James Gibbs' Rules for Drawing the several Parts of Architecture

My previous post looked at Palladio Londinensis' instructions for the use of geometry to design of entrances.* I found that essential information necessary to the layouts was left out/ not understood/missing.  Given that background, reading and writing about this book by James Gibbs has been a pleasure.

 

RULE for DRAWING the several PARTS of ARCHITECTURE

IN A More exact and easy manner that has been heretofore practiced by which all FRACTIONS, in dividing the principal MEMBERS and their Parts, are avoided.

 
By JAMES GIBBS

The Third Edition, 

London      1753**

This is a small book, 28 pages of text, 64 engravings. Gibbs is simplifying the design of columns. He discusses the complexity of dividing a module (the diameter of given circle) into minutes and seconds; that it's difficult to "divide the small parts with a compasses" and may "occasion mistakes".

He starts, "Of Columns and their Measures". The heights of columns are listed:  "The Tuscan - 7 diameters. The Doric - 8 Diameters. The Ionic - 9 diameters. The Corinthian - 10 diameters. The Roman or Composite - 10 Diameters." Next he discusses Entablatures, then his 64 Plates.

I am curious about how did masons and carpenters working on ordinary vernacular buildings use Practical Geometry. Can Gibbs' engravings tell me about vernacular design c.1730-50?  

Here are Gibbs' notes on 6 doors.

 

Plate XXVII shows 3 door frames: Tuscan, Dorick, and Ionick.

Each door has a segmented line on the left side. The divisions start at the top of the base of the columns. The Tuscan and Dorick lines both have 5 sections, one of which is the entablature's height.

The Ionick door has 6 sections, one of which is the entablature.

 

Those sections are the modules for all the parts of the door. The module is a length, a diameter of a circle drawn by a compass. So how does builder choose how big to make it? Where does he begin? 

Gibbs writes, "First find the Diameter of the Column, give 6 Diameters from middle to middle of the Columns..." 

From that diameter comes the sizes: the spacing of the columns, the width and height of the door opening. The door frame is a 'semidiameter', half a diameter, a radius.

 

Gibb's drawings are spare, clean.  His explanation, The Ionick Door, Plate XXXVII, second paragraph, for "The Geometric Rule to find the height of the Pediment..."  is easy to follow. ***

 

Vernacular buildings in the Colonies had doors with similar entablatures. Do the entrances for the Rockingham, VT, Meetinghouse follow Gibbs' instructions?  I will check.

 

 

 

Gibbs' Plate XLII,  'Three Doors with Archtraves'. 

Gibbs focuses on the architraves. I am looking at the doors. I want to know if our American builders use these rules to layout doors.****

The doors begin with a square whose length is the width of the door. The diameter of the square is divided into 6 parts. One part is the width of the frame, the Architrave, which today we would specify as the molding or trim. The middle door is taller: it adds one more part (1/6) to the width and height of its trim. The diagonal of both squares "gives the bigness of the pilaster upon which the Scroll is fixed."

 

The geometry for dividing a diameter - or any line - into 6 equal parts:

Using your line as the length of the sides, draw a square. 1) Add the diagonals . 2) Add the center lines. 3) Add the 4 lines from corner to opposite center point. Note the points where the  lines intersect.  4) Connect those points with lines.

You have divided the square into 3 long rectangles, and your line into 3 equal parts. See '1/3,1/3/1/3' above the square.

The distance between the center line of the square and the closest vertical line is 1/6 of your line . See "1/6" below the square, lower right. 

                                                                                                                  

 

*  https://www.jgrarchitect.com/2024/12/palladio-londiensis-frontispieces-c1755.html

**I am reading this through the University of Notre Dame  https://www3.nd.edu › Gibbs-Park-folio-18 

The first edition was published in 1732. It was available for purchase in the Colonies. I am always interested to see what words and phrases are capitalize in books printed in this era. 

