# theorem

## Definitions

• WordNet 3.6
• n theorem an idea accepted as a demonstrable truth
• n theorem a proposition deducible from basic postulates
• ***
Webster's Revised Unabridged Dictionary
• Theorem (Math) A statement of a principle to be demonstrated.
• Theorem That which is considered and established as a principle; hence, sometimes, a rule. "Not theories, but theorems, the intelligible products of contemplation, intellectual objects in the mind, and of and for the mind exclusively.""By the theorems ,
Which your polite and terser gallants practice,
I re-refine the court, and civilize
Their barbarous natures."
• v. t Theorem To formulate into a theorem.
• ***
Century Dictionary and Cyclopedia
• n theorem A universal demonstrable proposition. In the strict sense, a theorem must be true; it cannot be self-evident; it must be capable of being rendered evident by necessary reasoning and not by induction merely; and it must be a universal, not a particular proposition. But a proposition the proof of which is excessively easy or involves no genuine diagrammatic reasoning is not usually called a theorem.
• n theorem In geometry, a demonstrable theoretical proposition. There is a traditional distinction between a problem and a theorem, to the effect that a problem is practical, while a theorem is theoretical. Pappus, who makes this distinction, admits that it is not generally observed by the Greek geometers, and it has not been in general use except by editors and students of Euclid. It is recommended, however, by the circumstance that a theorem in the general and best sense is a universal proposition, and as such substantially a statement that something is impossible, while the kind of proposition called in geometry a problem is a statement that something is possible; the former demands demonstration only, while the latter requires solution, or the discovery of both method and demonstration.
• n theorem The proposition that the velocity of a liquid flowing from a reservoir is equal to what it would have if it were to fall freely from the level in the reservoir; or, more generally, if p is the pressure, p the density, V the potential of the forces, q the resultant velocity, A a certain quantity constant along a streamline, then
• n theorem given by Daniel Bernoulli (1700–82) in 1738.
• n theorem The generalized multiplication theorem of determinants (1812).
• n theorem given by the eminent English mathematician George Boole (1815–64).
• n theorem The proposition that in the impact of inelastic bodies vis viva is always lost.
• n theorem The proposition that in explosions vis viva is always gained. These theorems are all due to the eminent mathematician General L. N. M. Carnot (1753–1823), who published in 1803 and and in 1786.
• n theorem The proposition that the ratio of the maximum mechanical effect to the whole heat expended in an expansive engine is a function solely of the two temperatures at which the heat is received and emitted: given in 1824 by Sadi Carnot (1796–1832): often called Carnot's principle.
• n theorem given by John Casey in 1866.
• n theorem The proposition that if the order of a group is divisible by a prime number, then it contains a group of the order of that prime. The extension of this—that if the order of a group is divisible by a power of a prime, it contains a group whose order is that power—is called Cauchy and Sylow's theorem, or simply Sylow's theorem, because proved by the Norwegian L. Sylow in 1872.
• n theorem The rule for the development of determinants according to binary products of a row and a column.
• n theorem The false proposition that the sum of a convergent series whose terms are all continuous functions of a variable is itself continuous.
• n theorem Certain other theorems are often referred to as Cauchy's, with or without further specification. All these propositions are due to the extraordinary French analyst, Baron A. L. Cauchy (1789–1857).
• n theorem given by E. Cesaro in 1885. It is an extension of Ceva's theorem.
• n theorem given by B. P. E. Clapeyron (1799–1868): otherwise called the theorem of three moments.
• n theorem given by L. Crocchi in 1880.
• n theorem given by Morgan W. Crofton in 1868. Certain symbolic expansions and a proposition in least squares are also so termed.
• n theorem Same as De Moivre's property of the circle (which see, under circle).
• n theorem A certain proposition in probabilities. All these are by Abraham De Moivre (1667–1754).
• n theorem The proposition that if two triangles ABC and A′ B′ C′ are so placed that the three straight lines through corresponding vertices meet in a point, then also the three points of intersection of corresponding sides (produced if necessary) lie in one straight line, and conversely. Both were discovered by Gérard Desargues (1593–1662).
• n theorem named from G. Dostor, by whom it was given in 1870. Certain corollaries from this in regard to the ellipse and hyperbola are also known as Dostor's theorems.
• n theorem so that in a synclastic surface ρ1 and ρ2 are the maximum and minimum radii of curvature, but in an anticlastic surface, where they have opposite signs, they are the two minima radii.
• n theorem The proposition that in every polyhedron (but it is not true for one which enwraps the center more than once) the number of edges increased by two equals the sum of the numbers of faces and of summits.
