κεῖτο, χέλυν ἐρατὴν ἐπ’ ἀριστερὰ χειρὸς ἐέργων.

And probably the basis of the idea is the same. The really correct Greek expression for ‘on the left hand’ I take to be χειρὸς ἐξ ἀριστερᾶς, which is used by Euripides[681].

Sense altered in later Greek.

But in the later Greek the idea of the point of arrival prevailed over that of the point of departure: and, conventionally at least, the ἐπιδέξια, with its equivalent ἐνδέξια, came to mean simply ‘on the right,’ and ἐπ’ ἀριστερὰ, ‘on the left.’ It is worth notice, that we have a like ambiguous use in English of the word towards. Sometimes towards the left means being on the left: sometimes it means moving from the right in the direction of the left: and a room ‘towards the south’ means one with its windows on the north, looking out over the south, like as the star Arctus looks out towards the left of Ulysses[682].