***For  more information about pediments see my posts about Vignola's Rule for Pediments 

**** Today, a builder has a catalogue of doors to choose from. The doors may look different, but their widths and height are  similar: exterior doors are 3' x 6'8", 3'x7'. Other sizes must be special ordered or custom-made.  Before the Industrial Revolution there was no such uniformity.

 

Palladio Londinensis' Frontispieces, c.1755

:

Reader beware: This post is a work in progress.  I thought this was a simple post: I wanted to share the 'Diameters', because visually, with no words, they show how Practical Geometry was used.   

However, I am also reading James Gibbs' Rules for Drawing the Several Parts of Architecture..." * I found I was comparing of English pattern books c.1755. It was too much for one post. I edited. 

This post is about Salmon's illustrations. I've written a companion piece using James Gibbs' engravings.

These engravings are from Palladio Londinensis,The London Art of Building,  a builder's manual produced and published by William Salmon from 1734 to 1755.  Salmon was a carpenter and builder northeast of London. His book was readily available in bookshops and libraries in Britain and  the Colonies from the 1750's into the early 1800's.**

 

 

William Salmon's  Composite Order, Plate XXVI 

He wrote "..the Height of the Door is 3 Diameters, and hath a manner of pannelling different from all the foregoing; also the Entablature is 1/5 the length of the Pilaster, as may be seen from the Circles." 

The diameters Salmon mentions have no numerical value, nor do the Circles. They are the proportions for the door: 1wide/3 tall, and then for the pilasters and the entablature (the part of the door frame above the door itself and below the pediment): 5/1.  

A builder would have known generally how much space - width and height - he had to work with.  The circles and the diameters (semi-circles) were units of measure, the 'module' for that door's layout and design. Stepping off the module and adjusting its length, ie: its diameter, to fit the space he had, the builder could find the actual lengths of the door, its surround, and the entablature.** The layout of the frontispiece, the piece at the top, could come later. 

 

Before standardize dimensions, lengths were 'stepped off' using a compass. The diameter is the visual symbol of the compass' span and the act of swinging it. Salmon's book included drawings of diameters in rows - 'stepped off'. 

This illustration, from a 1950's text book for technical drawing, shows the compass stepping off 3 times.  

 

 

 The 'Doric Order Frontispiece and Door, Plate XXI'.

The height of the entablature is set by the length of the pilasters. The diameters on the right side, the modules, divide the length of the pilasters into 4 parts. 1 more part is added for the entablature.

The pediment is laid out by Vignola's Rule**  

 Salmon gives no geometric relationship between the door's proportions and the pilasters.

Is the circle drawn on the door its module? 
The door's length is 2 large circles plus a small one. The upper large circle encloses 4 small circles, so the whole door is 9 small circles tall. 

How would a carpenter find the diameter for the smaller circle if he began with the large one? It can be done, but not easily or quickly. Using the small circle as the module would be easier.

 The geometry:  Lay out 4 circles on a line. The length of the line from the outside edge of the first to the outside edge of the last is the large circle's diameter.

The point where the 2nd and 3rd circles cross the line is the center of the large circle. The circle's radius is the length of the line from the center to the outside edge of the first small circle.

Using his compass the builder could step off 4 small circles, or one big one for the width of the Dorick door, and 9 small circles for its height.

 

This 'Corinthian Order, Plate XV' door is 2-1/2 circles. The surround is 5 circles, the entablature is 1. 

The geometry of the door,  2-1/2 circles does not determine the size of the lower panel, the upper opening, or the size of the panes of glass. Salmon doesn't seem to understand that these sizes could have been derived from the proportions of the door itself. 

There is no indication that the pilasters' width or height might have been chosen to be in proportion to the door, or vice versa.

 

 

 

'A Dorick Entrance, Plate XXII' is an arched entry without a door, 5 modules long and, as the circle tells us, 3 modules wide.

The capitals of the pilasters around the arch are located at the center of the big circle. But the columns on each side of the opening and their pedestals do not use the proportions of the entry's 5 small circles.   

 

 

Here is the very simple geometry: the 3 circles.

