early 15c., "estimated value or worth, proportional estimation according to some standard; monetary amount; a proportional part," from Old French rate "price, value" and directly from Medieval Latin rata (pars) "fixed (amount)," from Latin rata "fixed, settled," fem. past participle of reri "to reckon, think" (from PIE root *re- "to reason, count").
Meaning "degree of speed" (properly ratio between distance and time) is attested from 1650s. Currency exchange sense of "basis of equivalence upon which one currency is exchanged for another" is recorded by 1727. Meaning "fixed public tax assessed on property for some local purpose" is by 1712.
First-rate, second-rate, etc. are 1640s, from British Navy division of ships into six classes based on size and strength. Phrase at any rate originally (1610s) meant "at any cost," hence "positively, assuredly." weakened sense of "at least" is attested by 1760. Rate-payer "one who is assessed and pays a local tax" is by 1825.
Old English fyrst "foremost, going before all others; chief, principal," also (though rarely) as an adverb, "at first, originally," superlative of fore; from Proto-Germanic *furista- "foremost" (source also of Old Saxon fuirst "first," Old High German furist, Old Norse fyrstr, Danish første, Old Frisian ferist, Middle Dutch vorste "prince," Dutch vorst "first," German Fürst "prince"), from PIE *pre-isto-, superlative of *pre-, from root *per- (1) "forward," hence "in front of, before, first, chief."
The usual Old English superlative word was not fyrst, but forma, which shows more clearly the connection to fore. Forma became Middle English firme "first, earliest," but this has not survived.
First aid is that given at the scene, pending the arrival of a doctor. First lady as an informal title for the wife of a U.S. president was in use by 1908, short for First lady of the land (by 1863 with reference to the president's wife); the earlier title was simply Lady (1841). First name is attested from mid-13c. First base "a start" in any sense (1938) is a figurative use from baseball.
First fruits is from late 14c. as "earliest productions of the soil;" 1590s as "first results" of any activity or endeavor. First love is from 1741 as "one's first experience of romantic love;" 1971 as "one's favorite occupation or pastime." First floor is from 1660s as "story built on or just above the ground" (now U.S.); 1865 as "story built next above the ground."
1560s, "that which is first," from first (adj.). Meaning "first day of the month" is by 1590s. In music, "instrument or voice that takes the highest or chief part of its class," 1774. From 1909 as the name of the lowest gear in an engine. In British schools colloquial use, "highest rank in an examination," 1850.
"to scold, chide vehemently, rebuke," late 14c., raten, probably from Old French rateir, variant of reter "to impute blame, accuse, find fault with," from Latin reputare "to count over, reflect," in Vulgar Latin, "to impute, blame," from re- "repeatedly" (see re-) + putare "to judge, suppose, believe, suspect" (originally "to clean, trim, prune," from PIE root *pau- (2) "to cut, strike, stamp"). Related: Rated; rating.
Old French reter also was borrowed into Middle English as retten "to blame" (c. 1300); also "to attribute, impute" (late 14c.), "to consider, think about" (late 14c.).
also firsthand, "direct from the source or origin," 1690s, from the image of the "first hand" as the producer or maker of something.
"of a second class or group," 1660s, originally of ships, "of the second rate as to size, strength, etc.;" see rate (n.). Related: Second-rater.