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Circuit theorem
The Extra Element Theorem (EET) is an analytic technique developed by R. D. Middlebrook for simplifying the process of deriving driving point and transfer
Extra_element_theorem
signal-flow analysis by John Choma, and was made popular in the extra element theorem by R. D. Middlebrook and the asymptotic gain model of Solomon Rosenstark
Blackman's_theorem
Theorem in electrical circuit analysis
impedances, connected in wye or in delta. Extra element theorem Maximum power transfer theorem Millman's theorem Source transformation von Helmholtz, Hermann
Thévenin's_theorem
DC circuit analysis technique
law Millman's theorem Source transformation Superposition theorem Thévenin's theorem Maximum power transfer theorem Extra element theorem Mayer, Hans Ferdinand
Norton's_theorem
developed many of the tools of D-OA including the Extra element theorem and the General Feedback Theorem. His goal with D-OA was to fundamentally change
R._D._Middlebrook
See Figure 2. The asymptotic gain model is a special case of the extra element theorem. As follows directly from limiting cases of the gain expression
Asymptotic_gain_model
Topics referred to by the same term
technology Electronic energy transfer Epoxyeicosatrienoic acid Extra element theorem School of Engineering of Terrassa (Catalan: Escola d'Enginyeria
EET
Product of any collection of compact topological spaces is compact
Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named
Tychonoff's_theorem
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
Type of electronic amplifier
transistor amplifying stage with negative feedback Extra element theorem Frequency compensation Miller theorem is a powerful tool for determining the input/output
Negative-feedback_amplifier
Numerical method for solving physical or engineering problems
problems with boundary layers. The mixed finite element method is a type of finite element method in which extra independent variables are introduced as nodal
Finite_element_method
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Classification theorem in group theory
In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s
Feit–Thompson_theorem
On the intersection form of a smooth, closed 4-manifold with a spin structure
form is even. By a theorem of Cahit Arf, any even unimodular lattice has signature divisible by 8, so Rokhlin's theorem forces one extra factor of 2 to divide
Rokhlin's_theorem
Theorem in quantum information science
Hilbert space only up to a phase factor i.e. as an element of projectivised Hilbert space. To prove the theorem, we select an arbitrary pair of states | ϕ ⟩
No-cloning_theorem
On polynomial rings over fields
In mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in
Hilbert's_syzygy_theorem
Geometric theorem
The Banach–Tarski paradox is a theorem in set-theoretic geometry that states the following: Given a solid ball in three-dimensional space, there exists
Banach–Tarski_paradox
Equations of degree 5 or higher cannot be solved by radicals
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial
Abel–Ruffini_theorem
Subfield of automated reasoning and mathematical logic
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving
Automated_theorem_proving
Square matrices satisfy their characteristic equation
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix
Cayley–Hamilton_theorem
ISBN 0-13-436049-4. Richard R Spencer & Ghausi MS (2003). Example 10.7 pp. 723-724. ISBN 0-201-36183-3. Asymptotic gain model Blackman's theorem Extra element theorem
Return_ratio
On algebraic independence of logarithms
easier to state. For example, the Hermite–Lindemann theorem becomes the statement that any nonzero element of L {\displaystyle \mathbb {L} } is transcendental
Baker's_theorem
Fundamental theorem in condensed matter physics
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves
Bloch's_theorem
Planar graph drawn by relaxing springs
the equations geometrically produces a planar embedding. Tutte's spring theorem, proven by W. T. Tutte (1963), states that this unique solution is always
Tutte_embedding
Number divisible only by 1 and itself
than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself
Prime_number
Theorem about a certain class of control-flow graphs
programming language theory, the structured program theorem, generally called the Böhm–Jacopini theorem, states that a class of control-flow graphs (historically
Structured_program_theorem
Concept in differential geometry
closely related to the curvature of the connection, via the Ambrose–Singer theorem. The study of Riemannian holonomy has led to a number of important developments
Holonomy
Key result in general relativity
theorem states the following: Given an asymptotically flat initial data set, one can define the energy-momentum of each infinite region as an element
Positive_energy_theorem
Self-adjusting binary search tree
accesses. Static optimality theorem—Let q x {\displaystyle q_{x}} be the number of times element x is accessed in S. If every element is accessed at least once
Splay_tree
Streaming algorithm
