Definitions of the properties of circles, 1847.
© Science Museum / Science & Society Picture Library
Diagrams illustrating: 1) Equal circles are those whose diameters are equal. 2) A right line is said to touch a circle when it meets the circle, and being produced does not cut it. 3) Circles are said to touch one another which meet but do not cut one another. 4) Right lines are said to be equally distant from the centre of a circle when the perpendiculars drawn to them from the centre are equal. Book 3 from 'The first six books of the Elements of Euclid: in which coloured diagrams and symbols are used instead of letters for the greater ease of learners' by Oliver Byrne, published in London in 1847. Euclid's (330-275 BC) achievements are impresive, given that there was little algebra or arithmetic at the time, and limited understanding of infinity.