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the principal orbit type theorem states that compact Lie group acting smoothly on a connected differentiable manifold has a principal orbit type. Suppose
Principal_orbit_type_theorem
Transformations induced by a mathematical group
belongs to ( H ) {\displaystyle (H)} . A maximal orbit type is often called a principal orbit type. Orbits and stabilizers are closely related. For a fixed
Group_action
Function describing an electron in an atom
level corresponding to the principal quantum number n; type is a lower-case letter denoting the shape or subshell of the orbital, corresponding to the angular
Atomic_orbital
Branch of mathematics that studies algebraic structures
basis theorem Hopkins–Levitzki theorem Krull's principal ideal theorem Levitzky's theorem Galois theory Abel–Ruffini theorem Wedderburn–Artin theorem Jacobson
List of abstract algebra topics
List_of_abstract_algebra_topics
Mathematical function
orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals in the linear combination of atomic orbitals
Gaussian_orbital
Correspondsnce between Higgs bundles and fundamental group representations
where two orbits are identified if their closures intersect. These moduli spaces are called the Betti moduli spaces. The nonabelian Hodge theorem can be
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
Classification used in differential geometry and general relativity
theorem states that there are precisely six possible types of algebraic symmetry. These are known as the Petrov types: Type I: four simple principal null
Petrov_classification
Movement of an object which leaves at least one point unchanged
orbital poles. Either type of rotation is involved in a corresponding type of angular velocity (spin angular velocity and orbital angular velocity) and
Rotation
Parameter in the Mandelbrot set
critical value, and by Tan Lei's theorem, also in the Mandelbrot set near any Misiurewicz parameter for which the repelling orbit has a non-real multiplier.
Misiurewicz_point
Topological space
subspace p. Then a principal orbit of the adjoint representation of H on p is an isoparametric manifold in p. Non principal orbits are examples of the
Isoparametric_manifold
Result of repeatedly applying a mathematical function
values fn(x) is called the orbit of x. If f n (x) = f n+m (x) for some integer m > 0, the orbit is called a periodic orbit. The smallest such value of
Iterated_function
Bundle theorem Butterfly theorem – About the midpoint of a chord of a circle, through which two other chords are drawn Carnot's theorem – Theorem in Euclidean
List_of_circle_topics
When an idea extends to a principal ideal in an extension of algebraic number fields
everywhere) provides such an extension. This statement, now known as the principal ideal theorem, was proved in 1930 by Philipp Furtwängler, following its reformulation
Principalization_(algebra)
Representation theory
In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
Star at the centre of the Solar System
and a central subject of astronomical research since antiquity. The Sun orbits the Galactic Center at a distance of 24,000 to 28,000 light-years. Its mean
Sun
Approximation method in quantum physics
atomic orbitals. These atomic orbitals are called Slater-type orbitals. Furthermore, it is very common for the "atomic orbitals" in use to actually be composed
Hartree–Fock_method
Method for describing the electronic structure of molecules using quantum mechanics
molecular orbital is best characterized by that type. This method of quantifying orbital contribution as a linear combination of atomic orbitals is used
Molecular_orbital_theory
Concept in mathematics
simplicity theorem remains valid except when G is split of type A1, B2, or G2, or non-split (that is, unitary) of type A2. For k = F3, the theorem holds except
Reductive_group
Study of sudden qualitative behavior changes caused by small parameter changes
"small" or "type I" homoclinic bifurcation. In 2D there is also the "big" or "type II" homoclinic bifurcation in which the homoclinic orbit "traps" the
Bifurcation_theory
Vector used in astronomy
_{i=1}^{3}L_{i}B_{i}\right)B_{j}=0.} Astrodynamics Orbit Eccentricity vector Orbital elements Bertrand's theorem Binet equation Two-body problem Goldstein, H
Laplace–Runge–Lenz_vector
Concept in continuum mechanics
formulation and proof of the following important theorems and corollary, cf. Ziółkowski (2022). Theorem I. The radial lines (rays) coming out from the origin
Stress_triaxiality
Study of vector bundles, principal bundles, and fibre bundles
