I. THE ORDER OF DISCOVERY

Hanses numbers the occurrences of λεπτή in accordance with the habits of some earlier scholars who, having come to think of the ‘gamma-acrostic’ as a unit that was the most important and prominent part of the passage, consider its constituent elements as the first and second appearance of λεπτή and the one in line 784 as the third. Since Hanses is above all interested in showing that there is a fourth, heavily hinted at in various ways in the lines of the passage and the preceding section of the poem, he has no reason to reconsider the numbering. But because the clues provided by Aratus are insistently numerical, it is important that the occurrences of the adjective be ordered as they will be found by an attentive reader. As Danielewicz's discussion makes clear, the two horizontal instances of λεπτή are in plain sight and will be noted first, resulting in the following order:Footnote ⁴

1. 1) the λεπτή in 783,

2. 2) the λεπτή in 784,

3. 3) the vertical acrostic λεπτή, which is completed only in 787,Footnote ⁵

4. 4) the diagonal acrostic, which can only be found, as Hanses notes, after recognition of the vertical one.

This is a useful observation because it allows us to reconstruct how Aratus intended his clues to be read—a bit of mild irony inasmuch as we are using the solution to elucidate the clues rather than the other way round. Those clues to us are, in essence:

1. A) pay close attention to the horns on either side (778, κεράων ἑκάτερθε);

2. B) then be on the lookout for different shapes of horns (780, ἀλλοῖαι μορφαί);

3. C) observe the plural of the preceding clue, for it is reinforced by emphasis on third and fourth (781, τρίτη … τετάρτῃ, and elsewhere), as Hanses notes.

The horns we are meant to look at first, it seems, cannot be the two parts of the ‘gamma-acrostic’, which a reader will not see first, but those I number 1 and 2, namely the anaphoric λεπτὴ μὲν … λεπτὴ δὲ … of 783–4.Footnote ⁶ Altogether this tells us what we are looking for: two additional instances of the word λεπτή after these. We know we are looking for λεπτή because this is what is repeated in the ‘horns’, and we know we are looking for two more instances because of the repeated emphasis on the numbers three and four throughout this section of the poem. As I suggested above, 3 is the vertical acrostic, and Aratus gives us a hint about 4, as Hanses points out, with the words τέτρατον ἐκ τριτάτοιο (786, ‘the fourth from the third’).

How does the fourth come from the third? Not, as Hanses would have it, by ‘glancing across the page from the Γ in the direction of the third λεπτή’ (emphasis mine), by which he means the λεπτή in 784. This is wrong on two counts: first, because that λεπτή is not, as we have seen, really the third; second, because the direction is wrong. The fourth, Aratus tells us, comes from or out of (ἐκ) the third, so we cannot be meant to find it by looking toward the third. Once we recall which one is truly the third and look for what comes out of it, we can spot the fourth: the diagonal λεπτή literally proceeds from the initial Λ of the third (which is also shared by the first, but this fact is not relevant to the immediate point I am making).Footnote ⁷

II. A ‘LAMBDA-ACROSTIC’?

Schematically, then, we may represent the acrostic visually in this way (omitting 2, which is not part of the acrostic arrangement):

We have then not merely a ‘gamma-acrostic’ but a three-pronged one formed by two orthogonal lines and a bisecting one. Perhaps the whole figure taken together has some significance, though I confess I cannot say that at the moment I know what it may be.Footnote ⁸ This does not mean we need to dispense with the Γ, merely acknowledge it as only one possible configuration among a set of shifting visual possibilities, each element of which is potentially polysemous itself. I would further argue that, just as taking 1 and 3 together gives us a Γ, taking 3 and 4 together gives us another alphabetic acrostic, this time in the shape of Λ, and in fact the two occurrences of λεπτή are visual extensions of the lines that form the legs of their shared initial lambda. At least in part it is plausible to imagine that this enlarged ‘lambda-acrostic’ is a visual reference to the word λεπτός itself, with its initial letter inscribed into the poem.

