mediate

What it means

1. transitiveTo resolve differences, or to bring about a settlement, between conflicting parties.

   Negotiators managed to mediate a ceasefire.

2. intransitiveTo intervene between conflicting parties in order to resolve differences or bring about a settlement.

   "Nay," replied Charles, gravely, "this is carrying your anger too far. Allow me to mediate between you. I must entreat, nay, I command, the Lady Francesca's presence."

   1834, L[etitia] E[lizabeth] L[andon], chapter XLII, in Francesca Carrara. […], volume III, London: Richard Bentley, […], (successor to Henry Colburn), →OCLC, page 352

3. To divide into two equal parts.

   1 more example

   Then, Meaſuring Land, by vvalking over it, they ſtyled a Double-ſtep (i.e. the Space from the elevation of one Foot, to the ſame Foot ſet dovvn again, mediated by a ſtep of the other Foot) a Pace, equal to 5 Foot; a Thouſand of vvhich Paces made a Mile, vvhich is a Meaſure ſerving for any diſtance on Earth, and even for the Height of the Sphears.

   1694, William Holder, “Of Measure in General. § More Particularly of Time; and Difficulties Concerning It.”, in A Discourse Concerning Time, […], London: […] J[ohn] Heptinstall, for L[uke] Meredith, […], →OCLC, page 6

In a sentence

Negotiators managed to mediate a ceasefire.

Where it comes from

1. Late Latinmediātus
2. Middle Englishmediat(e)“intermediate; intercessory”
3. Englishmediate

The adjective is first attested in the 1440s in Middle English, the verb in 1538; from Middle English mediat(e) (“intermediate; intercessory”), borrowed from Late Latin mediātus, perfect passive participle of mediō (“to divide in the middle; (in Medieval Latin) to be in the middle, be or become between, mediate”) (see -ate (verb-forming suffix) and -ate (adjective-forming suffix)), from medius (“middle”) + -ō (verb-forming suffix).