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From: Webster's Revised Unabridged Dictionary (1913)

 Mean, n.
 1. That which is mean, or intermediate, between two extremes of place, time, or number; the middle point or place; middle rate or degree; mediocrity; medium; absence of extremes or excess; moderation; measure.
    But to speak in a mean, the virtue of prosperity is temperance; the virtue of adversity is fortitude.   --Bacon.
    There is a mean in all things.   --Dryden.
    The extremes we have mentioned, between which the wellinstracted Christian holds the mean, are correlatives.   --I. Taylor.
 2. Math. A quantity having an intermediate value between several others, from which it is derived, and of which it expresses the resultant value; usually, unless otherwise specified, it is the simple average, formed by adding the quantities together and dividing by their number, which is called an arithmetical mean.  A geometrical mean is the nth root of the product of the n quantities being averaged.
 3. That through which, or by the help of which, an end is attained; something tending to an object desired; intermediate agency or measure; necessary condition or coagent; instrument.
    Their virtuous conversation was a mean to work the conversion of the heathen to Christ.   --Hooker.
    You may be able, by this mean, to review your own scientific acquirements.   --Coleridge.
    Philosophical doubt is not an end, but a mean.   --Sir W. Hamilton.
 Note:In this sense the word is usually employed in the plural form means, and often with a singular attribute or predicate, as if a singular noun.
    By this means he had them more at vantage.   --Bacon.
    What other means is left unto us.   --Shak.
 4. pl. Hence: Resources; property, revenue, or the like, considered as the condition of easy livelihood, or an instrumentality at command for effecting any purpose; disposable force or substance.
    Your means are very slender, and your waste is great.   --Shak.
 5. Mus. A part, whether alto or tenor, intermediate between the soprano and base; a middle part. [Obs.]
    The mean is drowned with your unruly base.   --Shak.
 6. Meantime; meanwhile. [Obs.]
 7. A mediator; a go-between. [Obs.]
    He wooeth her by means and by brokage.   --Chaucer.
 By all means, certainly; without fail; as, go, by all means.
 By any means, in any way; possibly; at all.
    If by any means I might attain to the resurrection of the dead.   --Phil. iii. ll.
 -- By no means, or By no manner of means, not at all; certainly not; not in any degree.
    The wine on this side of the lake is by no means so good as that on the other.   --Addison.

From: Webster's Revised Unabridged Dictionary (1913)

 Ar·ith·met·ic·al a. Of or pertaining to arithmetic; according to the rules or method of arithmetic.
 Arithmetical complement of a logarithm. See Logarithm.
 Arithmetical mean. See Mean.
 Arithmetical progression. See Progression.
 Arithmetical proportion. See Proportion.