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arithmetically
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Arithmetical
(gcide) | Arithmetical \Ar`ith*met"ic*al\, a.
Of or pertaining to arithmetic; according to the rules or
method of arithmetic.
[1913 Webster]
Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
[1913 Webster] |
Arithmetical complement of a logarithm
(gcide) | Logarithm \Log"a*rithm\ (l[o^]g"[.a]*r[i^][th]'m), n. [Gr.
lo`gos word, account, proportion + 'ariqmo`s number: cf. F.
logarithme.] (Math.)
One of a class of auxiliary numbers, devised by John Napier,
of Merchiston, Scotland (1550-1617), to abridge arithmetical
calculations, by the use of addition and subtraction in place
of multiplication and division.
Note: The relation of logarithms to common numbers is that of
numbers in an arithmetical series to corresponding
numbers in a geometrical series, so that sums and
differences of the former indicate respectively
products and quotients of the latter; thus,
0 1 2 3 4 Indices or logarithms
1 10 100 1000 10,000 Numbers in geometrical progression
Hence, the logarithm of any given number is the
exponent of a power to which another given invariable
number, called the base, must be raised in order to
produce that given number. Thus, let 10 be the base,
then 2 is the logarithm of 100, because 10^2 = 100,
and 3 is the logarithm of 1,000, because 10^3 =
1,000.
[1913 Webster]
Arithmetical complement of a logarithm, the difference
between a logarithm and the number ten.
Binary logarithms. See under Binary.
Common logarithms, or Brigg's logarithms, logarithms of
which the base is 10; -- so called from Henry Briggs, who
invented them.
Gauss's logarithms, tables of logarithms constructed for
facilitating the operation of finding the logarithm of the
sum of difference of two quantities from the logarithms of
the quantities, one entry of those tables and two
additions or subtractions answering the purpose of three
entries of the common tables and one addition or
subtraction. They were suggested by the celebrated German
mathematician Karl Friedrich Gauss (died in 1855), and are
of great service in many astronomical computations.
Hyperbolic logarithm or Napierian logarithm or {Natural
logarithm}, a logarithm (devised by John Speidell, 1619) of
which the base is e (2.718281828459045...); -- so called
from Napier, the inventor of logarithms.
Logistic logarithms or Proportional logarithms, See under
Logistic.
[1913 Webster] LogarithmeticArithmetical \Ar`ith*met"ic*al\, a.
Of or pertaining to arithmetic; according to the rules or
method of arithmetic.
[1913 Webster]
Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
[1913 Webster] |
Arithmetical complement of a number
(gcide) | Complement \Com"ple*ment\, n. [L. complementun: cf. F.
compl['e]ment. See Complete, v. t., and cf. Compliment.]
1. That which fills up or completes; the quantity or number
required to fill a thing or make it complete.
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2. That which is required to supply a deficiency, or to
complete a symmetrical whole.
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History is the complement of poetry. --Sir J.
Stephen.
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3. Full quantity, number, or amount; a complete set;
completeness.
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To exceed his complement and number appointed him
which was one hundred and twenty persons. --Hakluyt.
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4. (Math.) A second quantity added to a given quantity to
make it equal to a third given quantity.
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5. Something added for ornamentation; an accessory. [Obs.]
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Without vain art or curious complements. --Spenser.
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6. (Naut.) The whole working force of a vessel.
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7. (Mus.) The interval wanting to complete the octave; -- the
fourth is the complement of the fifth, the sixth of the
third.
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8. A compliment. [Obs.] --Shak.
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Arithmetical compliment of a logarithm. See under
Logarithm.
Arithmetical complement of a number (Math.), the difference
between that number and the next higher power of 10; as, 4
is the complement of 6, and 16 of 84.
Complement of an arc or Complement of an angle (Geom.),
the difference between that arc or angle and 90[deg].
Complement of a parallelogram. (Math.) See Gnomon.
