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Hyperbola (X)

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 Book Id: WPLBN0079619704 ► Abstract Description DetailsThe Hyperbola and Its Connexion to the Natural Logarithm by Patrick Bruskiewich; published by
 Book Id: WPLBN0007574270 Subjects: “with, Ellipse, Hyperbola:, Hyperbola: ► Abstract Description Details...Ellipse to Hyperbola: “with This String I Thee Wed” by Apostol; Tom M.; Mnatsakanian; Mamikon A.; published by Mathematical Association of America on 2016-08-23T10:06:03Z...
 Book Id: WHEBN0000014052 Subjects: Ellipse, Circle, Parabola Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case. ... ... Hyperbolas in the physical world: three cones of light of different widths ... ...and its housing. Each cone of light intersects a nearby vertical wall in a hyperbola. ... ...ola. Hyperbolas produced by interference of waves ... ...terference of waves In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve, lyin... ...s geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are... ..., that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the four kinds of conic section, formed by the intersec... ... cone but does not pass through the apex of the cones, then the conic is a hyperbola. Hyperbolas arise in many ways: as the curve ... ... principle is the same), and so on. Each branch of the hyperbola has two arms which become straighter (lower curvature) further ou...
 Book Id: WPLBN0001862866 Subjects: Angles (Geometry), Hyperbola, Geometry, Hyperbola ► Abstract
 Book Id: WPLBN0011878841 Subjects: Hyperbola, Fusing Process, Offset, Hyperbola Collections: Periodicals: Journal and Magazine Collection ► Abstract Description Details...A Study of Radii of Curvature by Fusing Process and Improvement of Coupling Efficiency in Hyperbola Fiber Microlens by None; published by National Sun Yat-Sen University on 2012-08-16...
 Book Id: WHEBN0026205122 Subjects: Spacetime, Geometry, Year Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...ptotes are red. In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfies ... ...ies x^2 - y^2 = 1 . In the study of indefinite orthogonal groups, the unit hyperbola forms the basis for an alternative radial length ... ... Whereas the unit circle surrounds its center, the unit hyperbola requires the conjugate hyperbola y^2 - x^2 = 1 to complement it i... ...jugate hyperbola y^2 - x^2 = 1 to complement it in the plane. This pair of hyperbolas share the asymptotes y = x and y = −x. When the conjugate of the... ...olas share the asymptotes y = x and y = −x. When the conjugate of the unit hyperbola is in use, the alternative radial length is r = \sqrt {y^2 - x^2}... ...tive radial length is r = \sqrt {y^2 - x^2} . The unit hyperbola is a special case of the rectangular hyperbola, with a particular... ...e. As such, its eccentricity equals \sqrt{2}. The unit hyperbola finds applications where the circle must be replaced with the hyp... ...of spacetime as a pseudo-Euclidean space. There the asymptotes of the unit hyperbola form a light cone. Further, the attention to areas of hyperbolic ... ...incent led to the logarithm function and the modern parametrization of the hyperbola by sector areas. When the notions of conjugate hyperbolas and hyp...
 Book Id: WPLBN0000333746 Subjects: Hyperbola, Math, Calculus, Hyperbola ► Abstract
 Book Id: WPLBN0012628432 Collections: Periodicals: Journal and Magazine Collection ► Abstract Description Details...Geometry of the Space of Closed Curves in the Complex Hyperbola by Fujioka; Atsushi; Kurose; Takashi; 藤岡; 敦; 黒瀬; 俊; Fujioka; Atsushi; Kurose; Takashi; 藤岡; 敦; 黒瀬; 俊; published by Faculty of Mathematics, Kyushu University on 2016-07-01T04:26:53Z...
 Book Id: WHEBN0018388859 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...Discovery The nine-point hyperbola was first discovered by E.F. Allen and his work was published in... ...ing complex numbers in his book Inverse Geometry (1933) and apply it to hyperbolas using split complex numbers using the equation zz* = 1 for hype... ...quation zz* = 1 for hyperbolas in the split-complex plane. The nine-point hyperbola was recalled by Isaak Yaglom when describing Minkowskian geome... ...imple Non-Euclidean Geometry and its Physical Basis (1979). For Yaglom, a hyperbola is a Minkowskian circle . He says on page 193 :...the midpoints ... ...ches its incircle s (Fig.173). Construction Starting out with a right hyperbola, we can find a focus and its reflection on the line of reflection... ...nts, we use a drafting compass to find two alternate points on the right hyperbola. When you draw a line through one of those points and the constru... ...f those points and the constructed foci point you get another point on the hyperbola. A triangle can be constructed where all three vertices are the ... ... order to construct the nine-point circle. Similarly given a rectangular hyperbola, this same nine-point circle can be constructed using the same me... ...sing the same methods used above when complete; the rectangular nine-point hyperbola would look like this. * Nine-Point Circle Hyperbolas *Allen, ...
