Palladio Londinensis' Frontispieces, c.1755

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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 

Serlio's Lines

 Lines

That's the word they used.   Lines.  An important word, often capitalized.         

Sebastiano Serlio writes, ".... if the architect wants to build a temple door which is proportional to the place, he should take the width of the central body of the temple, that is the floor space - or between the walls if it is small, and between the pillars if it has transepts. From this width he should draw the same height which will make a perfect square. 

... He should draw two diagonal lines and then the two other lines from the bottom corners to the top [center.] The "lines will form the opening of the door, and they will also enable the ornaments to be carved, as is shown... If 3 doors... were to be built in the face of a temple, the same proportions could be used in the smaller sides." *

We use this word: "line".  Usually we add helpful adjectives. 

 Metaphoric lines: "toe the line", "step over the line", life line; or bus and subway lines. 

Demarcation lines: fence line, property line, finish line, white line, sight line.

Rope that becomes a line: tow line, clothes line, fishing line, electric line.   

And in construction: chalk line, plumb line.  

The line shown here can be either. a chalk line that can be rewound into the case, or a plumb line by hanging the line on a peg and using the case as the plumb bob.

 We check that a foundation, a frame is true with matching diagonal lines.

There is also 'straight line', an oxymoron in geometry. 

 

Serlio's definition is geometric; a line is "a straight and continuous representation from one point to another, having length without width."  Here is his diagram shown above, rotated and then all 4 diagrams overlaid to make one 'star'.

He ends Book I: On Geometry, " However, honest reader, although the things resulting from the various intersections of lines is infinite, to avoid being long-winded I shall come to an end." 

 Do we, in 2022, know what these words, the various intersections of lines mean? What results from them?

The easiest answer is the lines can divide a rectangle or trapezoid in half, vertically or horizontally, or in 3, 4, 5, 6 (etc.) equal parts.

Any 2 points can establish a line, so lines can create simple or complex patterns.

Here is one of Serlio's designs that begins with a square and its diagonals. Every dimension on the plan comes from that initial diagram.

This villa comes from Serlio's Book  VI: On Geometry, titled: Treatise: On Domestic Architecture, written c. 1545-9, Plate XXXVIII, Project 28, of 73 plates.

Serlio drew in the lines for his readers.They were not laid out first. The lines come from the geometry. The placement of columns, walls, openings come from the "various intersections of lines".

He also gives dimensions: those little hatch marks in the center. 

 

Here's the geometry:

The plan is a square. It is divided into 4 parts horizontally and vertically - 16 equal squares. the top row is: 1 square, 2 squares, 1 square. The  bottom row matches it.  The vertical rows also repeat the pattern: square, double square, square. The center space is 'left over' - 2 squares x 2 squares.  That space is divided into 9 equal squares. The columns mark the intersections.

 

All of this can be easily laid out with Lines. The diagonals neatly cross the corners of the structure and the 4 columns in the central room.
The Lines Serlio used (shown above) to locate the door can also be laid out here. They cross at the center of the walls.

Serlio drew the lines that show the widths of walls, openings, and columns. How did he knows where those lines should be?  I followed his lead.

His design is a square: I drew squares. I located the center of each side of the plan and added the Lines from center point to center point. This divided the plan into 4 smaller squares. Now there were 4 points of intersection, plus the one in the center.

 

 

These points allowed more Lines to be added.

The Lines laid out the wall locations. They are at the back of the niches and the fireplaces. They told the mason where to begin his work. He could add the decorative niches, pilasters and mantles in front of the structure. The fireplace flues would line up.   

 

Don't miss the wonderful details: the circular stair - lower left - is at an intersection. The main stair fits neatly into the lower left square, the octagon room in the lower right.
 

So, the columns?

 The Lines  - the diagonals that Serlio used in his drawing for locating the door  - locate the columns. They are on the 'third points'  in the space: dividing the center hall into 9 squares.

This is  a simplified version of the star I drew above. It is the 'Rule of Thirds' that we use when we compose images on our cell phones, that artists consider when they compose a painting.

 

 

 Here is a detail showing how the Lines of the column locations are extended into the loggia 'G'. The Lines determine the placement of the outer side of the square columns. The center space - where G is on the center of 5 Lines - is divided into 4 spaces, easily done using the star. 2 of the spaces equal the opening between the columns, 1 is the width of the columns.  Note that the width of the columns is also the width of the walls.  

