it out but it is well worth reading ):
...he must have knowledge of drawing s that he can readily make sketches to show the appearance of the work which he proposes. Geometry, also, is of much assistance in architecture, and in particular it teaches us the use of the rule and compasses, by which especially we acquire  readiness for making plans for buildings in their grounds, and rightly apply the square, the level and the plummet. .. It is true that it is by arithmetic that the total of buildings is calculated and measurements are computed, but difficult questions involving symmetry are solved by means of geometrical theories and methods.

Chapter II, The Fundamental Principles of Architecture

1: Architecture depends on Order, Arrangement, Eurythmy, Symmetry, Propriety, and Economy.   
Vitruvius then writes a paragraph for each idea. Again I am quoting pieces, and suggest you enjoy reading the whole
2: Order gives due measure to the members of a work considered separately, and symmetrical agreement to the proportions of the whole... selection of the modules from the members of the work itself, and starting from these individual parts of members, constructing the whole work to correspond.
3. Eurythmy is beauty and fitness in the adjustments of the members. This is found when the members of a work are at a height suited to their breadth, of a breadth suited to their length, and in a word that they all correspond symmetrically.
4. Symmetry is a proper agreement between the members of the work itself, and relationship between the different parts and the whole general scheme, in accordance to a certain part selected as a standard.

Vitruvius then  mentions how in the human body there is a kind of symmetrical harmony -   which becomes in the Renaissance the Vitruvian Man.

Chapter III.
Buildings must be ... built with due reference to durability, convenience and beauty. Beauty is when the appearance of the work is pleasing and in good taste, and when its members are in due proportion according to correct principles of geometry.

Book IX, Introduction
Vitruvius praises the Greek writers, specifically Aristotle, Democritus, Plato and Pythagoras. He specifically discusses Plato and Pythagoras.

3. ... Of their many discoveries that have been useful for the development of humans life, I will site a few examples.
4. First of all, among the many very useful theorems of Plato, I will cite one as demonstrated by him.
Paragraphs 4 and 5 are examples of  Plato's teachings of geometry.Paraphrasing, a square field needs to be doubled in size, and still be square. Vitruvius says finding the side of the new square cannot be done with arithmetic and describes this :

A-B-C-D is a square. A-C is its diagonal. The triangle A-B-C is the same size as A-C-D. Using A-C as the side of the new square , see that A-C-E-F is made up of 4 triangles, each the size of the original 2 in A-B-C-D.
Look at that! A-C-E- F is twice as big!

 Paragraphs 6,7, and 8 describe Pythagoras'  knowledge of the 3/4/5 right triangle:
7. ...When Pythagoras discovered this fact, he had no doubt that the Muses had guided him in the discovery, and it is said that he very gratefully offered sacrifice to them. 

Book IX goes on to discuss the zodiac, planets, astrology, phases of the moon and sundials.

I have not yet read Plato or Pythagoras on geometry.
Next post will be a brief review of  the use of geometry in Medieval Europe.

Vitruvius, The Ten Books on Architecture, translated by Morris Hicky Morgan, Harvard University, 1916, reprinted by Dover Publications, Inc. 1960

Tuesday, March 14, 2017

Jackson, NY, House - geometry, dating, some beautiful craftsmanship, Part 6 of 6

This is the last post of 6 about a c. 1820 18' x 36' wing on a  Jackson, NY,  farm house. I assume the reader has read the earlier posts.

Practical Geometry

A measured frame is always, for me, an opportunity to learn how Practical Geometry was used.

Here is the framing for the west side of the wing.

and here the geometry:

The basic geometry for the building is 2 squares, each 18 ft x 18 ft. The floor plan is 18 ft wide by 36 ft long. The framing elevation is also 2 squares 18 ft x 18 ft. I show only the right half.

The 2nd floor height is half the height of the square - 9 ft.

The Rule of Thirds lines cross at A  the height of the wall.
The lines also cross at B  the center line of the window farthest to the right.

