The atomic theory was not generally accepted in the time of Democritus, largely because of its deterministic character, for it allows no chance, choice, or free will.

One thing of course was a fundamental necessity to the atomic world-view. There must be empty space for the atoms to move about in. The hallmark of Democritus’s thought, as Aristotle noted approvingly, was a determination to account for apparent fact and not be led astray by abstract argument. Hence he said that Parmenides’s denial of the existence of void could not be upheld. It was contrary to common sense. Aware however that he was flying in the face of that great authority, he made his denial with a kind of schoolboy daring, for according to Aristotle he put it in the form: ‘What is not does exist, no less than what is.’ If material atoms were the only real substance, then empty space was not real in the same sense. Dimly aware that there must be some way out, the atomists did not yet command a language capable of such a phrase as ‘not in the same sense’, and paradox was their only resource.

Eudoxes... not only based the method [of exhaustion] on rigorous demonstration... but he actually applied the method to find the volumes (1) of any pyramid, (2) of the cone, proving (1) that any pyramid is one third part of the prism which has the same base and equal height, and (2) that any cone is one third part of the cylinder which has the same base and equal height. Archimedes, however, tells us the remarkable fact that these two theorems were first discovered by Democritus, though he was not able to prove them (which no doubt means, not that he gave no sort of proof, but that he was not able to establish the propositions by the rigorous methods of Eudoxes. Archimedes adds that we must give no small share of the credit for these theorems to Democritus... another testimony to the marvellous powers, in mathematics as well as in other subjects, of the great man who, in the words of Aristotle, "seems to have thought of everything". ...Democritus wrote on irrationals; he is also said to have discussed the question of two parallel sections of a cone (which were evidently supposed to be indefinitely close together), asking whether we are to regard them as equal or unequal... Democritus was already close on the track of infinitesimals.

[http://plato.stanford.edu/entries/democritus/ Democritus in Stanford Encyclopedia of Philosophy]

Fortune is lavish with her favors, but not to be depended on. Nature on the other hand is self-sufficing, and therefore with her feebler but trustworthy [resources] she wins the greater [meed] of hope.

In the weightiest matters we must go to school to the animals, and learn spinning and weaving from the spider, building from the swallow, singing from the birds,—from the swan and the nightingale, imitating their art.

Men have made an idol of luck as an excuse for their own thoughtlessness. Luck seldom measures swords with wisdom. Most things in life quick wit and sharp vision can set right.

Neither art nor wisdom may be attained without learning.

It is better to correct your own faults than those of another.

Those who have a well-ordered character lead also a well-ordered life.

Good means not [merely] not to do wrong, but rather not to desire to do wrong.

There are many who know many things, yet are lacking in wisdom.

Fame and wealth without wisdom are unsafe possessions.

Making money is not without its value, but nothing is baser than to make it by wrong-doing.

You can tell the man who rings true from the man who rings false, not by his deeds alone, but also by his desires.

False men and shams talk big and do nothing.

My enemy is not the man who wrongs me, but the man who means to wrong me.

The enmity of one's kindred is far more bitter than the enmity of strangers.

The friendship of one wise man is better than the friendship of a host of fools.

No one deserves to live who has not at least one good-man-and-true for a friend.

Seek after the good, and with much toil shall ye find it; the evil turns up of itself without your seeking it.

For a man petticoat government is the limit of insolence.

(Democritus said he would rather discover a single demonstration than win the throne of Persia.)

[http://www.iep.utm.edu/democrit/ Democritus in The Internet Encyclopedia of Philosophy]

Immoderate desire is the mark of a child, not a man.

An evil and foolish and intemperate and irreligious life should not be called a bad life, but rather, dying long drawn out.

δοκεῖ δὲ αὐτῶι τάδε· ἀρχὰς εἶναι τῶν ὅλων ἀτόμους καὶ κενόν, τὰ δ'ἀλλα πάντα νενομίσθαι [δοξάζεσθαι]. (Diogenes Laërtius, Democritus, Vol. IX, 44)

νόμωι (γάρ φησι) γλυκὺ καὶ νόμωι πικρόν, νόμωι θερμόν, νόμωι ψυχρόν, νόμωι χροιή, ἐτεῆι δὲ ἄτομα καὶ κενόν (Tetralogies of Thrasyllus, 9; Sext. Emp. adv. math. VII 135)

We know nothing accurately in reality, but [only] as it changes according to the bodily condition, and the constitution of those things that flow upon [the body] and impinge upon it.

Medicine heals diseases of the body, wisdom frees the soul from passions.

Coition is a slight attack of apoplexy. For man gushes forth from man, and is separated by being torn apart with a kind of blow.

Πολλοὶ πολυμαθέες νοῦν οὐκ ἔχουσιν.

Good breeding in cattle depends on physical health, but in men on a well-formed character.

Man is a universe in little [Microcosm].

Now, that we do not really know of what sort each thing is, or is not, has often been shown.

Now, that we do not really know of what sort each thing is, or is not, has often been shown.

Verily we know nothing. Truth is buried deep.

In fact we do not know anything infallibly, but only that which changes according to the condition of our body and of the [influences] that reach and impinge upon it.

There are two forms of knowledge, one genuine, one obscure. To the obscure belong all of the following: sight, hearing, smell, taste, feeling. The other form is the genuine, and is quite distinct from this. [And then distinguishing the genuine from the obscure, he continues:] Whenever the obscure [way of knowing] has reached the minimum sensibile of hearing, smell, taste, and touch, and when the investigation must be carried farther into that which is still finer, then arises the genuine way of knowing, which has a finer organ of thought.

Of practical wisdom these are the three fruits: to deliberate well, to speak to the point, to do what is right.

He who intends to enjoy life should not be busy about many things, and in what he does should not undertake what exceeds his natural capacity. On the contrary, he should have himself so in hand that even when fortune comes his way, and is apparently ready to lead him on to higher things, he should put her aside and not o'erreach his powers. For a being of moderate size is safer than one that bulks too big.

If any one hearken with understanding to these sayings of mine many a deed worthy of a good man shall he perform and many a foolish deed be spared.

If one choose the goods of the soul, he chooses the diviner portion; if the goods of the body, the merely mortal.

'Tis well to restrain the wicked, and in any case not to join him in his wrong-doing.

'Tis not in strength of body nor in gold that men find happiness, but in uprightness and in fulness of understanding.

Repentance for one's evil deeds is the safeguard of life.

He who does wrong is more unhappy than he who suffers wrong.

'Tis a grievous thing to be subject to an inferior.

Many who have not learned wisdom live wisely, and many who do the basest deeds can make most learned speeches.

And yet it will be obvious that it is difficult to really know of what sort each thing is.