 

 

Since each was drawn with a compass, each has a center. Therefore the big circle which encloses them is easy to draw; it has a radius  of 1-1/2 little circles.

 

London and the Colonies in the 18th C. needed builders. Some were well trained; others not quite.  Along with instructions for laying out Entrances, William Salmon's book included chapters on 'Geometric Problems', 'Prices of the Labor and Materials' for the trades as well as 'all sorts of Iron Work', information about staircases, lumber, roof framing, 'Chimnies', and the 5 Orders of Columns. 

The polite conclusion is  that Palladio Londinensis helped builders educate themselves, that in spite of its shortcomings it was a useful reference. Even so, I find his explanations inadequate and sloppy.

 

* James Gibbs, Rules for Drawing the Several Parts of Architecture..., London, 1753. The print and drawings are clearer and much easier to read online. 

**My copy:  Salmon, William, Palladio Londinensis,  London, 1755, Gale Ecco reprint. The original is often found in historic libraries. One is in the library of Gunston Hall, in Virginia, .

***Today doors and their surrounds come in standard sizes. Before the Industrial Revolution, a door and its frontispiece might be match another next door, or not. 

**** See my blog posts about Andeas Palladio's 'module',  https://www.jgrarchitect.com/2024/05/a-daisy-wheel-is-module.html, and https://www.jgrarchitect.com/2020/04/practical-geometry-lesson-3.html

***** Yes, I wrote a post about that too: https://www.jgrarchitect.com/2024/05/how-to-layout-pediment-350-years-of.html 

From a Circle to the Pythagorean Triangle via the Schifferstadt House.

The  geometry used to lay out the Schiefferstadt House, 1755, was the 3/4/5 rectangle. Probably.

'Probably' because Practical Geometry, the use of geometry in construction, was taught by doing, not by reading and writing. The drawings we have assume a knowledge of basic geometric patterns. Written records are rare and incomplete.

The stone walls for the House were laid one row after another, consecutively. Unlike wood frame structures which are form and infill, in masonry buildings the  form and the skin are one. 

This is the back of the house, showing not just the main stone house and the brick wing, but the extensive stone foundation.

Every wall of the House needed to be trued as it was built. Here is a wall in the cellar: laid up stone.  Consider how hard those slabs would have been to adjust later on. The walls were trued with a plumb line and the lines of 3/4/5 triangle as they rose.*  

 

The frame of a wood structures determines its size, its corners, its form. The parts for the frame, the studs and braces, are cut and assembled. The shape can be adjusted, changed, trued using lines, even after it is raised. This image of a barn frame is from Wm Pain's The  Carpenter's Pocket Dictionary, 1781, redrawn by Eric Sloane.**  

The stone and brick buildings I have studied use the 3/4/5 triangle. Chimney blocks are 3/4/5 rectangles. 

So, why didn't I immediately try the 3/4/5 triangle when I looked at the house geometry? Well, I wondered if the Schiefferstadts'  traditional building patterns, brought with them from Germany, would be different from those I'd studied before, the vernacular housing built by English, Dutch, and French immigrants. Those began with the circle and its square. I began there too, looking for differences. I missed the obvious: the stone. The 3/4/5 rectangle easily fits the plans, the simple solution. KISS***

 

Then, as I was playing with the circle and its square (left image), this happened.

I saw that when I begin with the square derived from the radius, its circle and lines (left image), I can easy to locate 6 other points around the circumference , making 12 equidistant points around the circumference, (center image). I saw that circle geometry 'finds' the 3/4/5 rectangle (right image); that the Pythagorean Theorem is a 'short cut' using the 3 and 4 units that are already there.

On the left: the 12 pointed daisy wheel.  On the right: the 3/4/5 rectangle with units, and the 3/4/5 triangle.

 

 

 

 

 

 

*The walls are 'kept in line'. I am often surprised to realize that a common phrase, such as '"staying in line", probably began as construction lingo.

