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Method for computing the relation of two integers with their greatest common divisor
arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest
Extended_Euclidean_algorithm
Algorithm for computing greatest common divisors
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers
Euclidean_algorithm
Algorithm for computing the greatest common divisor
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor
Binary_GCD_algorithm
Commutative ring with a Euclidean division
ring of integers), but lacks an analogue of the Euclidean algorithm and extended Euclidean algorithm to compute greatest common divisors. So, given an
Euclidean_domain
Concept in modular arithmetic
RSA algorithm. A benefit for the computer implementation of these applications is that there exists a very fast algorithm (the extended Euclidean algorithm)
Modular multiplicative inverse
Modular_multiplicative_inverse
Topics referred to by the same term
a quotient and a remainder Euclidean algorithm, a method for finding greatest common divisors Extended Euclidean algorithm, a method for solving the Diophantine
Euclidean
Algorithm for fast modular multiplication
are coprime. It can be constructed using the extended Euclidean algorithm. The extended Euclidean algorithm efficiently determines integers R′ and N′ that
Montgomery modular multiplication
Montgomery_modular_multiplication
Error correction code
Sugiyama's adaptation of the Extended Euclidean algorithm. Correction of unreadable characters could be incorporated to the algorithm easily as well. Let k 1
BCH_code
Mathematical algorithm
{n}}} . Solutions to this equation are easily obtained using the extended Euclidean algorithm. To find the needed a {\displaystyle a} , b {\displaystyle b}
Pollard's rho algorithm for logarithms
Pollard's_rho_algorithm_for_logarithms
Largest integer that divides given integers
identity. Numbers p and q like this can be computed with the extended Euclidean algorithm. gcd(a, 0) = |a|, for a ≠ 0, since any number is a divisor of
Greatest_common_divisor
Relating two numbers and their greatest common divisor
called Bézout coefficients for (a, b); they are not unique. The extended Euclidean algorithm can be used to compute a minimal pair of Bézout coefficients
Bézout's_identity
Fast greatest common divisor algorithm
GCD algorithm, named after D. H. Lehmer, is a fast GCD algorithm for multiple-precision arithmetic, which improves on the simpler Euclidean algorithm by
Lehmer's_GCD_algorithm
About simultaneous modular congruences
m_{1}} and m 2 {\displaystyle m_{2}} may be computed by the extended Euclidean algorithm. A solution is given by x = a 1 m 2 n 2 + a 2 m 1 n 1 . {\displaystyle
Chinese_remainder_theorem
Algorithm for public-key cryptography
de ≡ 1 (mod λ(n)); d can be computed efficiently by using the extended Euclidean algorithm, since, thanks to e and λ(n) being coprime, said equation is
RSA_cryptosystem
Digital verification standard
computed before the message is known. It may be computed using the extended Euclidean algorithm or using Fermat's little theorem as k q − 2 mod q {\displaystyle
Digital_Signature_Algorithm
Algebraic structure
may be computed by using the extended Euclidean algorithm (see Modular multiplicative inverse § Extended Euclidean algorithm). Let F {\displaystyle F} be
Finite_field
Exponentation in modular arithmetic
multiplicative inverse d of b modulo m (for instance by using extended Euclidean algorithm). More precisely: c = be mod m = d−e mod m, where e < 0 and b
Modular_exponentiation
Error-correcting codes
decoding algorithm. In 1975, another improved BCH scheme decoder was developed by Yasuo Sugiyama, based on the extended Euclidean algorithm. In 1977,
Reed–Solomon_error_correction
'Best' approximation of a function by a rational function of given order
divergent series. One way to compute a Padé approximant is via the extended Euclidean algorithm for the polynomial greatest common divisor. The relation R (
Padé_approximant
Overview of and topical guide to algorithms
Regular expression Parsing Earley parser CYK algorithm Euclidean algorithm Extended Euclidean algorithm Sieve of Eratosthenes Integer factorization Primality
Outline_of_algorithms
NP-hard problem in combinatorial optimization
deterministic algorithm and within ( 33 + ε ) / 25 {\displaystyle (33+\varepsilon )/25} by a randomized algorithm. The TSP, in particular the Euclidean variant
Travelling_salesman_problem
Mathematical algorithm
Kuṭṭaka algorithm has much similarity with and can be considered as a precursor of the modern day extended Euclidean algorithm. The latter algorithm is a
Kuṭṭaka
Division with remainder of integers
are called integer division algorithms, the best known of which being long division. Euclidean division, and algorithms to compute it, are fundamental
Euclidean_division
calculus algorithm Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Euclidean algorithm: computes the greatest common divisor Extended Euclidean
List_of_algorithms
Number which when multiplied by x equals 1
