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Antilogarithm

Antilogarithm An`ti*log"a*rithm, n. (Math.) The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine. -- An`ti*log`a*rith"mic, a.

Antilogarithm An`ti*log"a*rithm, n. (Math.) The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine. -- An`ti*log`a*rith"mic, a.

Antilogarithmic

Antilogarithm An`ti*log"a*rithm, n. (Math.) The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine. -- An`ti*log`a*rith"mic, a.

Antilogarithm An`ti*log"a*rithm, n. (Math.) The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine. -- An`ti*log`a*rith"mic, a.

Arithmetical complement of a logarithm

Arithmetical 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.

Arithmetical 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.

Binary logarithms

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). 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.

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). 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.

Hyperbolic logarithm

Hyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. 2. (Rhet.) Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. ``This hyperbolical epitaph.' --Fuller. Hyperbolic functions (Math.), certain functions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc. Hyperbolic logarithm. See Logarithm. Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector.

Hyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. 2. (Rhet.) Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. ``This hyperbolical epitaph.' --Fuller. Hyperbolic functions (Math.), certain functions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc. Hyperbolic logarithm. See Logarithm. Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector.

Index of a logarithm

3. A table for facilitating reference to topics, names, and the like, in a book; -- usually alphabetical in arrangement, and printed at the end of the volume. 4. A prologue indicating what follows. [Obs.] --Shak. 5. (Anat.) The second digit, that next pollex, in the manus, or hand; the forefinger; index finger. 6. (Math.) The figure or letter which shows the power or root of a quantity; the exponent. [In this sense the plural is always indices.] Index error, the error in the reading of a mathematical instrument arising from the zero of the index not being in complete adjustment with that of the limb, or with its theoretically perfect position in the instrument; a correction to be applied to the instrument readings equal to the error of the zero adjustment. Index expurgatorius. [L.] See Index prohibitorius (below). Index finger. See Index, 5. Index glass, the mirror on the index of a quadrant, sextant, etc. Index hand, the pointer or hand of a clock, watch, or other registering machine; a hand that points to something. Index of a logarithm (Math.), the integral part of the logarithm, and always one less than the number of integral figures in the given number. It is also called the characteristic. Index of refraction, or Refractive index (Opt.), the number which expresses the ratio of the sine of the angle of incidence to the sine of the angle of refraction. Thus the index of refraction for sulphur is 2, because, when light passes out of air into sulphur, the sine of the angle of incidence is double the sine of the angle of refraction. Index plate, a graduated circular plate, or one with circular rows of holes differently spaced; used in machines for graduating circles, cutting gear teeth, etc. Index prohibitorius [L.], or Prohibitory index (R. C. Ch.), a catalogue of books which are forbidden by the church to be read; the index expurgatorius [L.], or expurgatory index, is a catalogue of books from which passages marked as against faith or morals must be removed before Catholics can read them. These catalogues are published with additions, from time to time, by the Congregation of the Index, composed of cardinals, theologians, etc., under the sanction of the pope. --Hook. Index rerum [L.], a tabulated and alphabetized notebook, for systematic preservation of items, quotations, etc.

3. A table for facilitating reference to topics, names, and the like, in a book; -- usually alphabetical in arrangement, and printed at the end of the volume. 4. A prologue indicating what follows. [Obs.] --Shak. 5. (Anat.) The second digit, that next pollex, in the manus, or hand; the forefinger; index finger. 6. (Math.) The figure or letter which shows the power or root of a quantity; the exponent. [In this sense the plural is always indices.] Index error, the error in the reading of a mathematical instrument arising from the zero of the index not being in complete adjustment with that of the limb, or with its theoretically perfect position in the instrument; a correction to be applied to the instrument readings equal to the error of the zero adjustment. Index expurgatorius. [L.] See Index prohibitorius (below). Index finger. See Index, 5. Index glass, the mirror on the index of a quadrant, sextant, etc. Index hand, the pointer or hand of a clock, watch, or other registering machine; a hand that points to something. Index of a logarithm (Math.), the integral part of the logarithm, and always one less than the number of integral figures in the given number. It is also called the characteristic. Index of refraction, or Refractive index (Opt.), the number which expresses the ratio of the sine of the angle of incidence to the sine of the angle of refraction. Thus the index of refraction for sulphur is 2, because, when light passes out of air into sulphur, the sine of the angle of incidence is double the sine of the angle of refraction. Index plate, a graduated circular plate, or one with circular rows of holes differently spaced; used in machines for graduating circles, cutting gear teeth, etc. Index prohibitorius [L.], or Prohibitory index (R. C. Ch.), a catalogue of books which are forbidden by the church to be read; the index expurgatorius [L.], or expurgatory index, is a catalogue of books from which passages marked as against faith or morals must be removed before Catholics can read them. These catalogues are published with additions, from time to time, by the Congregation of the Index, composed of cardinals, theologians, etc., under the sanction of the pope. --Hook. Index rerum [L.], a tabulated and alphabetized notebook, for systematic preservation of items, quotations, etc.