bundle construction theorem and the same process works for any fibre bundle described by transition functions, not just principal bundles or vector bundles
Gauge_theory_(mathematics)
Intrinsic quantum property of particles
discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to the
Spin_(physics)
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 : C n → C m
Singular_value_decomposition
German polymath and scholar (1777–1855)
Gauss produced the second and third complete proofs of the fundamental theorem of algebra. He also introduced the triple bar symbol (≡) for congruence
Carl_Friedrich_Gauss
Mathematics glossary
homotopy type of a sphere. Hopf 1. Heinz Hopf. 2. Hopf invariant. 3. The Hopf index theorem. 4. Hopf construction. Hurewicz The Hurewicz theorem establishes
Glossary of algebraic topology
Glossary_of_algebraic_topology
Vector bundles theorem
theory, the Kobayashi–Hitchin correspondence (or Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
Atomic model introduced by Niels Bohr in 1913
from the same premises of eq. (1a) plus the virial theorem, stating that, for an elliptical orbit, T = − 1 2 U ( 1 c ) . {\displaystyle T=-{\frac
Bohr_model
List of definitions of terms and concepts commonly used in aerospace engineering
current orbital state vectors (position and velocity). Parallel axis theorem – also known as Huygens–Steiner theorem, or just as Steiner's theorem, named
Glossary of aerospace engineering
Glossary_of_aerospace_engineering
American Jewish mathematician
Rosenberg, he is one of the namesakes of the Hochschild–Kostant–Rosenberg theorem which describes the Hochschild homology of some algebras. His students
Bertram_Kostant
Array of numbers
authors define a principal submatrix as one in which the first k rows and columns, for some number k, are the ones that remain; this type of submatrix has
Matrix_(mathematics)
a distinguished homogeneous boundary orbit: the Shilov boundary is the unique closed G {\displaystyle G} -orbit in ∂ D {\displaystyle \partial D} . Equivalently
Shilov_boundary
Mathematics of smooth surfaces
the definitions of the fundamental forms and Taylor's theorem in two dimensions. The principal curvatures can be viewed in the following way. At a given
Differential geometry of surfaces
Differential_geometry_of_surfaces
Concepts from linear algebra
lemma, see Roman 2008, p. 186, Theorem 8.2; Shilov 1977, p. 109; Hefferon 2001, p. 364; and Beezer 2006, p. 469, Theorem EDELI. By doing Gaussian elimination
Eigenvalues_and_eigenvectors
Set of points equidistant from a center
it is closed; Sn is also bounded, so it is compact by the Heine–Borel theorem. More generally, in a metric space (E,d), the sphere of center x and radius
Sphere
{\mathcal {O}}_{X}(-1)} . theorem See Zariski's main theorem, theorem on formal functions, cohomology base change theorem, Category:Theorems in algebraic geometry
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
American mathematician
as the Gershgorin circle theorem has been used as a basis for extension. In 1964 Brenner reported on Theorems of Gersgorin Type. In 1967 at University of
Joel_Lee_Brenner
Branch of mathematics
Euler proved a theorem expressing the curvature of a space curve on a surface in terms of the principal curvatures, known as Euler's theorem. Later in the
Differential_geometry
Lie group of complex numbers of unit modulus; topologically a circle
questions are: What structure does the orbit of a point have? For instance, is it dense in the group? Is the orbit of a point equidistributed? What is the
Circle_group
Plane curve
Ellipses are common in physics, astronomy and engineering. For example, the orbit of each planet in the Solar System is approximately an ellipse with the
Ellipse
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
Algebraic construct classifying topological spaces
1980s involving a van Kampen type theorem for higher homotopy groupoids have allowed new calculations on homotopy types and so on homotopy groups. See
Homotopy_group
Internal groupoid in the category of smooth manifolds
at a point x ∈ M {\displaystyle x\in M} is a principal G x {\displaystyle G_{x}} -bundle over the orbit O x {\displaystyle {\mathcal {O}}_{x}} at that
Lie_groupoid
Dynamical system
In mathematics, the replicator equation is a type of dynamical system used in evolutionary game theory to model how the frequency of strategies in a population
Replicator_equation
Plane curve: conic section
orbits most commonly resemble hyperbolas or ellipses. The parabolic orbit is the degenerate intermediate case between those two types of ideal orbit.