than k different values. The following theorem is easy to prove: Theorem 1. Each heavy-hitter of b is an element of a k-reduced bag for b. The first pass
Misra–Gries heavy hitters algorithm
Misra–Gries_heavy_hitters_algorithm
Study of rational collective decision-making
impossibility theorem is what often comes to mind when one thinks about impossibility theorems in voting. There are several famous theorems concerning social
Social_choice_theory
Bound lattice in which every element has a complement
bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0
Complemented_lattice
Algebraic structure with addition and multiplication
theorems concerning a PID, the most important one is the structure theorem for finitely generated modules over a principal ideal domain. The theorem may
Ring_(mathematics)
Berta Karlik discovered that the element 85 astatine is a product of the natural decay processes. Bohr–van Leeuwen theorem In her 1919 thesis, Hendrika Johanna
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
Type of logical system
to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization
First-order_logic
Reciprocal work theorem in engineering
theorem has applications in structural engineering where it is used to define influence lines and derive the boundary element method. Betti's theorem
Betti's_theorem
Form of mathematical proof
1000 AD, who applied it to arithmetic sequences to prove the binomial theorem and properties of Pascal's triangle. Whilst the original work was lost
Mathematical_induction
Measure of algorithmic complexity
describe the length of the string, before writing out the string itself. Theorem. (extra information bounds, subadditivity) K ( x | y ) ≤ K ( x ) ≤ K ( x ,
Kolmogorov_complexity
originally given as a theorem by Brouwer (1975) containing no "extra" restriction on R {\displaystyle R} under the name The Bar Theorem. However, the proof
Bar_induction
On linear-time algorithms for graph logic
In the study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs
Courcelle's_theorem
Set with associative invertible operation
third element within the same set and the following conditions must hold: the operation is associative, it has an identity element, and every element of
Group_(mathematics)
Mathematical problem
and Gödel's incompleteness theorem in the 1920s and 1930s. First, note that Garrett Birkhoff proved with his HSP theorem that the equational theory of
Tarski's high school algebra problem
Tarski's_high_school_algebra_problem
Theories in mathematical logic
for which the sentences of the theory are all true (by the completeness theorem, satisfiability is equivalent to consistency); be complete: for any statement
List_of_first-order_theories
Commutative ring with no zero divisors other than zero
two nonzero elements is nonzero. In an integral domain, every nonzero element a has the cancellation property, that is, if a ≠ 0, ab = ac implies b =
Integral_domain
Conjecture on zeros of the zeta function
hypothesis is true, then the theorem is true. If the generalized Riemann hypothesis is false, then the theorem is true. Thus, the theorem is true!! Care should
Riemann_hypothesis
Construction in algebra
identity 1 of H is required to be in A). The Nichols–Zoeller freeness theorem of Warren Nichols and Bettina Zoeller (1989) established that the natural
Hopf_algebra
that a theorem is beautiful when they really mean to say that it is enlightening. We acknowledge a theorem's beauty when we see how the theorem 'fits'
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
Mergelyan's theorem — generalization of Stone–Weierstrass theorem for polynomials Müntz–Szász theorem — variant of Stone–Weierstrass theorem for polynomials
List of numerical analysis topics
List_of_numerical_analysis_topics
Mathematical function between groups that preserves multiplication structure
this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, h ( e G ) = e H {\displaystyle h(e_{G})=e_{H}}
Group_homomorphism
10th episode of the 6th season of Futurama
episode by what David X. Cohen described in an interview as a mathematical theorem proved by Keeler, who has a Ph.D. in Mathematics. The title and the story's
The_Prisoner_of_Benda
Statement that is taken to be true
knowledge. They are accepted without demonstration. All other assertions (theorems, in the case of mathematics) must be proven with the aid of these basic
Axiom
Branch of mathematics
Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th
Topology
Theory of algebraic structures in general
of A and returns a single element of A. Thus, a 0-ary operation (or nullary operation) can be represented simply as an element of A, or a constant, often
Universal_algebra
Group in group theory and physics
the diagonal with −1.) By Bass's theorem, it has a polynomial growth rate of order 4. One can generate any element through ( 1 a c 0 1 b 0 0 1 ) = y
Heisenberg_group
System of mathematical set theory
finitely axiomatizable, while ZFC and MK are not. A key theorem of NBG is the class existence theorem, which states that for every formula whose quantifiers
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Search algorithm finding the position of a target value within a sorted array
