Etymology
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invincible (adj.)

early 15c., from Old French invincible (14c.) or directly from Latin invincibilis "unconquerable," from in- "not" (see in- (1)) + vincibilis "to be gained, easily maintained, conquerable," from vincere "to overcome" (from nasalized form of PIE root *weik- (3) "to fight, conquer"). Related: Invincibly.

The noun meaning "one who is invincible" is from 1630s. Invincible ignorance, an ignorance which the person having it lacks means to overcome, is from Church Latin ignorantia invincibilis (Aquinas). The Invincible Armada was the Spanish of 1588. Related: Invincibly.

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invincibility (n.)
1670s, from invincible + -ity. Invincibleness is recorded from 1610s.
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*weik- (3)

Proto-Indo-European root meaning "to fight, conquer."

It forms all or part of: convict; convince; evict; evince; invictus; invincible; Ordovician; province; vanquish; victor; victory; Vincent; vincible.

It is the hypothetical source of/evidence for its existence is provided by: Latin victor "a conqueror," vincere "to conquer, overcome, defeat;" Lithuanian apveikiu, apveikti "to subdue, overcome;" Old Church Slavonic veku "strength, power, age;" Old Norse vigr "able in battle," Old English wigan "fight;" Welsh gwych "brave, energetic," Old Irish fichim "I fight," second element in Celtic Ordovices "those who fight with hammers."

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inexpugnable (adj.)
late 15c., from Old French inexpugnable (14c.) or directly from Latin inexpugnabilis "not to be taken by assault, not to be rooted out, invincible," from in- "not" (see in- (1)) + expugnabilis "assailable," from expugnare (see expugn). Figurative sense, in reference to arguments, etc., is from 1530s.
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armada (n.)
"fleet of warships," 1530s (armado), from Spanish armada "an armed force," from Medieval Latin armata "armed force" (see army). Current form of the word is from 1590s. The fleet sent by Philip II of Spain against England in 1588 was being called the Spanish Armada by 1613, the Invincible Armada by 1632.
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invictus 

Latin adjective, "unconquered, unsubdued, invincible," from in- "not, opposite of" (see in- (1)) + victus, past participle of vincere "to conquer, overcome" (from nasalized form of PIE root *weik- (3) "to fight, conquer").

It matters not how strait the gate,
How charged with punishments the scroll,
I am the master of my fate,
I am the captain of my soul.
[William Ernest Henley, "Invictus"]
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Occam's razor (n.)

when two competing hypotheses explain the data equally well, choose the simpler. Or, as Sir William Hamilton puts it, "Neither more, nor more onerous, causes are to be assumed, than are necessary to account for the phenomena." Named for English philosopher William of Ockham or Occam (c. 1285-c. 1349), "The Invincible Doctor," who expressed it with Entia non sunt multiplicanda praeter neccssitatem.

So called after William of Occam (died about 1349): but, as a historical fact, Occam does not make much use of this principle, which belongs rather to the contemporary nominalist William Durand de St. Pourçain (died 1332). [Century Dictionary]
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adamant (n.)
Old English aðamans "a very hard stone;" the modern word is a mid-14c. borrowing of Old French adamant "diamond; magnet" or directly from Latin adamantem (nominative adamas) "adamant, hardest iron, steel," also used figuratively, of character, from Greek adamas (genitive adamantos), name of a hypothetical hardest material, noun use of an adjective meaning "unbreakable, inflexible," which was metaphoric of anything unalterable (such as Hades), a word of uncertain origin.

It is perhaps literally "invincible, indomitable," from a- "not" (see a- (3)) + daman "to conquer, to tame," from PIE root *deme- "to constrain, force, break (horses)" (see tame (adj.)). "But semantically, the etymology is rather strange," according to Beekes, who suggests it might be a foreign word altered in Greek by folk etymology, and compares Akkadian (Semitic) adamu.

Applied in antiquity to a metal resembling gold (Plato), white sapphire (Pliny), magnet (Ovid, perhaps through confusion with Latin adamare "to love passionately"), steel, emery stone, and especially diamond, which is a variant of this word. "The name has thus always been of indefinite and fluctuating sense" [Century Dictionary].
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bogey (n.2)

in golf, c. 1891, originally "number of strokes a good player is supposed to need for a given hole or course;" later, "score one over par" (1946); from the same source as bogey (n.1), on the notion of a "phantom" opponent, represented by the "ground score." The word was in vogue at the time in Britain through the popularity of a music-hall tune "Hush, Hush, Hush, Here Comes the Bogey Man."

One popular song at least has left its permanent effect on the game of golf. That song is 'The Bogey Man.' In 1890 Dr. Thos. Browne, R.N., the hon. secretary of the Great Yarmouth Club, was playing against a Major Wellman, the match being against the 'ground score,' which was the name given to the scratch value of each hole. The system of playing against the 'ground score' was new to Major Wellman, and he exclaimed, thinking of the song of the moment, that his mysterious and well-nigh invincible opponent was a regular 'bogey-man.' The name 'caught on' at Great Yarmouth, and to-day 'Bogey' is one of the most feared opponents on all the courses that acknowledge him. [1908, cited in OED]

Other early golfing sources give it an American origin. As a verb, attested by 1948.

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phalanx (n.)

1550s, "line of battle in close ranks," from Latin phalanx "compact body of heavily armed men in battle array," or directly from Greek phalanx (genitive phalangos) "line of battle, battle array," also "finger or toe bone," originally "round piece of wood, trunk, log," a word of unknown origin. Perhaps from PIE root *bhelg- "plank, beam" (source of Old English balca "balk;" see balk (n.)).

In anatomy, originally the whole row of finger joints, which fit together like infantry in close order. Figurative sense of "number of persons banded together in a common cause" is attested from 1600 (compare Spanish Falangist, member of a fascist organization founded in 1933).

The celebrated Macedonian phalanx was normally drawn up sixteen ranks deep, the men being clad in armor, bearing shields, and armed with swords and with spears from 21 to 24 feet long. In array the shields formed a continuous bulwark, and the ranks were placed at such intervals that five spears which were borne pointed forward and upward protected every man in the front rank. The phalanx on smooth ground, and with its flanks and rear adequately protected, was practically invincible; but it was cumbrous and slow in movement, and if once broken could only with great difficulty be reformed. [Century Dictionary]
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