** Wm Pain, The Carpenter's Pocket Directory, London, 1781.

     Eric Sloane, An Age of Barns, Voyageur Press, Minneapolis, MN, 2001, p.37. originally published by Funk&Wagnals, c. 1967.  

*** KISS: "keep it simple, stupid"

The earlier posts on the Schiefferstadt House:  

https://www.jgrarchitect.com/2024/08/a-closer-look-at-schiefferstadt-house.html

https://www.jgrarchitect.com/2024/07/the-geometry-of-schiefferstadt-house.html

A closer look at the Schiefferstadt House practical geometry

Please see my update:  https://www.jgrarchitect.com/2024/09/from-circle-to-pythagorean-triangle-via.html
I am not deleting this post because of my last paragraphs: I find the ways the Lines and layouts in Practical Geometry overlap need more consideration.* 

The lay out of the Schiefferstadt House,* uses a geometric pattern that was well known at the 1750's: the rule for drawing a square starting with a radius and a circle.

The diagram begins with the daisy wheel, scribed by a compass or a divider.  The 'petals' created by the 6 arcs of the radius around the circle make 6 points on the circumference.

The length of the radius for the circle is the width of the house.

 

 

 

When those points of the daisy wheel are joined they create Lines - dashed lines in the diagram. (Basic Euclidean geometry : 2 points are required to create a Line.)  The arcs of the radii cross those Lines to lay out a square. **

When one point of the divider, still opened to the width of the radius of the circle, is set on each of the 2 upper corners of the square, and the arcs swung, the arcs cross the circumference at the top of the circle.  Stepping off the radius around the circumference, will locate 6 more points.  All 12 points are equidistant from each other; all can be used for layout and design.

There is also a short cut to those upper 2 points; the place where the arcs cross the daisy wheel petals are points. 2 points = a Line. That Line extended is the same Line shown in my next diagram.  

 

The carpenter of the Schiefferstadt House could have used this geometry to step off  a rectangle about 18 units wide x 26 units long.  If his compass was open to a 2 ft span, the floor plan would have been 36 ft.wide  x 52 ft long. He would have trued his rectangle by checking that his diagonals matched, just as builders do today.

*

However the carpenter could also have used the square and its diagonal to lay out the plan. Those arcs would cross the circumference at the same place (dashed line), but they would cross the vertical lines of the rectangle about one unit higher than if the 12 points had been used (see the points where the dashed and red lines cross the circumference).  

This would make the floor plan 36 ft wide x 54 ft long. That's not much longer,  probably of little consequence to the design. However if the mason and the the framer were not using the same geometric progression (both using the first diagram or both using the second) the stone foundation and the interior wood frame would not have fit together. 

 

The drawings made c. 1978 for the restoration of the Schiefferstadt House may give me more information. The Frederick County Landmarks Foundation is sending prints. 

I will be looking for the simplest and quickest layout. I find that a builder tends to use the same same geometric progression for his plans and elevations. The geometry is one of his tools. The repetition of one pattern and one unit of measurement would be efficient and leave fewer chances for mistakes.  

If another layout is introduced it is usually the work of a craftsman whose work comes later - the finish carpenter adding a mantle, or the mason building a firebox and flu. Each might prefer a different system.

* The Schiefferstadt House, Frederick, Maryland, built in 1755, owned by The Frederick County Landmarks Foundation.  See my previous post for the geometry of the floor plan: https://www.jgrarchitect.com/2024/07/the-geometry-of-schiefferstadt-house.html

 

**2  basic practical geometry diagrams:

The diagram laying out how the radius of a circle can become the side of a square.

 Audel's Carpenters and Builders Guides , published in 1923, shows this diagram.

100 years ago, this geometry was common and practical knowledge.

The geometry of the Schiefferstadt House, Frederick, MD, 1758

The Schiefferstadt House 

 

 

This stone house, in Frederick, Maryland, was built c. 1755 for Elias Bruner, the son of German immigrants.

In the spring of 2023 the board of the Preservation Trades Network toured the house when we were in Frederick to plan the 2023 International Preservation Trades Workshops. The guides of the Schiefferstadt House showed us the house from cellar to attic, sharing both the original construction and the on-going work of maintenance and restoration. 