a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot
Binary_search
Two-dimensional manifold
not be surfaces in the extrinsic sense. However, the Whitney embedding theorem asserts every surface can in fact be embedded homeomorphically into Euclidean
Surface_(topology)
Matrix decomposition
n } {\displaystyle i>\min\{m,n\}} . The geometric content of the SVD theorem can thus be summarized as follows: for every linear map T : K n → K m
Singular_value_decomposition
Duality for locally compact abelian groups
bidual (the dual of its dual). The Fourier inversion theorem is a special case of this theorem. The subject is named after Lev Pontryagin, who laid down
Pontryagin_duality
British-Lebanese mathematician (1929–2019)
specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in
Michael_Atiyah
Mathematical-logic system based on functions
– A virtual machine designed for the lambda calculus Scott–Curry theorem – A theorem about sets of lambda terms To Mock a Mockingbird – An introduction
Lambda_calculus
Set of vectors used to define coordinates
of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite linear combination of elements
Basis_(linear_algebra)
Type of binary relation
m)].} Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set. Equivalently, assuming
Well-founded_relation
1969 non-fiction book by G. Spencer-Brown
mathematical conjectures of very long standing, such as the four color theorem, Fermat's Last Theorem, and the Goldbach conjecture, are provable using extensions
Laws_of_Form
Differential form
{\displaystyle n} , a volume form is an n {\displaystyle n} -form. It is an element of the space of sections of the line bundle ⋀ n ( T ∗ M ) {\displaystyle
Volume_form
Particular class of sets which can be described entirely in terms of simpler sets
basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true,
Constructible_universe
Element of a unital algebra over the field of real numbers
number system. Hurwitz and Frobenius proved theorems that put limits on hypercomplexity: Hurwitz's theorem says finite-dimensional real composition algebras
Hypercomplex_number
Theories of higher-dimensional general relativity
appears in string theory and M-theory as a central element for mathematical consistency, where extra dimensions are essential for mathematical consistency
Higher-dimensional Einstein gravity
Higher-dimensional_Einstein_gravity
Field in which every sum of two squares is a square
of a field F {\displaystyle F} is an extension obtained by adjoining an element 1 + λ 2 {\displaystyle {\sqrt {1+\lambda ^{2}}}} for some λ {\displaystyle
Pythagorean_field
Theory in abstract algebra
Eduard Kummer around the 1840s in his pioneering work on Fermat's Last Theorem. The main statements do not depend on the nature of the field – apart from
Kummer_theory
Mathematical group
started with Camille Jordan's theorem that the projective special linear group PSL(2, q) is simple for q ≠ 2, 3. This theorem generalizes to projective groups
Group_of_Lie_type
Branch of mathematics that studies sets
uncountable, that is, one cannot put all real numbers in a list. This theorem is proved using Cantor's first uncountability proof, which differs from
Set_theory
Set of functions between two fixed sets
cardinal dimension of a function space with no extra structure can be found by the Erdős–Kaplansky theorem. Function spaces appear in various areas of mathematics:
Function_space
Progression-free set of numbers
1942 that Salem–Spencer sets can have nearly-linear size. However a later theorem of Klaus Roth shows that the size is always less than linear. For k = 1
Salem–Spencer_set
Methods of mathematical approximation
polarisation Eigenvalue perturbation Homotopy perturbation method Interval finite element Lyapunov stability Method of dominant balance Order of approximation Perturbation
Perturbation_theory
Branch of numerical analysis
divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite
Numerical methods for partial differential equations
Numerical_methods_for_partial_differential_equations
Mathematics of real numbers and real functions
is an upper bound that is smaller than all of the others. Most of the theorems that are proved in real analysis rely on completeness in one way or another
Real_analysis
Czech-Canadian mathematician
Mathematica, Extra Volume ICM III, archived from the original on 2020-07-27, retrieved 2017-03-22 Weisstein, Eric W. "Art Gallery Theorem." From MathWorld--A
Václav_Chvátal
Analysis of datasets using techniques from topology
first classification theorem for persistent homology appeared in 1994 via Barannikov's canonical forms. The classification theorem interpreting persistence
Topological_data_analysis
Unsolved problem in geometry
conjecture and provided some of Hodge's motivation. Theorem (Lefschetz theorem on (1,1)-classes) Any element of H 2 ( X , Z ) ∩ H 1 , 1 ( X ) {\displaystyle
Hodge_conjecture
Type of mathematical proof
method of exhaustion (e.g., the first computer-assisted proof of four color theorem in 1976), though such approaches can also be challenged on the basis of
Proof_by_exhaustion
Category whose objects are sets and whose morphisms are functions