 Book Id: WPLBN0002823946 Subjects: Math, Algebra, Conic sections Collections: Math, Algebra, Hyperbolas series, Educational Videos ► Abstract Description DetailsProof of the hyperbola foci formula Excerpt DetailsIdentifying and graphing circles, ellipses, parabolas, and hyperbolas. Table of Contents Detailshyperbola, foci, focuses, conic
 Book Id: WPLBN0006994128 Subjects: Cross Correlation Function, Tdoa, Hyperbola, Hyperbola ► Abstract
 Book Id: WHEBN0000039739 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...e between the mirrors. In conic section s, it is said of two ellipse s, two hyperbola s, or an ellipse and a hyperbola which share both foci with e... ...pse and a hyperbola which share both foci with each other. If an ellipse and a hyperbola are confocal, they are perpendicular to each other. In opt...
 Book Id: WPLBN0002823945 Subjects: Math, Algebra, Conic sections Collections: Math, Algebra, Hyperbolas series, Educational Videos ► Abstract Description DetailsIntroduction to the foci (focuses) of a hyperbola Excerpt DetailsIdentifying and graphing circles, ellipses, parabolas, and hyperbolas. Table of Contents Detailshyperbola, foci, focuses, conic
 Book Id: WPLBN0012208447 Collections: Periodicals: Journal and Magazine Collection ► Abstract
 Book Id: WHEBN0022058210 Subjects: Plane (geometry) Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...centrally symmetric convex shapes.[1] It is constructed by replacing the corners of a regular octagon with a section of a hyperbola that is tangent to... ...rs are clipped by a point that lies halfway between their centres, generating the required curve, which turns out to be a hyperbola. ... ...hyperbola. Construction of the smoothed octagon (black), the tangent hyperbola (red) and the asym... ...d octagon (black), the tangent hyperbola (red) and the asymptotes of this hyperbola (green), and the tangent sides to the hyperbola (blue). ... ... \ell = \sqrt{2} - 1 m = \sqrt[4]{\frac{1}{2}} The hyperbola is then given by t... ...x=\frac{m}{\ell} \cosh{t}\\y = m \sinh{t} \end{cases}-\inftyhyperbola that forms the cor... ... -\frac{\ln{2}}{4}hyperbola are ... ... y= \pm \left(\sqrt{2} + 1 \right) \left( x-2 \right) The lines asymptotic to the hyperbola are simply ...
 Book Id: WPLBN0002823983 Subjects: Test Prep, IIT JEE Collections: IIT JEE series, Educational Videos ► Abstract Description Details2010 IIT JEE Paper 1 Problem 46 Circle Hyperbola Intersection Table of Contents Details2010, IIT, JEE, Paper, Problem, 46, Circle, Hyperbola, Intersection
 Book Id: WPLBN0012146660 Collections: Periodicals: Journal and Magazine Collection ► Abstract
 Book Id: WHEBN0014412213 Subjects: Geometry, Fermat point, Mathematical Reviews Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... 1.1 Gibert's proof using the Kiepert hyperbola 1.2 Dao's lemma on the... ... 1.2 Dao's lemma on the rectangular hyperbola 2 See al... ... Proofs Gibert's proof using the Kiepert hyperbola Lester's circle theorem follows from a more ge... ...(2000); namely, that every circle whose diameter is a chord of the Kiepert hyperbola of the triangle and is perpendicular to its Euler line passes thr... ...he Fermat points.[1][2] Dao's lemma on the rectangular hyperbola Dao's theorem... ... Dao's theorem on a rectangular hyperbola In 2014, Đào Thanh Oai showe... ...anh Oai showed that Gibert's result follows from a property of rectangular hyperbolas. Namely, let H and G lie on one branch of a rectangular hyperbol... ...llel to the line HG, Let K_+ and K_- two points on the hyperbola the tangents at which intersect at a point E on the line HG. If t... ..._- intersects HG at D, and the perpendicular bisector of DE intersects the hyperbola at G_+ and G_-, then the six points F_+,F_-,E,F,G_+,G_- lie on a ...
