Owen Biddle's 'Young Carpenter's Assistant' , Plate I, G

A note on Owen Biddle's Plate I, Diagram G. in his pattern book for beginning carpenters. *

 

I wrote about Diagram G on this post: https://www.jgrarchitect.com/2020/06/practical-geometry-lessons-lesson-5.html

I said that Biddle was not just introducing his 'carpenter assistant' to geometry; in Diagram G Biddle was explaining how to layout a square corner to work out a structural detail, cut a board, or set a frame on site.

Since then I have explored the theoretical geometry of that diagram.

The number of right angles which can be drawn in a circle is infinite. The rule always works. That understanding is part of why geometry is seen as mystical or sacred.

This 'squaring the circle' diagram is from

Robert Lawlor's Sacred Geometry*. (page 77, diagram 7.5)

It uses a geometry similar geometry to Biddle's diagram G: a diameter and an angle. Here the diameters are evenly spaced and the same angle  is used at every point on the circumference. But the angle is not 90*. It is not a 'square angle'.

This is decorative, not structural.

The shapes do not close. The line continues for 5 rotations. It does not create a square, but seeks to define the perimeter of a circle with straight lines. 

,

I am often told that I work with Sacred Geometry, that the geometric patterns I recover are theoretical, mystical, and sacred. I agree they are geometry. No, they are not sacred. They are practical. They are geometry used in construction.

Here is how Biddle's diagram comes about: 

Begin with  a point  - A

Choose a radius - A-B,  and draw a circle. Using the daisy wheel find the diameter - B- A- C, dotted and dashed line.

Pick a point on the circumference of the circle - D.

Here I have chosen 3 different D's  at random.

Connect B-D and D-C.

Each diagram will have a 90* (right) angle at the intersection of  B-D-C.

Wherever the D is placed. the angle will be 90*.

Biddle's Diagram G begins with my line B-D.

It describes how to find my 90* angle of B-D-C. (his a-b-c) The answer is to find the diameter of a circle (a-d-c) that intersects a. That will give c. That will give the 90* the carpenter needs.

 

By Hound and Eye* has a very similar diagram for drawing a right angle .
The book is a  guide to furniture design, full of practical geometry. Each geometric problem is described step by step; practice work sheets are included.

This pattern is the beginning of a handmade try square. 

 

*Owen Biddle's The Young Carpenter's Assistant, 1805, Philadelphia. Dover Publishing  reprint,  See my Bibliography for more information.

*Robert Lawlor, Sacred Geometry, Philosophy and Practice, 1982, Thames and Hudson, London.

*Geo.R. Walker & Jim Tolpin, By Hound and Eye, A Plain & Easy Guide to Designing Furniture with No Further Trouble, 2013,  Lost Art Press, Kentucky The diagram shown above is from page 57.

This pattern is 4 overlapping hexagons.

My granddaughter, who is 7, watched me add the images to this post.

She wanted us to 'square the circle'. I did, using right angles where the diameters met the circumference. That produced these overlapping 6 hexagons, not squares.

She watched closely and observed that accurate work was not easy: my lines did not always cross exactly in the center of the circle. When we finished she asked me to erase all the diameters. This is the result. Maybe she will show me later what she added to the copy I printed for her. 

PRACTICAL GEOMETRY - Lesson 3

The drawing of 'stepping off' is from Audels Carpenters and Builders Guide, NYC, 1923, p.640.

The holes in the daisy wheel are lower left, center, upper right.  There are others which do not photograph as well. This sheathing board was given to me by the crew that deconstructed the barns. It travels with me when I present on Practical Geometry.

 

The posts in this series  Lessons 1-7  are :

 https://www.jgrarchitect.com/2020/04/lessons.html

 https://www.jgrarchitect.com/2020/04/practical-geometry-lessons-2.html

 https://www.jgrarchitect.com/2020/04/practical-geometry-lesson-3.html

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

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

https://www.jgrarchitect.com/2020/06/practical-geometry-lessons-lesson-5.html

https://www.jgrarchitect.com/2020/06/practical-geometry-lesson-5-addendum.html

https://www.jgrarchitect.com/2020/08/lesson-6-rule-of-thirds-part-1_21.html

https://www.jgrarchitect.com/2020/08/lesson-6-rule-of-thirds-part-2-serlio.html

 

https://www.jgrarchitect.com/2020/09/lesson-7-how-to-layout-frame-with-lines.html

 

God with His Compass

This is referred to as 'God Measuring the World'.

 I think the title could be 'God Creating the World'.

The image is c. 1250. It is the frontispiece of German Bible. The person who drew this was most likely a monk.