In her complement (Her.), said of the moon when represented
as full.
[1913 Webster] |
Arithmetical compliment of a logarithm
(gcide) | Complement \Com"ple*ment\, n. [L. complementun: cf. F.
compl['e]ment. See Complete, v. t., and cf. Compliment.]
1. That which fills up or completes; the quantity or number
required to fill a thing or make it complete.
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2. That which is required to supply a deficiency, or to
complete a symmetrical whole.
[1913 Webster]
History is the complement of poetry. --Sir J.
Stephen.
[1913 Webster]
3. Full quantity, number, or amount; a complete set;
completeness.
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To exceed his complement and number appointed him
which was one hundred and twenty persons. --Hakluyt.
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4. (Math.) A second quantity added to a given quantity to
make it equal to a third given quantity.
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5. Something added for ornamentation; an accessory. [Obs.]
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Without vain art or curious complements. --Spenser.
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6. (Naut.) The whole working force of a vessel.
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7. (Mus.) The interval wanting to complete the octave; -- the
fourth is the complement of the fifth, the sixth of the
third.
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8. A compliment. [Obs.] --Shak.
[1913 Webster]
Arithmetical compliment of a logarithm. See under
Logarithm.
Arithmetical complement of a number (Math.), the difference
between that number and the next higher power of 10; as, 4
is the complement of 6, and 16 of 84.
Complement of an arc or Complement of an angle (Geom.),
the difference between that arc or angle and 90[deg].
Complement of a parallelogram. (Math.) See Gnomon.
In her complement (Her.), said of the moon when represented
as full.
[1913 Webster] |
arithmetical mean
(gcide) | Mean \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.
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But to speak in a mean, the virtue of prosperity is
temperance; the virtue of adversity is fortitude.
--Bacon.
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There is a mean in all things. --Dryden.
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The extremes we have mentioned, between which the
wellinstracted Christian holds the mean, are
correlatives. --I. Taylor.
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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.
[1913 Webster]
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.
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Their virtuous conversation was a mean to work the
conversion of the heathen to Christ. --Hooker.
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You may be able, by this mean, to review your own
scientific acquirements. --Coleridge.
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Philosophical doubt is not an end, but a mean. --Sir
W. Hamilton.
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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.
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By this means he had them more at vantage.
--Bacon.
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What other means is left unto us. --Shak.
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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.
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Your means are very slender, and your waste is
great. --Shak.
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5. (Mus.) A part, whether alto or tenor, intermediate between
the soprano and base; a middle part. [Obs.]
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The mean is drowned with your unruly base. --Shak.
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6. Meantime; meanwhile. [Obs.] --Spenser.
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7. A mediator; a go-between. [Obs.] --Piers Plowman.
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He wooeth her by means and by brokage. --Chaucer.
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By all means, certainly; without fail; as, go, by all
means.
By any means, in any way; possibly; at all.
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If by any means I might attain to the resurrection
of the dead. --Phil. iii.
ll.
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By no means, or By no manner of means, not at all;
certainly not; not in any degree.
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The wine on this side of the lake is by no means so
good as that on the other. --Addison.
[1913 Webster]Arithmetical \Ar`ith*met"ic*al\, a.
Of or pertaining to arithmetic; according to the rules or
method of arithmetic.
[1913 Webster]
Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
[1913 Webster] |
Arithmetical mean
(gcide) | Mean \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.
[1913 Webster]
But to speak in a mean, the virtue of prosperity is
temperance; the virtue of adversity is fortitude.
--Bacon.
[1913 Webster]
There is a mean in all things. --Dryden.
[1913 Webster]
The extremes we have mentioned, between which the
wellinstracted Christian holds the mean, are
correlatives. --I. Taylor.
[1913 Webster]
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.
[1913 Webster]
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.
[1913 Webster]
Their virtuous conversation was a mean to work the
conversion of the heathen to Christ. --Hooker.