inverse of 3 mod 11 is four because 4 ⋅ 3 ≡ 1 (mod 11). The extended Euclidean algorithm may be used to compute it. The sedenions are an algebra in which
Multiplicative_inverse
Vector quantization algorithm minimizing the sum of squared deviations
is the minimum Euclidean distance assignment. Hartigan, J. A.; Wong, M. A. (1979). "Algorithm AS 136: A k-Means Clustering Algorithm". Journal of the
K-means_clustering
Dijkstra notation with non-deterministic conditionals
b hold the greatest common divisor of A and B. Dijkstra sees in this algorithm a way of synchronizing two infinite cycles a := a - b and b := b - a in
Guarded_Command_Language
Greatest common divisor of polynomials
polynomial GCD allows extending to univariate polynomials all the properties that may be deduced from the Euclidean algorithm and Euclidean division. Moreover
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Algorithm used for points in euclidean space
in Voronoi diagrams. Although the algorithm may be applied most directly to the Euclidean plane, similar algorithms may also be applied to higher-dimensional
Lloyd's_algorithm
Maximally even rhythm
The Euclidean rhythm in music was discovered by Godfried Toussaint in 2004 and is described in a 2005 paper "The Euclidean Algorithm Generates Traditional
Euclidean_rhythm
Representation of modular integers by "small" fractions
complexity of the Euclidean algorithm. More precisely, given the two integers m and a appearing in Thue's lemma, the extended Euclidean algorithm computes three
Thue's_lemma
Public-key cryptosystem
the modular multiplicative inverse can be computed using the extended Euclidean algorithm. An alternative is to compute s − 1 {\displaystyle s^{-1}} as
ElGamal_encryption
A prime p divides a^p–a for any integer a
values of y, e and n is easy if one knows φ(n). In fact, the extended Euclidean algorithm allows computing the modular inverse of e modulo φ(n), that is
Fermat's_little_theorem
Form of public key cryptography
of r {\displaystyle r} modulo q {\displaystyle q} using the Extended Euclidean algorithm. The inverse will exist since r {\displaystyle r} is coprime
Merkle–Hellman knapsack cryptosystem
Merkle–Hellman_knapsack_cryptosystem
topics named after the Greek mathematician Euclid. Euclidean algorithm Extended Euclidean algorithm Euclidean division Euclid–Euler theorem Euclid number Euclid's
List of things named after Euclid
List_of_things_named_after_Euclid
Algorithm for integer factorization
residue classes modulo n {\displaystyle n} , performed using the extended Euclidean algorithm. In particular, division by some v mod n {\displaystyle v{\bmod
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Algorithm for finding shortest paths
path problem. A* search algorithm Bellman–Ford algorithm Euclidean shortest path Floyd–Warshall algorithm Johnson's algorithm Longest path problem Parallel
Dijkstra's_algorithm
Arithmetic in a field with a finite number of elements
multiplication by the inverse modulo p, which may be computed using the extended Euclidean algorithm. A particular case is GF(2), where addition is exclusive OR (XOR)
Finite_field_arithmetic
Method for division with remainder
result of Euclidean division. Some are applied by hand, while others are employed by digital circuit designs and software. Division algorithms fall into
Division_algorithm
Computation modulo a fixed integer
solving Bézout's equation a x + m y = 1 for x, y, by using the Extended Euclidean algorithm. In particular, if p is a prime number, then a is coprime with
Modular_arithmetic
One over a whole number
fraction can be converted into an equivalent whole number using the extended Euclidean algorithm. This conversion can be used to perform modular division: dividing
Unit_fraction
Problem of inverting exponentiation in groups
means congruence modulo p {\displaystyle p} in the integers. The extended Euclidean algorithm finds k {\displaystyle k} quickly. With Diffie–Hellman, a cyclic
Discrete_logarithm
Cryptographic algorithm created by Adi Shamir
A is B such that A*B % p == 1). This can be computed via the extended Euclidean algorithm http://en.wikipedia.org/wiki/Modular_multiplicative_inverse#Computation
Shamir's_secret_sharing
Mathematical puzzle
Coconuts, a copy of the story as it appeared in the Saturday Evening Post The Monkey and the Coconuts: An Introduction to the Extended Euclidean Algorithm
The_monkey_and_the_coconuts
Quantum algorithm for integer factorization
using the Euclidean algorithm. If this produces a nontrivial factor (meaning gcd ( a , N ) ≠ 1 {\displaystyle \gcd(a,N)\neq 1} ), the algorithm is finished
Shor's_algorithm
Kind of error correction code
{\displaystyle a(x)} and b ( x ) {\displaystyle b(x)} using the extended euclidean algorithm, so that a ( x ) ≡ b ( x ) ⋅ v ( x ) mod g ( x ) {\displaystyle
Binary_Goppa_code
English mathematician (1682–1716)
he had lived we would have known something." Cotes's spiral Extended Euclidean algorithm Newton–Cotes formulas Lituus (mathematics) Gowing 2002, p. 5
Roger_Cotes
Least common multiple Euclidean algorithm Coprime Euclid's lemma Bézout's identity, Bézout's lemma Extended Euclidean algorithm Table of divisors Prime