I have not drawn all the lines for the Rule of Thirds star. They run from all the corners to all the centers of the sides of the square.

The larger square can be divided into 4 smaller squares. One is outlined on the lower left.
The window next to the door is located at the center of the right half the lower left square  - at C. 

Dating the wing by its technology

The sheathing boards are cut by a sash saw. The house was framed 'pre-circular saw' which seems to be c. 1830.

The mortise and tendon frame is augmented by nailed framing members. The frame itself is cut, not hewn. Nails begin to be manufactured in the early 1800's and come into general use by 1820.

There is both a Rumford fireplace and space provided for a cast iron stove, especially the framing for the chimney which begins on the 2nd fl. Cast iron stoves began to be manufactured c. 1820. Rumford fireplaces were still being built.

The brick used for the fireplace, the chimneys and the nogging is soft and water struck, still baked in a kiln fired by charcoal.

For pictures of these details please see the earlier posts in this series.

Beautiful craftsmanship

The top plate of the frame has unusual bird's mouth  - the joint which seats the rafter on the plate. Here is a quiet piece of craft known only to the carpenters until the frame was uncovered.

As the corner boards were removed from the house the boards looked worn out, rotted, junk. The framers disconnected the boards and saw how carefully shaped and pieced the boards were, not only as a graceful edge, but to resist rain and wind.

This particular corner detail was also used by the Shakers locally in Lebanon, NY, and in Harvard, MA.
It was also used on the 1837 house of Elizabeth Cady Stanton in Seneca Falls, NY.

I keep this section in my office .

The frieze board and its molding comes to the eave return and curls into a point at the intersection of the walls.

A Look Back

This was my first view of this house.

Below is what it looked like in 1820.

The link to  the men who took down and repaired this house, Green Mountain Timber Frames: .

Monday, March 13, 2017

Jackson, NY, House, The Frame, Part 5 of 6

In 1981, the Washington County, NY, Information, Tourism and Historic Preservation people documented every 'old house' in the county they could. This is the picture which accompanied the form, and the only picture known showing anything of the rest of the  house.

The land was part of lot #12 of the Grand Division of Cambridge Patent. The town of Jackson, where this house is, split off from Cambridge in 1814. The Parrish family owned the farm from 1846 until  1929 when Charles T. Hayes bought the farm. His son, Charles J. Hayes was the source for those gathering information.

Who added the left wing to this house around 1820?  Who wanted stylish design - the Federal front door and moldings - and technological improvements - the cast iron wood stove in the north room?

Usually a new owner, a new wife, better finances, will mean new construction. Here there is no easy answer.  Before the Parrishes, several families owned this land. However, from 1796 to 1839, Garrit Wendell, a well-respected lawyer and leading citizen of Cambridge, the town next door, was the owner. Wendell was born in Watervliet, NY, in 1769. He married Rebekah of Dutch descent; they had 2 children. He died in 1840; his wife in 1843. I found no record that he ever lived in Jackson. Wendell may have leased this house to William Mushet who is mentioned in a deed.  Mushet was not wealthy; he contributed $6 to help build the Washington Academy in 1814, while Wendell's subscription was $500.

Why would Wendell renovate and update this farm? I have not found an answer.

The frame is 'Dutch'; it is made up of a series of  bents, here 12, approximately 3 ft apart, for the 36 ft. length.
This implies that the framer had been trained in the local Dutch vernacular tradition as practiced in upper Hudson River valley.

The last bent on the left side has been removed by the timber framers in this picture.

 An 'English' frame would have had 4 bents: one at each end, one on either side of the center door and its hall.
Mixing framing traditions is not uncommon in this part of eastern New York and western New England. Here the frame is Dutch and the exterior appearance, Federal., based on English architecture.

The south end of the frame shows the braces set just below the gable end rafters. These were on both ends of the wing. The original house had also braced this new wing. Green Mountain Timber Framers who were deconstructing the house felt the frame move and secured it with cross bracing, visible here.

