## Tuesday, August 25, 2020

## Friday, August 21, 2020

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

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.

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

## Thursday, August 6, 2020

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

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.

**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'.**

**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.

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

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

**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.