List_of_number_theory_topics
planar by a certifying algorithm that outputs either a planar embedding or a Kuratowski subgraph. The extended Euclidean algorithm for the greatest common
Certifying_algorithm
Algorithm in computational number theory
Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Public-key encryption scheme
{p}}\\m_{q}&=c^{{\frac {1}{4}}(q+1)}{\bmod {q}}\end{aligned}}} Use the extended Euclidean algorithm to find y p {\displaystyle y_{p}} and y q {\displaystyle y_{q}}
Rabin_cryptosystem
Topics referred to by the same term
the twin study Ethylene-ethyl acid, used in hot-melt adhesive Extended Euclidean algorithm Extreme event attribution, the science of quantifying the degree
EEA_(disambiguation)
Some polynomial Diophantine equations can be solved using the extended Euclidean algorithm, which works as well with polynomials as it does with integers
Polynomial Diophantine equation
Polynomial_Diophantine_equation
Type of plane partition
of points { p 1 , … p n } {\displaystyle \{p_{1},\dots p_{n}\}} in the Euclidean plane. In this case, each point p k {\displaystyle p_{k}} has a corresponding
Voronoi_diagram
Algebraic structure
divisor that is monic (leading coefficient equal to 1). The extended Euclidean algorithm allows computing (and proving) Bézout's identity. In the case
Polynomial_ring
Shape with three sides
generally, four points in three-dimensional Euclidean space determine a solid figure called tetrahedron. In non-Euclidean geometries, three "straight" segments
Triangle
Area of discrete mathematics
graph is the special case of a Euclidean graph. The Euclidean graph allows its edges to have the length of the Euclidean distance between its endpoints
Graph_theory
Shortest network connecting points
A Euclidean minimum spanning tree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
On short connecting nets with added points
the Euclidean Steiner tree problem is NP-hard, and hence it is not known whether an optimal solution can be found by using a polynomial-time algorithm. However
Steiner_tree_problem
develops Kuṭṭaka, an algorithm very similar to the Extended Euclidean algorithm. 499: Aryabhata describes a numerical algorithm for finding cube roots
Timeline of scientific discoveries
Timeline_of_scientific_discoveries
Indian inventions
Kuṭṭaka algorithm has much similarity with and can be considered as a precursor of the modern day extended Euclidean algorithm. The latter algorithm is a
List of Indian inventions and discoveries
List_of_Indian_inventions_and_discoveries
Finding the smallest circle that contains all given points
Welzl's minidisk algorithm has been extended to handle Bregman divergences which include the squared Euclidean distance. Megiddo's algorithm is based on the
Smallest-circle_problem
Statistical method in data analysis
cluster. At each step, the algorithm merges the two most similar clusters based on a chosen distance metric (e.g., Euclidean distance) and linkage criterion
Hierarchical_clustering
Triangulation method
of Delaunay triangulation extends to three and higher dimensions. Generalizations are possible to metrics other than Euclidean distance. However, in these
Delaunay_triangulation
Algorithm to multiply two numbers
multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient
Multiplication_algorithm
ring of univariate polynomials over a field. In this case, the extended Euclidean algorithm may be used for computing the above unimodular matrix; see Polynomial
Linear_equation_over_a_ring
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
{\displaystyle a} and b {\displaystyle b} will be integers. Using the Extended Euclidean Algorithm, compute the inverse of b {\displaystyle b} modulo p {\displaystyle
Okamoto–Uchiyama_cryptosystem
Integer factorization algorithm
Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and
Pollard's_rho_algorithm
Mathematical procedure
extension of the Euclidean algorithm can find any integer relation that exists between any two real numbers x1 and x2. The algorithm generates successive
Integer_relation_algorithm
Type of algebraic curve
over the field K {\displaystyle K} . The algorithm works as follows Using the extended Euclidean algorithm compute the polynomials d 1 , e 1 , e 2 ∈
Imaginary_hyperelliptic_curve
Partition of the Euclidean plane
tesselation or a sectional Dirichlet tesselation, is a partition of the Euclidean plane into polygonal cells defined from a set of circles. The cell for
Power_diagram
Result on periodic sequences
theorem above. The proof comes from, and is closely related to the extended Euclidean algorithm, much like the proof of Bézout's identity. Let u , v {\displaystyle
Fine_and_Wilf's_theorem
Density-based data clustering algorithm
HDBSCAN* algorithm. pyclustering library includes a Python and C++ implementation of DBSCAN for Euclidean distance only as well as OPTICS algorithm. SPMF
DBSCAN
Ancient algorithm for generating prime numbers
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking
Sieve_of_Eratosthenes
British mathematician and cryptographer
