Etymology
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cartomancy (n.)
"divination by means of playing-cards," 1852, from combining form of card (n.1) + -mancy.
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astromancy (n.)
"astrology, art of judging occult influences of stars and planets on human affairs," 1650s; see astro- + -mancy "divination by means of."
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catoptromancy (n.)
"divination by means of a mirror," 1610s, from Latinized combining form of Greek katoptron "mirror" (see catoptric) + -mancy "divination by means of."
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arithmancy (n.)
"divination by numbers," 1570s, from Greek arithmos "number" (see arithmetic) + -mancy "divination by means of." Alternative arithmomancy is recorded from 1620s.
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pegomancy (n.)

"divination by fountains," 1727, from Latinized form of Greek pēgē "fountain, spring" (a word of unknown origin, possibly Pre-Greek) + -mancy "divination by means of."

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psephomancy (n.)

"divination by means of pebbles drawn from a heap," 1727, from Greek psēphos "pebble" (a word of uncertain origin) + -mancy "divination by means of."

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ornithomancy (n.)

"divination by means of birds," 1650s; see ornitho- + -mancy. Middle English had it as ornomanci (late 15c.). Related: Ornithomantic.

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oneiromancy (n.)

"divination through dreams," 1650s; see oneiro- "dream" + -mancy "divination by means of." Greek had oneiromantis "an interpreter of dreams." Related: oneiromantic.

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psychomancy (n.)

1680s, "divination by consulting the souls of the deceased;" see psycho- + -mancy. The word was revived or re-coined in occultism by 1853. Related: Psychomantic; psychomancer.

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ophiomancy (n.)

"the ancient art of divination by the movements and coilings of snakes, 1753, from ophio- "snake, serpent" + -mancy "divination by means of." Related: Ophiomantic; ophiomancer.

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