• n theorem One of a variety of theorems sometimes referred to as Euler's, with or without further specification; as, the theorem that (xd/dx + yd/dy)r f(x, y) = n f(x, y); the theorem, relating to the circle, called by Euler and others Fermat's geometrical theorem; the theorem on the law of formation of the approximations to a continued fraction; the theorem of the 2, 4, 8, and 16 squares; the theorem relating to the decomposition of a number into four positive cubes. All the above (except that of Fermat) are due to Leonhard Euler (1707–831.
• n theorem One of a number of arithmetical propositions which Fermat, owing to pressure of circumstances, could only jot down upon the margin of books or elsewhere, and the proofs of which remained unknown for the most part during two centuries, and which are still only partially understood—especially the following, called the last theorem of Fermat: the equation x + y = z, where n is an odd prime, has no solution in integers.
• n theorem The proposition that, if from the extremities A and B of the diameter of a circle lines AD and BE be drawn at right angles to the diameter, on the same side of it, each equal to the straight line AI or BI from A or B to the middle point of the are of the semicircle, and if through any point C in the circumference, on either side of the diameter AB, lines DCF, ECG be drawn from D and E to cut AB (produced if necessary) in F and G, then AG + BF = AB: distinguished as Fermat's geometrical theorem. This is shown in the figure by arcs from A as a center through G and from B as a center through F meeting at H on the circle.
• n theorem The proposition that light travels along the quickest path.
• n theorem given in 1820 by Sir J. F. W. Herschel (1792–1872).
• n theorem The proposition that forced vibrations follow the period of the exciting cause.
• n theorem given by the Rev. Hamnet Holditch (born 1800).
• n theorem The proposition that an equilibrium ellipsoid may have three unequal axes.
• n theorem One of a variety of other propositions relating to the transformation of Laplace's equation, to the partial determinants of an adjunct system, to infinite series whose exponents are contained in two quadratic forms, to Hamilton's equations, to distance-correspondences for quadric surfaces, etc. All are named from their author, K. G. J. Jacobi (1804–51).
• n theorem The proposition that the order of a group is divisible by that of every group it contains: also called the fundamental theorem of substitutions. Both by, J. L. Lagrange (1736–1813).
• n theorem A proposition relating to the apparent curvature of the geocentric path of a comet. Both are named from their author, J. H. Lambert (1728–77).
• n theorem where the modulus of x is comprised between R and R′ : given by P. A. Laurent (1813–54).
• n theorem is equal to the same after development of (Du + Dv) by the binomial theorem, where Du denotes differentiation as if u were constant, and Dv differentiation as if u were constant.
• n theorem given by S. A. J. Lhuilier (1750–1840).
• n theorem a monodromic function fz can always be found having for critical points α0, α1, … αn, etc., and such that
• n theorem φn being a function for which αn is not a critical point: given by G. Mittag-Leffler.
• n theorem The proposition that the three diagonals of a quadrilateral circumscribed about a circle are all bisected by one diameter of the circle.
• n theorem One of the two propositions that the surface of a solid of revolution is equal to the product of the perimeter of the generating plane figure by the length of the path described by the center of gravity, and that the volume of such a solid is equal to the area of the plane figure multiplied by the same length of path. Various other theorems contained in the collection of the Greek mathematician Pappus, of the third century, are sometimes called by his name.
• n theorem A certain proposition concerning uniform functions connected by an algebraic relation.
• n theorem The proposition that a quantity of the form R = √u + v cannot differ from αu + βv by more than R tan ½ε where α = cos (θ + ε)/cos ½ε, β = sin (θ + ε)/cos ½ε, ε = ½(Θ—θ), tan Θ ⟩ u/v ⟩ tan θ. Both were given by General J. V. Poncelet (1788–l877).
• n theorem The proposition that if a point be taken on each of the edges of any tetrahedron and a sphere be described through each vertex and the points assumed on the three adjacent edges, the four spheres will meet in a point: given by Samuel Roberts in 1881.
• n theorem where α, β, etc., are all the prime numbers one greater than the double of divisors of n: given in 1840 by K. G. C. von Staudt (1798–1867).
• n theorem given by James Stirling (1696–1770).
• n theorem The proposition that every quaternary cubic is the sum of the cubes of five linear forms.
• n theorem The proposition that if λ1, λ2, etc., are the latent roots of a matrix m, then
• n theorem given by the great algebraist J. J. Sylvester (born 1814).
• n theorem given by H. M. L. Tanner in 1879.
• n theorem where d represents the differential of the function u.
• n theorem named after the discoverer, John Wallis (1616–1703).
• n theorem where v is the velocity, r the radius vector of the point whose mass is m and its coördinates x, y, z, while X, Y, Z are the components of the force, f the force, and ⟩ the distance of two particles: given in 1872 by A. J. F. Yvon-Villarceau (1813–83). It much resembles the theorem of the virial.
• n theorem Synonyms See inference.
• theorem To reduce to or formulate as a theorem.
• ***
Chambers's Twentieth Century Dictionary
• n Theorem thē′ō-rem a proposition to be proved
• ***