Each dimension comes directly from the first geometry, the square and its diagonals.

 

The Front Elevation! 

 

That simple layout creates the structure of the villa. Visually the walls became a backdrop for columns, arches, niches, friezes, lintels, dormers, balconies. However it is the geometry which holds all those pieces together.

Note that those square columns, here on the front of the house, have round pilasters added to their front sides, with doubled pilasters on the corners. And don't miss the chimneys!

* Sebastiano Serlio, Book I: On Geometry, See my bibliography: https://www.jgrarchitect.com/2019/06/bibliography-includiung-websites.html

                                Book  VI: On Geometry, On Domestic Architecture,  A Dover Publication edition, 1996, of work originally published by The Architectural History Foundation, NY, and the MIT Press, Cambridge, MA, 1978.

Owen Biddle's "The Young Carpenter's Assistant"

 Owen Biddle's pattern book The Young Carpenter's Assistant was published  in Philadelphia in 1805.
I am rereading it, looking especially at his use of Practical Geometry.



His first drawings, A and B, on Plate 1 are a plan and section of a drafting board. His instructions include how to construct the frame and the panel, and how to locate the small wood buttons which will keep the dampened paper in place while it dries by the fireplace to become "smooth as a drum head" .*
Drawing C is a T Square whose construction is also described.
He lists the tools a student would need; including a small compass, often called a 'bow pen'.

The rest of Plate 1, Plates 2, 3, with Biddle's descriptions explain "the most useful geometric problems every Carpenter ought to be acquainted with."*

I read between the lines: What was common knowledge that did not need explanation?

- 'Carpenter's Assistants' might have been men who needed to learn more about construction but had not had regular apprenticeships. Many apprentices ran away before completing their training; the most famous one is Benjamin Franklin.
 -  The carpenter's assistant had little experience with paper for architectural drawings. He used a convenient board, a compass, a straight edge, and an awl when he needs to work out a design. These designs are often found on boards during renovation.
-  Biddle specified the compass to be small because there are many different sized compasses. The ones shown here are in a cabinet maker's shop. The biggest is about 16" tall
-  Geometry was a practical tool in construction.

Biddle had set up a school to teach 'architecture' to carpenters.  Assistants might not have been trained to draw in their apprenticeships. Those who designed might not trained under a master builder.  Biddle himself was a contractor becoming an architect.





Biddle has  includes 2 drawings of the same construction. Biddle first explains the design, Plate 15. Then he details how to make the construction drawing become an inviting illustration for a potential client, Plate 16.

Here is Plate 15. In his description Biddle says he gives 'the lines of a pitch pediment frontispiece'.  He writes about 'Lines' as Serlio did: the Lines for layout and design. He adds that the  "Column is made 10 diameters in height." The use of diameter of the column as a measurement is discussed by Palladio.


Biddle says for the best appearance "the door should be as wide as  half its height"*. The scale on the right side of the drawing is labeled '10 diameters'. Did the 'door' consisted of just the part that's hinged? No, Biddle's dimensions include the door and its surround. Here is the door with a height of 10 units divided into 2 red squares, each  5 units square.

As I followed Biddle's notes and dimensions on the drawing I learned how he thought about construction and design: his unit is the door and its frame: the 'door'  itself was not the measure; the door frame between the columns is. The column's height includes its base and its capital, but not the lower base  which is noted as 8" high. This allows the base to be adjusted to fit the vagaries of the location.

Of course the fanlight is a semicircle. The frame is half the height of the squares of the door. 
The key stone of the semicircular fanlight was the center of the square, the height of the pediment 3/4 of the square.

The roof pitch falls exactly along the Lines which cross the square and locate its 3/4 mark.

The notes on the right side about the height of the little columns in the architrave and the  return of the eaves reference the span of the door which is derived from the height of the columns.




Biddle notes at the bottom of the actual door its width: 9 parts.  the parts lay out the panels. The panels themselves are 3 parts wide. Their length and spacing is also determined by the 9 parts.
The fan light's rays are also set by the 9 units. . The tic marks for the 9 units extended to the arc of the fan light layout the fins. The rhythm for the main fins is 1,2,3,2,1.  In the center of the 'petals' of the fan lights are more tic marks - the centers of the arcs that create the tracery.