Our visit was well worth our time; many thanks to the Schiefferstadt staff and volunteers.

We saw many practical built-in systems for cooling and heating. 
The black blob in the lower left corner of this picture is one of several vents for the very effective basement cold storage vault. 

Under one kitchen window is a very useful drainage sill. 

 

 

 

 

 A close up of the trough with its lip and spout.  

The kitchen help need not carry the dirty dish water over to the door; instead it can be efficiently discarded out the window. 

 

I have seen a trough like this only once before, in medieval military barracks
in Switzerland.

The HABS drawing of the first floor plan shows the original stone house at the top of the drawing. The brick wing was built later. 

That first, 1637, house is outlined in red.

Stone walls are usually built between 2 lines, set to keep the walls straight. Here either the exterior line or the interior line could have set the governing dimensions.   

In both cases the practical geometry of the Line and its arc created the plan. First: The exterior geometry:

Using the width of the main house (red arrows) as a radius for a circle, I drew the daisy wheel with its 6 'petals',  noting the points around the circle where the arcs cross the circumference. The points connect the lines which lay out the long walls - see the red dots and vertical dashed lines at the top of the drawing.

The arcs of this daisy wheel create 6 points  If I rotated the wheel to begin the arcs not on the corners of the house, but at the center of the lower wall, the petals will be perpendicular to the side walls, parallel to the front and back walls. This adds 6 more points to the circumference - noted here as black dots, 12 points in all equally spaced*.

 2 of the new points lay out the location of the 4th wall, here at the top of the drawing, noted with red dots and a horizontal dashed line.

 

However, the plan for the house could also have been laid out from the inside. The exterior sides of the stone foundation walls could have been irregular, sloping away from the house below grade, only becoming straight  once they were above grade. I have seen this often in houses built before 1900. As in the first layout the width is the governing dimension. The geometry, a square and its diagonal, lays out the interior walls.

The builders dug into the side of the hill to set the foundation. When they set their governing lines which layout did they use? The exterior or the interior plan? Perhaps the exterior plan was concept, drawn during a consultation with the owner, then staked on site, perhaps with offset lines like those we use today. Then the interior dimensions could have been used when the workmen were on site, in the future cellar.

On the drawing are faint pencil lines of diagonals and an arc, using the exterior width as the side of the square. They don't quite fit. They are an exploration,  an essential part of discovering what geometry the builder used.

 

 

The house has a center entrance, a room on each side. Within both walls on either side of the center hall are fireplaces and flues. Here is the kitchen fireplace.

 

 

 

 

 Fireplaces on both sides of the center hall itself send heat to iron boxes on the first and second floor. This picture is a 2nd floor heating box, set into the wall between 2 rooms so it will radiate heat into both rooms. It's an early version of the radiator.

 

The flues of those first floor fireplaces join to become one chimney as they exit the roof.

Here 2 members of the Preservation Trades Network board and a staffer for the House stand in the first floor hall under the arch created by those flues as they come together overhead. One fire box is visible on the left. The one on the right has been closed.

This 3D drawing of the House is helpful even if not quite accurate. The flues come together over the first floor, not the second  as shown here.

However it explains how 'wishbone' masonry chimney blocks were located and the flues joined to become one chimney at the ridge of the roof.  

Each wing of the chimney required its own foundation which would have been built as the stone walls of the house were laid up.

I found as I studied the layout that while I could easily layout the exterior dimensions, I did not have enough experience with stone construction to understand how the masons would have worked once they set up the lines for the foundation walls. How did the masons measure where to set the chimney foundations?

A timber framer can begin the house frame with a sill set on the foundation after it is complete. I know those frames and foundations well. The joist pockets for the wood interior frame of the Schiefferstadt House had to be set in the stone as the wall was built. How did they know where to place them?

