Etymology
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compost (n.)

late 14c., compote, "mixture of stewed fruits, a preserve," from Old French composte "mixture of leaves, manure, etc., for fertilizing land" (13c.), also "condiment," from Vulgar Latin *composita, noun use of fem. of Latin compositus, past participle of componere "to put together," from com "with, together" (see com-) + ponere "to place" (see position (n.)).

The fertilizer sense is attested in English from 1580s, and the French word in this sense is a 19th century borrowing from English. The condiment sense now goes with compote, a later borrowing from French.

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compost (v.)

late 15c., "to manure with compost;" 1829, "to make into compost;" from compost (n.). Related: Composted; composting.

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heap (v.)
Old English heapian "collect, heap up, bring together;" from heap (n.). Related: Heaped; heaping. Compare Old High German houfon, German haufen "to heap," also a verb from a noun.
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heap (n.)

Old English heap "pile (of things); great number, crowd, multitude (of persons)," from West Germanic *haupaz (source also of Old Saxon hop, Old Frisian hap, Middle Low German hupe, Dutch hoop, German Haufe "heap"), of uncertain origin. The group is perhaps related to Old English heah "high" (see high), but OED suggests a common origin with Latin cubare "lie down," and Boutkan says it is probably not Indo-European at all.

Slang meaning "old car" is attested from 1924. Earlier it meant "slovenly woman" (1806). As a characteristic word in American Indian English speech, "a lot, a great deal," by 1832.

One grain of sand does not make a heap. A second grain of sand added to the first does not make a heap. Indeed each and every grain of sand, when added to the others, does not make a heap which was not a heap before. Therefore, all the grains of sand in existence can still not a heap make. [the fallacy of the heap, as described in Malcolm Murray and Nebojsa Kujundzic, "Critical Reflection," 2005]
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scrap-heap (n.)

1803, "place where scrap is collected," later especially "place in a railroad yard, etc., where old iron is collected," from scrap (n.1) + heap (n.).

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compote (n.)

1690s, "fruit preserved in syrup," from French compote "stewed fruit, fruit preserved in syrup," from Old French composte (13c.) "mixture, compost," from Vulgar Latin *composita, fem. of compositus "placed together," past participle of componere  "to put together, to collect a whole from several parts," from com "with, together" (see com-) + ponere "to place" (past participle positus; see position (n.)). Etymologically the same word as compost (n.).

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manure (n.)

"dung or compost used as fertilizer, any substance (especially the excrement of livestock) added to the soil to render it more fertile," 1540s, from manure (v.).

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accumulate (v.)
1520s, "to heap up" (transitive), from Latin accumulatus, past participle of accumulare "to heap up, amass," from ad "to," here perhaps emphatic (see ad-), + cumulare "heap up," from cumulus "heap" (from suffixed form of PIE root *keue- "to swell"). From 1759 in intransitive sense of "grow in size or number." Related: Accumulated; accumulating.
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cumulate (v.)

1530s, "gather into a heap or mass" (transitive), from Latin cumulatus "heaped, increased, augmented," past participle of cumulare "to heap," from cumulus "mound, heap" (from suffixed form of PIE root *keue- "to swell"). Related: Cumulated; cumulating; cumulant.

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