Etymology
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investigate (v.)

c. 1500, back-formation from investigation or else from Latin investigatus, past participle of investigare "to trace out, search after," figuratively "search into, investigate," from in- "in, into" (from PIE root *en "in") + vestigare "to track, trace," from vestigium "footprint, track" (see vestige). Related: Investigated; investigating.

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march (n.1)

"act of marching;" 1580s, "a measured and uniform walk; a regular advance of a body of persons in which they keep time with each other," from march (v.) or else from French marche (n.), from marcher (v.). As "an advance from one halting place to another," also the distance so covered, from 1590s.

The musical sense of "strongly rhythmic composition" is attested from c. 1600, from the earlier meaning "rhythmic drumbeat for marching" (1570s). The earliest sense of the word in English is "footprint, track" (early 15c.), from a sense in Old French. Transferred sense of "forward motion" (as in march of progress, etc.) is from 1620s.

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branch (n.)

c. 1300, braunch, "division or subdivision of the stem of a tree or bush" (also used of things resembling a branch in its relation to a trunk, such as geographic features, lines of family descent), from Old French branche "branch, bough, twig; branch of a family" (12c.), from Late Latin branca "footprint," later "a claw, paw," which is of unknown origin, said to be probably from Gaulish. The connecting notion would be the shape (compare pedigree).

In English it replaced native bough. The meaning "local office of a business" is recorded by 1817, from the earlier sense of "component part of a system" (1690s).

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carbon (n.)

non-metallic element occurring naturally as diamond, graphite, or charcoal, 1789, coined 1787 in French by Lavoisier as charbone, from Latin carbonem (nominative carbo) "a coal, glowing coal; charcoal," from PIE root *ker- (3) "heat, fire."

Carbon 14, the long-lived radioactive isotope used in dating organic deposits, is from 1936. Carbon-dating (using carbon 14) is recorded from 1958. Carbon cycle is attested from 1912; carbon footprint was in use by 2001. Carbon-paper "paper faced with carbon, used between two sheets for reproduction on the lower of what is drawn or written on the upper" is from 1855, earlier it was carbonic paper (1850).

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spur (n.)

Old English spura, spora "metal implement worn on the heel to goad a horse" (related to spurnan "to kick"), from Proto-Germanic *spuron (source also of Old Norse spori, Middle Dutch spore, Dutch spoor, Old High German sporo, German Sporn "spur"), from PIE *spere- "ankle" (see spurn). Related to Dutch spoor, Old English spor "track, footprint, trace."

Generalized sense of "anything that urges on, stimulus," is from late 14c. As a sharp projection on the leg of a cock, from 1540s. Meaning "a ridge projecting off a mountain mass" is recorded from 1650s. Of railway lines from 1837. "Widely extended senses ... are characteristic of a horsey race" [Weekley]. Expression on the spur of the moment (1801) preserves archaic phrase on the spur "in great haste" (1520s). To win one's spurs is to gain knighthood by some valorous act, gilded spurs being the distinctive mark of a knight.

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pedigree (n.)

early 15c., pedigrue, "genealogical table or chart," from Anglo-French pe de gru, a variant of Old French pied de gru "foot of a crane," from Latin pedem accusative of pes "foot" (from PIE root *ped- "foot") + gruem (nominative grus) "crane," cognate with Greek geranos, Old English cran; see crane (n.)).

On old manuscripts, "descent" was indicated by a forked sign resembling the branching lines of a genealogical chart; the sign also happened to look like a bird's footprint. On this theory the form was influenced in Middle English by association with degree. This explanation dates back to Skeat and Sweet in the late 1800s. The word obviously is of French origin, and pied de gru is the only Old French term answering to the earliest English forms, but this sense is not attested in Old French (Modern French pédigree is from English). Perhaps it was a fanciful extension developed in Anglo-French. Other explanations are considered untenable.

The crane was at the time in question very common in England and France, and it figures in many similes, proverbs, and allusions. The term appears to be extant in the surname Pettigrew, Pettygrew .... [Century Dictionary] 

Meaning "ancestral line" is mid-15c.; of animals, c. 1600. Related: Pedigreed.

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track (n.)

late 15c., "footprint, mark left by anything," from Old French trac "track of horses, trace" (mid-15c.), possibly from a Germanic source (compare Middle Low German treck, Dutch trek "drawing, pulling;" see trek). Meaning "lines of rails for drawing trains" is from 1805. Meaning "branch of athletics involving a running track" is recorded from 1905. Meaning "single recorded item" is from 1904, originally in reference to phonograph records. Meaning "mark on skin from repeated drug injection" is first attested 1964.

Track record (1955) is a figurative use from racing, "performance history" of an individual car, runner, horse, etc. (1907, but the phrase was more common in sense "fastest speed recorded at a particular track"). To make tracks "move quickly" is American English colloquial first recorded 1835; to cover (one's) tracks in the figurative sense first attested 1898; to keep track of something is attested from 1883. American English wrong side of the tracks "bad part of town" is by 1901. Track lighting attested from 1970.

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