Etymology
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alectryomancy (n.)
"divination by means of a cock and grains of corn," 1680s, from -mancy "divination" + Latinized form of Greek alektryon "cock," literally "warder-off, fighter," related to alexein "to ward off, drive or keep off" (see Alexander, and compare Alekto, name of one of the three Furies). Perhaps originally a personal name, applied at first to the fighting cock, then to cocks generally. Earlier form of the word in English was alectoromancy (1650s). Letters of the alphabet were traced on the ground and a grain of corn was placed on each.
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mantis (n.)

1650s, "type of insect that holds its forelegs in a praying position" (especially the praying mantis, Mantis religiosa), Modern Latin, from Greek mantis, used of some sort of elongated insect with long forelimbs (Theocritus), literally "one who divines, a seer, prophet," from mainesthai "be inspired," related to menos "passion, spirit," from PIE *mnyo-, suffixed form of root *men- (1) "to think," with derivatives referring to qualities and states of mind or thought (compare mania and -mancy).

The insects, which live in temperate and tropical regions worldwide, are so called for its way of holding the enlarged forelimbs as if in prayer. The mantis shrimp (by 1853; earlier sea-mantis, 1690s) is so called for its resemblance to the insect.

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scapulimancy (n.)

divination by means of the cracks in a shoulder-blade put into a fire, 1871, from combining form of scapula + -mancy "divination by means of." Related: Scapulimantic.

With haruspication may be classed the art of divining by bones, as where North American Indians would put in the fire a certain flat bone of a porcupine, and judge from its colour if the porcupine-hunt would be successful. The principal art of this kind is divination by a shoulder-blade, technically called scapulimancy or omoplatoscopy. This is especially found in vogue in Tartary, where it is ancient, and whence it may have spread into all other countries where we hear of it. [Edward B. Tylor, "Primitive Culture," 1871]
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*men- (1)

Proto-Indo-European root meaning "to think," with derivatives referring to qualities and states of mind or thought.

It forms all or part of: admonish; Ahura Mazda; ament; amentia; amnesia; amnesty; anamnesis; anamnestic; automatic; automaton; balletomane; comment; compos mentis; dement; demonstrate; Eumenides; idiomatic; maenad; -mancy; mandarin; mania; maniac; manic; mantic; mantis; mantra; memento; mens rea; mental; mention; mentor; mind; Minerva; minnesinger; mnemonic; Mnemosyne; money; monition; monitor; monster; monument; mosaic; Muse; museum; music; muster; premonition; reminiscence; reminiscent; summon.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit manas- "mind, spirit," matih "thought," munih "sage, seer;" Avestan manah- "mind, spirit;" Greek memona "I yearn," mania "madness," mantis "one who divines, prophet, seer;" Latin mens "mind, understanding, reason," memini "I remember," mentio "remembrance;" Lithuanian mintis "thought, idea," Old Church Slavonic mineti "to believe, think," Russian pamjat "memory;" Gothic gamunds, Old English gemynd "memory, remembrance; conscious mind, intellect."

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