Among the most famous was Pythagoras ( 560 BC ) who is credited with the rule of the squares of the sides of a right-angled triangle, which he almost certainly learned as a young man during his travels in Egypt and Babylonia. He noticed the mathematical relationship between notes of the musical scale and the length of 'pan-pipes' and also that there were definite numerical relationships between the periods of the orbits of the various celestial bodies 'around the earth'. The Pythagoreans discovered irrational numbers ( such as pi ) and three of the five regular solids ( cube, pyramid and dodecahedron ). They placed the known planets in order of distance from the earth based on on their periods - Earth as centre ( obviously ! ) followed by the Moon,Mercury,Venus,Mars,Jupiter and Saturn. The planets Uranus, Neptune and Pluto were not discovered until modern times; after the invention of the telescope, although technically, Uranus could have been seen without one and probably was!) The Pythagoreans believed that the most perfect shape was that of the sphere and naturally, they assumed that everything in heaven was perfect and unchanging. The planets moved in perfect, crystal spheres around the earth, which was corrupt and immovable at the centre of the Universe. They also believed in a musical aspect to the heavens; the Music of the Spheres was to have a profound effect on the thinking of Johannes Kepler, the German mathematician who solved the problem of planetary orbits, in his book Harmonica Mundi, published in 1618.
Democritos ( 460 BC ) taught that solid matter is made of indivisible and invisible 'atoms' which are perpetually in motion. The world was thus composed of lumps of matter in a sea of emptiness - the void. Collections of atoms were thought to 'gravitate' together as a result of a 'vortex' formed between them ; even the idea of spherical bubbles of atoms or universes beyond our own was considered. Unfortunately, although close to our own ideas about matter, the theories of the atomists failed to replace those of Empedocles, who introduced the four 'elements' - earth, air,fire and water - as the 'roots of all things' and the two forces, love and hate. Empedocles saw the universe as a crystal sphere studded with lumps of fire - the stars - although he did realise that the Moon shone by reflecting the light of the Sun. He taught that light takes time to travel through space (a result that was not confirmed until 1675 by Ole Romer). He also discussed light and vision, taking the view that luminous bodies emit something which meets rays from the eyes. He even had a theory of the creation of the universe not unlike that of our own Big Bang theory.
The elemental theory persisted, in the form of alchemy, into the late 17th century and beyond. It was present in the philosophy of Aristotle ( 384 - 322 BC ) who believed in the natural place and natural motion of all things. Objects fall to the ground because of their 'gravity' while smoke rises because of its 'levity'. The natural place of 'earthy' materials was at the centre of the earth; the more of the earth-element a body contained, the harder it strove to get there. Thus, according to Aristotle, heavier objects would fall to the ground faster than lighter ones. Water spreads over the ground because that is its natural place. Air covers the earth like a blanket and fire belongs above air, hence fire burns upwards. This was a beautifully logical non-theory which explained everything without explaining anything. It was Galileo's vehement criticism of this patently absurd theory of Aristotle's which was to bring him into so much conflict with the established body of learning , particularly over Aristotle's theory of moving bodies. In Aristotle's view, a force was always needed to produce what he termed 'forced' motion as opposed to natural motion. Thus a projectile flew through the air under the action of a force, returning to the ground only when this force was expended. This caused problems to gunners trying to apply the theory to cannonballs in the 16th century and it was eventually proved to be incorrect by the work of Galileo and Newton. It is surprising how many people even today still cling to the Aristotelian belief that a force is needed to keep something in motion.
In Aristotle's universe, the stars and other celestial bodies moved in perfectly circular paths on concentric crystal spheres centred on the earth. The force needed to keep the spheres in motion was provided by the outermost sphere of the stars or 'Prime Mover'. He even suggested that behind this sphere an 'unmoved mover' drove the whole system, thereby invoking some kind of divine intervention. The earth was at the centre of a finite universe - how could there be a centre to infinity after all ? That the earth did not move was apparent from the absence of rushing winds or the unsteadiness which would result - nor was it spinning about an axis, or objects released from a height would not fall vertically to the ground ( this of course is exactly what does happen ! ). The fact that these 'theories' were accepted unchallenged reveals that the Greeks placed greater authority in the thoughts that came into their conscious minds than they did in the evidence of their other senses, although the degree of accuracy needed to test them was probably beyond their capability to measure. They did not, however, quite believe that the earth was flat - later 'wise men' would promote this particular idea. That the earth was round could be ascertained from the way the masts of ships disappeared over the horizon, and from the shape of the earth's shadow as it eclipsed the Moon. Besides, the symmetry of a spherical universe was too beautiful to be upset by a non-spherical earth ( the earth in fact is not perfectly spherical - it has a pronounced equatorial bulge and is in fact slighlty pear-shaped ).
Aristotle laid the foundations of logical deduction and, as a zoologist, he was second to none; he classified over 500 types of mammals and dissected many of them and their embryos. He was more of a scientist than his tutor Plato, who followed the teaching of Socrates ( 470 - 399 BC ) who favoured abstract theoretical arguments over careful investigation of phenomena and the formulation of hypotheses to explain them. Plato's theory of 'Realism' holds that the natural world does not provide a reliable guide to the true or perfect reality, which can only be discovered through contemplation or revelation ( in this respect it is similar to the teachings of Islam). To Plato experiment and observation were not only irrelevant but positively misleading in the search for knowledge.It did not seem that observations should be checked or that results could be obtained from them by the use of mathematics.
However, later Greek 'scientists' such as Eratosthenes ( 235 BC ) succeeded in measuring the circumference of the earth and Hipparchos ( 150 BC ) compiled the first star catalogue in the western world. He discovered the precession of the equinoxes, measured the distances of the Sun and Moon and established the length of the year as 365.2467 days ( it is actually 365.2422 days long ). Aristarchos of Samos ( 310 - 230 BC ) also measured the Sun and Moon distances, although not very accurately, but he did put forward the first 'heliocentric' theory of the solar system. He could not however, account for the failure to observe the apparent shift in position ( parallax ) of the stars which should result from the earth's motion. This is not surprising for the simple fact that the stars are so far away that their parallax is always less than one second of arc; to measure it required the invention of the telescope and very accurate observations which were not successful until F W Bessel measured the parallax of the faint star 61 Cygni in 1838. The time of the heliocentric theory was not yet - it would have to wait another 17 centuries before a Polish canon named Niklas Koppernigk ( Copernicus ) could revive it.