Here's what I see:
God is holding the world in His left hand. His right hand holds His compass, ready to be turned in an arc. He has set His feet to steady Himself in a door frame.  His right foot is outside the frame; His toes catching the sill. 

His brass compass is long - 24"? It has a well wrought hinge which might have a nut on the right side and a handle long enough for easy grasping.  Its wing has generous length, allowing God to adjust His dimension.
The accuracy of the depiction of the compass and the posture of God tell me that the illustrator knew personally how a mason or carpenter used a compass. It was a portrait of God. The model could have been a friend or himself.


Earth appears to be a flat disk, a plate, with the darkness upon the deep, the light divided from the darkness, and the earth without form - just as described in Genesis. 

God has put one compass point into the center of the world. He has set His width to a pleasing radius. He is drawing a circle, the first step in compass layout; or perhaps He has just finished drawing the circle: He has just laid out the World.  He pays close attention on His first day as He creates the World. He sees that it is good.
If He were dividing the firmament from the depths  - measuring - His compass width would be smaller.

In case you don't know this part of the Bible:

The  Bible (using 17th c. English, the King James Version of the Bible,  not the Latin this monk probably knew):
"In the beginning God created the heaven and the earth.
And the earth was without form, and void; and darkness was upon the face of the deep. and the spirit of God moved upon the face of the waters.
And God said let there be light. And there was light.
And God saw the light, that it was good; and God divided the light from the darkness.
And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.
  Genesis, Chapter 1.1-6.

The sun and the moon are not created until the fourth day in verse 16.

See also Proverbs, Chapter 8. 22-29.

Portraits of Master Builders with Their Compasses, Part 2

My previous post had portraits of men who designed and built - Master Builders - with their compasses. 
Here are a few more.
Before 1800, in the States especially, the word 'architect' referred to master carpenters and masons, not a specialized group of people who had not trained in actual hands-on construction.
For more clarification look up the word 'architect' in the OED - the Oxford English Dictionary - which gives origins, sources, and historic uses of words. Its first definition of 'architect' is 'master builder'.

Men who drew and designed buildings, machines, and equipment used compasses. They often had other jobs too - painters, builders, tool makers, teachers, surveyors, erstwhile inventors.They are well-rounded, experienced craftsmen.


Here is James Watt, a famous Scottish inventor with his compass. He vastly improved the efficiency of the steam engine, working on the refinements from about 1765 to 1790. While he refined the parts of the steam engine, he made mathematical instruments and was a land surveyor. 
The Britannica has an excellent biography on him. 

This sculpture is in the  National Museum of Scotland in Edinburgh.
 
For more pictures and information about James Watt  see my blog post:
 https://www.jgrarchitect.com/2019/09/john-haviland-his-pattern-book.html

By the mid-1800's men who drew buildings were beginning to call themselves 'Architects', no longer 'Master Builders'.
Asher Benjamin and others designers are said to have joined together as 'architects' teaching in Boston in the 1840's.*
New York architects created the American Institute of Architects in 1857.
MIT, founded in 1868, was the first school to train architects. The department was, and is, called  Course IV. William Ware, mentioned below, was its first Director.
The street directories in Lawrence Massachusetts,  1845-1880, show men who first advertise themselves as carpenters, later listing themselves as builders, and then as architects.

John Haviland called himself an architect. He apprenticed to an architect in England, then sought to become an engineer in Russia, before migrating to the States in 1816. Here he is, with his compass.



For information about the portrait see the blog post listed above for James Watt.






Edward Shaw published his pattern book in 1854. He referred to himself as an architect.

His book discusses design and relationships between parts. It also includes detailed information for carpenters, masons, plasterers.  
I wrote about this illustration and the tools shown here in this blog post:
https://www.jgrarchitect.com/2012/02/edward-shaw-uses-tools.html
 

Le Pere Soubise is the legendary founder and saint of the Campagnons Passants Charpentiers de Devoir.


There is more about le Pere Soubise and his compass here: https://www.jgrarchitect.com/2018/02/how-practical-geometry-is-practical.html  

This portrait of le Pere Soubise dates from c.1880. This implies that large compasses were still known and used in the late 19th century.

An engraving of Giacoma Barozzi da Vignola (1507-1573) with his compass.
Vignola trained under Serlio, then worked in France for Francis I at the same time Serlio was there. He wrote Canon of the Five Orders of Architecture in 1562. It was widely available, reprinted, and translated into many languages. This image is from the edition translated by John Leeke into English in 1669, now available through Dover Publications.  