 Book Id: WPLBN0002823993 Subjects: Test Prep, IIT JEE Collections: IIT JEE series, Educational Videos ► Abstract Description Details2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity Table of Contents Details2010, IIT, JEE, Paper, 1, Problem, 50, Hyperbola, Eccentricity
 Book Id: WPLBN0008640233 Subjects: Technical Note, Estimating, Herrnstein's Collections: National Center for Biotechnology Information ► Abstract Description DetailsWilkinson's Method of Estimating the Parameters of Herrnstein's Hyperbola by McDowell; J. J; published by on 2006-02-15
 Book Id: WHEBN0000958449 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...onal when they are reflections of each other over the asymptote of a given hyperbola. Two particular hyperbolas are frequently used in the plane: :(A)... ...lane, where any particular line can represent the class. Thus, for a given hyperbola and asymptote A, a pair of lines (a, b) are hyperbolic orthogonal... ...orthogonal to the tangent at the curve, is extended from the circle to the hyperbola by the hyperbolic orthogonal concept. See Lewis & Wilson or Felsa... ...taneity of events relative to the timeline. In Minkowski's development the hyperbola of type (B) above is in use (see the wikisource link below). Two ... ...z's are zero, x≠0, t1≠0, then \frac t x = \frac{x_1} {t_1}. Given a hyperbola with asymptote A, its reflection in A produces the conjugate hype... ...ection in A produces the conjugate hyperbola. Any diameter of the original hyperbola is reflected to a conjugate diameter. The directions indicated by... ...for space and time axes in relativity. As E. T. Whittaker wrote in 1910, " hyperbola is unaltered when any pair of conjugate diameters are taken as ne... ...so that all lines have a slope in the real projective line. Then whichever hyperbola (A) or (B) is used, the operation is an example of a hyperbolic i...
 Book Id: WPLBN0002824007 Subjects: Test Prep, IIT JEE ► Abstract Description Details...How a tangent line relates to a hyperbola. Might be useful for some competitive exams where there isn't time to derive (like we are doing in this video)... Table of Contents Detailshyperbola, tangent, line, conic, section
 Book Id: WPLBN0009243748 Subjects: Caltech Library Services, Behavior, Ellipse ► Abstract Description DetailsTransition Behavior of K-Surface from Hyperbola to Ellipse by Qiao; S.; Zheng; G.; Zhang; H.; Ran; L.; published by Emw on 2012-12-26T10:08:06Z
 Book Id: WHEBN0000969610 Subjects: Orbit, Geometry, Semi-major axis Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...ne segment associated with most conic sections (that is, with ellipses and hyperbolas) that is at right angles with the semi-major axis and has one en... ...f the axes of symmetry for the curve: in an ellipse, the shorter one; in a hyperbola, the one that does not intersect the hyperbola. Ellipse The sem... ...i, p and q are the distances from each focus to any point in the ellipse. Hyperbola In a hyperbola, a conjugate axis or minor axis of length 2b, cor... ...major axis, the latter connecting the two vertices (turning points) of the hyperbola, with the two axes intersecting at the center of the hyperbola. T... ..., ±b) of the minor axis lie at the height of the asymptotes over/under the hyperbola's vertices. Either half of the minor axis is called the semi-mino... ... the semi-minor and semi-major axes' lengths appear in the equation of the hyperbola relative to these axes as follows: :\frac{x^2}{a^2} - \frac{y^2... ...hrough the eccentricity, as follows: :b = a \sqrt{e^2-1}. Note that in a hyperbola b can be larger than a. Semi-minor and semi-major axes of an elli...
