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likeness, neighborhood, resemblance, contiguity, nearness, propinquity, similarity.

      In mathematics, approximation is not guesswork, not looseness, and not error. The process of approximation is as exact and correct at every point as that by which an absolute result is secured; the result only fails of exactness because of some inherent difficulty in the problem. The attempt to "square the circle" gives only an approximate result, because of the impossibility of expressing the circumference in terms of the radius. But the limits of error on either side are known, and the approximation has practical value. Outside of mathematics, the correct use of approximation (and the kindred words approximate and approximately) is to express as near an approach to accuracy and certainty as the conditions of human thought or action in any given case make possible. Resemblance and similarity may be but superficial and apparent; approximation is real. Approach is a relative term, indicating that one has come nearer than before, tho the distance may yet be considerable; an approximation brings one really near. Nearness, neighborhood, and propinquity are commonly used of place; approximation, of mathematical calculations and abstract reasoning; we speak of approach to the shore, nearness to the town, approximation to the truth.

      Antonyms:

difference, distance, error, remoteness, unlikeness, variation.

      Prepositions:

      The approximation of the vegetable to the animal type.

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      Synonyms:

accouterments, armor, harness, mail, weapons.

      Arms are implements of attack; armor is a defensive covering. The knight put on his armor; he grasped his arms. With the disuse of defensive armor the word has practically gone out of military use, but it is still employed in the navy, where the distinction[56] is clearly preserved; any vessel provided with cannon is an armed vessel; an armored ship is an ironclad. Anything that can be wielded in fight may become a weapon, as a pitchfork or a paving-stone; arms are especially made and designed for conflict.

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      Synonyms:

armament, forces, military, soldiers,
array, host, multitude, soldiery,
force, legions, phalanx, troops.

      An army is an organized body of men armed for war, ordinarily considerable in numbers, always independent in organization so far as not to be a constituent part of any other command. Organization, unity, and independence, rather than numbers are the essentials of an army. We speak of the invading army of Cortes or Pizarro, tho either body was contemptible in numbers from a modern military standpoint. We may have a little army, a large army, or a vast army. Host is used for any vast and orderly assemblage; as, the stars are called the heavenly host. Multitude expresses number without order or organization; a multitude of armed men is not an army, but a mob. Legion (from the Latin) and phalanx (from the Greek) are applied by a kind of poetic license to modern forces; the plural legions is preferred to the singular. Military is a general word for land-forces; the military may include all the armed soldiery of a nation, or the term may be applied to any small detached company, as at a fort, in distinction from civilians. Any organized body of men by whom the law or will of a people is executed is a force; the word is a usual term for the police of any locality.

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      Synonyms:

accuse, charge, impeach, prosecute,
censure, cite, indict, summon.

      Arraign is an official word; a person accused of crime is arraigned when he is formally called into court, the indictment read to him, and the demand made of him to plead guilty or not guilty; in more extended use, to arraign is to call in question for fault in any formal, public, or official way. One may charge another with any fault, great or trifling, privately or publicly, formally or informally. Accuse is stronger than charge, suggesting more of the formal and criminal; a person may charge a[57] friend with unkindness or neglect; he may accuse a tramp of stealing. Censure carries the idea of fault, but not of crime; it may be private and individual, or public and official. A judge, a president, or other officer of high rank may be impeached before the appropriate tribunal for high crimes; the veracity of a witness may be impeached by damaging evidence. A person of the highest character may be summoned as defendant in a civil suit; or he may be cited to answer as administrator, etc. Indict and arraign apply strictly to criminal proceedings, and only an alleged criminal is indicted or arraigned. One is indicted by the grand jury, and arraigned before the appropriate court.

      Antonyms:

acquit, discharge, exonerate, overlook, release,
condone, excuse, forgive, pardon, set free.

      Prepositions:

      Arraign at the bar, before the tribunal, of or for a crime; on or upon an indictment.

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