I tried to draw this clearly. What resulted was a jumble of lines. I'll try words:
Biddle began with the diameter of the column. He used 10 diameters to create 2 squares for door and 3/4 of the square for a fanlight and architrave. His 5 unit width is divided into 10 units, 9 of which are the physical door. The Lines inform all his design.
Biddle uses 10 parts because he supposes
"that the door is for a town house with a narrow front..."  The parts will be in proportion to each other, but take up less space.


The  square shown here has already been divided into 4 equal parts. The Lines divide the 4 rectangles into 5 rectangles. The bottom and top lines defining the square are thus divided into 5 equal parts.



Plate 16

Here is the same entrance shaded. He writes " ...the student should make it his business to understand the effects of light and shade..."  He explains how to think about shading in 2 paragraphs, where "the shade should be strong", where the part should be "bright".

Plates 17 and 18  are similar: one drawing setting up the design itself, the next explaining how to shade the design.  









* Plates 1, 2, 3, 15, and 16, and their descriptions
Owen Biddle, The Young Carpenter's Assistant; or, A System of Architecture Adapted to the Style of Building in the United States, 1805, Benjamin Johnson, Philadelphia, and Ronalds & London, New York. Reprint 2006, Dover Publications, Inc.

2 good biographies of  Biddle: 1) the introduction to the Dover Edition of Biddle book by Bryan Clark Green. 2) an article by Micheal J. Lewis in  American Architects and Their Books to 1848, edited by Hafertepe and O'Gorman, 2001, U.Mass Press.

John Haviland and James Watt with their compasses

Portraits of master carpenters and architects with their compasses are part of my presentations: how I show people that we really did use geometry and compasses for design and layout.

I collect these images as someone else might collect old maps or historic recipes.



This is John Haviland, 1792-1852, an emigre to Philadelphia. He designed many Gothic inspired public works around Philadelphia.
The portrait is now in the NY Metropolitan Museum of Art. I have cropped it so his compass (which shines) can be clearly seen.

 Like Owen Biddle, Haviland taught 'carpenter's assistants' in Philadelphia. In 1833, 28 years after Biddle's death, he reprinted Biddle's pattern book.
He also wrote his own 3 volume pattern book, beginning in 1818. The Met has one copy; the other is in a library in Australia.I have not yet read it.








James Watt  (1736-1819) was a famous Scottish inventor and mechanical engineer.

Soon after he died Sir Francis Chantrey was asked to create this sculpture to honor him.
Watts is shown designing the double acting beam engine. a new and powerful steam engine which changed manufacturing. It drove machinery all over the world.
Note that he is designing with his compass.





This sculpture sits in the entry hall of the National Museum of Scotland in Edinburgh. It is on loan from the Heriot-Watt University in Edinburgh, named after him and George Heriot.
(Heriot (1563-1624) was a goldsmith who left his money to educate the orphaned sons of freemen in Edinburgh.)  

I had come to Edinburgh after presenting on Practical Geometry at the IPTW 2019 in Stirling, Scotland, September 5-7. I was enjoying the museum with friends, including a 3 yr old who needed to visit the sharks and dinosaurs, when I came upon James Watt.
What fun to share a 3 yr old's enthusiasm and come across one of mine in the process!

For an interesting look at James Watt and his world,  read this blog  written by an intern at the Engine Shed, the center (run by Historic Environment Scotland) where my IPTW conference had just been held.
https://blog.engineshed.scot/2019/06/17/5-things-james-watt/

The Geometry of Fences, c. 1830

Asher Benjamin's The Architect or Practical House Carpenter, published in 1830, includes a plate with 3 designs for fashionable fencing,  2 for gates. The lower drawing also includes a post.



While Benjamin includes a scale between the middle and the lower illustrations, he gives no other dimensions or information. He assumes the reader will know how to lay out the design.

The 2 right hand designs are repeated diagonals. quite simple to draw: cross your rectangle, lay in the horizontal and vertical center lines, embellish as you wish.
The bottom drawing is the fence for the gate above and shows the post and its ball.

What about the fence with curved balusters and the gate below it with rectangles and crosses?




