Ah Phoebus, numbers, numbers. A can of worms you have opened.
Of all Alexander’s set pieces the transmittal of Hydaspes is possibly (leaving aside Diodorus’ version of Granicus) the most muddled. What is clear is the fact that there were three staging points: Craterus, Meleagher et al in the middle and Alexander at the crossing point. What is also clear is that Alexander left clear instructions that neither of these two move until the battle was clearly in Alexander’s favour.
That leaves just who Alexander took with him to make the assault on the army of Porus. This too is a relatively straightforward in Arrian's text (nothing is ever straightforward with numbers):
He then picked the select body-guard called the Companions, as well as the cavalry regiments of Hephaestion, Perdiccas, and Demetrius, the cavalry from Bactria, Sogdiana, and Scythia, and the Daan horse-archers; and from the phalanx of infantry the shield-bearing guards, the brigades of Clitus and Coenus, with the archers and Agrianians.
This would amount to some 13,000 infantry and cavalry: 3,000 “hoplites” of the line, 3,000 (or more) “Guards”, 2,000 Agrianes and Archers and 5,000 cavalry. With this force Alexander would take on Porus. A rather eloquent comment on the size of Porus’ army one might think in passing. Demonstrably Alexander was not facing 200 elephants spaced “at about 100 feet” with infantry filling the spaces and extending beyond – a line some six or more kilometres long.
Anyway, Alexander crosses with half the royal hypaspists (in one boat?!) and the rest follow. Arrian, making clear what forces Alexander took into battle, then lists them again (pardon my presumption in correcting Arrian’s error in transmission):
[…] he selected the choice guard of cavalry, and the best men from the other cavalry regiments, and brought them up from column into line on the right wing. In front of all the cavalry he posted the horse-archers, and placed next to the cavalry in front of the other infantry the royal shield-bearing guards under the command of Seleucus. Near these he placed the [royal foot-guard, and next to these] the other shield-bearing guards (regular hypaspists) and the two regiments of the phalanx, as each happened at the time to have the right of precedence. On each side, at the extremities of the phalanx, his archers, Agrianians and javelin-throwers were posted.
It is this force that the following battle narrative – in all sources – has engage the entire army of Porus. Arrian is clear, at the close, that the losses (aside possibly from the “200 other horsemen”) he enumerates are from this force:
Of Alexander’s forces, about 8o of the 6,ooo foot-soldiers who were engaged in the first attack were killed…
This, palpably, is pap. Diodorus might well be closer to the truth if one reads the narrative of all three sources: 750 represents a little shy of 10% of the “infantry” (some 8,000 or so).
Again, the other units did not cross until the battle was decided and only participated in the follow on slaughter “round up” after Alexander’s original slaughter cordon was breached. Another comment on the size of Porus’ army: it was cordoned off and surrounded by 13,000 combatants.