Encryption Using a Finite Field" (A couple of typos in this pdf: Extended Euclidean Algorithm modulus should be (p-1) instead of p. Enc and Dec are performed
Malcolm_J._Williamson
Approach to quantum gravity utilizing Wick rotations
In theoretical physics, Euclidean quantum gravity exploits the Wick rotation to describe gravity according to the principles of quantum mechanics. This
Euclidean_quantum_gravity
Algorithm for integer multiplication
The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a
Karatsuba_algorithm
Number-theoretic algorithm
replace r0 with m - r0, which will still be a root of -d). Then the Euclidean algorithm can be employed to find r 1 ≡ m ( mod r 0 ) {\displaystyle r_{1}\equiv
Cornacchia's_algorithm
Decomposition of a number into a product
efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist. The presumed difficulty
Integer_factorization
Formula for the "volume" of an n-simplex
theorem comes from the following algorithm for realizing a Euclidean Distance Matrix or a Gramian Matrix. Input Euclidean Distance Matrix Δ {\displaystyle
Cayley–Menger_determinant
exist positive integers ri and si, that can be found using the Extended Euclidean algorithm, such that r i . m i + s i . M / m i = 1 {\displaystyle r_{i}
Secret sharing using the Chinese remainder theorem
Secret_sharing_using_the_Chinese_remainder_theorem
Proof that a number is prime
calculation of gcd, done for large numbers usually using the Extended Euclidean algorithm, over the number of primes provided. Each operation takes between
Primality_certificate
Feature detection algorithm in computer vision
required for finding the Euclidean-distance-based nearest neighbor, an approximate algorithm called the best-bin-first algorithm is used. This is a fast
Scale-invariant feature transform
Scale-invariant_feature_transform
Arithmetic operation
integers as result, is sometimes called Euclidean division, because it is the basis of the Euclidean algorithm. Give the integer quotient as the answer
Division_(mathematics)
Physical simulation to visualize graphs
Force-directed graph drawing algorithms are a class of algorithms for drawing graphs in an aesthetically-pleasing way. Their purpose is to position the
Force-directed_graph_drawing
Smallest convex set containing a given set
of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its
Convex_hull
Multiplication algorithm
The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen
Schönhage–Strassen_algorithm
Algorithm for supervised learning of binary classifiers
In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. A binary classifier is a function that can decide whether
Perceptron
Condition under which an odd prime is a sum of two squares
{p}}} . Once x {\displaystyle x} is determined, one can apply the Euclidean algorithm with p {\displaystyle p} and x {\displaystyle x} . Denote the first
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Branch of mathematics
geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance,
Geometry
Asymmetric key encryption algorithm
mod q {\displaystyle u_{q}=x^{d_{q}}{\bmod {q}}} . Using the Extended Euclidean Algorithm, compute r p {\displaystyle r_{p}} and r q {\displaystyle r_{q}}
Blum–Goldwasser_cryptosystem
localization and mapping (SLAM) and relative position tracking, the algorithm was extended to 3D point clouds and has wide applications in computer vision
Normal distributions transform
Normal_distributions_transform
Machine learning paradigm
supervised learning (SL) is a type of machine learning paradigm where an algorithm learns to map input data to a specific output based on example input-output
Supervised_learning
Topological space that locally resembles Euclidean space
mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional
Manifold
Graph of intervisible locations in computational geometry
graphs have therefore been extended to the realm of time series analysis. Visibility graphs may be used to find Euclidean shortest paths among a set of
Visibility_graph
Function for machine learning algorithms
examples. It was conceived by Google researchers for their prominent FaceNet algorithm for face detection. Triplet loss is designed to support metric learning
Triplet_loss
Mathematical space with a notion of distance
geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are
Metric_space
Mathematical treatise by Euclid
Euclidean geometry, elementary number theory, and incommensurability. These include the Pythagorean theorem, Thales' theorem, the Euclidean algorithm
Euclid's_Elements
Root-finding algorithm for polynomials
p-f_{0}g_{0}=f_{0}\Delta g+g_{0}\Delta f} using any variant of the extended Euclidean algorithm to obtain the incremented approximations f 1 = f 0 + Δ f {\displaystyle
Splitting_circle_method
EXTENDED EUCLIDEAN-ALGORITHM
EXTENDED EUCLIDEAN-ALGORITHM
Biblical
large; extended (name of a woman)
Boy/Male
Hindu, Indian, Marathi
Continuous Extended
Boy/Male
Indian
Servant of the expander, Extender
Girl/Female
Indian, Sanskrit
Awakened; Roused; Expanded
Girl/Female
Biblical
Large; extended (name of a woman).