Logarithmetic

Logarithmetic Log`a*rith*met"ic, Logarithmetical Log"a*rith*met"ic*al, a. See Logarithmic.

Logarithmetic Log`a*rith*met"ic, Logarithmetical Log"a*rith*met"ic*al, a. See Logarithmic.

Logarithmetical

Logarithmetic Log`a*rith*met"ic, Logarithmetical Log"a*rith*met"ic*al, a. See Logarithmic.

Logarithmetic Log`a*rith*met"ic, Logarithmetical Log"a*rith*met"ic*al, a. See Logarithmic.

Logarithmetically

Logarithmetically Log`a*rith*met"ic*al*ly, adv. Logarithmically.

Logarithmetically Log`a*rith*met"ic*al*ly, adv. Logarithmically.

Logarithmic

Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

Logarithmic

Tangent Tan"gent, n. [L. tangens, -entis, p. pr. of tangere to touch; akin to Gr. ? having seized: cf. F. tangente. Cf. Attain, Contaminate, Contingent, Entire, Tact, Taste, Tax, v. t.] (Geom.) A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced. See Trigonometrical function, under Function. Artificial, or Logarithmic, tangent, the logarithm of the natural tangent of an arc. Natural tangent, a decimal expressing the length of the tangent of an arc, the radius being reckoned unity. Tangent galvanometer (Elec.), a form of galvanometer having a circular coil and a short needle, in which the tangent of the angle of deflection of the needle is proportional to the strength of the current. Tangent of an angle, the natural tangent of the arc subtending or measuring the angle. Tangent of an arc, a right line, as ta, touching the arc of a circle at one extremity a, and terminated by a line ct, passing from the center through the other extremity o.

Tangent Tan"gent, n. [L. tangens, -entis, p. pr. of tangere to touch; akin to Gr. ? having seized: cf. F. tangente. Cf. Attain, Contaminate, Contingent, Entire, Tact, Taste, Tax, v. t.] (Geom.) A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced. See Trigonometrical function, under Function. Artificial, or Logarithmic, tangent, the logarithm of the natural tangent of an arc. Natural tangent, a decimal expressing the length of the tangent of an arc, the radius being reckoned unity. Tangent galvanometer (Elec.), a form of galvanometer having a circular coil and a short needle, in which the tangent of the angle of deflection of the needle is proportional to the strength of the current. Tangent of an angle, the natural tangent of the arc subtending or measuring the angle. Tangent of an arc, a right line, as ta, touching the arc of a circle at one extremity a, and terminated by a line ct, passing from the center through the other extremity o.

Logarithmic curve

Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

Logarithmic spiral

Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

Logarithmic spiral

Spiral Spi"ral, n. [Cf. F. spirale. See Spiral, a.] 1. (Geom.) A plane curve, not re["e]ntrant, described by a point, called the generatrix, moving along a straight line according to a mathematical law, while the line is revolving about a fixed point called the pole. Cf. Helix. 2. Anything which has a spiral form, as a spiral shell. Equiangular spiral,a plane curve which cuts all its generatrices at the same angle. Same as Logarithmic spiral, under Logarithmic. Spiral of Archimedes, a spiral the law of which is that the generatrix moves uniformly along the revolving line, which also moves uniformly.

Spiral Spi"ral, n. [Cf. F. spirale. See Spiral, a.] 1. (Geom.) A plane curve, not re["e]ntrant, described by a point, called the generatrix, moving along a straight line according to a mathematical law, while the line is revolving about a fixed point called the pole. Cf. Helix. 2. Anything which has a spiral form, as a spiral shell. Equiangular spiral,a plane curve which cuts all its generatrices at the same angle. Same as Logarithmic spiral, under Logarithmic. Spiral of Archimedes, a spiral the law of which is that the generatrix moves uniformly along the revolving line, which also moves uniformly.

Logarithmical

Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.

Logarithmically

Logarithmically Log`a*rith"mic*al*ly, adv. By the use of logarithms.

