Why is the ninth month called September?
Old English springan "to leap, burst forth, fly up" (class III strong verb; past tense sprang, past participle sprungen), from Proto-Germanic *sprenganan (cf. Old Norse, Old Frisian springa, Middle Dutch springhen, Old High German springan, German springen), from PIE *sprengh- "rapid movement" (cf. Sanskrit sprhayati "desires eagerly," Greek sperkhesthai "to hurry").
In Middle English, it took on the role of causal sprenge, from Old English sprengan (as still in to spring a trap, etc.). Slang meaning "to pay" (for a treat, etc.) is recorded from 1906. Meaning "to announce suddenly" (usually with on) is from 1876. Meaning "to release" (from imprisonment) is from 1900.
"season following winter," 1540s, earlier springing time (late 14c.), spring-time (late 15c.), spring of the year (1520s), which had replaced Old English Lent by late 14c. From spring (v.); also see spring (n.3). The notion is of the "spring of the year," when plants "spring up" (cf. spring of the leaf, 1530s).
Other Germanic languages tend to take words for "fore" or "early" as their roots for the season name, cf. Danish voraar, Dutch voorjaar, literally "fore-year;" German Frühling, from Middle High German vrueje "early." In 15c., the season also was prime-temps, after Old French prin tans, tamps prim (French printemps, which replaced primevère 16c. as the common word for spring), from Latin tempus primum, literally "first time, first season."
Spring fever was Old English lenctenadle; first record of spring cleaning is in 1857 (in ancient Persia, the first month, corresponding to March-April, was Adukanaiša, which apparently means "Irrigation-Canal-Cleaning Month;" Kent, p.167). Spring chicken "small roasting chicken" (usually 11 to 14 weeks) is recorded from 1780; transferred sense of "young person" first recorded 1906. Spring training first attested 1897.
"source of a stream or river," Old English, from spring (v.) on the notion of the water "bursting forth" from the ground. Rarely used alone, appearing more often in compounds, e.g. wyllspring "wellspring." Figurative sense of "source or origin of something" is attested from early 13c.
"act of springing or leaping," mid-15c., from spring (v.). The elastic coil that returns to its shape when stretched is so called from early 15c., originally in clocks and watches. As a device in carriages, coaches, etc., it is attested from 1660s. The oldest noun sense (c.1300) is a general one of "action or time of rising or springing into existence." It was used of sunrise, the waxing of the moon, rising tides, etc., and is preserved in spring (n.1).
(Heb. 'ain, "the bright open source, the eye of the landscape"). To be carefully distinguished from "well" (q.v.). "Springs" mentioned in Josh. 10:40 (Heb. 'ashdoth) should rather be "declivities" or "slopes" (R.V.), i.e., the undulating ground lying between the lowlands (the shephelah) and the central range of hills.