Parabola
Approximation method in statistics
after reading Gauss's work, Laplace, after proving the central limit theorem, used it to give a large sample justification for the method of least squares
Least_squares
Type of mathematical functions
theorem was able to create a global meromorphic function from a given and principal parts (Cousin I problem), and Weierstrass factorization theorem was
Function of several complex variables
Function_of_several_complex_variables
Class of problems in classical mechanics
thus the orbit will not be closed. In that case, the particle will eventually pass arbitrarily close to every point within the annulus. Two types of central
Classical central-force problem
Classical_central-force_problem
comparing the rate of orbital precession of two stars on different orbits, it is possible in principle to test the no-hair theorems of general relativity
Tests_of_general_relativity
Fractal named after mathematician Benoit Mandelbrot
is the uncountable set of values of c in the complex plane for which the orbit of the critical point z = 0 {\textstyle z=0} under iteration of the quadratic
Mandelbrot_set
Type of mathematical space
parabolic type. They are homogeneous Riemannian manifolds under any maximal compact subgroup of G, and they are precisely the coadjoint orbits of compact
Generalized_flag_variety
Description of a quantum-mechanical system
together orbit each other about a common center of mass, and constitute a two-body problem to solve. The motion of the electron is of principal interest
Schrödinger_equation
Laws in physics about force and motion
that orbits will be conic sections, that is, ellipses (including circles), parabolas, or hyperbolas. The eccentricity of the orbit, and thus the type of
Newton's_laws_of_motion
Property of certain dynamical systems
and the energy level set is compact, this implies the Liouville–Arnold theorem; i.e., the existence of action-angle variables. General dynamical systems
Integrable_system
Method for estimating the unknown parameters in a linear regression model
residuals when regressors have finite fourth moments and—by the Gauss–Markov theorem—optimal in the class of linear unbiased estimators when the errors are
Ordinary_least_squares
Curve from a cone intersecting a plane
Pascal's theorem concerns the collinearity of three points that are constructed from a set of six points on any non-degenerate conic. The theorem also holds
Conic_section
Iranian mathematician (1977–2017)
on the dynamics of moduli spaces that became known as the "magic wand theorem". Mirzakhani died from breast cancer on 14 July 2017 at the age of 40.
Maryam_Mirzakhani
Circus skill manipulating objects
Claude Shannon, builder of the first juggling robot, developed a juggling theorem, relating the time balls spend in the air and in the hands: (F+D)H=(V+D)N
Juggling
further simplified with the use of group theory and in particular Bloch's theorem, which leads to the result that the energy eigenvalues depend on the crystal
Korringa–Kohn–Rostoker_method
Orientation-preserving mapping class group of the torus
of the orbit of z. This also means that we can construct fundamental domains, which (roughly) contain exactly one representative from the orbit of every
Modular_group
2009 Spanish film
refuses. Hypatia theorizes that the Earth orbits around the Sun in an elliptical orbit, not a circular orbit, with the Sun at one of the foci. Cyril convinces
Agora_(film)
Energy level of a quantum system
motion and spin–orbit coupling result in breaking the degeneracy in energy levels for different values of l corresponding to a single principal quantum number
Degenerate_energy_levels
Formulation of classical mechanics
_{0}\in M} in the configuration space be fixed. The existence and uniqueness theorems guarantee that, for every v 0 , {\displaystyle \mathbf {v} _{0},} the initial
Hamilton–Jacobi_equation
Change in sea level due to gravity
combined with inertial effects associated with the Earth–Moon system’s orbital motion and the Earth's rotation. While these astronomical forcings generate
Tide
System of stars and interstellar matter
largest galaxies known—supergiants with one hundred trillion stars, each orbiting its galaxy's center of mass. Most of the mass in a typical galaxy is in
Galaxy
Alternative mathematical ordering
Huntington, Edward V. (July 1935), "Inter-Relations Among the Four Principal Types of Order" (PDF), Transactions of the American Mathematical Society