III. THREE (Γ), FOUR (Δ) AND THIRTY (Λ)

Once we have restored the proper order of discovery, there is a correspondence to note with regard to the gamma-acrostic, namely the fact that its form is apparent only after we have revealed the third occurrence of λεπτή, and that form is Γ, precisely the alphabetic numeral 3.Footnote ⁹ In other words, Aratus has given us not merely what we moderns call a ‘gamma-acrostic’, that is, an acrostic that happens to resemble a gamma, but an acrostic that is a gamma. The poet thus composes signs from other signs—letters writ large by means of other letters—and inscribes them into the passage that holds the greatest visual interest for readers. This is of particular interest in light of Katharina Volk's recent and convincing exploration of the ‘numerous ways in which Aratus’ signs evoke the notion of writing’ and the methods by which Aratus provides and arranges signifying phenomena in written form.Footnote ¹⁰ A poet as concerned with writing, letters and celestial arrangements as Aratus is one whom we may easily imagine moving beyond the simple geometry of a gamma-acrostic, reimagining it as an actual letter and then playing with the numerical significance of the sign.

We have seen that the fourth λεπτή is meant to come from the third, and I believe that Aratus has meant us to find his Λ through the use of another alphabetic/numerical correspondence, in this case, a Δ (the numeral 4) coming from the Γ (3), which is precisely what the poet told us. I have supposed earlier that we are dealing with a Λ acrostic, but that letter emerges in the end only because—aside from the bottom horizontal stroke—it consists of the same shape as a Δ. There is another hint, too, in Aratus’ signal that the fourth arises from the third when the κεραῖαι are bluntedFootnote ¹¹ (ἀμβλείῃσι κεραίαις), for in the space of the phantom bottom stroke of the Δ we find the etymological partner to ἀμβλείῃσι, namely the verb ἄμβλυνται.Footnote ¹² Moreover, even the Λ is not numerically inappropriate in the context; as the alphabetic numeral for 30 it could be taken to represent the number of days in a lunar month.Footnote ¹³

IV. HORNS

I suggested above in Section II that the horns we are instructed to look at closely (778) are the words λεπτὴ μὲν … λεπτὴ δὲ … in 783–4. This may seem initially less appealing than the idea of the two parts of the gamma Γ being the horns, but the anaphoric μὲν/δὲ structure (my 1 and 2) is what we see first (πρῶτον, 778). Moreover, when we consider the semantic range of κέρας, which covers, among other things, the two parts of a bow on either side of its handle, two wings of the line of an army and two branches of a river, it hardly seems to be stretching plausibility to imagine that these words of the poem could be taken as verbal κέρατα.

There can also be no doubt that there is a great deal of emphasis on horns in the passage and its surrounding context. In addition to the instance of κέρας in 778, the word reappears in 788 and 794, as does a related verb in 780 (κερόωσι) and the near synonym κεραία in 785 and 790. Aside from literally referring to horns, the nouns κέρας and κεραία have wide semantic ranges (see LSJ s.vv.), many of which involve the joining of two similar linear elements at a common point. While it is not at all a stretch to think of the Γ and the Λ shapes of the acrostic as easily fitting into this general notion, we can be even more specific. Both κέρας and κεραία can refer to a peak, that is, a point where vertical converging lines meet, and κεραία is used by Sextus Empiricus to refer to the leg of a compass, an instrument that resembles exactly a Λ. The word κεραία even has a specific use referring to portions of letterforms (‘apex of a letter’), although the LSJ entry elides some complexity in that definition. More specifically important to us here—and LSJ does not hint at this at all—are the clear instances in which κεραῖαι is the precise word used in Greek for the lines that form letters. Thus we have examples such as Apollonius Dyscolus (De Constr. 1.47): τοῦ Α τὴν κεραίαν ἀπήλειψε (‘he erased the stroke of the alpha’). This usage covers the two legs of a lambda, as can be unmistakably seen from Ps.-Galen, De pond. et mens. (fr. 56a Hultsch): πλάγιον δὲ Λ εἰς μὲν τὰ δεξιὰ ταῖς κεραίαις νεῦον δραχμὴν δηλοῖ, <, εἰς δὲ τὰ εὐώνυμα ἡμίσειαν, > (‘a lambda on its side pointing with its legs to the right indicates “drachma,” like so <; pointing to the left, “half drachma”, like so >’).Footnote ¹⁴

We begin, then, with one sort of ‘horns’ in λεπτὴ μὲν … λεπτὴ δὲ … and we are told what we are looking for and where to search for a third and fourth form of ‘horns’ through the repeated punning emphasis on κέρας/κεραία. As with most riddles we cannot initially solve, once a solution is revealed, it appears simple and obvious in retrospect. We should be grateful to Hanses for making Aratus' acrostic puzzle look so simple and obvious that we can see connections we could not before.