 Book Id: WPLBN0001158742 Subjects: Conic sections, Geometry, Analytic, Curves Collections: Geometry, Math, Canadian Libraries Collection ► Abstract Full Text Search Details...y.org RBOLA, TREATED GEOMETRICALLY Title: THE PARABOLA, ELLIPSE, AND HYPERBOLA, TREATED GEOMETRICALLY Author: ROBERT WILLIAM GRIFFIN Language: E... ...f even the elementary Geometrical properties of the Parabola, Ellipse, and Hyperbola a knowledge which may be attained, in a very short time, by any o... ... traced the analogy between the properties of con- jugate diameters of the Hyperbola, and those of the El- lipse, further than has been done in any ot... ...PTER II. THE ELLIPSE, 46 PROBLEMS ON THE ELLIPSE, ... 110 CHAPTER III. THE HYPERBOLA, Ill APPENDIX, 178 CHAPTER I. THE PARABOLA. DEFINITIONS. A PARAB... ...e Cor. 5, Prop. xvi. ; Cor., Prop, xxi., and Prop. xxix. CHAPTER III. THE HYPERBOLA. DEFINITIONS. A HYPERBOLA is the curve traced out by a point whic... .... Supplemental Chords, Transverse Axis, Conjugate Axis, as on page 71. Two hyperbolas are said to be conjugate when the transverse axis of each is the... ... axis of each is the conjugate axis of the other. If the axes be equal the hyperbola is said to be Rect- angular or Equilateral. Tangents to the curve... ...ve whose points of contact are at infinity are called Asymptotes. 112 The Hyperbola. [CHAP. in. PROPOSITION I. The focus, directrix, and eccentricity... ...ola. [CHAP. in. PROPOSITION I. The focus, directrix, and eccentricity of a hyperbola being given, to determine any number of points on the curve. Fig....
 Book Id: WPLBN0005815879 Subjects: Technical Note Collections: National Center for Biotechnology Information ► Abstract Description DetailsWilkinson's method of estimating the parameters of Herrnstein's hyperbola by McDowell; J. J; published by on 2006-02-15
 Book Id: WHEBN0042433934 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... Y Y = Arctg X: The Hyperbola of the World Order Cat... ... Y Y = Arctg X: The Hyperbola of the World Order Cat...
 Book Id: WPLBN0001137395 Collections: American Libraries Collection ► Abstract
 Book Id: WPLBN0012777217 Subjects: Gas Pipes Localization, Gpr, Dictionary Collections: Periodicals: Journal and Magazine Collection ► Abstract Description Details...Sparse Decomposition of the Gpr Useful Signal from Hyperbola Dictionary by Terrasse; Guillaume; Nicolas; Jean-Marie; Trouvé; Emmanuel; Drouet; Émeline; published by Hal Ccsd on 2016-10-24...
 Book Id: WHEBN0001929759 Subjects: Reflection seismology, Normal moveout Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...e seismic velocity obtained from the best fit of the traveltime curve by a hyperbola.. The hyperbolic approximation to the traveltime curve (two-way t...
 Book Id: WPLBN0002823981 Subjects: Test Prep, IIT JEE Collections: IIT JEE series, Educational Videos ► Abstract Description Details2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 4 Table of Contents Details2010, IIT, JEE, Paper, Problem, 45, Circle, Hyperbola, Common, Tangent, Part
 Book Id: WPLBN0008494767 Subjects: Research Article, Animals., Fitting Collections: National Center for Biotechnology Information ► Abstract Description DetailsTwo Methods for Fitting a Rectangular Hyperbola to Data from Several Animals. by Nimmo; I A; published by on 2005-09-07
 Book Id: WHEBN0032103199 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...owing species:[1] Hesperorhipis albofasciata Fall, 1930 Hesperorhipis hyperbola Knull, 1938 ...
 Book Id: WPLBN0002823979 Subjects: Test Prep, IIT JEE Collections: IIT JEE series, Educational Videos ► Abstract Description Details2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 2 Table of Contents Details2010, IIT, JEE, Paper, Problem, 45, Circle, Hyperbola, Common, Tangent, Part
 Book Id: WPLBN0005725631 Subjects: Research Article Collections: National Center for Biotechnology Information ► Abstract Description DetailsTwo methods for fitting a rectangular hyperbola to data from several animals. by Nimmo; I A; published by on 2005-09-07
 Book Id: WHEBN0000240796 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...ith the celestial equatorial coordinate system Σ(α, δ)ellipse and lower, a hyperbola Polar distance (geometry), more correctl...
 Book Id: WPLBN0002823980 Subjects: Test Prep, IIT JEE ► Abstract Description Details2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 3 Table of Contents Details2010, IIT, JEE, Paper, Problem, 45, Circle, Hyperbola, Common, Tangent, Part
 Book Id: WPLBN0011660888 ► Abstract Description Details...A General Bayesian Framework for Ellipse-Based and Hyperbola-Based Damage Localisation in Anisotropic Composite Plates by Fendzi; Claude; Mechbal; Nazih; Rebillat; Marc; Guskov; Mikhail; Coffignal; G.; published by Hal Ccsd on 2015-07-11...