Above is the west (road) facade of the frame. 12 bents. Each 6"x 6" post is mortised into the sill. The
3"x 8" joists are mortised through the posts and pegged at the second floor height. A 3" x 6" rim joist is then attached below the joist and pegged.

The next bent can now be slid into place because its mortise is ready to receive the rim joist. Its floor joist can be slid into place because the easing on the 6"x 6" post runs across the face of the post, not just at the mortise. Then the intermediate stud is set below and above the rim joist and a 2"x 8" joist nailed to it. Some of the joists are notched to make the 2nd floor level.

Here is another set of post and joists. The setting of the secondary joists - about half on the left side, the rest on the right - might be because the framers worked from each end of the wing toward the front door.
The parts for these bents might have been cut ahead of time and assembled on site. They are quite uniform.

Here is a look along the 2nd floor joists on the east side, Reused posts are visible. The south sill was also a reused timber, a plate with notches for rafters and the necessary holes for pegs.

The door frame is not neat. There is some fudging - an extra post to set the door in the center, Framing for the stair opening seems to have been  figured out on the job.

Similarly the extra 2 joists, one 6"x 8",  the other 2"x 8", which carry the chimney above the stove pipe seems to intrude into the rhythm of the frame a decision made on the spot.

The framing of  the gable ends includes both mortised and nailed joints.

Mortise and tendon framing does not need nails. We used it extensively as a framing system before 1800  partly because nails were hand made from scarce iron ore not easily processed.
The invention in the early 1800's of nail making machines changed how we framed. Here, c. 1820, both wood pegs and iron nails  are used to hold the wood together. This is a transitional frame.

Here are details at the gable and at the 2nd floor. The left photograph shows the nailed north gable on the ground after it was taken down.  The right photograph is the braces mortised into the 2nd floor beam.

Here is the plate, with its unusual bird's mouth - the mortise which holds the rafters.  I and the framers, and others who know historic framing in the Hudson River Valley, had never seen this joint before. The plate is mortised to the posts.

Notice on the framing layout that the rafters do not line up with the posts. This means the walls and the roof were thought of as separate entities.

The last part of this 6 part series will review some of the exterior details and the geometry based on the frame.

The link to  the men who took down and repaired this house, Green Mountain Timber Frames: .

Wednesday, January 18, 2017

The pattern books of Asher Benjamin

This is a post about 2 of Asher Benjamin's pattern booksThe American Builder's Companion and The Architect, or Practical House Carpenter.

I like reading Asher Benjamin's pattern books.
He says practical and personal things when you least expect it.In  his notes about chimney pieces, he adds," Care should be taken, however, not to overload them (the whole mantle) with ornaments, as they are exposed and liable to be broken."* 1
This is a real person. He writes for "all practical house carpenters... particularly those who reside in the country, where they have no opportunity of consulting with an architect." *2  He is talking directly to them.

 My friends have just bought a farm with fields, barns - and an old house - in Ohio  They have many questions. The land was first settled in 1805. The house may have been built soon after that. Its shape and proportions are Federal: center entrance, 2 windows each side, 5 above, end chimneys.

Since Benjamin's pattern books were used extensively as guides by house wrights and joiners in the states west of the Appalachians from before 1800 through the 1860's, I mailed my friends two of his pattern books for their use: The American Builder's Companion, first published in 1806, the 6th edition (which I sent) in 1827,  and The Architect, or Practical House Carpenter, published in 1830, and reprinted through 1850.

This post is an addendum to the books - to help them discover Asher Benjamin's writing for themselves, especially since I live so far away. I also wanted my friends to see how design  and construction techniques evolved in those years and how to read them in their new house.

Three examples:
The mantle of this fireplace in the dining room appears to be original. (The firebox was reconfigured and then closed over the years as central heat became possible and then efficient.)