First: the fence with curved balusters: 
The center of the rail is the center of the arc. The extended arc becomes a semi-circle  whose radius appears to be the distance to the edge of the bottom rail from the center and the height to the post below the ball and its base.

The arc determines the curve of the baluster. The circle using the same radius, centered on the baluster, follows the reverse curve. Both balusters are shown in red. 
Using Benjamin's scale the balusters could be cut from boards about 3 feet long and 8 inches wide. They are all the same shape.




The circles intersect  - see the vertical dashed lines in black. That intersection gives the spacing for the balusters.
Drawing the next circle using the point where the first circle's circumference crosses the center line, adding the vertical at the intersection, the placement for the balusters, noted in red. continues.
o







The gate seems at first glance to be more complex.

 
In my exploration I decided the size and the structure of the gate was known - its width, the framing members, the depth of the bottom rail. The black rectangle outline is what's left - the space for the fret work.
The diagonals are easy to draw - corner to corner. The space can be easily divided in half horizontally and vertically. I have not noted those lines.
But what about the inner rectangle?  The little corner squares?







Two radii are drawn; both A and B are arcs the height of the space, their centers are in the bottom corners, they arc from the top to the bottom - follow A and B's arrows.  They cross at C which is both the vertical center of the rectangle and the depth of the cross brace.







Reverse the arcs.  Now A and B land on the bottom rail  and mark the placement of the vertical braces. C marks the horizontal brace .







The horizontal and vertical braces are noted in red.

The rectangle of the space could be larger or smaller without changing the way the design developed or the general appearance. The proportions would still relate to each other.


The reader in 1830 - probably a house carpenter - would not have required my explanation to copy or adapt the  designs for his own use. He would have learned Practical Geometry as an apprentice. He would have read the design development automatically; he needed no words of explanation.
He might have drawn  his own small diagram on a board. Then he would have drawn the arcs full size on his framing floor - or table, as this is not very big - and found his lengths. The diagram would have remained until all the parts were made.


Plate XXXIII, Asher Benjamin's The Architect or Practical House Carpenter, 1830, L. Coffin, Boston. From the Dover Reprint first published in 1988.


This Asher Benjamin pattern book especially interests me because a diary was written by a local farmer in this period. Its author notes that his friend, a carpenter, traveled twice to Albany to buy his copy of the pattern book when it was first published. The details in several local houses seem to indicate that the joiner worked directly from Benjamin's plates.
 

Practical Geometry, Drawing the Diagrams #2, the 3/4/5 Triangle

Here's the second diagram I taught at the 2016 PTN Workshops.

I did not lay it out as I have done here. Today I think this diagram would have been a good handout.I could have drawn it; the participants could have followed along and had a cheat sheet to take home.

4/18/2017: this diagram is awkward. I will redraw and simplify.

Using the  3/4/5 triangle for construction

 3/4 5 triangles always have a 90* angle where the side with 3 units meets the side with 4 units.

Draw a line and mark off your unit.



Lay out lines of 3 units, 4 units and 5 units.
On my diagram:  A-B = 3 units
                            A-C = 4 units
                            B-D = 5 units

Swing an arc from either end of A-B; one arc with a 4 unit radius, one arc with a 5 unit radius,
Where the arcs cross is E.





Draw lines from A to B  to E to A.
This is a 3/4/5 triangle. The corner at A is 90*

For fun I have laid out another triangle beginning with 5 units, use 3 and 4 units for the radii of the arcs. It is another 3/4/5 triangle with a 90* corner.

We used Gunston Hall, built of brick by George Mason from 1755 to 1759, as an example. Mason  was a real mason; he gave George Washington advice about mortar recipes. He would have used the 3/4/5 triangle when he built walls or, as a Master Mason, instructed others. The triangle was/is one way to keep brick square and true.
It would have been ordinary for him to use 3/4/5 geometry to design his house.

The base of the brick work at Gunston Hall is 4 units. The height of the brick work of the end wall at Gunston Hall measures 3 units. The diagonal is 5 units.

The floor plan is also laid put using the 3/4/5 triangle. See my post for more information and drawings:  http://www.jgrarchitect.com/2014/05/gunston-hall-ason-neck-virginia.html

I asked the participants at the PTN session to divide the width of the Gunston Hall side elevation into 4 equal parts. I wanted them to draw the geometry for themselves, to see it come to life.