it is an element of some larger Grothendieck universe.) However, one does not work directly with the "category of all sets". Instead, theorems are expressed
Category_of_sets
Branch of mathematics that studies the properties of groups
is known that V above decomposes into irreducible parts (see Maschke's theorem). These parts, in turn, are much more easily manageable than the whole
Group_theory
Completion of the usual space with "points at infinity"
over a (commutative) field. Equivalently Pappus's hexagon theorem and Desargues's theorem are supposed to be true. A large part of the results remain
Projective_space
Determinant of the matrix of first derivatives of a set of functions
Roth used this result about generalized Wronskians in his proof of Roth's theorem. For more general conditions under which the converse is valid see Wolsson
Wronskian
Type of infinite structure
o-minimal structures. There is a cell decomposition theorem, Whitney and Verdier stratification theorems and a good notion of dimension and Euler characteristic
O-minimal_theory
Pictorial representation of the behavior of subatomic particles
x = e i k x {\displaystyle A_{kx}=e^{ikx}\,} and the Fourier inversion theorem tells you the inverse: A k x − 1 = e − i k x {\displaystyle A_{kx}^{-1}=e^{-ikx}\
Feynman_diagram
In mathematics, invertible homomorphism
{\displaystyle 1+3=4.} This is a special case of the Chinese remainder theorem which asserts that, if m {\displaystyle m} and n {\displaystyle n}
Isomorphism
Submodule of a mathematical ring
maximal left ideal); see Krull's theorem for more. A left (resp. right, two-sided) ideal generated by a single element x is called the principal left (resp
Ideal_(ring_theory)
In arithmetic geometry, a Frobenioid is a category with some extra structure that generalizes the theory of line bundles on models of finite extensions
Frobenioid
Observational basis of thermodynamics
now known as the first and second laws were established. Later, Nernst's theorem (or Nernst's postulate), which is now known as the third law, was formulated
Laws_of_thermodynamics
Algebraic structure associated with a topological space
via Morse homology, or by taking the output of the universal coefficient theorem when applied to a cohomology theory such as Čech cohomology or (in the
Homology_(mathematics)
Set whose pairs have minima and maxima
(help), Theorem 4.10, p. 89. Davey & Priestley (2002) harvtxt error: multiple targets (2×): CITEREFDaveyPriestley2002 (help), Theorem 10.21, pp. 238–239
Lattice_(order)
Various systems of symbolic logic
article. In general, one may take as the extra axiom any classical tautology that is not valid in the two-element Kripke frame ∘ ⟶ ∘ {\displaystyle \circ
Intuitionistic_logic
How spheres of various dimensions can wrap around each other
representing maps, and any element of non-zero degree is nilpotent; the nilpotence theorem on complex cobordism implies Nishida's theorem.[citation needed] Example:
Homotopy_groups_of_spheres
Smooth manifold with an inner product on each tangent space
fundamental form). This result is known as the Theorema Egregium ("remarkable theorem" in Latin). A map that preserves the local measurements of a surface is
Riemannian_manifold
Isomorphism type of ordered sets
Relevant theorems of this sort are expanded upon below. More examples can be given now: The set of positive integers (which has a least element), and that
Order_type
Type of mathematical function
theory Liouville's theorem (differential algebra) – Criterion for integration in terms of elementary functions Richardson's theorem: Undecidability of
Elementary_function
Löwenheim–Skolem theorem states that if a first-order theory has an infinite model then it has a model of any given infinite cardinality lower bound An element of a
Glossary_of_set_theory
Group of even permutations of a finite set
A4 is the smallest group demonstrating that the converse of Lagrange's theorem is not true in general: given a finite group G and a divisor d of |G|,
Alternating_group
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
Male
English
Short form of Latin Clementius, CLEMENT means "gentle and merciful." meaning "gentle and merciful." In the bible, this is the name of a companion of Paul.
Male
Slovene
Slovene form of Greek Klementos, KLEMEN means "gentle and merciful."
Male
Polish
 Danish, German, Polish and Swedish form of Greek Klementos, KLEMENS means "gentle and merciful."
Surname or Lastname
English, French, and Dutch
English, French, and Dutch : from the Latin personal name Clemens meaning ‘merciful’ (genitive Clementis). This achieved popularity firstly through having been borne by an early saint who was a disciple of St. Paul, and later because it was selected as a symbolic name by a number of early popes. There has also been some confusion with the personal name Clemence (Latin Clementia, meaning ‘mercy’, an abstract noun derived from the adjective; in part a masculine name from Latin Clementius, a later derivative of Clemens). As an American family name, Clement has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Male
Italian
 Italian, Portuguese and Spanish form of Latin Clementius, CLEMENTE means "gentle and merciful."
