How did Lucretius know about atoms?

Lucretius, answered from the texts and cited to the page.

Lucretius answers

You ask how I knew of atoms, and I will answer as I answer Memmius: I did not see them, and I do not pretend to. What I saw is the thing that points to them. Let rays of the sun be let into a darkened house, and you will watch many tiny bodies mingle in many ways through the empty space, right in the light, as though in some everlasting strife they waged war and battle, troop against troop, harried with constant meetings and partings.¹

That is a likeness and image ever passing before our eyes, and a little thing can give a picture of great things and afford traces of a concept.¹ Look then at what those motes do. You see many of them stirred by unseen blows change their course and turn back, driven now this way, now that, in every direction.² The blows are not seen, and yet the dust is shoved.

So I reason from what the eyes can bear witness to toward what they cannot. The first-beginnings move of themselves; the bodies formed of a tiny union, nearest to their powers, are smitten by their unseen blows; these rouse bodies a little larger; and so the movement climbs upward and comes forth at last to our senses.² The mote you can see is moved by a cause you cannot, and the cause must be a body too small for sight.

I knew them also by what they must be if anything is to endure. The senses are only the beginning of the road, and the keen mind can come to know what the eyes cannot descry, just as it can know what is devoid of colour or smell.³ And if things are created mortal, soft or brittle or hollow, then immortal foundations must be placed beneath them, lest you see all things pass away utterly into nothing.³

The doctrine is Epicurus's, and I follow in his footprints; what I have added is the Latin and the song. But the proof is open to any man who will stand in a sunbeam and look.

Sources

For look closely, whenever rays are let in and pour the sun's light through the dark places in houses: for you will see many tiny bodies mingle in many ways all through the empty space right in the light of the rays, and as though in some everlasting strife wage war and battle
On the Nature of Things, pp. 69–70
For you will see many particles there stirred by unseen blows change their course and turn back, driven backwards on their path, now this way, now that, in every direction everywhere.
On the Nature of Things, pp. 69–70
yet that the keen mind can come to know them no less than it can mark those devoid of other things.
On the Nature of Things, pp. 94–95