Lesson 6: The Rule of Thirds, Part 1of 2

 

The Rule of Thirds is what artists call the grid that appears on your cell phone. It helps you compose and edit.

A variation of this is used in Practical Geometry. 

 

 

 

 

 

Sebastiano Serlio used this diagram in his book, On Architecture, published  in 1545.  He writes simple instructions for the reader; he says to construct the 'lines'. 

Note that the triangle (with its base at the bottom of the drawing) intersects the diagonals at the the upper corners of the door.  The width of the square is divided into thirds.  

Check how the division into thirds in the square above this drawing  lines up with those intersections.  Serlio is using a a variation of the Rule of Thirds.

 

 

Like Owen Biddle (see Lesson 5) Serlio sets out basic Geometry as used in construction in Book 1.

Then he explains how to solve problems.  He does not show how he knows where to draw the lines shown above. He assumes the reader knows. 

 Here are the instructions:

 

Draw a square;

Add the diagonals to your square. Where they cross in the center. You have point 1.  

 

 

 

 

 

 

Divide one side of your square in half. Now you have  points 1 and 2.
With 2 points you can draw a line.

 

 

 

 

 

      

Add diagonals in each new rectangle.            

 

 

 

 

 

 

 Add the diagonals from the square.                                            

If you were drawing this for a construction project on wood, on masonry, or on paper, you would not have separate squares.  All lines would be on your first square.  I have drawn each step without the extra lines for clarity.

Do you see that the center line does not pass through the intersection of the diagonals? If you were the builder you would know that your diagonals will match when the line in centered. In this diagram they don't. So you would move  your center line.

This is the diagram for Serlio's drawing for the door.

 

 For the Rule of Thirds (as we know it today) add the diagonals for the rectangles on both sides of the square.            

Note that you have intersections (4 points) not just where the lines  divide the square into smaller squares, but where the diagonals cross those lines.  2 points above the horizontal center line and 2 points below. Or: 2 on the right side of the vertical center line and 2 on the left.

I have deliberately not added black points where the lines cross. You who are reading this will see it more clearly if you find those points yourself. 

 

Connect those new points and extend the lines across the square. 
You have drawn the Rule of Thirds.

 

 

 

   

Similar diagonals could be drawn from the left to the right side and vice versa. 

 I drew all the diagonals on graph paper to make it easier to follow.  The next lines to add would be the diagonals of the small squares.
The line does not come back to its beginning until it has continued through the complete pattern. 

 

 

A post on Serlio. https://www.jgrarchitect.com/2017/04/serlio-writes-about-practical-geometry.html 

 

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 

 

English Construction Tools, 1669

John Leeke translated Giacomo Barozzi da Vignola's Regola delli cinque ordini from Italian into English in 1669.

While Leeke himself is worth attention; he was a mathematician, a professor, and land surveyor and well as fluent in Italian. He also helped rebuild London after its disastrous fire in 1666.  Here I want to focus on the frontispiece for his translation.

Leeke calls the translation
THE REGULAR ARCHITECT
He adds Vignola's title.

Then he writes
For the USE and BENEFIT of
Free Masons, Carpenters, Joyners, Carvers, Painters,    Bricklayers Plaisterers:
In General
For all Ingenious Persons that are concerned in the Famous Art of BUILDING 


This cartouche fills half the frontispiece. It celebrates the tools used by all those craftsmen.
Sitting on a column base are:
A compass
A carpenter square
A horizontal level
A vertical level
A measure with a curved side and regular marks
Draped around the cartouche is a Line, its spool on one end, its plumb bob on the other.

These are the tools for people who built.



130 years earlier most of the same tools are on Serlio's frontispiece which he engraved about 1540, for his book, On Architecture.
The original is black and white. This cartouche is on the cover of the 1998 translation by Hart and Hicks.
I use the color image because it makes the tools easier to see:

A compass in front of a ring - a perfect circle.
The compass pierces the scroll of the cartouche and is held in place by the ring.
A large carpenter square spearing a tetrahedron
A straight edge spearing a cube incised with diagonals, graduated circles and squares. The size of each is determined by those on either side.
A round rule pierces both the tetrahedron and the cube.
A Line with a handle is in the lower left corner, entangled in the scrolling, ending with a knot and a tassel beside the handle.
Serlio does not include any levels.



 Walther Hermann Ryff, of Nuremberg, c. 1500- 1548, considered Serlio his mentor. He did not train under him.
Ryff was probably a pharmacist and published many works on medicine.

He also published Vitruvius first in Latin and then in German 1548.
This book, with a title of over 30 words, is referred to as Architecture. Part of the title says it is "The hardest, most necessary, belonging to the whole architecture of mathematical and mechanical art, regular report, and vastly clear, understandable information..."
 
This engraving is the frontispiece for his book. Many tools!
4 compasses are easily seen. 
Here's a close up of one, with an impressive arm that would have guaranteed accuracy - along with a knife, a plane, and calipers. 

Edward Shaw published his pattern book, The Modern Architect, in 1854, in Boston. It also had a frontispiece displaying tools,.
His engraving is in black and white: The color rendering is for clarity.

He includes:
A small compass in hand
A rule in hand
A large compass in the foreground
A hammer.
A large carpenter square
A cylinder which might be a chalk line
A saw in hand
A drawing and a portfolio of drawings
against the tool box:
A straight edge or rule
A vertical level
A brace is in the tool box.




A part of the original engraving showing most of the tools.

 The 12 presentations and workshops I gave this past year began with the portraits of master builders holding their compasses, and these engravings of their tools.
When my audience understood what tools were available before the Industrial Revolution they enjoyed seeing how a compass and a straight edge could layout a  rectangle, and then a building. Next they drew them themselves. They saw for themselves how the compass creates the first dimension and determines the next dimensions.
    
Practical Geometry was the tool  which translated a design from an idea to construction.  It was the Practical, not Theoretical, use of Geometry.

   



Note: our contemporary John Leeke is the 8th great-grandson of the man mentioned above. Yes, I asked and he told me so.