| slovo | definícia |
arithmetic
(encz) | arithmetic,aritmetika |
arithmetic
(encz) | arithmetic,početní adj: Zdeněk Brož |
arithmetic
(encz) | arithmetic,počty |
Arithmetic
(gcide) | Mathematics \Math`e*mat"ics\, n. [F. math['e]matiques, pl., L.
mathematica, sing., Gr. ? (sc. ?) science. See Mathematic,
and -ics.]
That science, or class of sciences, which treats of the exact
relations existing between quantities or magnitudes, and of
the methods by which, in accordance with these relations,
quantities sought are deducible from other quantities known
or supposed; the science of spatial and quantitative
relations.
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Note: Mathematics embraces three departments, namely: 1.
Arithmetic. 2. Geometry, including Trigonometry
and Conic Sections. 3. Analysis, in which letters
are used, including Algebra, Analytical Geometry,
and Calculus. Each of these divisions is divided into
pure or abstract, which considers magnitude or quantity
abstractly, without relation to matter; and mixed or
applied, which treats of magnitude as subsisting in
material bodies, and is consequently interwoven with
physical considerations.
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Arithmetic
(gcide) | Arithmetic \A*rith"me*tic\, n. [OE. arsmetike, OF. arismetique,
L. arithmetica, fr. Gr. ? (sc. ?), fr. ? arithmetical, fr. ?
to number, fr. ? number, prob. fr. same root as E. arm, the
idea of counting coming from that of fitting, attaching. See
Arm. The modern Eng. and French forms are accommodated to
the Greek.]
1. The science of numbers; the art of computation by figures.
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2. A book containing the principles of this science.
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Arithmetic of sines, trigonometry.
Political arithmetic, the application of the science of
numbers to problems in civil government, political
economy, and social science.
Universal arithmetic, the name given by Sir Isaac Newton to
algebra.
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arithmetic
(wn) | arithmetic
adj 1: relating to or involving arithmetic; "arithmetical
computations" [syn: arithmetical, arithmetic]
n 1: the branch of pure mathematics dealing with the theory of
numerical calculations |
| | podobné slovo | definícia |
arithmetic
(encz) | arithmetic,aritmetika arithmetic,početní adj: Zdeněk Brožarithmetic,počty |
arithmetic mean
(encz) | arithmetic mean,aritmetický průměr Zdeněk Brož |
arithmetical
(encz) | arithmetical,aritmetický adj: Zdeněk Brožarithmetical,matematický |
arithmetically
(encz) | arithmetically,matematicky |
arithmetician
(encz) | arithmetician,matematik n: Zdeněk Brožarithmetician,počtář n: Zdeněk Brož |
Arithmetic of sines
(gcide) | Arithmetic \A*rith"me*tic\, n. [OE. arsmetike, OF. arismetique,
L. arithmetica, fr. Gr. ? (sc. ?), fr. ? arithmetical, fr. ?
to number, fr. ? number, prob. fr. same root as E. arm, the
idea of counting coming from that of fitting, attaching. See
Arm. The modern Eng. and French forms are accommodated to
the Greek.]
1. The science of numbers; the art of computation by figures.
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2. A book containing the principles of this science.
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Arithmetic of sines, trigonometry.
Political arithmetic, the application of the science of
numbers to problems in civil government, political
economy, and social science.
Universal arithmetic, the name given by Sir Isaac Newton to
algebra.
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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.
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Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
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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.
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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.
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Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
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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.
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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.
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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.
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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.
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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.
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Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
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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.
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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.
[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.
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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.
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Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
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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.
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Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
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Arithmetical proportion
(gcide) | Arithmetical \Ar`ith*met"ic*al\, a.
Of or pertaining to arithmetic; according to the rules or
method of arithmetic.
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Arithmetical complement of a logarithm. See Logarithm.
Arithmetical mean. See Mean.
Arithmetical progression. See Progression.
Arithmetical proportion. See Proportion.
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Arithmetically
(gcide) | Arithmetically \Ar`ith*met"ic*al*ly\, adv.
Conformably to the principles or methods of arithmetic.
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Arithmetician
(gcide) | Arithmetician \A*rith`me*ti"cian\, n. [Cf. F. arithm['e]ticien.]
One skilled in arithmetic.
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Binary arithmetic
(gcide) | Binary \Bi"na*ry\, a. [L. binarius, fr. bini two by two, two at
a time, fr. root of bis twice; akin to E. two: cf. F.
binaire.]
Compounded or consisting of two things or parts;
characterized by two (things).
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Binary arithmetic, that in which numbers are expressed
according to the binary scale, or in which two figures
only, 0 and 1, are used, in lieu of ten; the cipher
multiplying everything by two, as in common arithmetic by
ten. Thus, 1 is one; 10 is two; 11 is three; 100 is four,
etc. --Davies & Peck.
Binary compound (Chem.), a compound of two elements, or of
an element and a compound performing the function of an
element, or of two compounds performing the function of
elements.
