Meaning of "match Greek with Greek"

Question

From Christmas Storms and Sunshine by Elizabeth Gaskell (4th paragraph):

Jenkins had his wife too. Wives were wanting to finish the completeness of the quarrel, which existed one memorable Christmas week, some dozen years ago, between the two neighbours, the two compositors. And with wives, it was a very pretty, a very complete quarrel. To make the opposing parties still more equal, still more well-matched, if the Hodgsons had a baby ("such a baby!—a poor, puny little thing"), Mrs. Jenkins had a cat ("such a cat! a great, nasty, miowling tom-cat, that was always stealing the milk put by for little Angel's supper"). And now, having matched Greek with Greek, I must proceed to the tug of war. It was the day before Christmas; such a cold east wind! such an inky sky! such a blue-black look in people's faces, as they were driven out more than usual, to complete their purchases for the next day's festival.

What does having matched Greek with Greek mean? Is this some quote or allusion? What is its origin?

Answer 1

The allusion is to the proverb when Greek meets Greek, then comes the tug of war, which means that a battle-royal can be expected between two adversaries of equal strength and determination.

So far as I can tell from your snippet, the author means that having set up such an encounter, she is now going to see the results.