Leucippus is beleived to have lived in the 5th Century BC.
Today, science and philosophy are clearly separated disciplines but the the classic Greek philosophers practiced both disciplines at the same time and findings in one disciplines had direct repercussions on the other and both views had to be consistent with one another. In other words, a Greek philosopher could not profess a scientific view of the world as being completely material and in philosophy believe in gods existing on another universe on the other.
Leucippus was an atomist meaning that for him the the world is constituted of atoms, void and movement, nothing more.
Although this world view is simple, it has major implications.
The world is populated by what he called simulacrums which are atoms circulating in the void. These simulacrums detach themselves from the objects of which they are originally part of and circulate around in the void.
For example when someone speaks, what you are hearing is the result of simulacrums that have detached themselves from the speaker and have hit you.
This has major implications because the consequence of this world view is that the world as we know it is in it’s entirely material. There are no gods and souls, or rather if there are such things, they are material, they are not part of another realm or dimension but exist in the same world as ours, are governed by the same laws as us humans.
As are all humans, animals and things, gods and the soul are constituted by atoms, they are material and not as Plato will state, and after him all religions, on another existential plane altogether.
In other words, contrarily to Plato, Leucippus states that there is no dualism, immaterial soul and gods on one plane and body and material things on another. His view of the world is immanent, everything that exists does so on the same plane.
So, the soul and gods (the Greeks were polytheists) are not governed by principles that would be different from our world, but are part of it and governed by the same rules.
In consequence the world and what happens cannot be explained by saying that the Gods wanted things to happen so and that being in another universe we humans cannot understand their purpose,
It also means that since the rules that govern our existence do not have their origin in a different world we should be able to understand them and find rational explanations.
Another consequence, is that since the Gods do not really govern our existence and destiny, then we can directly change our destiny and we are, up to a certain point, responsible for what happens to us.
And of course there is no transcendence. For the atomists, you don’t look for explanations by looking upwards to another world or realm but you are rather looking horizontally in your own world for explanations.
The object of Greek classical philosophy was to make man as happy as possible. In other words, Greek philosophy was a practical philosophy. It’s purpose was not to create conceptual constructions (as will later happen specially starting with Hegel) but to give man a modus operandi on how to be as happy as possible in his life.
This meant that the philosophy one was adhering to had visible effects in his life. You could not profess to be a cynic and act as a idealist.
Today it is perfectly possible to profess one philosophy and act totally the opposite. The best example that comes to mind would be Marx who, as everyone knows, was professing power for the workers, but lived in an expensive house in London, with servants and who insisted that his wife’s noble title be printed on his name card.
This visibility of philosophy in life translated itself in all aspects of life such as diet and clothing.
Pythagoreans for instance conveyed the sense of purity that was their philosophy by always wearing clean white clothes, while cynics tended to wear always the same clothes for several year, never washing and appearing rather filthy.
To become a happy man, three basic principles must be observed:
Be a peace with yourself
Be at peace with others
Be at peace with the world