The mantle  - called a 'Chimney Piece' by Asher Benjamin - has only proportions - barely any moldings, no pattern, no emphasis or flourish.  Those proportions, however, are closely aligned with the shape of the  mantle -  illustrated in Plate 37 of  The American Builder's Companion (shown here). The shelf is narrow and extended on the ends; the board below it is wide; the side pieces are topped with a bead so that they read as columns. It is as if the joiner created a background, a base ready for embellishment.


This would seem to imply that the chimney piece was built before 1830, following the late Georgian style. This style is often referred to as Federal, Adamesque, or Neo-Classical by historians, but also called 'Colonial' by many.

But... What often happened was that the joiner simply copied what he remembered from where he came from - which might have been 30 years ago. Unless someone signed and dated his work, the age of a piece cannot be easily pinned down.

Still, the joiner who built the mantel in my friends' house did not know or disdained this mantle illustrated in Benjamin's next book, The Architect, or Practical House Carpenter, published in 1830.

This is a dramatic departure from the designs in the earlier book: Greek Revival in no uncertain terms!
The chimney piece thrusts itself into the room. The side pieces are real columns set in front of the sides of the mantle. The shelf above has become an unadorned detail with no softening molding above that frieze with its bold, dramatic Greek Key.

Here is the floor plan. The columns are not just round, but fluted.  The mantel shelf is thin, but wide and deep, adding to the sense of the fireplace jutting into the room.

My friends' dining room is quiet - not like this!

The farm house staircase is the second example.
The newel shown here is elegant and flowing, a fitting ending to the rail and balusters.

Not Greek Revival. Maybe tinged with Gothic Revival and Italianate sentiments, or inspired by Renaissance Revival furniture.

Definitely not late Georgian.

Below is Plate XLIII on stair construction from The American Builder's Companion. It includes practical drawings including diagrams for laying out curved stairs. In the upper right is a careful drawing showing where to place newel posts on stair landings. I've added a circle to highlight that detail.

On the right side is drawn a newel post, a very plain newel that is securely anchored to the step, has a little entasis in the shaft, and ends with an elliptic knob that fits the hand.  It comes from a different era than the one in the photograph.

Below is part of Plate XXXIV from The American Builder's Companion, showing what Benjamin calls 'Banisters' and we now refer to as balusters.
There is some relationship between these illustrations and those in the photograph - a solid base, a tapering of the shaft. but not much else.

On the right side of the Plate a line is divided into 6 equal parts. The placement of the curves and ornamentation, the size of the base, is determined by those parts. The balusters in the photograph do not follow those proportions.

If the rest of the house was built c.1810, then the newel and its balusters now in the house are later renovations.

The final example is the hand rail, sinuous, beautiful.  That smooth changing slope of wood was the goal of stair builders since the first awkward attempts in the 1750's.

Benjamin dedicated 10 Plates and more than 15 pages of text in his 1806 and 1830 pattern books to the design and fabrication of that curve.

This is highly technical, and hard to explain on paper with words. Benjamin does it so well that craftsmen today look to his directions.
The railing does not fall at a consistent rate. Lumber is not necessarily curved to match the changes in direction; and yet, the aim is achieved: a smooth continuous flow of wood from the upper landing to the newel at the bottom step.

I have added circles on the smaller print - Plate 48  from The American Builder's Companion- to highlight where Benjamin said the curve was to be to be modified.

Plate LXI from  The Architect, or Practical House Carpenter  shows how "to find the moulds for a stair rail with a semi-circle of 8 winders." Figure 6, upper left, shows how to lay them out on a plank.

The polished sloping hand rail invites us to run our hand along its length, and perhaps even to try sliding down around that curve! It is a beautiful work of art.

revised 1/19/2017
*1 The American Builder's Companion,the sixth edition (1827), Plate XXXVII

*2  The Architect, or Practical House Carpenter, 1830, Third Edition, Preface, page v.