| 单词 | apollonian parabola |
| 释义 | > as lemmasApollonian parabola 2. Of Apollonius of Perga, a famous Greek geometer and investigator of conic sections. Frequently in Apollonian parabola. ΘΚΠ the world > relative properties > number > geometry > [adjective] > branches of stereometrical1656 Apollonian1704 Euclidean1714 isoperimetrical1743 stereotomical1828 stereotomic1860 stereometric1862 graphic1865 parabolic1872 metageometrical1882 pangeometrical1882 Riemannian1889 synthetic1889 polygonometric1890 Lobachevskian1896 topological1913 1704 J. Harris Lexicon Technicum I Helicoid Parabola, or the Parabolick Spiral, is a Curve which arises from the Supposition of the Axis of the common Apollonian Parabola's being bent round into the Periphery of a Circle. 1728 E. Chambers Cycl. at Hyperbola Apollonian Hyperbola is..the Hyperbola of the first Kind: Thus call'd in Contradistinction to the Hyperbola's of the higher Kinds. 1798 Atwood in Philos. Trans. (Royal Soc.) 88 208 The Apollonian or conic parabola. 1992 Math. Rev. 93 M. The turning rule and moving curve procedure which Descartes applies to the Apollonian parabola to obtain his ‘Cartesian parabola.’ Apollonian parabola a. Mathematics. A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side; the curve traced by a point whose distance from a given point (the focus) is equal to its distance from a given straight line (the directrix); a curve that is the graph of an equation of the type y2 = 2px, or y = ax2, where p and a are constants. Also more fully (now historical) Apollonian parabola (see Apollonian adj. 2).All three definitions are equivalent. The path of a projectile under the influence of gravity follows a curve of approximately this shape. The parabola is one of the conic sections, along with the circle, ellipse, and hyperbola.biquadratic, helicoid parabola: see the first element. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > conic section > parabola parabola1559 parabolic1657 parabole1676 1559 P. Morwyng tr. C. Gesner Treasure of Euonymus 71 A parabolæ is a deuision of a Geometrical figure, called conus [L. parabola conifectio]. 1579 L. Digges & T. Digges Stratioticos 188 I demaunde whether then this Eleipsis shal not make an Angle with the Parabola Section equal to the distaunce betweene the grade of Randon proponed, and the grade of vttermost Randon. 1656 T. Hobbes Six Lessons Ep. Ded. in Elements Philos. I have exhibited and demonstrated the proportion of the Parabola and Parabolasters to the Parallelograms of the same height and base. 1696 W. Whiston New Theory of Earth i. 13 The Orbits describ'd will be one of the other Conick Sections, either Parabola's or Hyperbola's. 1704 J. Harris Lexicon Technicum I Helicoid Parabola, or the Parabolick Spiral, is a Curve which arises from the Supposition of the Axis of the common Apollonian Parabola's being bent round into the Periphery of a Circle. 1706 W. Jones Synopsis Palmariorum Matheseos 246 'Tis evident the Parabola has but one Focus. 1760 L. Sterne Life Tristram Shandy II. iii. 22 He found the precise path to be a Parabola,—or else an Hyperbola. 1828 O. Gregory Hutton's Course Math. (ed. 9) II. 136 The Area or Space of a Parabola, is equal to Two-Thirds of its Circumscribing Parallelogram. 1868 J. N. Lockyer Elem. Lessons Astron. (1870) xxiii. 124 The orbit of a comet is generally best represented by what is called a parabola; that is, an infinitely long ellipse. 1935 C. J. Smith Intermediate Physics (ed. 2) v. xlvi. 769 For most pure metals the curve showing the variation of resistance with temperature measured on the gas scale is almost a perfect parabola. 1993 Math. Rev. 93 M. 6499/2 The turning rule and moving curve procedure which Descartes applies to the Apollonian parabola to obtain his ‘Cartesian parabola’. < as lemmas |
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