Binary logarithms, a system of logarithms devised by Euler
for facilitating musical calculations, in which 1 is the
logarithm of 2, instead of 10, as in the common
logarithms, and the modulus 1.442695 instead of .43429448.
Binary measure (Mus.), measure divisible by two or four;
common time.
Binary nomenclature (Nat. Hist.), nomenclature in which the
names designate both genus and species.
Binary scale (Arith.), a uniform scale of notation whose
ratio is two.
Binary star (Astron.), a double star whose members have a
revolution round their common center of gravity.
Binary theory (Chem.), the theory that all chemical
compounds consist of two constituents of opposite and
unlike qualities.
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Decimal arithmetic
(gcide) | Decimal \Dec"i*mal\, a. [F. d['e]cimal (cf. LL. decimalis), fr.
L. decimus tenth, fr. decem ten. See Ten, and cf. Dime.]
Of or pertaining to decimals; numbered or proceeding by tens;
having a tenfold increase or decrease, each unit being ten
times the unit next smaller; as, decimal notation; a decimal
coinage.
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Decimal arithmetic, the common arithmetic, in which
numeration proceeds by tens.
Decimal fraction, a fraction in which the denominator is
some power of 10, as 2/10, [frac25x100], and is usually
not expressed, but is signified by a point placed at the
left hand of the numerator, as .2, .25.
Decimal point, a dot or full stop at the left of a decimal
fraction. The figures at the left of the point represent
units or whole numbers, as 1.05.
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Dyadic arithmetic
(gcide) | Dyadic \Dy*ad"ic\, a. [Gr. ?, fr. ? two.]
Pertaining to the number two; of two parts or elements.
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Dyadic arithmetic, the same as binary arithmetic.
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Logarithmetic
(gcide) | Logarithmetic \Log`a*rith*met"ic\, Logarithmetical
\Log"a*rith*met"ic*al\, a.
See Logarithmic.
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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 |
Mental arithmetic
(gcide) | Mental \Men"tal\, a. [F., fr. L. mentalis, fr. mens, mentis, the
mind; akin to E. mind. See Mind.]
Of or pertaining to the mind; intellectual; as, mental
faculties; mental operations, conditions, or exercise.
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What a mental power
This eye shoots forth! --Shak.
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Mental alienation, insanity.
Mental arithmetic, the art or practice of solving
arithmetical problems by mental processes, unassisted by
written figures.
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Political arithmetic
(gcide) | Arithmetic \A*rith"me*tic\, n. [OE. arsmetike, OF. arismetique,
L. arithmetica, fr. Gr. ? (sc. ?), fr. ? arithmetical, fr. ?
to number, fr. ? number, prob. fr. same root as E. arm, the
idea of counting coming from that of fitting, attaching. See
Arm. The modern Eng. and French forms are accommodated to
the Greek.]
1. The science of numbers; the art of computation by figures.
[1913 Webster]
2. A book containing the principles of this science.
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Arithmetic of sines, trigonometry.
Political arithmetic, the application of the science of
numbers to problems in civil government, political
economy, and social science.
Universal arithmetic, the name given by Sir Isaac Newton to
algebra.
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Sexagenary arithmetic
(gcide) | Sexagesimal \Sex`a*ges"i*mal\, a. [Cf. F. sexag['e]simal.]
Pertaining to, or founded on, the number sixty.
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Sexagesimal fractions or Sexagesimal numbers (Arith. &
Alg.), those fractions whose denominators are some power
of sixty; as, 1/60, 1/3600, 1/216000; -- called also
astronomical fractions, because formerly there were no
others used in astronomical calculations.
Sexagesimal arithmetic, or Sexagenary arithmetic, the
method of computing by the sexagenary scale, or by
sixties.
Sexagesimal scale (Math.), the sexagenary scale.
[1913 Webster]Sexagenary \Sex*ag"e*na*ry\, a. [L. sexagenarius, fr. sexageni
sixty each, akin to sexaginta sixty, sex six: cf.
sexag['e]naire. See Six.]
Pertaining to, or designating, the number sixty; poceeding by
sixties; sixty years old.
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Sexagenary arithmetic. See under Sexagesimal.
Sexagenary scale, or Sexagesimal scale (Math.), a scale
of numbers in which the modulus is sixty. It is used in
treating the divisions of the circle.
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Sexagesimal arithmetic
(gcide) | Sexagesimal \Sex`a*ges"i*mal\, a. [Cf. F. sexag['e]simal.]
Pertaining to, or founded on, the number sixty.
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Sexagesimal fractions or Sexagesimal numbers (Arith. &
Alg.), those fractions whose denominators are some power
of sixty; as, 1/60, 1/3600, 1/216000; -- called also
astronomical fractions, because formerly there were no
others used in astronomical calculations.
Sexagesimal arithmetic, or Sexagenary arithmetic, the
method of computing by the sexagenary scale, or by
sixties.
Sexagesimal scale (Math.), the sexagenary scale.