 Book Id: WHEBN0003286916 Subjects: Physics, Music, Astronomy Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... as the harmonic law) Quasi-harmonic motion: Unit hyperbola#Parametrization Musica universalis (in m...
 Book Id: WPLBN0002823978 Subjects: Test Prep, IIT JEE ► Abstract Description Details2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tan Table of Contents Details2010, IIT, JEE, Paper, Problem, 45, Circle, Hyperbola, Common, Tangent, Part
 Book Id: WPLBN0008632302 Subjects: Articles, Naturalistic, Allocation Collections: National Center for Biotechnology Information ► Abstract Description Details...Application of Herrnstein's Hyperbola to Time Allocation of Naturalistic Human Behavior Maintained by Naturalistic Social Reinforcement by Beardsley; Scott D.; McDowell; J. J; published by on 2005-12-28...
 Book Id: WHEBN0001499625 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...ause the equation describing the path of the object through spacetime is a hyperbola, as can be seen when graphed on a Minkowski diagram. The proper ... ... the equation of motion results in :x^2-c^2t^2=c^4/\alpha^2, which is a hyperbola. Hyperbolic motion is easily visualized on a Minkowski diagram, ... ..., where the motion of the accelerating particle is along the x-axis. Each hyperbola is defined by :X=c^2/\alpha.Rindler coordinates* :*Wikisource t...
 Book Id: WPLBN0002823982 Subjects: Test Prep, IIT JEE Collections: IIT JEE series, Educational Videos ► Abstract Description Details2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 5 Table of Contents Details2010, IIT, JEE, Paper, Problem, 45, Circle, Hyperbola, Common, Tangent, Part
 Book Id: WPLBN0008597436 Subjects: Research Article, Asymptote, Changes Collections: National Center for Biotechnology Information ► Abstract Description Details...Falsification of Matching Theory: Changes in the Asymptote of Herrnstein's Hyperbola as a Function of Water Deprivation. by McDowell; J J; Dallery; J; published by on 2005-12-08...
 Book Id: WHEBN0001139981 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...In mathematics, a hyperbolic angle is a geometric figure that divides a hyperbola. The science of hyperbolic angle parallels the relation of an ord... ...d position", and subsequently as a measure of an interval on a branch of a hyperbola. A hyperbolic angle in standard position is the angle at (0, 0) ... ...> a > 1 so that (a,  b) and (c,  d) determine an interval on the hyperbola xy = 1. Then the squeeze mapping with diagonal elements b and a m... ...lar sector of u radians is u. (The area of the whole circle is 2π.) As the hyperbola x y = 1, associated with the hyperbolic angle, has shortest diame... ...ll √2 times the legs of right triangles determined by the ray, circle, and hyperbola. There is also a projective resolution between circular and hype... ... to be parallel to P1P2. The same construction can also be applied to the hyperbola. If P0 is taken to be the point (1, 1), P1 the point (x1, 1/x1),... ...ean plane steadily moving orthogonal to a ray from the origin traces out a hyperbola. In Euclidean space, the multiple of a given angle traces equal... ... upon the hyperbolic line. pp 5-6, Fig 15.1 History The quadrature of the hyperbola is the evaluation of the area swept out by a radial segment from ... ...pt out by a radial segment from the origin as the terminus moves along the hyperbola, just the topic of hyperbolic angle. The quadrature of the hyperb...
 Book Id: WPLBN0002313338 Subjects: Conic sections, Curves Collections: Canadian Libraries Collection ► Abstract
 Book Id: WPLBN0006380304 Subjects: Research Article Collections: National Center for Biotechnology Information ► Abstract Description Details...Falsification of matching theory: changes in the asymptote of Herrnstein's hyperbola as a function of water deprivation. by McDowell; J J; Dallery; J; published by on 2005-12-08...
 Book Id: WHEBN0001139926 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...ed by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy = 1. A hyperbolic sector in standard position has a = 1 and b... ...ive except in the case p = −1 corresponding to the quadrature of the hyperbola. The other cases are given by Cavalieri's quadrature formula. Whe... ...arithm since it is obtained by integrating, or finding the area, under the hyperbola. The natural logarithm is a transcendental function, an entity b...
 Book Id: WPLBN0002313337 Collections: History, Literature, American Libraries Collection ► Abstract
 Book Id: WPLBN0006073334 Subjects: Articles Collections: National Center for Biotechnology Information ► Abstract Description Details...Application of Herrnstein's hyperbola to time allocation of naturalistic human behavior maintained by naturalistic social reinforcement by Beardsley; Scott D.; McDowell; J. J; published by on 2005-12-28...
