-logy

early 15c., "correspondence, proportion," from Old French analogie or directly from Latin analogia, from Greek analogia "proportion," from ana "upon, according to" (see ana-) + logos "ratio," also "word, speech, reckoning" (from PIE root *leg- (1) "to collect, gather," with derivatives meaning "to speak, to 'pick out words'").

A Greek mathematical term given a wider sense by Plato. The meaning "partial agreement, likeness or proportion between things" is from 1540s. In logic, "an argument from the similarity of things in some ways inferring their similarity in others," c. 1600.

early 15c., "defense, justification," from Late Latin apologia, from Greek apologia "a speech in defense," from apologeisthai "to speak in one's defense," from apologos "an account, story," from apo "away from, off" (see apo-) + logos "speech" (see Logos).

In classical Greek, "a well-reasoned reply; a 'thought-out response' to the accusations made," as that of Socrates. The original English sense of "self-justification" yielded a meaning "frank expression of regret for wrong done," attested by 1590s, but this was not the main sense until 18c. In Johnson's dictionary it is defined as "Defence; excuse," and adds, "Apology generally signifies rather excuse than vindication, and tends rather to extenuate the fault, than prove innocence," which might indicate the path of the sense shift. The old sense has since tended to go with the Latin form apologia (1784), a word known from early Christian writings in defense of the faith.