Again a handout with step by step instructions would have been helpful.   

Not everyone knew how to divide a line into parts; but those who did showed those who didn't. It was a excellent group.

One of the first figures in the pattern books on Practical Geometry is the division of a line by a perpendicular. Here is  Figure 5, Plate II, of  Asher Benjamin's The American Builder's Companion, first edition published 1806.











 Asher Benjamin's Figure 3, Plate II,  shows a
simply drawn 3/4/5 triangle expressed with units 6/8/10
with short arc lines at c, the top, to show the use of a compass to make a circle with the radius determined.

His description assumes a familiarity with the language of geometry and compasses.

"To make a perpendicular with a 10 foot rod. Let b a be 6 feet; take eight feet in your compasses; from b make the arch c, with the distance ten feet from a; make the intersection at c, and draw the perpendicular, c b. "

Practical Geometry - as described by those who used it, Part 2

The last post  discussed how Asher Benjamin and Owen Biddle presented Practical Geometry in their pattern books in 1805 and 1806.
This post focuses on Minard Lefever, and finally Peter Nicholson, who inspired them all.

Minard Lefever ( 1798-1854) wrote 5 pattern books between 1829 and 1856.
The Modern Builder's Guide was published in September 1833, in New York.
In his Preface Lefever says "...it will be proper to specify the authors whom I have either consulted or made extractions from,..."
One of these was Peter Nicholson.  Because Lefever copies Nicholson's drawings  directly I will post only the latter's introductory geometry.

Lefever writes 35 pages of  descriptions for 21 plates on "Geometry Adapted to Practical Carpentry".
Here are Plate 8  and Plate 20.


















Minard Lefever, The Modern Builder's Guide, NY, 1833, reprint by Dover Publications, NY, 1969.






Peter Nicholson (1765-1844) practiced architecture, mathematics, and engineering in Scotland.  He taught and wrote 27 books.  The Carpenter's New Guide was first  published in 1792 in Great Britain. His books were regularly reprinted in the States.

The book reproduced here was printed in Philadelphia in 1830, his 10th Edition with, he writes,"6 new Plates".  The book is 121 pages long not including the Index.
27 of those pages are of - as his title page says - Practical Geometry for Carpentry and Joinery, "the whole founded on the geometric principals; the theory and practice well explained and fully exemplified" on 10 copper-plates.

In the Preface he says, "...it is Geometry which lays down all the first principals of building, measures lines, angles, and solids, and gives rules for describing the various kinds of figures used in buildings; therefore, as a necessary introduction to the art treated of, I have first laid down, and explained in the terms of workmen, such problems of Geometry as are absolutely prerequisite to the well understanding and putting into practice the necessary lines for Carpentry."

His introductory geometry plates match those of Asher Benjamin, Owen Biddle and Minard Lefever, all of whom acknowledge him in their prefaces.

Nicholson's Plate 10 is Lefever's Plate 8.

I will bring this book to the 2016 IPTN Workshops in September. It is fragile.

If you would like to read the titles of Peter Nicholson's books, they are listed at the end of his Wikipedia biography.

Other architectural historians must have looked at the first pages of these books. Everyone cannot have just turned to the illustrations of mantles and window casings, building plans and elevations and ignored the plates on geometry. Why hasn't someone else wondered out loud why so many pages on geometry were included in a book about construction?

Someone must have considered that if Nicholson's The Carpenter's New Guide went through 10 editions and was published in the States as well as Great Britain - as well as being directly copied - that carpenters were reading it, using it, that his information was useful, that maybe we should understand what he wrote.

The builders who came before us used geometry to design and build. The knowledge was taught to the next generation hands-on. Books were not needed.
Boys were 'apprenticed', learned their craft and became 'journeymen', traveling to sites to earn and learn. Eventually these men became full carpenters, 'masters', and were admitted to a guild. The guild system was not always possible in the States. Men quit their apprenticeships. moved west or into cities. The skills and knowledge that masters were expected to impart had to be taught in other ways. Asher Benjamin and others set up a school in Boston. The pattern book was another solution - a way for 'young carpenters'  (to quote Owen Biddle) to teach themselves the necessary construction skills, beginning with geometry.

Part 1 can be read here: http://www.jgrarchitect.com/2016/08/practical-geometry-as-described-by.html