Cyclic_order
Branch of mathematics
accelerated motion, and Nicole Oresme gave a graphical proof of the mean speed theorem, representing displacement by the area under a velocity-time graph. Oresme
Mathematical_analysis
Algebraic geometry analog of a principal bundle in algebraic topology
integrals as being examples of torsors. Beauville–Laszlo theorem Moduli stack of principal bundles Cox ring Demazure, Michel; Gabriel, Pierre (2005)
Torsor_(algebraic_geometry)
Statistical modeling method
effects estimation is an alternative approach to analyzing this type of data. Principal component regression (PCR) is used when the number of predictor
Linear_regression
Turning force around an axis
principle of moments, also known as Varignon's theorem (not to be confused with the geometrical theorem of the same name) states that the resultant torques
Torque
Set of statistical processes for estimating the relationships among variables
theory of least squares in 1821, including a version of the Gauss–Markov theorem. The term "regression" was coined by Francis Galton in the 19th century
Regression_analysis
Lie group of Lorentz transformations
be written as the quotient space SO+(1, 3) / SO(3), due to the orbit-stabilizer theorem. Furthermore, this upper sheet also provides a model for three-dimensional
Lorentz_group
Physical theory with fields invariant under the action of local "gauge" Lie groups
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local
Gauge_theory
Parafoil Paraformer Parallax barrier Parallel Worlds (book) Parallel axis theorem Parallelogram of force Paramagnetism Parameterized post-Newtonian formalism
Index_of_physics_articles_(P)
Principal bundle associated to a vector bundle
called smooth frames on M {\displaystyle M} . The cross-section theorem for principal bundles states that the frame bundle is trivial over any open set
Frame_bundle
Hypothesis about sapient life and the universe
three spatial dimensions, the orbit of a planet about its Sun cannot remain stable. The same is true of a star's orbit around the center of its galaxy
Anthropic_principle
Technique to solve partial differential equations
scientific machine learning (SciML), leveraging the universal approximation theorem and high expressivity of neural networks. In general, deep neural networks
Physics-informed neural networks
Physics-informed_neural_networks
Space of complex matrices with positive definite imaginary part
structures, so the Siegel upper half-space as a homogeneous space is the orbit of a fixed Kähler structure modulo its isotropy: H g = S p ( 2 g , R ) /
Siegel_upper_half-space
Mathematical group
Mathematicae. 3: 149–179. Brown, Ronald; Humphries, Stephen P. (1986). "Orbits under symplectic transvections. I". Proceedings of the London Mathematical
Symplectic_group
equations of mathematical physics. In 1896 he gave a proof of the prime number theorem that defines the frequency of prime numbers among the integers (also see
Meanings of minor-planet names: 10001–11000
Meanings_of_minor-planet_names:_10001–11000
Energy needed to remove an electron
provided by Koopmans' theorem, which involves the highest occupied molecular orbital or "HOMO" and the lowest unoccupied molecular orbital or "LUMO", and states
Ionization_energy
List of definitions of terms and concepts used in electrical engineering and electronics
Stokes' theorem A theorem about integration of three-dimensional functions, much used in analysis of electric fields. storage tube A type of cathode
Glossary of electrical and electronics engineering
Glossary_of_electrical_and_electronics_engineering
List of scientists who are Christians
Bolzano–Weierstrass theorem. He also gave the first purely analytic proofs of the fundamental theorem of algebra and the intermediate value theorem. Adam Sedgwick
List of Christians in science and technology
List_of_Christians_in_science_and_technology
Brightest star in the constellation Lyra
planet on an eccentric orbit. Dust would collect in orbits that have mean-motion resonances with this planet—where their orbital periods form integer fractions
Vega
Rate of change of velocity
explains tangent, (principal) normal and binormal, is described by the Frenet–Serret formulas. Uniform or constant acceleration is a type of motion in which
Acceleration
Exact solution for the Einstein field equations