## Quotations

• Albert Camus “To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”

## Etymology

Webster's Revised Unabridged Dictionary
L. theorema, Gr. a sight, speculation, theory, theorem, fr. to look at, a spectator: cf. F. théorème,. See Theory
Chambers's Twentieth Century Dictionary
Gr. theōrēmatheōrein, to view—theasthai, to see.

## Usage

### In literature:

We state therefore a theorem which is practically demonstrated; there is no sensation in matter.
"The Right Knock" by Helen Van-Anderson
But just demonstrate this theorem, Hoggy, old boy.
"At Good Old Siwash" by George Fitch
Be this as it may, few theorems appear to us more promising of interest.
"Blackwood's Edinburgh Magazine, Volume 56, Number 347, September, 1844" by Various
The period passed like a moment, as theorem after theorem was disposed of.
"Peggy" by Laura E. Richards
According to his disciple, M'Culloch, Ricardo's great merit was that he 'laid down the fundamental theorem of the science of value.
"The English Utilitarians, Volume II (of 3)" by Leslie Stephen
I could not have believed that any one would consider a theorem or a page of French difficult.
"Elizabeth Hobart at Exeter Hall" by Jean K. Baird
It is the result of experience of a mathematical theorem concerning unique distributions.
"Life and Matter" by Oliver Lodge
Dear girl, it seems that always I must woo you in metaphysics and express my ardour in theorems.
"The Jessica Letters: An Editor's Romance" by Paul Elmer More
In it he developed the law of three centers, now known as Kennedy's theorem.
"Kinematics of Mechanisms from the Time of Watt" by Eugene S. Ferguson
Brook Taylor, well known to mathematicians as the discoverer of "Taylor's theorem," entered as a Fellow Commoner 3rd April 1701.
"St. John's College, Cambridge" by Robert Forsyth Scott
This is not put forward as an obvious result; it depends upon a refined dynamical theorem.
"The Story of the Heavens" by Robert Stawell Ball
Such were a few of the theorems to which his discovery of this nebula led him.
"Sir William Herschel: His Life and Works" by Edward Singleton Holden
Big, perilous theorem, hard for king and priest; 'Pursue the West but long enough, 'tis East!
"Christopher Columbus and His Monument Columbia" by Various
Yet, here was a woman whose mind he had to respect, using the term as a proved theorem.
"In the Heart of a Fool" by William Allen White
This is the theorem of these volumes.
"The Stones of Venice, Volume III (of 3)" by John Ruskin
Really, all geometrical theorems are laws of external nature.
"Analysis of Mr. Mill's System of Logic" by William Stebbing
The following theorem covers a large number of important cases.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 2" by Various
Generally speaking, Aristotle says, Begging the Question consists in not demonstrating the theorem.
"Logic, Inductive and Deductive" by William Minto
Theoreme, as I will declare in the booke of proofes.
"The Path-Way to Knowledg" by Robert Record
Whence I seem to gather the two following Theorems.
"Opticks" by Isaac Newton
***

### In poetry:

For, as their nurses dandle them
They crow binomial theorem,
With views (it seems absurd to us)
On differential calculus.
"My Dream" by William Schwenck Gilbert
Alone to the weight of impassivity,
Incest of spirit, theorem of desire,
Without will as chalky cliffs by the sea
Empty as the bodiless flesh of fire:
"Last Days Of Alice" by Allen Tate