And why did they need compasses? The compass was a tool of layout - for design, for setting proportions. A ruler could then be used to measure those proportions. 
   
*I had the citation about 10 years ago, but cannot find it now. Perhaps it could not be substantiated.
I apologize for the type size changes. If I understood what causes them I would fix them.

Portraits of Master Builders with Their Compasses, Part I

This past year I have given 8 presentations on Practical Geometry, the last 3 at the International Preservation Trades Workshop (IPTW) in Stirling, Scotland. My workshop begins with a power point introduction about how geometry was used in construction. Then we practice using compasses, straightedges, pencils, and twine (chalk lines, anyone?) to layout and design frames and buildings. 
 
 
The portraits here of master builders holding a compass, the symbol of their profession,  are part of those presentations.

Sebastiano Serlio, 1475-1554, master builder and author of    'On Architectura'
 posthumous portrait by Bastolomeo Passerotti c. 1575, 
now in the Martin von Wagner Museum,  University of Wurtzburg.

I wrote an introduction to Serlio here: https://www.jgrarchitect.com/2017/04/serlio-writes-about-practical-geometry.html

 Andrea Palladio,  1508-1580
architect and author of The 4 Books of Architecture, 1570

The engraving and the painting it came from may have been made 100 years after Palladio died. 




https://www.jgrarchitect.com/2017/04/palladio-discusses-geometry.html

James Gibbs, born in Scotland, died in England: 1682 - 1754. Architect of St. Martin's in the Field church, 1722. author of the Book of Architecture. 1728. This book of engravings of his buildings is known to have been in the Colonies. It influenced a great many designs.

Portrait in the Scottish National Portrait Gallery

William Buckland - 1734-1774
 
indentured to  George Mason of Gunston Hall, 1755 

Master Builder in Virginia and Maryland

Note his compass on the table below his hand 

I write about him here: https://www.jgrarchitect.com/2014/05/gunston-hall-ason-neck-virginia.html







Peter Nicholson  - 1765 -1844  
Author of texts for master builders, architects and engineers, and mathematicians beginning in 1793 , extending through the 1840's. His books were in print many years after he died and went through many editions both in London and in the States. Asher Benjamin and Owen Biddle credit him in their pattern books. Minard Lefever says (here I paraphrase):  "Refer to Nicholson . He's the master!"

For more on Peter Nicholson see: https://www.jgrarchitect.com/2018/09/practical-geometry-what-our-ancestors.htm
 

Much of what I taught this year is not yet on this blog.  It should be, so this is a beginning.

The Compass in Construction

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

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

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

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

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



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

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



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

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






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

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

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

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






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





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

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

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

Bow compasses

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

carpenter squares in 1503

Here are carpenter squares in use in the early 16th century in Germany.

The print comes from Robert Lawlor's Sacred Geometry, Philosophy and Practice, p. 7. The wood cut by Gregor Riesch is from his book Margarita Philosophical, published in Baden,1503. Lawlor's description reads:

"Geometry as a contemplative practice is personified by an elegant and refined woman, for geometry functions as an intuitive, synthesizing, creative yet exact activity of mind associated with the feminine principle. But when these geometric laws come to be applied in the technology of daily life they are represented by the rational masculine principle: contemplative geometry is transformed into practical geometry."

I add this to the posts on carpenter squares, geometry, and regulating lines to follow up on some ideas I'm thinking about.

a) Carpenter squares were in regular use centuries before Silas Hawes of Shaftsbury, Vermont, made his first steel square in 1815, beginning what became The Eagle Square Co. Local lore wants Hawes to be the inventor of the carpenter square, but it isn't so.

b)The practice of geometry has since its beginning been an intellectual, philosophical process - 'contemplative' in the words of Lawlor - as well as a practical skill called Practical Geometry.

c) The intertwining of design - contemplative and theoretical  - and practice in construction unraveled during the Industrial Revolution. As the master-carpenter and master-mason evolved into the separate professions of architect, engineer, and builder each lost parts of the knowledge and skills, as well as the understanding and appreciation of what the others was doing.

d) Notes added 1/7/2019:
The woodcut is a wonderful window into geometry, crafts, tools, even education in late Middle Ages.
The woman is using a compass,  a tool that historians often overlook.
The famous Geometers (Google it!) were men - some of our best thinkers: Plato, Archimedes, Pythagoras, etc., not 'contemplative' nor 'feminine' as Robert Lawlor writes. I would describe them excellent, theoretical, logical, careful thinkers who also understood how to use Geometry for Practical purposes..
The word 'feminine' has little relevance in a discussion about Theoretical and Practical Geometry.