Laudator Temporis Acti

Diogenes Laertius, Lives of the Philosophers 8.9 (on Pythagoras, tr. R.D. Hicks):

He divides man's life into four quarters thus: "Twenty years a boy, twenty years a youth, twenty years a young man, twenty years an old man; and these four periods correspond to the four seasons, the boy to spring, the youth to summer, the young man to autumn, and the old man to winter," meaning by youth one not yet grown up and by a young man a man of mature age.

Διαιρεῖται δὲ καὶ τὸν τοῦ ἀνθρώπου βίον οὕτως· "Παῖς εἴκοσι ἔτεα, νεηνίσκος εἴκοσι, νεηνίης εἴκοσι, γέρων εἴκοσι. αἱ δὲ ἡλικίαι πρὸς τὰς ὥρας ὧδε σύμμετροι· παῖς ἔαρ, νεηνίσκος θέρος, νεηνίης φθινόπωρον, γέρων χειμών." ἔστι δ' αὐτῷ ὁ μὲν νεηνίσκος μειράκιον, ὁ δὲ νεηνίης ἀνήρ.

By Pythagoras' reckoning I'm still a young man, but by no other.

Philo, Creation of the World 103-105 (tr. C.D. Yonge), follows Solon and Hippocrates in adopting seven-year divisions:

[103] And besides what has been already said, the growth of men from infancy to old age, when measured by the number seven, displays in a most evident manner its perfecting power; for in the first period of seven years, the putting forth of the teeth takes place. And at the end of the second period of the same length, he arrives at the age of puberty: at the end of the third period, the growth of the beard takes place. The fourth period sees him arrive at the fullness of his manly strength. The fifth seven years is the season for marriage. In the sixth period he arrives at the maturity of his understanding. The seventh period is that of the most rapid improvement and growth of both his intellectual and reasoning powers. The eighth is the sum of the perfection of both. In the ninth, his passions assume a mildness and gentleness, from being to a great degree tamed. In the tenth, the desirable end of life comes upon him, while his limbs and organic senses are still unimpaired: for excessive old age is apt to weaken and enfeeble them all.

[104] And Solon, the Athenian lawgiver, described these different ages in the following elegiac verses:

In seven years from th' earliest breath,
The child puts forth his hedge of teeth;
When strengthened by a similar span,
He first displays some signs of man.
As in a third, his limbs increase,
A beard buds o'er his changing face.
When he has passed a fourth such time,
His strength and vigour's in its prime.
When five times seven years o'er his head
Have passed, the man should think to wed;
At forty two, the wisdom's clear
To shun vile deed of folly or fear:
While seven times seven years to sense
Add ready wit and eloquence.
And seven years further skill admit
To raise them to their perfect height.
When nine such periods have passed,
His powers, though milder grown, still last;
When God has granted ten times seven,
The aged man prepares for heaven.

[105] Solon therefore thus computes the life of man by the aforesaid ten periods of seven years. But Hippocrates the physician says that there are seven ages of man, infancy, childhood, boyhood, youth, manhood, middle age, old age; and that these too, are measured by periods of seven, though not in the same order. And he speaks thus: "In the nature of man there are seven seasons, which men call ages; infancy, childhood, boyhood, and the rest. He is an infant till he reaches his seventh year, the age of the shedding of his teeth. He is a child till he arrives at the age of puberty, which takes place in fourteen years. He is a boy till his beard begins to grow, and that time is the end of a third period of seven years. He is a youth till the completion of the growth of his whole body, which coincides with the fourth seven years. Then he is a man till he reaches his forty-ninth year, or seven times seven periods. He is a middle aged man till he is fifty-six, or eight times seven years old; and after that he is an old man."

Censorinus, On the Day of Birth 14, also discusses the periods of life. I don't have access to the translations of Censorinus by William Maude (New York: Cambridge Encyclopedia Co., 1900) or Holt Parker (Chicago: University of Chicago Press, 2007), and I don't have time to translate this lengthy chapter myself, but here is the Latin:

