"of, pertaining to, or of the nature of mathematics," early 15c., from Medieval Latin mathematicus "of or belonging to mathematics," from Latin mathematica (see mathematic) + -al (1). Also, by 1765, "pertaining to the quadrivium," comprising arithmetic, geometry, astronomy, and music. It also could include optics. Related: Mathematically.

The four mathematical arts are arithmetic, geometry, music, and astronomy; these anciently were termed the quadrivium, or fourfold way of knowledge. [Sir John Hawkins, "A General History of the Science and Practice of Music," Sir John Hawkins, 1776]

"to go in procession," 1814, "A colloquial or humorous back-formation" from procession [OED]. Accent on second syllable. The earlier verb was procession (1540s).

early 14c., proces, "fact of being carried on" (as in in process), from Old French proces "a journey; continuation, development; legal trial" (13c.) and directly from Latin processus "a going forward, advance, progress," from past-participle stem of procedere "go forward" (see proceed).

Meaning "course or method of action, continuous action or series of actions or events" is from mid-14c.; sense of "continuous and regular series of actions meant to accomplish some result" (the main modern sense) is from 1620s. Meaning "a projection from the main body of something," especially a natural appendage, is from 1570s. Legal sense of "course of action of a suit at law, the whole of the proceedings in any action at law" is attested from early 14c.; hence **due process** "fair treatment" at law, considered as a right (mid-15c.).

1530s, "begin legal action against, summon in a court of law," from French processer "to prosecute," from proces (see process (n.)). Meaning "prepare or treat by special process, subject to special process" is from 1881, from the noun in English. Of persons, "to register and examine," by 1935, in reference to the U.S. Army. Related: Processed; processing.

1620s, "action of leaping or springing back" (a sense now obsolete); 1640s, "outcome, effect, consequence;" 1650s, "decision, outcome of an action or process;" from result (v.). Related: **Results** "favorable or desirable consequences" (by 1922). Mathematical sense of "quantity or value ascertained by a calculation" is by 1771.

by 1717, in algebra textbooks, in phrase to the nth, a mathematical term indicating an indefinite number, in which n is an abbreviation for (whole) number (n.). Figurative (non-mathematical) use is by 1852.

1560s, originally in the mathematical sense, from irrational + -ity. Meaning "unreasonableness, absurdity" is from 1640s.

"mathematical science," late 14c. as singular noun, mathematik (replaced since early 17c. by mathematics, q.v.), from Old French mathematique and directly from Latin mathematica (plural), from Greek mathēmatike tekhnē "mathematical science," feminine singular of mathēmatikos (adj.) "relating to mathematics, scientific, astronomical; pertaining to learning, disposed to learn," from mathēma (genitive mathēmatos) "science, knowledge, mathematical knowledge; a lesson," literally "that which is learnt;" from manthanein "to learn," from PIE root *mendh- "to learn."

As an adjective, "pertaining to mathematics," from c. 1400, from French mathématique or directly from Latin mathematicus.

according to OED, the plural form of index preferable in scientific and mathematical senses of that word.