Logarithmically Log`a*rith"mic*al*ly, adv. By the use of logarithms.

logarithms

Logistic Lo*gis"tic, Logistical Lo*gis"tic*al, a. [Gr. ? skilled in calculating, ? to calculate, fr. lo`gos word, number, reckoning: cf. F. logistique.] 1. Logical. [Obs.] --Berkeley. 2. (Math.) Sexagesimal, or made on the scale of 60; as, logistic, or sexagesimal, arithmetic. Logistic, or Proportional, logarithms, certain logarithmic numbers used to shorten the calculation of the fourth term of a proportion of which one of the terms is a given constant quantity, commonly one hour, while the other terms are expressed in minutes and seconds; -- not now used.

Logistic Lo*gis"tic, Logistical Lo*gis"tic*al, a. [Gr. ? skilled in calculating, ? to calculate, fr. lo`gos word, number, reckoning: cf. F. logistique.] 1. Logical. [Obs.] --Berkeley. 2. (Math.) Sexagesimal, or made on the scale of 60; as, logistic, or sexagesimal, arithmetic. Logistic, or Proportional, logarithms, certain logarithmic numbers used to shorten the calculation of the fourth term of a proportion of which one of the terms is a given constant quantity, commonly one hour, while the other terms are expressed in minutes and seconds; -- not now used.

Naperian logarithms

Napierian Na*pie"ri*an, Naperian Na*pe"ri*an,, a. Of, pertaining to, or discovered by, Napier, or Naper. Naperian logarithms. See under Logarithms.

Napierian Na*pie"ri*an, Naperian Na*pe"ri*an,, a. Of, pertaining to, or discovered by, Napier, or Naper. Naperian logarithms. See under Logarithms.

Proportional logarithms

Proportional Pro*por"tion*al, a. [L. proportionalis: cf. F. proportionnel.] 1. Having a due proportion, or comparative relation; being in suitable proportion or degree; as, the parts of an edifice are proportional. --Milton. 2. Relating to, or securing, proportion. --Hutton. 3. (Math.) Constituting a proportion; having the same, or a constant, ratio; as, proportional quantities; momentum is proportional to quantity of matter. Proportional logarithms, logistic logarithms. See under Logistic. Proportional scale, a scale on which are marked parts proportional to the logarithms of the natural numbers; a logarithmic scale. Proportional scales, compasses, dividers, etc. (Draughting), instruments used in making copies of drawings, or drawings of objects, on an enlarged or reduced scale.

Proportional Pro*por"tion*al, a. [L. proportionalis: cf. F. proportionnel.] 1. Having a due proportion, or comparative relation; being in suitable proportion or degree; as, the parts of an edifice are proportional. --Milton. 2. Relating to, or securing, proportion. --Hutton. 3. (Math.) Constituting a proportion; having the same, or a constant, ratio; as, proportional quantities; momentum is proportional to quantity of matter. Proportional logarithms, logistic logarithms. See under Logistic. Proportional scale, a scale on which are marked parts proportional to the logarithms of the natural numbers; a logarithmic scale. Proportional scales, compasses, dividers, etc. (Draughting), instruments used in making copies of drawings, or drawings of objects, on an enlarged or reduced scale.

Proportionallogarithms

, those logarithms (devised by John Speidell, 1619) of which the base is 2.7182818; -- so called from Napier, the inventor of logarithms. Logistic or Proportionallogarithms., See under Logistic.

, those logarithms (devised by John Speidell, 1619) of which the base is 2.7182818; -- so called from Napier, the inventor of logarithms. Logistic or Proportionallogarithms., See under Logistic.

- In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another...

- The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately...

- mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base...

- binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5. The binary logarithm is the...

- mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828...

- In the mathematics of the real numbers, the logarithm logb a is a number x such that bx = a, for given numbers a and b. Analogously, in any group G, powers...

- In complex analysis, a complex logarithm of the non-zero complex number z, denoted by w = log z, is defined to be any complex number w for which e w =...

- The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and...

- functions, Euler laid the foundation for the modern introduction of natural logarithm as the inverse function for the natural exponential function, f(x) = ex...

- elliptic-curve-based protocols, it is ****umed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base...

- The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately...

- mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base...

- binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5. The binary logarithm is the...

- mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828...

- In the mathematics of the real numbers, the logarithm logb a is a number x such that bx = a, for given numbers a and b. Analogously, in any group G, powers...

- In complex analysis, a complex logarithm of the non-zero complex number z, denoted by w = log z, is defined to be any complex number w for which e w =...

- The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and...

- functions, Euler laid the foundation for the modern introduction of natural logarithm as the inverse function for the natural exponential function, f(x) = ex...

- elliptic-curve-based protocols, it is ****umed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base...

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