Online Etymology Dictionary

pegomancy: "divination by fountains," 1727, from Gk., from pege "fountain, spring" (of unknown origin) + manteia "oracle, divination."
arithmancy: 1570s, "divination by numbers," from Gk. arithmos "number" + -manteia "divination."
necromancy: c.1300, "divination by communication with the dead," from O.Fr. nygromancie, from M.L. nigromantia (1212), from L. necromantia "divination from an exhumed corpse," from Gk. nekromanteia, from nekros "dead body" (see necro-) + manteia "divination, oracle," from manteuesthai "to prophesy," from mantis "prophet" (see mania). Spelling infl. in M.L. by niger "black," on notion of "black arts." Modern spelling is c.1550 from attempts to correct M.E. nygromauncy.
augury: late 14c., "divination from the flight of birds," from O.Fr. augure "divination, soothsaying, sorcery, enchantment," from L. augurium (see augur). Fig. sense of "presage, omen, portent, indication" is from 1797 (also often in pl. as auguries).
gyromancy: 1557, "a method of divination by walking in a circle till the person falls down from dizziness, the inference being drawn from the place in the circle at which he fell," from M.L. gyromantia, from Gk. gyyros "circle" + manteia "divination, oracle."
bibliomancy: 1753, "divination by opening a book (especially the Bible) at random," the first verse presenting itself being taken as a prognostication of future events, from biblio- + manteia "divination." Before the Bible, in pagan times, Homer (sortes Homericæ) and Virgil (sortes Virgilianæ) were similarly used.
tephromancy: 1652, "divination by means of ashes," from Gk. tephra "ashes" + manteia "divination," from mantis "prophet" (see mania).
-mancy: combining form meaning "divination by means of," from O.Fr. -mancie, from L.L. -mantia, from Gk. manteia "oracle, divination," from mantis "seer, prophet, soothsayer," related to mania "madness, frenzy" (see mania).
geomancy: "art of divination by means of signs derived from the earth," mid-14c., from Fr. geomancie, from L. geomantia, from late Gk. *geomanteia, from geo-, comb. form of ge "earth" + manteia "divination."
myomancy: 1725, divination by the movements of mice, from Gk. myo-, comb. form of mys (see mouse) + -mancy, from Gk. manteia "oracle, divination" (see -mancy).
catoptromancy: "divination by means of a mirror," 1613, from Gk. katoptron "mirror."
sciomancy: "divination by communication with shades of the dead," 1623, from Mod.L. sciomantia, from Gk. skio- "shadow" + manteia (see -mancy).
auspicious: 1590s, "of good omen," from L. auspicium "divination by observing the flight of birds," from auspex (gen. auspicis) "augur," lit. "one who takes signs from the flight of birds."
alectryomancy: "divination by means of a cock and grains of corn," 1650s, from Gk. alektryon "cock" + manteia "oracle." The first element is lit. "warder-off, fighter," related to alexein "to ward off, drive or keep off" (see Alexander).
jinx (n.): 1911, Amer.Eng., from 17c. jyng "a charm, a spell," originally "wryneck," a bird used in witchcraft and divination, from L. iynx "wryneck," from Gk. iynx. The verb is 1917 in Amer.Eng., from the noun.
palmistry: "divination from the palm of the hand," c.1420, from palme (see palm (1)) + obscure second element, perhaps -estre (as in M.E. webbestre "weaver") or -rie (as in M.E. archerie "archery").
ophidian: "pertaining to snakes," 1883, from Gk. ophidion, dim. of ophis "serpent," of unknown origin. Hence, ophiolatry "serpent-worship" (1862), and the 2c. sect of the Ophitæ, who revered the serpent as the symbol of divine wisdom. Also ophiomancy (1683), the ancient art of divination by the movements of snakes.
chiromancy: "divination by the hand, palmistry," 1528, from Fr. chiromancie, from L. chiromantia, from Late Gk. kheiromanteia, from kheiro-, comb. form of kheir "hand" + -mantia (see -mancy).
divine (v.): "to conjure, to guess," originally "to make out by supernatural insight," early 14c., from L. divinus (see divine (adj.)), which also meant "soothsayer." Hence, divination (late 14c.), from O.Fr., from L. divinationem (nom. divinatio) "the power of foreseeing, prediction," from divinatus, pp. of divinare, lit. "to be inspired by a god." Divining rod (or wand) attested from 1650s.
rhabdomancy: 1646, "use of divining rod" (especially to discover ores or underground water), from Gk. rhabdos "rod, twig, stick" + manteia "divination, oracle." Gk. rhabdos is from PIE *werbh- (cf. Lith. virbas "twig, branch, scion, rod," L. verbena "leaves and branches of laurel"), from base *werb- "to turn, bend" (see warp).
mirror: early 13c., from O.Fr. mireor "a reflecting glass," earlier miradoir (11c.), from mirer "look at," from V.L. *mirare, from L. mirari "to wonder at, admire" (see miracle). Fig. usage is attested from c.1300. The verb. meaning "to reflect" is first attested 1820 in Keats's "Lamia." Used in divination since classical and biblical times; mirrors in modern England are the subject of at least 14 known superstitions, according to folklorists. Belief that breaking one brings bad luck is attested from 1777.