 Book Id: WHEBN0002523065 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...a point-to-point vehicle traveling outside the atmosphere ., FlightGlobal Hyperbola, Rob Coppinger, 29 Feb 2008 , the SpaceShipThree concept spacec...
 Book Id: WPLBN0002824062 ► Abstract
 Book Id: WPLBN0007677240 ► Abstract Description Details...A General Bayesian Framework for Ellipse-Based and Hyperbola-Based Damage Localisation in Anisotropic Composite Plates by Fendzi; Claude; Mechbal; Nazih; Rebillat; Marc; Guskov; Mikhail; Coffignal; G.; published by Hal Ccsd on 2015-07-11...
 Book Id: WHEBN0023968676 Subjects: Midpoint, Radical axis, Saddle point Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... Helmholtz decomposition Hesse normal form Hyperbola I Inflection point ... ... U Unit circle Unit hyperbola V Vector area ... ... Helmholtz decomposition Hesse normal form Hyperbola I Inflection point ... ... U Unit circle Unit hyperbola V Vector area ...
 Book Id: WPLBN0001582674 Subjects: Conic sections, Geometry, Analytic, Curves Collections: Geometry, Math, American Libraries Collection ► Abstract Full Text Search Details...AM GRIFFIN Classic Literature Collection World Public Library.org HYPERBOLA, TREATED GEOMETRICALLY Title: THE PARABOLA, ELLIPSE AND HYPE... ...GREEN, AND CO. DUBLIN UNIVERSITY PRESS SERIES. THE PARABOLA, ELLIPSE, AND HYPERBOLA, TREATED GEOMETRICALLY. BY ROBERT WILLIAM GRIFFIN, A.M., LLC, EX-... ... traced the analogy between the properties of con- jugate diameters of the Hyperbola, and those of the El- lipse, further than has been done in any ot... ...e Cor. 5, Prop. xvi. ; Cor., Prop, xxi., and Prop. xxix. CHAPTEE III. The Hyperbola. uefinitions. A Hyperbola is the curve traced out by a point whic... ...Sxippkmental Chords, Transverse Axis, Conjugate Axis, as on page 71. , Two hyperbolas are said to be conjugate when the transverse axis of each is the... ... axis of each is the conjugate axis of the other- If the axes be equal the hyperbola is said to be Meet- angular or Equilateral. Tangents to the curve... ...ve whose points of contact are at infinity are called Asymptotes. 112 The Hyperbola. [chap. in. Peoposition I. The focus, directrix, and eccentricity... ...ola. [chap. in. Peoposition I. The focus, directrix, and eccentricity of a hyperbola being given, to determine any number of points on the curve. Let ... ...H is || Op; .-. H'F iH'p = A'F : A'6 ; ..H'F:H'p = HF:Hp. CHAP. iii.J The Hyperbola. 113 Hence PF : Pp = FH: Hp (Lemma, page 47.) = FA:AO=t:l. (2, VI...
 Date: 1753-01-01, Vol. 25 Book Id: WPLBN0004352205 Collections: Periodicals: Journal and Magazine Collection ► Abstract Description Details...Description: The Construction and Properties of a New Quadratrix to the Hyperbola, By Mr. Perks. Communicated by Mr Abr. de Moivre, F. R. S Perks, M.; de Moivre, A Philosophical Transactions (1683-1775). 1753-01-01. 25:2253–2262...
 Book Id: WHEBN0001944319 Subjects: Greek language, Plutarch, Euclid Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...the then-long-standing problem of doubling the cube using the parabola and hyperbola. Life and work Menaechmus is remembered by mathematicians for ... ...discovered the conic sections, that is, the ellipse, the parabola, and the hyperbola, as a by-product of his search for the solution to the Delian pro...
 Date: 1811-01-01, Vol. 101 Book Id: WPLBN0004358724 Collections: Periodicals: Journal and Magazine Collection ► Abstract Description Details...Description: On the Rectification of the Hyperbola by Means of Two Ellipses; Proving That Method to be Circuitous, and Such as Requires Much More Calculation Than Is Requisite by an Appropriate Theorem: In Which Process a New Theorem for the Rectification of That Cu...
 Book Id: WHEBN0018480091 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...rld history Y Y = Arctg X: The Hyperbola of the World Order Cat... ...rld history Y Y = Arctg X: The Hyperbola of the World Order Cat...
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