[1913 Webster]
You may be able, by this mean, to review your own
scientific acquirements. --Coleridge.
[1913 Webster]
Philosophical doubt is not an end, but a mean. --Sir
W. Hamilton.
[1913 Webster]
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.
[1913 Webster]
By this means he had them more at vantage.
--Bacon.
[1913 Webster]
What other means is left unto us. --Shak.
[1913 Webster]
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.
[1913 Webster]
Your means are very slender, and your waste is
great. --Shak.
[1913 Webster]
5. (Mus.) A part, whether alto or tenor, intermediate between
the soprano and base; a middle part. [Obs.]
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The mean is drowned with your unruly base. --Shak.
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6. Meantime; meanwhile. [Obs.] --Spenser.
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7. A mediator; a go-between. [Obs.] --Piers Plowman.
[1913 Webster]
He wooeth her by means and by brokage. --Chaucer.
[1913 Webster]
By all means, certainly; without fail; as, go, by all
means.
By any means, in any way; possibly; at all.
[1913 Webster]
If by any means I might attain to the resurrection
of the dead. --Phil. iii.
ll.
[1913 Webster]
By no means, or By no manner of means, not at all;
certainly not; not in any degree.
[1913 Webster]
The wine on this side of the lake is by no means so
good as that on the other. --Addison.
[1913 Webster]Arithmetical \Ar`ith*met"ic*al\, a.
Of or pertaining to arithmetic; according to the rules or
method of arithmetic.
[1913 Webster]
Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
[1913 Webster] |
Arithmetical progression
(gcide) | Progression \Pro*gres"sion\, n. [L. progressio: cf. F.
progression.]
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1. The act of moving forward; a proceeding in a course;
motion onward.
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2. Course; passage; lapse or process of time.
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I hope, in a short progression, you will be wholly
immerged in the delices and joys of religion.
--Evelyn.
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3. (Math.) Regular or proportional advance in increase or
decrease of numbers; continued proportion, arithmetical,
geometrical, or harmonic.
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4. (Mus.) A regular succession of tones or chords; the
movement of the parts in harmony; the order of the
modulations in a piece from key to key.
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Arithmetical progression, a progression in which the terms
increase or decrease by equal differences, as the numbers
[lbrace2]2, 4, 6, 8, 1010, 8, 6, 4, 2[rbrace2] by the
difference 2.
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Geometrical progression, a progression in which the terms
increase or decrease by equal ratios, as the numbers
[lbrace2]2, 4, 8, 16, 32, 6464, 32, 16, 8, 4, 2[rbrace2]
by a continual multiplication or division by 2.
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Harmonic progression, a progression in which the terms are
the reciprocals of quantities in arithmetical progression,
as 1/2, 1/4, 1/6, 1/8, 1/10.
[1913 Webster]Arithmetical \Ar`ith*met"ic*al\, a.
Of or pertaining to arithmetic; according to the rules or
method of arithmetic.
[1913 Webster]
Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
[1913 Webster] |
Arithmetical proportion
(gcide) | Arithmetical \Ar`ith*met"ic*al\, a.
Of or pertaining to arithmetic; according to the rules or
method of arithmetic.
[1913 Webster]
Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
[1913 Webster] |
Arithmetically
(gcide) | Arithmetically \Ar`ith*met"ic*al*ly\, adv.
Conformably to the principles or methods of arithmetic.
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Logarithmetical
(gcide) | Logarithmetic \Log`a*rith*met"ic\, Logarithmetical
\Log"a*rith*met"ic*al\, a.
See Logarithmic.
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Logarithmetically
(gcide) | Logarithmetically \Log`a*rith*met"ic*al*ly\, adv.
Logarithmically.
[1913 Webster] Logarithmic |
arithmetically
(wn) | arithmetically
adv 1: with respect to arithmetic; "this problem is
arithmetically easy" |
|