Basic constructions
David Clayton in his book The Way of Beauty explains: “Quaternity represents the earth, or the entire material order, and is manifested as a square. The four traditional ‘elements‘ of earth, water, air and fire seem to correspond […] to the four basic states of matter which we call solid, liquid, gas and energy.” He later recounts how in the book of Genesis “the river of Eden splits into four heads, supplying the world’s rivers”, and how there are four Evangelists “whose foundational writings are spread throughout the four corners of the world.”
The square, along with the equilateral triangle, form the base grids of Cosmatesque ornaments. The quincunx is constructed from a square and the square allows divisions needed for the patterns.
The instructions in this tutorial will explain the drawing process of a square in what I was taught to call its static and dynamic variants.
The square is built out of a circle and its construction commences where the Vesica Piscis has ended.
A static square and a dynamic square inscribed within.
Materials:
compass
30cm ruler
H or 2H pencil
A4 printer paper
card or cutting mat
eraser
Notes:
Please follow instructions for the Vesica Piscis and then continue with the steps below on the same drawing
The Vesica Piscis construction will be shown in lighter grey
please use the contact button should you have any queries or would like to share your work
1) Find the two intersections where the vertical line cuts the circle circumference and name these points E and F.
2) Place the compass needle at point A and stretch the other compass leg to point Z. With radius AZ mark an arch, approx. 2/3 of a circle.
3) Place the compass needle at point E and, with the same radius AZ, mark an arch like the previous.
4) Place the compass needle at point B and, with the same radius AZ, mark an arch like the two previous.
5) Place the compass needle at point F and, with the same radius AZ, mark an arch like the three previous.
6) There should now be visible a flower shape with 4 petals and with its centre at point Z.
7) Starting top left, and going clockwise, name the petal tip points: G, H, I and J.
8) With a horizontal line join point G with point H.
9) With a vertical line join point H with point I.
10) With a horizontal line join point I with point J.
11) With a vertical line join point J with point G.
12) This completes the construction of a static square.
13) With a diagonal line join point E with point B.
14) With a diagonal line join point B with point F.
15) With a diagonal line join point F with point A.
16) With a diagonal line join point A with point E.
17) This completes the construction of a dynamic square within the static square.
18) The dynamic square within a static square construction has four isosceles-right-triangles, one in each corner. An arrangement used in Cosmatesque ornaments.