I asked Joe Lubozynski for help. He lives in the area, is an excellent architectural historian as well as craftsman. He knows historic stone construction and this house in particular. And he was willing to advise me. 

He and I reviewed how the house would have been built, beginning with digging into a slope (see the Architectural Cross Section above),  placing the footings, laying the stones for the walls and chimney foundations.  Then constructing the basement cold storage space with its vaulted cellar ceiling and placing the first floor frame.  

We considered whether the builders would have measured from the outside or the inside of the stone walls to place the joists. Our conclusion was obvious: it's much easier to set Lines from the inside of the walls and check them. The work would be done more accurately as well as more quickly.

At this point we drew the Rule of Thirds* diagram using the inside of the stone foundation as the rectangle.

 

  
The diagram easily located the floor joists. Note  how the inner sides of the floor joists are on the intersections of the diagonals. the diagonals cross, making 2 points. The points layout out the location of the joists and the joist pockets. See the 2 black lines with arrows on each end.The geometry is as simple as the layout of the foundation.

The chimney bases are white in this drawing in order to make the lines of the Rule of Thirds clear. 

 

 

The Rule of Thirds also locates the 2 foundations which support the fireplaces and chimneys. See the red arrows.

The measured drawings were done before the restoration of the house began. The fireplaces had been altered. The location of the masonry for the fireboxes and chimneys is an educated estimate. I have not measured the rebuilt and restored masonry. 

 

My conclusion? The technology of the Schiefferstat House is elegant and sophisticated for that period in the Colonies. The grand houses in New England and Virginia did not have the conveniences of this little house.  However, the practical geometry of the house is simple, traditional: very similar to what I've found from the same era in New England, New York, Virginia, and Louisiana.

* For information about Daisy Wheels,  drawings squares and rectangles with compasses, the Rule of Thirds, try:

https://www.jgrarchitect.com/2020/04/practical-geometry-lesson-4.html

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

 https://www.jgrarchitect.com/2022/10/serlios-lines.html

 

 

The Perfect Cube and its Sphere

 

 

This perfect cube and its square was drawn by Sebastiano Serlio, c. 1540.

It is an Euclidean solid: 6 square faces.  It is 'perfect': each side exactly like the others. A  perfect sphere would fit within it. A perfect circle fits its perfect square face. Another square is within that circle, and a smaller square within that. 

The shapes are bound by the diagonal Lines which create 2 points at the intersections for drawing the next square or circle.
That cube and sphere were not only theoretical ideals, they were practical, a layout tool, the pattern governing a design. The pattern book writers called this 'Practical Geometry'.

 

 

Serlio drew his tools in the lower right corner on the frontispiece to his book, 'On Architecture'. **

The perfect cube is in the lower right corner. His compass is in the middle surrounded by his straight edge, carpenter square, stylus. his line*. 

I've kept track of that pattern: the cube, its circle, the next smaller square and its circle, the diagonals. I want to understand how it is layout tool.

Some of what I've learned is posted here.

Hagia Sofia was built in the early 6th C. by Justinian I, the Byzantine Emperor in then Constantinople, now Istanbul. Earlier churches on the site had burned and the first dome of Hagia Sofia fell in.  The second is still standing 1500 yrs later.

 

 

 

 

 Here is what it looks like from the inside.

This is Bannister Fletcher's diagram** of the dome  formation for Hagia Sophia: the square with its circles. One is around it, the other within it. Their sizes are governed by the square.

This design can be seen in the mosques and churches built after Hagia Sophia in eastern Europe and around the Mediterranean.  The examples in western Europe which I have found are in Italy. 

The shaded areas are called 'pendentives'. There are several ways to build these, not to be discussed here.

 

A dome needs to be held up, of course. When it is the top of a silo, there is no structural problem - the dome is supported all the way around. 

 

 

 

 

But in a church or mosque - where people congregate - the dome needs to be on supports so it is visible. We need to be under it and in its space. 

The weight of the dome must be supported, and its thrust as well.

