Etymology
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Words related to *ker-

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, 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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carboniferous (adj.)
1799, "coal-bearing, containing or yielding carbon or coal," from Latin carbo (genitive carbonis) "coal" (see carbon) + -ferous "producing, containing, bearing," from ferre "to bear" (from PIE root *bher- (1) "to carry," also "to bear children").

Used in designating the rocks which formed the great coal-beds of England, France, Germany and the United States; from 1832 with reference to the geological period when these were laid down. As a stand-alone noun (short for Carboniferous Period) by 1907.
carbuncle (n.)
early 13c., "fiery jewel, gem of a deep red color, ruby," also the name of a semi-mythical gem from the East Indies formerly believed to be capable of shining in the dark, from Old North French carbuncle (Old French charbocle, charboncle) "carbuncle-stone," also "carbuncle, boil," from Latin carbunculus "red gem," also "red, inflamed spot," literally "a little coal," from carbo (genitive carbonis) "coal" (see carbon).

Originally of rubies, garnets, and other red jewels. In English the word was used of red, eruptive subcutaneous inflammations and tumors from late 14c. Also "red spot on the nose or face caused by intemperance" (1680s).
cremate (v.)

"to burn, destroy by heat" (especially a dead body, as an alternative to burial), 1851, a back-formation from cremation. Related: Cremated; cremating.

cremation (n.)

"act or custom of burning of the dead," 1620s, from Latin cremationem (nominative crematio), noun of action from past-participle stem of cremare "to burn, consume by fire" (also used of the dead), from PIE *krem-, extended form of root *ker- (3) "heat, fire."

The adoption of cremation would relieve us of a muck of threadbare burial-witticisms; but, on the other hand, it would resurrect a lot of mildewed old cremation-jokes that have had a rest for two thousand years. ["Mark Twain," "Life on the Mississippi," 1883]
hearth (n.)

Old English heorð "hearth, fireplace, part of a floor on which a fire is made," also in transferred use "house, home, fireside," from Proto-Germanic *hertha- "burning place" (source also of Old Saxon and Old Frisian herth, Middle Dutch hert, Dutch haard, German Herd "floor, ground, fireplace"), from PIE *kerta-, from root *ker- (3) "heat, fire." Hearth-rug is from 1824. Hearth-stone is from early 14c.

accretion (n.)
Origin and meaning of accretion

1610s, "act of growing by organic enlargement;" 1650s as "that which is formed by continued growth from without," from Latin accretionem (nominative accretio) "an increasing, a growing larger" (as of the waxing moon), noun of action from past-participle stem of accrescere "grow progressively, increase, become greater," from ad "to" (see ad-) + crescere "grow" (from PIE root *ker- (2) "to grow"). It goes with the verb accrue. Related: Accretional; accretionary.

accrue (v.)
Origin and meaning of accrue
formerly also accrew, mid-15c., "to fall to someone as an addition or increment," of property, etc., from Old French acreue "growth, increase, what has grown," fem. of acreu, past participle of acreistre (Modern French accroître) "to increase," from Latin accrescere "grow progressively, increase, become greater," from ad "to" (see ad-) + crescere "grow" (from PIE root *ker- (2) "to grow"). Related: Accrued; accruing.

Apparently an English verb from a French noun because there is no English noun to go with it until much later (the earliest seems to be now-obsolete accrue, 1570s), unless the record is defective. From late 15c. as "happen or result as a natural growth;" from 1881 as "gain by increment, accumulate." Alternative verb accrete "grow by adhesion" (1784) is rare, as is accresce (1630s), from Latin accrescere.
cereal (n.)

1832, "grass yielding edible grain and cultivated for food," originally an adjective (1818) "having to do with edible grain," from French céréale (16c., "of Ceres;" 18c. in grain sense), from Latin Cerealis "of grain," originally "of Ceres," from Ceres, Italic goddess of agriculture, from PIE *ker-es-, from root *ker- (2) "to grow." The application to breakfast food cereal made from grain is American English, 1899.

Ceres 

Roman goddess of agriculture (identified with Greek Demeter), also the name given to the first-found and largest asteroid (discovered 1801 by Piazzi at Palermo), from PIE *ker-es-, from root *ker- (2) "to grow." Her festival, Cerealia, was April 10.