Boy/Male
Afghan, Arabic, Pashtun
Intended; Proposed
Boy/Male
Arabic, German, Muslim
Intended; Proposed
Boy/Male
Arabic
Servant of the Extender; Creator
Boy/Male
Muslim
Intended, Aimed at, Object, Proposed
Boy/Male
Muslim
Servant of the expander, Extender
Girl/Female
Arabic, Muslim
Intended; Destined
Girl/Female
Muslim
Intended, Destined
Boy/Male
Muslim
Servant of the Extender, Creator.
Biblical
burning; adoration,extended land
Girl/Female
Australian, Biblical, British, Christian, English, German, Hawaiian, Hebrew
Large; Extended; Broad; Spacious; Wide
Boy/Male
Hindu
Constisting of extended troops
Boy/Male
Muslim/Islamic
Servant of the Extender and Creator
Boy/Male
Muslim
Servant of the Extender, Creator.
Boy/Male
Tamil
Constisting of extended troops
Surname or Lastname
English
English : extended form of Yates.
EXTENDED EUCLIDEAN-ALGORITHM
EXTENDED EUCLIDEAN-ALGORITHM
Boy/Male
Tamil
Ramendra | ராமேநà¯à®¤à¯à®°
God of gods
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Sanskrit, Sindhi, Telugu, Traditional
A Record of Victory
Surname or Lastname
German and Dutch
German and Dutch : from a short form of Hildebrand or other compound names with the same initial element, hild ‘strife’, ‘battle’.English : from the medieval female personal name Hilda (Old English Hild), representing a short form of compound names with the first element hild ‘strife’, ‘battle’. Compare Hilliard, for example.
Boy/Male
Hindu, Indian, Telugu
Lord Indra
Male
Greek
(ἸοÏδάνης) Greek masculine form of Hebrew unisex Yarden ("flowing down"), IORDANES means "the descender." In the bible, this is the name of the river in which Jesus was baptized by John the Baptist.
Boy/Male
Hindu, Indian
Part of Lady and Man; Slove
Boy/Male
Irish
Holy.
Boy/Male
African, Arabic, Swahili
Defender; Supporter; Protector; Granting Victory
Boy/Male
Norse
Wolf.
Girl/Female
Arabic, Hindu, Indian, Muslim
Explore; Provider of Food
EXTENDED EUCLIDEAN-ALGORITHM
EXTENDED EUCLIDEAN-ALGORITHM
EXTENDED EUCLIDEAN-ALGORITHM
EXTENDED EUCLIDEAN-ALGORITHM
EXTENDED EUCLIDEAN-ALGORITHM
v. t.
Outreaching; expansive; extended, superficially or otherwise.
v. t.
To enlarge, as a surface or volume; to expand; to spread; to amplify; as, to extend metal plates by hammering or rolling them.
n.
One who, or that which, extends or stretches anything.
v. t.
To increase in quantity by weakening or adulterating additions; as, to extend liquors.
a.
Purposed; designed; as, intended harm or help.
adv.
In an extended manner.
a.
Not extended.
a.
Extended in length; tiresome.
v. t.
To enlarge; to widen; to carry out further; as, to extend the capacities, the sphere of usefulness, or commerce; to extend power or influence; to continue, as time; to lengthen; to prolong; as, to extend the time of payment or a season of trail.
a.
Drawn out; extended.
a.
Extended horizontally; stretched out.
a.
Betrothed; affianced; as, an intended husband.
a.
Made tense; stretched out; extended; forcible; violent.
n.
Extended area.
v. t.
To stretch out; to prolong in space; to carry forward or continue in length; as, to extend a line in surveying; to extend a cord across the street.
a.
Capable of being extended, susceptible of being stretched, extended, enlarged, widened, or expanded.
n.
Related to Euclid, or to the geometry of Euclid.
v. t.
To bestow; to offer; to impart; to apply; as, to extend sympathy to the suffering.
imp. & p. p.
of Extend
a.
Extended.