par

The root par is one of the trickiest in English, because three different Latin words all collapsed into the same three letters. They have nothing to do with each other in meaning — you have to keep three separate stories in your head.

Branch 1 — parāre, "to make ready, prepare." This is the action branch. Picture a Roman cook or soldier getting things in place before they are needed. Add prefixes and you get a tidy family:
- pre- (beforehand) + parāre → prepare: make ready in advance; preparation is the act of doing so.
- re- (again) + parāre → repair: make ready again — i.e., fix what broke. The noun repairs and the adjectives repairable / reparable all sit here, plus irreparable (cannot be made ready again).
- The same re- pieces took a second, more abstract road into reparation — "making things right again" after a wrong, hence compensation and war reparations.
- se- (apart) + parāre → separate: literally "make ready apart," set things in their own places — hence to divide. separation is the noun.
- apparatus is "things made ready" — equipment prepared for a purpose; apparel (also from ad- + parāre) is the "gear" you put on, i.e. clothing. And pare is the plain verb "to make ready by trimming" — to peel or cut down.

Branch 2 — pār, "equal, on the same level." This is the equality branch. Pār simply meant two things weighing the same:
- par itself survives in "on a par with" and golf's "par." parity is the state of being equal; disparity (dis- = apart) is inequality; disparate means so unequal as to be unmatched.
- com- (together) + pār → compare: set two things side by side as equals to judge them. The whole sub-family follows — comparison, comparable, comparative, comparatively, comparability, comparably, incomparable, incomparably.
- pār also entered through French as peer — "an equal," hence both a member of the nobility and one's age-mates (peer-group); peerless is "having no equal." nonpareil (French non pareil, "not equal") means matchless. Even several belongs here, from Latin separ — "each its own, separate" — which slid into the vague "a few."

Branch 3 — parere, "to bring forth, give birth" (and, in a related sense, "to appear"). This branch is about producing and becoming visible:
- parent is "one who brings forth" a child.
- viviparous (vivi- = alive) means bringing forth live young.
- From the "appear" sense: ap- (toward) + parēre → apparent "coming into view, plainly seen"; trans- (through) + parēre → transparent "showing through."

A warning about two former members. impair is not from this root (it comes from Latin pejor, "worse") and parallel is Greek para- + allēlos, not Latin par. Both have been moved out of this family.