To contemporary ears “quaternion” refers to a number system discovered in the 19h century, but there were a couple precedents. Both refer to something related to a group of four things, but there is no relation to mathematical quaternions other than that they have four dimensions.
I’ve written before about Milton’s use of the word in Paradise Lost. Milton is alluding to the four elements of antiquity: air, earth, fire, and water.
I recently found out the word quaternion appears in the Latin Vulgate as well. Acts 12:4 records that Herod had Peter guarded by four squads of four soldiers each, “quattuor quaternionibus militum.”
Update: Thanks to Phil for pointing out in the comments that quaternion appears in the King James as well, “four quaternions of soldiers.”