[1] Igitur expositis iis, quae ante diem natalem sunt, nunc ut climactericoe anni noscantur, quid de gradibus aetatis humanae sensum sit, dicam. [2] Varro quinque gradus aetatis aequabiliter putat esse divisos, unumquemque scilicet praeter extremum in annos XV. itaque primo gradu usque annum XV pueros dictos, quod sint puri, id est inpubes. secundo ad tricensimum annum adulescentes, ab alescendo sic nominatos. in tertio gradu qui erant usque quinque et quadraginta annos, iuvenis annos appellatos eo quod rem publicam in re militari possent iuvare. in quarto autem adusque sexagensimum annum seniores vocitatos, quod tunc primum senescere corpus inciperet. inde usque finem vitae uniuscuiusque quintum gradum factum, in quo qui essent, senes appellatos, quod ea aetate corpus iam senio laboraret. [3] Hippocrates medicus in septem gradus aetates distribuit. finem primae putavit esse septimum annum, secundae quartum decimum, tertiae duodetricensimum, quartae tricensimum quintum, quintae duo et quadragensimum, sextae quinquagensimum sextum, septimae novissimum annum vitae humanae. [4] Solon autem decem partes fecit, et Hippocratis gradum tertium et sextum et septimum singulos bifariam divisit, ut unaquaeque aetas annos haberet septenos. [5] Staseas peripateticus ad has Solonis decem hebdomadas addidit duas, et spatium plenae vitae quattuor et octoginta annorum esse dixit; quem terminum si quis praeterit, facere idem quod stadiodromoe ac quadrigae faciunt, cum extra finem procurrunt. [6] Etruscis quoque libris fatalibus aetatem hominis duodecim hebdomadibus discribi Varro commemorat; quae duo ** ad decies septenos annos posse fatalia deprecando rebus divinis proferre, ab anno autem LXX nec postulari debere nec posse ab deis impetrari. ceterum post annos LXXXIIII a mente sua homines abire, neque his fieri prodigia. [7] sed ex eis omnibus proxime videntur adcessisse naturam, qui hebdomadibus humanam vitam emensi sunt. fere enim post septimum quemque annum articulos quosdam et in his aliquid novi natura ostendit, ut et in elegia Solonis cognoscere datur. ait enim in prima hebdomade dentes homini cadere, in secunda pubem apparere, in tertia barbam nasci, in quarta vires, in quinta maturitatem ad stirpem reliquendam, in sexta cupiditatibus temperari, in septima prudentiam linguamque consummari, in octava eadem manere (in qua alii dixerunt oculos albescere), in nona omnia fieri languidiora, in decima hominem morti fieri maturum. ** tamen in secunda hebdomade vel incipiente tertia vocem crassiorem et inaequabilem fieri, quod Aristoteles appellat tragizin, antiqui nostri irquitallire, et ipsos inde putant irquitallos appellari, quod tum corpus ircum olere incipiat. [8] de tertia autem aetate adulescentulorum tres gradus esse factos in Graecia priusquam ad viros perveniatur, quod vocent annorum XIIII παῖδα, μελλέφηβον autem XV, dein sedecim ἔφηβον, tunc septemdecim ἐξέφηβον. [9] praeterea multa sunt de his hebdomadibus quae medici ac philosophi libris mandaverunt, unde apparet, ut in morbis dies septimi suspecti sunt et crisimoe dicuntur, ita per omnem vitam septimum quemque annum periculosum et velut crisimon esse et climactericum vocitari. [10] sed ex his genethliaci alios aliis difficiliores esse dixerunt, et nonnulli eos potissimum, quos ternae hebdomades conficiunt, putant observandos, hoc est unum et vicensimum, et quadragensimum secundum, dein tertium et sexagensimum, postremum octogensimum et quartum, in quo Staseas terminum vitae defixit. [11] alii autem non pauci unum omnium difficillimum climactera prodiderunt, anno scilicet undequinquagensimo, quem conplent anni septies septeni; ad quam opinionem plurimorum consensus inclinat: nam quadrati numeri potentissimi ducuntur. [12] denique Plato ille veniat, veteris philosophiae sanctissimus, qui quadrato numero annorum vitam humanam consummari putavit, sed novenario, qui conplet annos octoginta et unum. fuerunt etiam qui utrumque reciperent numerum, undequinquagensimum et octogensimum unum, et minorem nocturnis genesibus, maiorem diurnis scriberent *. [13] plerique [aliter moti] duos istos numeros subtiliter dicreverunt, dicentes septenarium ad corpus, novenarium ad animum pertinere; hunc medicinae corporis et Apollini adtributum, illum Musis, quia morbos animi, quos appellant pathe, musice lenire ac sanare consueverit. [14] itaque primum climactera annum quadragensimum et nonum esse prodiderunt, ultimum autem octogensimum et unum; medium vero ex utroque permixtum anno tertio et sexagensimo, vel quem hebdomades novem vel septem enneades conficiunt. [15] hunc licet quidam periculosissimum dicant, quod ad corpus et ad animum pertineat, ego tamen ceteris duco infirmiorem. nam utrumque quidem supra dictum continet numerum, sed neutrum quadratum, et ut est ab utroque non alienus, ita in neutro potens. nec multos sane, quos vetustas claro nomine celebrat, hic annus absumpsit. [16] Aristotelen Stagiriten reperio; sed hunc ferunt naturalem stomachi infirmitatem crebrasque morbidi corporis offensiones adeo virtute animi diu sustentasse, ut magis mirum sit ad annos LXIII eum vitam pertulisse quam ultra non protulisse.

In the Λέξεις (Words) of Aristophanes of Byzantium, one of the sections is περὶ ὀνομασίας ἡλικιῶν (on the naming of periods of life). I don't have access to the edition of W. Slater, Aristophani Byzantii Fragmenta (Berlin, 1986), but the old edition of A. Nauck is available in its entirety in Google Book Search — Aristophanis Byzantii Grammatici Alexandrini Fragmenta (Halle, 1848), and in Nauck's edition the fragments on the naming of periods of life are on pp. 87-127.

Among modern authors, Sir Thomas Browne discusses the ages of man in his Pseudodoxia Epidemica 4.12. Shakespeare's lines in As You Like It are well-known:

All the world's a stage,
And all the men and women merely players;
They have their exits and their entrances;
And one man in his time plays many parts,
His acts being seven ages. At first the infant,
Mewling and puking in the nurse's arms;
Then the whining school-boy, with his satchel
And shining morning face, creeping like snail
Unwillingly to school. And then the lover,
Sighing like furnace, with a woeful ballad
Made to his mistress' eyebrow. Then a soldier,
Full of strange oaths, and bearded like the pard,
Jealous in honour, sudden and quick in quarrel,
Seeking the bubble reputation
Even in the cannon's mouth. And then the justice,
In fair round belly with good capon lin'd,
With eyes severe and beard of formal cut,
Full of wise saws and modern instances;
And so he plays his part. The sixth age shifts
Into the lean and slipper'd pantaloon,
With spectacles on nose and pouch on side,
His youthful hose, well sav'd, a world too wide
For his shrunk shank; and his big manly voice,
Turning again toward childish treble, pipes
And whistles in his sound. Last scene of all,
That ends this strange eventful history,
Is second childishness and mere oblivion;
Sans teeth, sans eyes, sans taste, sans every thing.