powwow: 1624, "priest, sorcerer," from a southern New England Algonquian language (probably Narragansett) powwow "shaman, medicine man, Indian priest," from a verb meaning "to use divination, to dream," from Proto-Algonquian *pawe:wa "he dreams, one who dreams." Meaning "magical ceremony among N.Amer. Indians" is recorded from 1663. Sense of "council, conference, meeting" is first recorded 1812. Verb sense of "to confer, discuss" is attested from 1780.
consider: late 14c., from O.Fr. considerer, from L. considerare "to look at closely, observe," lit. "to observe the stars," from com- "with" + sidus (gen. sideris) "constellation." Perhaps a metaphor from navigation, but more likely reflecting Roman obsession with divination by astrology. Tucker doubts the connection with sidus, however, since it is "quite inapplicable to desiderare," and suggests derivation instead from the root of Eng. side meaning "stretch, extend," and a sense for the full word of "survey on all sides" or "dwell long upon."
augur (n.): 1540s, from L. augur, a religious official in ancient Rome who foretold events by interpreting omens, perhaps originally meaning "an increase in crops enacted in ritual," in which case it probably is from Old L. *augos (gen. *augeris) "increase," and is related to augere "increase" (see augment). The more popular theory is that it is from L. avis "bird," since the flights, singing, and feeding of birds, along with entrails from bird sacrifices, were important objects of divination (cf. auspicious). The second element would be from garrire "to talk." The verb is c.1600, from the noun.
magpie: 1605, common European bird, known for its chattering, earlier simply pie; first element from Mag, nickname for Margaret, long used in Eng. proverbial and slang senses for qualities associated generally with women, especially in this case "idle chattering" (cf. Magge tales "tall tales, nonsense," c.1410; also Fr. margot "magpie," from Margot, pet form of Marguerite). Second element, pie, is the earlier name of the bird, from O.Fr. pie, from L. pica "magpie," fem. of picus "woodpecker," possibly from PIE base *pi-, denoting pointedness, of the beak, perhaps, but the magpie also has a long, pointed tail. The birds are proverbial for pilfering and hoarding, can be taught to speak, and have been regarded since the Middle Ages as a bird of ill omen.
"Whan pyes chatter vpon a house it is a sygne of ryghte euyll tydynges." [1507]
Divination by number of magpies is attested from c.1780 in Lincolnshire; the rhyme varies from place to place, the only consistency being that one is bad, two are good.
witch: O.E. wicce "female magician, sorceress," in later use esp. "a woman supposed to have dealings with the devil or evil spirits and to be able by their cooperation to perform supernatural acts," fem. of O.E. wicca "sorcerer, wizard, man who practices witchcraft or magic," from verb wiccian "to practice witchcraft" (cf. Low Ger. wikken, wicken "to use witchcraft," wikker, wicker "soothsayer"). OED says of uncertain origin. Klein suggests connection with O.E. wigle "divination," and wig, wih "idol." Watkins says the nouns represent a P.Gmc. *wikkjaz "necromancer" (one who wakes the dead), from PIE *weg-yo-, from *weg- "to be strong, be lively." That wicce once had a more specific sense than the later general one of "female magician, sorceress" perhaps is suggested by the presence of other words in O.E. describing more specific kinds of magical craft. In the Laws of Ælfred (c.890), witchcraft was specifically singled out as a woman's craft, whose practitioners were not to be suffered to live among the W. Saxons:
"Ða fæmnan þe gewuniað onfon gealdorcræftigan & scinlæcan & wiccan, ne læt þu ða libban."
The other two words combined with it here are gealdricge, a woman who practices "incantations," and scinlæce "female wizard, woman magician," from a root meaning "phantom, evil spirit." Another word that appears in the Anglo-Saxon laws is lyblæca "wizard, sorcerer," but with suggestions of skill in the use of drugs, since the root of the word is lybb "drug, poison, charm." Lybbestre was a fem. word meaning "sorceress," and lybcorn was the name of a certain medicinal seed (perhaps wild saffron). Weekly notes possible connection to Gothic weihs "holy" and Ger. weihan "consecrate," and writes, "the priests of a suppressed religion naturally become magicians to its successors or opponents." In Anglo-Saxon glossaries, wicca renders L. augur (c.1100), and wicce stands for "pythoness, divinatricem." In the "Three Kings of Cologne" (c.1400) wicca translates Magi:
"Þe paynyms ... cleped þe iij kyngis Magos, þat is to seye wicchis."
The glossary translates L. necromantia ("demonum invocatio") with galdre, wiccecræft. The Anglo-Saxon poem called "Men's Crafts" has wiccræft, which appears to be the same word, and by its context means "skill with horses." In a c.1250 translation of "Exodus," witches is used of the Egyptian midwives who save the newborn sons of the Hebrews: "Ðe wicches hidden hem for-ðan, Biforen pharaun nolden he ben." Witch in ref. to a man survived in dialect into 20c., but the fem. form was so dominant by 1601 that men-witches or he-witch began to be used. Extended sense of "young woman or girl of bewitching aspect or manners" is first recorded 1740. Witch doctor is from 1718; applied to African magicians from 1836.
"At this day it is indifferent to say in the English tongue, 'she is a witch,' or 'she is a wise woman.' " [Reginald Scot, "The Discoverie of Witchcraft," 1584]