This diagram from Mosque,**by David Macaulay, explains the problem and show.s the solution in the Byzantium empire: columns (blue) support arches (green) with  cylinders (brown) adding weight behind each arch. At the bottom of the drawing is the floor plan, a square which fits within the circle of the dome.

Other domes had been built. The Pantheon dome with its oculus, c. 120CE, is the best known example. However, the Pantheon's geometry is circular. Hagia Sophia adds the circle's square. Or perhaps the square's circle. 

When Hagia Sofia was being built the Roman Empire was collapsing. Western Europe built little except in  those ports where there was political power, trading, and influence from the cultures around the Mediterranean.

Venice, with its location and port, did flourish. It began to build  St. Marks Cathedral*** in 1000 CE.

 

These drawing of the plan and the interior are from Bannister Fletcher. **

The design shows many circles within their squares.

The large circles are domes, seen here from above. The square bases are visible too.

 

The small circles are the arched stone work of the columns which are shown as 4 black cubes around each circle within its square.

 

The ponderous columns are divided into 4 piers which makes them appear less massive and intimidating. They join at the springing points to support the arches.

This photograph is from Laurie Smith's' book, The Geometrical Design of Saint David's Cathedral Nave Ceiling.**

 

It's the ceiling under the new (c. 1535) roof for the cathedral.

The pattern is squares and the circles set side by side but not in a simple repetition. Laurie's compasses show the layout.
This ceiling pattern is obviously geometric but it is not in the lineage of the designs of Hajia Sofia or Serlio. It is, to quote Laurie Smith, " ...an exceptional carpentry idea and one that was unique to Wales.

These are the geometries used  for the pendants in St. David's Cathedral, as documented by Laurie Smith. The first 4 are based on the use of a compass, the next 2 on a diamond and a square. The last is related to, and perhaps growing out of, the circles and squares in ceiling pattern. 

 

These dome elevations and plans are part of William Ware's book, American Vignola, published in the States in 1903.**

 He describes the dome on the left (C) as "being generally a full hemisphere, constructed with a radius less than that of the sphere of which the pendentives form a part."  

If the same dome is erected upon  a vertical cylinder, visually a band below the dome, it is a 'drum' dome. Here: the dome on the right (D).

I have wondered why he did not recognize the lineage of the perfect square and its circle. He knew geometry.

 

The drum dome is the plan and elevation of the main dome at Massachusetts Institute of Technology, built in 1916.

 The glass blocks which fill the oculus of the MIT dome are set in Serlio's  pattern: the circle is the outer shape with its square and its circle set within it.

 To see the glass of the oculus, please follow the link, as the photographs are under copyright. https://capitalprojects.mit.edu/projects/great-dome-skylight-building-10 

 

A similar dome was placed over the Massachusetts Avenue entrance at MIT, built the the 1930's.

The glass curtain wall that faces Mass Ave is naturally based on the square and its circle. However the overlap of the square within the circle is not a simple repetition of square set next to square. The band between the squares  is a simplification (no curved lines) of the complex pattern seen in Saint David's Cathedral.

 

 

 

 I will update this post as I learn more.

 

*The tangled Line with its plumb bob is in the lower left corner. It can be tied to something and held taut with a plumb bob on the other end. It is not perfect. It is how we attempt to build perfectly, with no mistakes.

**  frontispiece, On Architecture, Sebastiano Serlio

**page 281, 288, A History of Architecture on the Comparative Method, Bannister Fletcher 

** page 11, Mosque, David Macaulay. 

** pages 7,15 and 31, The Geometrical Design of Saint David's Cathedral Nave Ceiling, Laurie Smith. Laurie's book can be purchased through me, as well as through the Carpenters Fellowship in the UK. 

** page 88, The American Vignola, William R. Ware

For more information please see my Bibliography: https://www.jgrarchitect.com/2022/03/a-bibliography-for-my-traditional.html

***I have lost the name of the engraver for the image of St.Marks. I don't know where I found it. The pictures of Hagia Sophia also cannot be credited. If you recognize what publication they appeared in, or who made the images, please let me know.