What does arch mean?
The definition of arch
Arch, a.
Etym: [See Arch-, pref.]

1 Chief; eminent; greatest; principal. The most arch act of piteous massacre. Shak.
2 Cunning or sly; sportively mischievous; roguish; as, an arch look, word, lad. [He] spoke his request with so arch a leer. Tatler.

Arch, n.
Etym: [See Arch-, pref.]

A chief. [Obs.] My worthy arch and patron comes to-night. Shak.

*arch.
Etym: [Gr. Arch, a.]

A suffix meaning a ruler, as in monarch (a sole ruler).
-ARCH -arch. [Gr. ‘archo`s chief, commander, ‘a`rchein to rule. See Arch, a.]
A suffix meaning a ruler, as in monarch (a sole ruler).