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Universal arithmetic
(gcide) | Arithmetic \A*rith"me*tic\, n. [OE. arsmetike, OF. arismetique,
L. arithmetica, fr. Gr. ? (sc. ?), fr. ? arithmetical, fr. ?
to number, fr. ? number, prob. fr. same root as E. arm, the
idea of counting coming from that of fitting, attaching. See
Arm. The modern Eng. and French forms are accommodated to
the Greek.]
1. The science of numbers; the art of computation by figures.
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2. A book containing the principles of this science.
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Arithmetic of sines, trigonometry.
Political arithmetic, the application of the science of
numbers to problems in civil government, political
economy, and social science.
Universal arithmetic, the name given by Sir Isaac Newton to
algebra.
[1913 Webster] |
arithmetic
(wn) | arithmetic
adj 1: relating to or involving arithmetic; "arithmetical
computations" [syn: arithmetical, arithmetic]
n 1: the branch of pure mathematics dealing with the theory of
numerical calculations |
arithmetic mean
(wn) | arithmetic mean
n 1: the sum of the values of a random variable divided by the
number of values [syn: arithmetic mean, first moment,
expectation, expected value] |
arithmetic operation
(wn) | arithmetic operation
n 1: a mathematical operation involving numbers |
arithmetic progression
(wn) | arithmetic progression
n 1: (mathematics) a progression in which a constant is added to
each term in order to obtain the next term; "1-4-7-10-13-
is the start of an arithmetic progression" |
arithmetical
(wn) | arithmetical
adj 1: relating to or involving arithmetic; "arithmetical
computations" [syn: arithmetical, arithmetic] |
arithmetically
(wn) | arithmetically
adv 1: with respect to arithmetic; "this problem is
arithmetically easy" |
arithmetician
(wn) | arithmetician
n 1: someone who specializes in arithmetic |
binary arithmetic operation
(wn) | binary arithmetic operation
n 1: an operation that follows the rules of Boolean algebra;
each operand and the result take one of two values [syn:
boolean operation, binary operation, {binary arithmetic
operation}] |
arithmetic and logic unit
(foldoc) | Arithmetic and Logic Unit
mill
(ALU or "mill") The part of the {central
processing unit} which performs operations such as addition,
subtraction and multiplication of integers and bit-wise
AND, OR, NOT, XOR and other Boolean operations. The
CPU's instruction decode logic determines which particular
operation the ALU should perform, the source of the operands
and the destination of the result.
The width in bits of the words which the ALU handles is
usually the same as that quoted for the processor as a whole
whereas its external busses may be narrower. Floating-point
operations are usually done by a separate "{floating-point
unit}". Some processors use the ALU for address calculations
(e.g. incrementing the program counter), others have
separate logic for this.
(1995-03-24)
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arithmetic mean
(foldoc) | arithmetic mean
The mean of a list of N numbers calculated by
dividing their sum by N. The arithmetic mean is appropriate
for sets of numbers that are added together or that form an
arithmetic series. If all the numbers in the list were
changed to their arithmetic mean then their total would stay
the same.
For sets of numbers that are multiplied together, the
geometric mean is more appropriate.
(2007-03-20)
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modular arithmetic
(foldoc) | modular arithmetic
modulo arithmetic
(Or "clock arithmetic") A kind of integer
arithmetic that reduces all numbers to one of a fixed set
[0..N-1] (this would be "modulo N arithmetic") by effectively
repeatedly adding or subtracting N (the "modulus") until the
result is within this range.
The original mathematical usage considers only __equivalence__
modulo N. The numbers being compared can take any values,
what matters is whether they differ by a multiple of N.
Computing usage however, considers modulo to be an operator
that returns the remainder after integer division of its first
argument by its second.
Ordinary "clock arithmetic" is like modular arithmetic except
that the range is [1..12] whereas modulo 12 would be [0..11].
(2003-03-28)
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modulo arithmetic
(foldoc) | modular arithmetic
modulo arithmetic
(Or "clock arithmetic") A kind of integer
arithmetic that reduces all numbers to one of a fixed set
[0..N-1] (this would be "modulo N arithmetic") by effectively
repeatedly adding or subtracting N (the "modulus") until the
result is within this range.
The original mathematical usage considers only __equivalence__
modulo N. The numbers being compared can take any values,
what matters is whether they differ by a multiple of N.
Computing usage however, considers modulo to be an operator
that returns the remainder after integer division of its first
argument by its second.
Ordinary "clock arithmetic" is like modular arithmetic except
that the range is [1..12] whereas modulo 12 would be [0..11].
(2003-03-28)
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peano arithmetic
(foldoc) | Peano arithmetic
Giuseppe Peano's system for representing {natural
numbers} inductively (induction) using only two symbols, "0"
(zero) and "S" (successor).
This system could be expressed as a recursive data type with the
following Haskell definition:
data Peano = Zero | Succ Peano
The number three, usually written "SSS0", would be Succ (Succ
(Succ Zero)). Addition of Peano numbers can be expressed as a
simple syntactic transformation:
plus Zero n = n
plus (Succ m) n = Succ (plus m n)
(1995-03-28)
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