The principles of geometry were recorded in a series of *theorems* expounded by the Greek mathematician Euclid around 300 BCE. One of the first principles he alludes to is a process of dividing a straight line into two equal parts. This is done by taking the line, AB, and drawing two circles of equal diameter, one circle at each end of the line, so that they overlap.

Drawing a vertical line between the points C & D will bisect the line AB into two equal lengths. This concept can be taken one stage further when the circles, both of equal diameter, are drawn such that the circumference of one circle touches the centre of the other circle. This geometric pattern was well known to the ancients and has been passed down to us with the title *Vesica Piscis*. The resultant area where the two circles overlap is known as the *Vesica*.

It produces some interesting characteristics. For example, it is possible from this use of the two circles to determine an angle of 30° and 60°. This is shown in the diagram below

This simple geometric structure immediately lends itself to the construction of another important figure -the equilateral triangle.

So, our ancestors, through their knowledge of geometry, were able to produce, with considerable accuracy, the three most common geometric forms in their construction armoury -the circle, the square and the equilateral triangle -the latter two being derived from the basic form -the circle.