In Miletus, about 550 B.C., together with our world-picture cosmology was born. This book tells the story. In Part One the reader is introduced in the archaic world-picture of a flat earth with the cupola of the celestial vault onto which the celestial bodies are attached. One of the subjects treated in that context is the riddle of the tilted celestial axis. This part also contains an extensive chapter on archaic astronomical instruments. Part Two shows how Anaximander (610-547 B.C.) blew (...) up this archaic world-picture and replaced it by a new one that is essentially still ours. He taught that the celestial bodies orbit at different distances and that the earth floats unsupported in space. This makes him the founding father of cosmology. Part Three discusses topics that completed the new picture described by Anaximander. Special attention is paid to the confrontation between Anaxagoras and Aristotle on the question whether the earth is flat or spherical, and on the battle between Aristotle and Heraclides Ponticus on the question whether the universe is finite or infinite. (shrink)

In ancient tradition, Pythagoras emerges as a wise teacher, an outstanding mathematician, an influential politician, and as a religious and ethical reformer. This volume offers a comprehensive study of Pythagoras, Pythagoreanism, and the early Pythagoreans through an analysis of the many representations of the individual and his followers.

Plato's geometrical theory of what we now call chemistry, set out in the Timaeus, uses triangles, his stoicheia, as the fundamental units with which he constructs his four elements. A paper claiming that these triangles can be divided indefinitely is criticized; the claim of an error here in the commentary by F.M. Cornford is unfounded. Plato's constructions of the elements are analyzed using simple point group theory. His procedure generates fully symmetric polyhedra, but Cornford's 'simpler' alternatives generate polyhedra with low (...) symmetries and multiple isomeric forms. However, Cornford's principle of constructing larger triangles by assembling smaller ones is still valid. (shrink)

It probes the work of Pythagoras, Galileo, Berkeley, Einstein, and others, exploring how "number magic" has influenced religion, philosophy, science, and mathematics.

What ought we to make of Aristotle's apparently disparate comments on bodies in motion? I argue that Aristotle is concerned with a higher level project than dynamics and that is the establishment of a coherent theory of change in general. This theory is designed to avoid the paradoxes and infinities that Aristotle finds in Eleatic, Heraclitean and atomist accounts, notably in relation to comparatives such as 'quicker' and 'slower'. This theory relies on a broad application of proportionality to all types (...) of change, not merely those we would label 'dynamics'. To support this I argue that Aristotle denied the existence of the void and the possibility of instantaneous change, and that he could accommodate 'threshold' changes within his scheme. If this is so, then the aims of Aristotle's comments on motion become more comprehensible, and it will be understandable why Aristotle was more concerned with the application of proportionality in general rather with the investigation of specific cases in dynamics. (shrink)