a pair of principal null congruences (one ingoing and one outgoing). The Weyl tensor is algebraically special, in fact it has Petrov type D. Note that
Kerr_metric
modern type theory. Advances were also made in ordinal analysis and the study of independence results in arithmetic such as the Paris–Harrington theorem. This
History_of_logic
History of maths
Hilbert's syzygy theorem is a prototype for a concept of dimension in homological algebra. 1893 David Hilbert A fundamental theorem in algebraic geometry
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
major deduction from the existence of octonions was the eight squares theorem, which follows directly from the product rule from octonions. It had also
History_of_quaternions
Hypothesis about quantum and statistical mechanics
theorem leaves open the possibility of non-ergodic states such as quantum scars. In addition to the conventional scarring, there are two other types of
Eigenstate thermalization hypothesis
Eigenstate_thermalization_hypothesis
Branch of geometry
foliation on the manifold, whose equivalence is the content of the Frobenius theorem. Contact geometry is in many ways an odd-dimensional counterpart of symplectic
Contact_geometry
Branch of applied mathematics
systems, as embodied within the most elementary formulation of Noether's theorem. These approaches and ideas have been extended to other areas of physics
Mathematical_physics
Application of game theory to evolving populations in biology
distribution. The distribution (an ESS) can be computed using the Bishop-Cannings theorem, which holds true for any mixed-strategy ESS. The distribution function
Evolutionary_game_theory
Intrinsic geometric structures in mathematics
e_{1}+\cos \theta \,e_{2}).} Thus E becomes a principal bundle with structure group K. Taking the G-orbit of the point ((1,0,0),(0,1,0),(0,0,1)), the space
Riemannian connection on a surface
Riemannian_connection_on_a_surface
Geometry problem about finding touching circles
Descartes's theorem in 1936, several people solved (independently) the mutually tangent case corresponding to Soddy's circles in d dimensions. The principal application
Problem_of_Apollonius
230 BC) theorized Earth's rotation around its own axis, as well as Earth's orbit around the Sun in a heliocentric cosmology. Seleucus of Seleucia (c. 190 –
History of gravitational theory
History_of_gravitational_theory
Little Company of Mary Hospital in Evergreen Park, Illinois. 1933 Sampling theorem By Vladimir Kotelnikov[citation needed] 1933 Tandem rotor helicopter By
Timeline of Russian innovation
Timeline_of_Russian_innovation
Area of geometry, about angles and lengths
properties of chords and inscribed angles in circles, and they proved theorems that are equivalent to modern trigonometric formulae, although they presented
Trigonometry
German-born theoretical physicist (1879–1955)
rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday. A family tutor, Max Talmud, said that only
Albert_Einstein
Property that is not changed by mathematical transformations
of the Riemannian metric g {\displaystyle g} . This is the Gauss–Bonnet theorem. The MU puzzle is a good example of a logical problem where determining
Invariant_(mathematics)
PRINCIPAL ORBIT-TYPE-THEOREM
PRINCIPAL ORBIT-TYPE-THEOREM
Boy/Male
Muslim
Orbit, Eye socket, Argument
Boy/Male
Indian
Orbit, Eye socket, Argument
Boy/Male
Tamil
Siddhant | ஸிதà¯à®¤à®¾à®‚தÂ
Rule, Principals
Siddhant | ஸிதà¯à®¤à®¾à®‚தÂ
Male
English
English surname transferred to forename use, derived from the Middle English word tye, TYE means "pasture."
Boy/Male
Hindu
Rule, Principals
Surname or Lastname
English (mainly East Anglia)
English (mainly East Anglia) : topographic name for someone who lived by a common pasture, Middle English tye (Old English tēag).North German : from a short form, Tide, of the personal name Dietrich.
Boy/Male
Hindu, Indian, Kannada, Marathi, Oriya, Sanskrit, Telugu
Principal; Controller
Boy/Male
British, English, Latin
Raven; Variant of Corbet; Black-haired; Dark as a Raven
Boy/Male
Hindu, Indian, Traditional
Protector of Earth
Boy/Male
Sikh
Beloved cherisher, Protector
Boy/Male
Tamil
Siddhanth Nair | ஸிதà¯à®¤à®¾à®‚த நீர
Principal
Siddhanth Nair | ஸிதà¯à®¤à®¾à®‚த நீர
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Circumference of the Orbit; Limit; Realm
Boy/Male
Tamil
Siddhanta | ஸிதà¯à®¤à®¾à®‚தாÂ
Rule, Principals
Siddhanta | ஸிதà¯à®¤à®¾à®‚தாÂ
Female
Hebrew
(×ï‹×¨Ö´×™×ª) Variant form of Hebrew Ora, ORIT means "light."
