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The Histories

§12.21.1-12.21.10

Mathematical Impossibility of Callisthenes' Issus Formation

Polybius demonstrates that Callisthenes' account of Alexander's battle formation at Issus is mathematically impossible, as the narrow space of less than fourteen stades could not accommodate the troops at a depth of eight men.

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§12.21.1

τὸ δὲ δὴ πάντων μέγιστον·1 ἤδη γὰρ σύνεγγυς ὄντα τοῖς πολεμίοις αὐτὸν εἰς ὀκτὼ ποιῆσαί φησι τὸ βάθος.

​And indeed the greatest thing of all: for he says that when he was already close to the enemy, he made the depth eight deep.

§12.21.2

ἐξ οὗ δῆλον ὅτι κατʼ ἀνάγκην ἐπὶ τετταράκοντα σταδίους ἔδει γενέσθαι τὸ μῆκος τῆς φάλαγγος.

​From which it is clear that of necessity the length of the phalanx must have become forty stades.

§12.21.3

εἰ δʼ ὅλως συνήσπισαν κατὰ τὸν ποιητὴν2 οὕτως ὥστε συνερεῖσαι πρὸς ἀλλήλους, ὅμως εἴκοσι σταδίων ἔδει τὸν τόπον ὑπάρχειν.

​But even if they locked shields completely, in the words of the poet, so as to press against one another, still the space must have been twenty stades.

§12.21.4

αὐτὸς δέ φησι λείπειν τῶν δεκατεττάρων σταδίων καὶ τούτου μέρος μέν τι πρὸς θαλάττῃ τοὺς ἡμίσεας ἐπὶ τοῦ δεξιοῦ· ἔτι δὲ τὴν ὅλην τάξιν ἀπὸ τῶν ὀρῶν ἱκανὸν τόπον ἀφεστάναι3 πρὸς τὸ μὴ τοῖς πολεμίοις ὑποπεπτωκέναι τοῖς κατέχουσι τὰς παρωρείας.

​But he himself says that it fell short of fourteen stades. ​And of this space, some part by the sea was occupied by the half of the cavalry on the right; and further, that the whole line was drawn up at a considerable distance from the mountains, so as not to be exposed to the enemy who occupied the foothills.

§12.21.6

ἴσμεν γὰρ ὃ ποιεῖ πρὸς τούτους ἐπικάμπιον. Ὑπολειπόμεθα καὶ νῦν ἡμεῖς τοὺς μυρίους πεζούς, πλείους ὄντας τῆς ἐκείνου προθέσεως.

​For we know what defensive flank he made against them. And now we ourselves leave out of account the ten thousand infantry, though they are more than his own estimate.

§12.21.7

ὥστʼ ἐκ τούτων ἕνδεκα σταδίους ἐπὶ τὸ πλεῖον ἀπολείπεσθαι τὸ τῆς φάλαγγος μῆκος κατʼ αὐτὸν τὸν Καλλισθένην, ἐν οἷς4 ἀνάγκη τοὺς τρισμυρίους καὶ δισχιλίους ἐπὶ τριάκοντα τὸ βάθος ὑπάρχειν συνησπικότας.

​So that from this, the length of the phalanx, according to Callisthenes himself, was at most eleven stades, in which it is necessary that the thirty-two thousand should be thirty deep, even when shields are locked.

§12.21.8

ὁ δέ φησιν εἰς ὀκτὼ τεταγμένων γενέσθαι τὴν μάχην.

​But he says that the battle was fought with them drawn up eight deep.

§12.21.9

τὰ δὲ τοιαῦτα τῶν ἁμαρτημάτων οὐδʼ ἀπολογίαν ἐπιδέχεται· τὸ γὰρ ἀδύνατον ἐν πράγμασιν αὐτόθεν ἔχει τὴν πίστιν.

​Errors of this kind do not even admit of defense; for the impossibility in facts has its proof immediately from itself.

§12.21.10

διόπερ ὅταν καὶ τὰ κατʼ ἄνδρα διαστήματα καὶ τὸ πᾶν τοῦ τόπου μέγεθος ὡρισμένον ὑποθῶσι καὶ τὸν ἀριθμὸν τῶν ἀνδρῶν, ἀναπολόγητον γίνεται τὸ ψεῦδος.

​Therefore, when they assume both the distance allowed for each man and the whole extent of the ground to be fixed, as well as the number of the men, the falsehood becomes indefensible.

Syntax notes4 items
  1. 12.21.1τὸ δὲ δὴ πάντων μέγιστον

    Accusative in apposition to the sentence (or nominative absolute), introducing the following statement as 'and what is indeed the greatest of all.'

  2. 12.21.3κατὰ τὸν ποιητὴν

    'According to the poet,' referring to Homer. It points to the Homeric description of closely-locked shields (synaspismos) as described in Iliad 13.131.

  3. 12.21.5ἀφεστάναι

    Infinitive in indirect discourse, continuing the report of Callisthenes' claims dependent on phēsi in 12.21.4. Its subject accusative is tēn holēn taxin.

  4. 12.21.7ἐν οἷς

    Relative clause whose antecedent is hendeka stadious (eleven stades). It means 'within which (eleven stades).'

Translated by Gemini 3.5 Flash (published 2026-05-25)urn:cts:greekLit:tlg0543.tlg001.humanitext-grc2:12.21.1-12.21.10