### In news:

JHANE BARNES Theorem from Couteur Designs/ A Division of Kenmark Group.
Greer's OC: Coffee bar Theorem now open.
Here's the news: Alain Connes — a French Fields medalist — has come up with a new proof of Morley 's theorem.
We Still Should Remember the Nyquist Sampling Theorem.
Yet there's plenty of drama and passion in the story of Fermat's last theorem.
Terry Gilliam's 'Zero Theorem ' sells round the world.
Voltage Pictures has sold territories including France, Germany and Italy on Terry Gilliam's "The Zero Theorem ," starring Christoph Waltz.
Infinite Monkey Theorem , Erbert and Gerbert's coming to Denver.
Dionne and the Sargent Theorem .
What do you think has been the key to Theorem 's successful growth over the past decade.
Taking the Fundamental Theorem challenge.
Roger Federer's future, the Jimmy Connors theorem and the Petko Dance.
Needy Gonzales Truth Theorem .
"What makes a theorem great.".
***

### In science:

Then, the second theorem reads Theorem 2 Let Wg : P [[x, p, ]] −→ bP [[bx, bp, ]] be the vector space isomorphism deﬁned in Theorem 1.
Matrix representation of the generalized Moyal algebra
We will start by showing how the two-dimensional analogue of Theorem 2 for Poisson processes is an immediate consequence of Theorem 3, the extension of Burke’s theorem given in the previous section, and the symmetry formula (20).
Random matrices, non-colliding processes and queues
Formally, this theorem does not depend on Theorem 2.1 but in fact its hypothesis are equivalent to the ones of Theorem 2.1 and its conclusions are corollaries of Theorem 2.1.
Random groups in the optical waveguides theory
Follows immediately from Theorem 2.8 and the Gantmacher-Krein theorem (see Chapter 2, Theorem 6 there) claiming that the eigenvalues of a totally positive matrix are distinct real numbers.
Moduli spaces of convex projective structures on surfaces
The convergence to a Brownian motion stated in Theorem 1 also follows, but this could have been obtained (avoiding an analysis of the inﬁnitesimal generator) by applying Theorem 17.1 of [Bil] and Theorem 2.1 of [DFGW].
Mott law as lower bound for a random walk in a random environment
The proof of Theorem 1.1 is ﬁnished since if ψ vanishes on an open set, it vanishes everywhere on X by the usual Carleman-type unique continuation theorem [3, Theorem 17.2.1].
Absence of super-exponentially decaying eigenfunctions on Riemannian manifolds with pinched negative curvature
In this section, we prove Theorem 1.4; we translate Theorem 1.4 into a purely combinatorial statement (Theorem 5.3 below) which we prove using a simple algorithm.
Desingularization of toric and binomial varieties
Our main results are the description of this subalgebra under various assumptions (Theorem 4.5 and Theorem 4.8) and the explicit formulas (Theorem 5.4) of the associated module of the TGWA.
Locally finite simple weight modules over twisted generalized Weyl algebras
By Theorem 1.3(a) the process eZ (n) is tight with respect to the annealed law given by the semi-direct product P∗ = P × P 0 ω . (See Theorem 1.1 for the analogous result for the discrete time simple random walk.) Proof of Theorem 1.5.
Random walk on the incipient infinite cluster on trees
For the purpose of proving Theorem 1.2, it actually suﬃces to use a weaker theorem (Theorem 2.1 of ) whose proof is signiﬁcantly simpler.
Central limit theorems for random polytopes in a smooth convex set
Minimax Theorems: In this section as an application of ubiquitous Hall’s theorem we discuss the theorem of Konig-Egervary.
The Friendship Theorem and Minimax Theorems
Menger’s Theorem: Perhaps the most important theorem in the entire graph theory is Menger’s theorem, the theorem first proved by K. Menger in 1927.
The Friendship Theorem and Minimax Theorems
Now, let us recall from [7, 6] the structure of cosemisimple corings, which is tightly related to the coring version of the Generalized Descent Theorem formulated in [6, Theorem 3.10]. A coring is said to be cosemisimple if it satisﬁes one of the equivalent conditions of the following theorem.
Galois Corings and a Jacobson-Bourbaki type Correspondence
The fundamental theorem here is a consequence of G¨odel’s completeness theorem called the compactness theorem: a theory T has a model if every ﬁnite subset of T has a model.
Integration in valued fields
It is easy to see that Theorem 4.2 follows from Theorem 4.5, because under the assumptions of Theorem 4.2, for M > λ and h suﬃciently large, we have N (f , h, hM ) = 1.
Constructive Function Theory on Sets of the Complex Plane through Potential Theory and Geometric Function Theory
***