Boy/Male
Muslim/Islamic
Orbit eye socket, Orgument, debate
Boy/Male
Hindu
Rule, Principals
Surname or Lastname
English
English : variant spelling of Corbett.
Boy/Male
Hindu
Principal
Boy/Male
English
Raven. Black-haired.
Boy/Male
Tamil
Adhikara | அதிகராÂ
Principal, Controller
PRINCIPAL ORBIT-TYPE-THEOREM
PRINCIPAL ORBIT-TYPE-THEOREM
Male
Hebrew
(ש×Ö¸×וּל) Hebrew name SHAUWL means "asked for, desired." In the bible, this is the name of many characters, including the first king of Israel.
Surname or Lastname
English
English : habitational name from Marbury in Cheshire, named in Old English as ‘stronghold by the lake’, from mere ‘pool’, ‘lake’ + burh ‘fortified place’ (dative byrig).
Girl/Female
Indian, Tamil
Broad Eye; Wide Eye
Girl/Female
Indian
Girl/Female
Biblical, Christian, German, Hebrew
The World; Loved One; Mole; Weasel
Boy/Male
Tamil
Sindhura | ஸிஂதà¯à®°à®¾
Surname or Lastname
English
English : habitational name from Healey near Manchester, named with Old English hēah ‘high’ + lēah ‘wood’, ‘clearing’. There are various other places in northern England, for example in Northumberland and Yorkshire, with the same name and etymology, and they may also have contributed to the surname.Variant of Irish Healy.
Male
Celtic
, chief leader.
Boy/Male
Australian, Chinese
Victory
Boy/Male
Hindu, Indian, Marathi
One God; The Supreme Being
PRINCIPAL ORBIT-TYPE-THEOREM
PRINCIPAL ORBIT-TYPE-THEOREM
PRINCIPAL ORBIT-TYPE-THEOREM
PRINCIPAL ORBIT-TYPE-THEOREM
PRINCIPAL ORBIT-TYPE-THEOREM
n.
The path described by a heavenly body in its periodical revolution around another body; as, the orbit of Jupiter, of the earth, of the moon.
n.
An orb or ball.
n.
In the antler of a stag, the third tyne above the base. This tyne appears in the third year. In those deer in which the brow tyne does not divide, the tres-tyne is the second tyne above the base. See Illust. under Rucervine, and under Rusine.
n.
A leader, chief, or head; one who takes the lead; one who acts independently, or who has controlling authority or influence; as, the principal of a faction, a school, a firm, etc.; -- distinguished from a subordinate, abettor, auxiliary, or assistant.
imp. & p. p.
of Type
n.
A principal or essential point or rule; a principle.
adv.
In a principal manner; primarily; above all; chiefly; mainly.
n.
A narrow fillet or band of cotton or linen; a narrow woven fabric used for strings and the like; as, curtains tied with tape.
n.
A combining form signifying impressed form; stamp; print; type; typical form; representative; as in stereotype phototype, ferrotype, monotype.
n.
The construction which gives shape and strength to a roof, -- generally a truss of timber or iron, but there are roofs with stone principals. Also, loosely, the most important member of a piece of framing.
a.
Relating to a type or types; belonging to types; serving as a type; typical.
n.
The cavity or socket of the skull in which the eye and its appendages are situated.
n.
A grove or clump of trees; as, a toddy tope.
n.
A tapeline; also, a metallic ribbon so marked as to serve as a tapeline; as, a steel tape.
n.
A single type; type, collectively; a style of type.
n. pl.
First principles; fundamental beginnings; elements; as. Newton's Principia.
v. t.
To represent by a type, model, or symbol beforehand; to prefigure.
n.
The skin which surrounds the eye of a bird.
a.
Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a state; the principal productions of a country; the principal arguments in a case.