The Lord Brouncker employed this series to square the hyperbola.
"Letters on England" by Voltaire
An oval is never mistaken for a circle, nor an hyperbola for an ellipsis.
"An Enquiry Concerning Human Understanding" by David Hume
The following analysis shows that with the aid of an hyperbola any arc, and therefore any angle, may be trisected.
"Scientific American Supplement, No. 787, January 31, 1891" by Various
It is easily seen that the curves traced by the shadow of the point P are hyperbolas whose convexity is turned toward A B.
"Scientific American Supplement, No. 810, July 11, 1891" by Various
There's nothing more to fear from your hyperbolas or parabolas or any other of your open curves!
"All Around the Moon" by Jules Verne
In the hyperbola we have the mathematical demonstration of the error of an axiom.
"Fables of Infidelity and Facts of Faith" by Robert Patterson
Griffin (R. W.) on Parabola, Ellipse, and Hyperbola.
"France and the Republic" by William Henry Hurlbert
It is said that he was the first to introduce the words ellipse and hyperbola.
"History of the Intellectual Development of Europe, Volume I (of 2)" by John William Draper
In such cases the orbit might be changed to a hyperbola, and then the comet would never return.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7" by Various
Just a plain hyperbola is bad enough.
"The Romantic Analogue" by W.W. Skupeldyckle
The planet would then have moved in a parabola, or an hyperbola, curves not returning into themselves.
"A System of Logic: Ratiocinative and Inductive" by John Stuart Mill
Two asymptotes and any two tangents to an hyperbola may be considered as a quadrilateral circumscribed about the hyperbola.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
It is natural, therefore, that circle, ellipse, parabola, and hyperbola should all be looked upon as lines.
"The Teaching of Geometry" by David Eugene Smith
The epithets hyperbolic and parabolic are of course derived from the conic hyperbola and parabola respectively.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 8" by Various
The geometry of the rectangular hyperbola is simplified by the fact that its principal axes are equal.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 2" by Various
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On the other hand, the curves of parabolas in the middle (resp. right) ﬁgure are the osculating parabolic congruence of a hyperbola (resp. an ellipse ).
Curvature Functionals for Curves in the Equi-Affine Plane
Region in the (ρ, η) plane allowed by constraints on |Vub /Vcb | (dotted semicircles), B 0 − ¯B 0 mixing (dashed semicircles), and CP-violating K − ¯K mixing (solid hyperbolae).
Present and Future Aspects of CP Violation
Equation (19) speciﬁes a hyperbola in the ( ¯̺, ¯η) plane.
Theoretical review of K physics
Vub/Vcb | which produces a circular ring and from a hyperbola deﬁned from the theoretical formula for ε.
Analysis of \epsilon'/\epsilon in the 1/N_c Expansion
The position of the hyperbola depends on mt , |Vcb |, and ˆBK .
Analysis of \epsilon'/\epsilon in the 1/N_c Expansion
This is valid since geodesics on the Taub-NUT space are hyperbolae , so in a scattering process r asymptotically approaches inﬁnity and there is only one turning point.
Radiation from SU(3) monopole scattering
The curve for N = 6 dominates that for N = 4, which in turn dominates the hyperbola for N = 2.
Increased Efficiency of Quantum State Estimation Using Non-Separable Measurements
The eq.(21) represents a hyperbola and shows that to an external observer a radially in-falling time like or null particle approaches the radius r = q(D)asymptotically but can never reach it.
Wormhole and C-field
Here we also see the s - r relationship represents a hyperbola.
Wormhole and C-field
For example, the constraint obtained from the C P -violating parameter ǫK in the neutral K system corresponds to the vertex A of the unitarity triangle lying on a hyperbola for ﬁxed values of the (imprecisely known) hadronic matrix elements , .
Unitarity Triangle from CP invariant quantities
Note that this has the required form (two hyperbolae with the same asymptotes, and possibly different intercepts).
Analogue spacetime based on 2-component Bose-Einstein condensates
It is known that for any point (p, q) ∈ R2 below the critical hyperbola the Hamiltonian system has a nontrivial solution (see [CdFM], [dFF], [HvdV], [FM] and [dFR]), whereas for points (p, q) on the critical hyperbola one ﬁnds the typical problems of non-compactness and non-existence of solutions (see [vdV] and [M]).
Perturbation from symmetry and multiplicity of solutions for strongly indefinite elliptic systems
We remark here that the pair (p, q) lies below the critical hyperbola; for any ﬁxed (p, q), the value of r, which identiﬁes the space E r , is not ﬁxed, but can be chosen in the range deﬁned by (60) (see Theorem 2.1).
Perturbation from symmetry and multiplicity of solutions for strongly indefinite elliptic systems
Let us ﬁx (p, q) below the critical hyperbola 1 N .
Perturbation from symmetry and multiplicity of solutions for strongly indefinite elliptic systems
Condition (81) deﬁnes a new region in the (p, q) plane which is contained in the subcritical region delimited by the critical hyperbola.
Perturbation from symmetry and multiplicity of solutions for strongly indefinite elliptic systems
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