Girl/Female
Arabic
Heavenly Smell
Surname or Lastname
English
English : patronymic from the personal name Clement. As an American family name, this form has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Male
English
English surname transferred to forename use, derived from Latin Clemens or Clement, CLEMENTS means "gentle and merciful."
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
English American Danish
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Male
Russian
(Климент) Russian form of Greek Klementos, KLIMENT means "gentle and merciful."
Boy/Male
English American Biblical Latin
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Girl/Female
Tamil
Extra ordinary
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Girl/Female
British, English, Latin
Dyer; Skillful; Dexterous; Adroit; Right-handed
Girl/Female
Latin
Adroit; skillful.
Surname or Lastname
English
English : patronymic from the personal name Clement.German, Dutch, and Danish : from the personal name Clemens (see Clement).Samuel Langhorne Clemens, better known by his pen name, Mark Twain, was descended from VA stock on his father’s side, from a Robert Clemens, who was born in Warwickshire, England, in 1634.
Girl/Female
Indian
Extra ordinary
Boy/Male
Australian, British, Danish, Dutch, English, Finnish, French, German, Irish, Latin, Swedish
Gentle; Merciful; Mild; Form of Clement
Male
Hungarian
Hungarian form of Greek Klementos, KELEMEN means "gentle and merciful."
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
Boy/Male
Arabic, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Deer
Male
Polish
Polish form of Latin Ivo, IWO means "yew tree."
Boy/Male
Hindu, Indian, Sanskrit, Traditional
A Sage; A Mythical Bird; Skylark; Strong and Fast
Boy/Male
Indian, Kannada
Son of the Moon
Boy/Male
Hindu
God of victory, Winner
Female
English
Contracted form of French Bernardine, BERNADINE means "bold as a bear."
Girl/Female
Gujarati, Hindu, Indian
Star; Faithful; Constant
Girl/Female
Latin
Circle of light.
Girl/Female
Tamil
A river, Moon light
Boy/Male
African, American, Australian, British, English, French, German, Teutonic
Archer's Bow; Young Archer; Yew Wood
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
n.
The four elements were, air, earth, water, and fire
n.
Any outline or sketch, regarded as containing the fundamental ideas or features of the thing in question; as, the elements of a plan.
v. t.
To constitute; to make up with elements.
a.
Acting with great force; furious; violent; impetuous; forcible; mighty; as, vehement wind; a vehement torrent; a vehement fire or heat.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
n.
The quotient of a unit divided by eleven; one of eleven equal parts.
a.
Beyond what is due, usual, expected, or necessary; additional; supernumerary; also, extraordinarily good; superior; as, extra work; extra pay.
n.
One of the ultimate, undecomposable constituents of any kind of matter. Specifically: (Chem.) A substance which cannot be decomposed into different kinds of matter by any means at present employed; as, the elements of water are oxygen and hydrogen.
n.
To overlay or coat with cement; as, to cement a cellar bottom.
n.
The elements of the alchemists were salt, sulphur, and mercury.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
n.
Something in addition to what is due, expected, or customary; something in addition to the regular charge or compensation, or for which an additional charge is made; as, at European hotels lights are extras.
n.
An infinitesimal part of anything of the same nature as the entire magnitude considered; as, in a solid an element may be the infinitesimal portion between any two planes that are separated an indefinitely small distance. In the calculus, element is sometimes used as synonymous with differential.
a.
Constituting one of eleven parts into which a thing is divided; as, the eleventh part of a thing.
n.
Sometimes a curve, or surface, or volume is considered as described by a moving point, or curve, or surface, the latter being at any instant called an element of the former.
v. t.
To compound of elements or first principles.
n.
One of the ultimate parts which are variously combined in anything; as, letters are the elements of written language; hence, also, a simple portion of that which is complex, as a shaft, lever, wheel, or any simple part in a machine; one of the essential ingredients of any mixture; a constituent part; as, quartz, feldspar, and mica are the elements of granite.
n.
One out of several parts combined in a system of aggregation, when each is of the nature of the whole; as, a single cell is an element of the honeycomb.
pl.
of Extra
n.
One of the necessary data or values upon which a system of calculations depends, or general conclusions are based; as, the elements of a planet's orbit.