The Stanford site has a good summary of the poem, Lucretius, and recent scholarship.
Here is an MIT site with a full translation of the poem. Below I copy a few passages that are of particular interest in Book I, concerning evidence for atoms (here, Lucretius calls them ‘germs’ or ‘seeds’, which are eternal, and remain true to type):
[N.B. The argument that knowledge and understanding of how the world works can liberate us from fear of the gods, and the argument for existence of the seeds.]
Substance is Eternal
This terror, then, this darkness of the mind,
Not sunrise with its flaring spokes of light,
Nor glittering arrows of morning can disperse,
But only Nature’s aspect and her law,
Which, teaching us, hath this exordium:
Nothing from nothing ever yet was born.
Fear holds dominion over mortality
Only because, seeing in land and sky
So much the cause whereof no wise they know,
Men think Divinities are working there.
Meantime, when once we know from nothing still
Nothing can be create, we shall divine
More clearly what we seek: those elements
From which alone all things created are,
And how accomplished by no tool of Gods.
Suppose all sprang from all things: any kind
Might take its origin from any thing,
No fixed seed required. Men from the sea
Might rise, and from the land the scaly breed,
And, fowl full fledged come bursting from the sky;
The horned cattle, the herds and all the wild
Would haunt with varying offspring tilth and waste;
Nor would the same fruits keep their olden trees,
But each might grow from any stock or limb
By chance and change. Indeed, and were there not
For each its procreant atoms, could things have
Each its unalterable mother old?
But, since produced from fixed seeds are all,
Each birth goes forth upon the shores of light
From its own stuff, from its own primal bodies.
And all from all cannot become, because
In each resides a secret power its own.
[N.B. The argument for discreteness of the seeds.]
“Nor nothing to nothing evermore return.
And, too, the selfsame power might end alike
All things, were they not still together held
By matter eternal, shackled through its parts,
Now more, now less. A touch might be enough
To cause destruction. For the slightest force
Would loose the weft of things wherein no part
Were of imperishable stock. But now
Because the fastenings of primordial parts
Are put together diversely and stuff
Is everlasting, things abide the same
Unhurt and sure, until some power comes on
Strong to destroy the warp and woof of each:
Nothing returns to naught; but all return
At their collapse to primal forms of stuff.”
[…]
[N.B. Examples of things not seen, yet still real as revealed by the senses.]
“Thus naught of what so seems
Perishes utterly, since Nature ever
Upbuilds one thing from other, suffering naught
To come to birth but through some other’s death.
And now, since I have taught that things cannot
Be born from nothing, nor the same, when born,
To nothing be recalled, doubt not my words,
Because our eyes no primal germs perceive;
For mark those bodies which, though known to be
In this our world, are yet invisible:
The winds infuriate lash our face and frame,
Unseen, and swamp huge ships and rend the clouds,
Or, eddying wildly down, bestrew the plains
With mighty trees, or scour the mountain tops
With forest-crackling blasts. Thus on they rave
With uproar shrill and ominous moan. The winds,
‘Tis clear, are sightless bodies sweeping through
[…]
Then too we know the varied smells of things
Yet never to our nostrils see them come;
With eyes we view not burning heats, nor cold,
Nor are we wont men’s voices to behold.
Yet these must be corporeal at the base,
Since thus they smite the senses: naught there is
Save body, having property of touch.
And raiment, hung by surf-beat shore, grows moist,
The same, spread out before the sun, will dry;
Yet no one saw how sank the moisture in,
Nor how by heat off-driven. Thus we know,
That moisture is dispersed about in bits
Too small for eyes to see. Another case:
A ring upon the finger thins away
Along the under side, with years and suns;
The drippings from the eaves will scoop the stone;
The hooked ploughshare, though of iron, wastes
Amid the fields insidiously. We view
The rock-paved highways worn by many feet;
And at the gates the brazen statues show
Their right hands leaner from the frequent touch
Of wayfarers innumerable who greet.
We see how wearing-down hath minished these,
But just what motes depart at any time,
The envious nature of vision bars our sight.
Lastly whatever days and nature add
Little by little, constraining things to grow
In due proportion, no gaze however keen
Of these our eyes hath watched and known. No more
Can we observe what’s lost at any time,
When things wax old with eld and foul decay,
Or when salt seas eat under beetling crags.
Thus Nature ever by unseen bodies works.”
[N.B.The atomistic theory also solves the problem of motion by introducing the Void.]
“The Void
But yet creation’s neither crammed nor blocked
About by body: there’s in things a void-
Which to have known will serve thee many a turn,
Nor will not leave thee wandering in doubt,
Forever searching in the sum of all,
And losing faith in these pronouncements mine.
There’s place intangible, a void and room.
For were it not, things could in nowise move;
Since body’s property to block and check
Would work on all and at an times the same.
Thus naught could evermore push forth and go,
Since naught elsewhere would yield a starting place.
But now through oceans, lands, and heights of heaven
By divers causes and in divers modes,
Before our eyes we mark how much may move,
Which, finding not a void, would fail deprived
Of stir and motion; nay, would then have been
Nowise begot at all, since matter, then,
Had staid at rest, its parts together crammed.
On the infinity of worlds…
Once more, we all from seed celestial spring,
To all is that same father, from whom earth,
The fostering mother, as she takes the drops
Of liquid moisture, pregnant bears her broods-
The shining grains, and gladsome shrubs and trees,
And bears the human race and of the wild
The generations all, the while she yields
The foods wherewith all feed their frames and lead
The genial life and propagate their kind;
Wherefore she owneth that maternal name,
By old desert. What was before from earth,
The same in earth sinks back, and what was sent
From shores of ether, that, returning home,
The vaults of sky receive. Nor thus doth death
So far annihilate things that she destroys
The bodies of matter; but she dissipates
Their combinations, and conjoins anew
One element with others; and contrives
That all things vary forms and change their colours
And get sensations and straight give them o’er.
And thus may’st know it matters with what others
And in what structure the primordial germs
Are held together, and what motions they
Among themselves do give and get; nor think
That aught we see hither and thither afloat
Upon the crest of things, and now a birth
And straightway now a ruin, inheres at rest
Deep in the eternal atoms of the world.