c. 1400, reguler, "belonging to or subject to a religious or monastic rule," from Old French reguler "ecclesiastical" (Modern French régulier) and directly from Late Latin regularis "containing rules for guidance," from Latin regula "rule, straight piece of wood" (from PIE root *reg- "move in a straight line"). The classical -a- was restored 16c.
In earliest use, the opposite of secular. Extended from late 16c. to shapes, verbs, etc., that followed predictable, proper, or uniform patterns. From 1590s as "marked or distinguished by steadiness or uniformity in action or practice;" hence, of persons, "pursuing a definite course, observing a universal principle in action or conduct" (c. 1600).
The sense of "normal, conformed or conforming to established customs" is from 1630s. The meaning "orderly, well-behaved" is from 1705. By 1756 as "recurring at repeated or fixed times," especially at short, uniform intervals. The military sense of "properly and permanently organized, constituting part of a standing army" is by 1706. The colloquial meaning "real, genuine, thorough" is from 1821.
Old English borrowed Latin regula and nativized it as regol "rule, regulation, canon, law, standard, pattern;" hence regolsticca "ruler" (instrument); regollic (adj.) "canonical, regular."
-ize
word-forming element used to make verbs, Middle English -isen, from Old French -iser/-izer, from Late Latin -izare, from Greek -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached.
The variation of -ize and -ise began in Old French and Middle English, perhaps aided by a few words (such as surprise, see below) where the ending is French or Latin, not Greek. With the classical revival, English partially reverted to the correct Greek -z- spelling from late 16c. But the 1694 edition of the authoritative French Academy dictionary standardized the spellings as -s-, which influenced English.
In Britain, despite the opposition to it (at least formerly) of OED, Encyclopaedia Britannica, the Times of London, and Fowler, -ise remains dominant. Fowler thinks this is to avoid the difficulty of remembering the short list of common words not from Greek which must be spelled with an -s- (such as advertise, devise, surprise). American English has always favored -ize. The spelling variation involves about 200 English verbs.