Euclid lived around 300 bC and published his Elementa (Gr. Stoicheia) as an overview of a specific kind of mathematical knowledge dating back to the Babylonian, Egyptian and earlier Greek thinkers as Thales and Pythagoras. Although it could be called a ‘state of the art’ at the time it was published, it remained intellectually the dominant approach until the later part of the 19th century – and in everyday didactics it
is still dominant. The way his work was and is kept is a good example of a codification of a certain approach, almost a cultural monopoly.
The relation with bodily movement can be seen throughout history in the geometrical design of disciplinary organizations of human bodies and their movements, beginning in the earliest monasteries, later in armies and social institutions such as homes for the poor, orphanages and schools. This aimed primarily at becoming disciplined into a well functioning member/ part of a group-body.
The Euclidian approach has been develop into mechanics by Archimedes from Syracuse (280-212 bC) who studied with followers of Euclid in Alexandria but developed into a more original worker. Not only did he invent the integral calculus, but he also experimented constantly and is widely remembered because of his many discoveries and practically oriented physical ‘laws’. He ran out of his bathtub, naked through the streets of Syracuse, shouting ‘Eureka’ (‘I have found it’) after he had discovered what has been called ‘The law of Archimedes’, while taking a bath. He also began to discover the specific weight of distinct metals and was an inventor of many practical devices (such as the screw of Archimedes), the compound pulley and war-machines that helped to ward of the Roman attack on Syracuse for three years, until they captured Syracuse and killed him.
There are some interesting examples of how movement is forcefully generated by arrangement of points and lines: the screw of Archimedes (which is still used for irrigation) turns in a straight line around one point.