Lexic.us

2. Noun. (mathematics) Any closed curve (similar to a figure eight) described by a Cartesian equation of the form $(x^2\; +\; y^2)^2\; =\; a^2\; (x^2\; -\; y^2)\backslash ,$. ¹

¹ Source: wiktionary.com

Definition of Lemniscate

1. [n -S]

Medical Definition of Lemniscate

1. A curve in the form of the figure 8, with both parts symmetrical, generated by the point in which a tangent to an equilateral hyperbola meets the perpendicular on it drawn from the center. Origin: L. Lemniscatus adorned with ribbons, fr. Lemniscus a ribbon having down, Gr. Source: Websters Dictionary (01 Mar 1998)

Lexicographical Neighbors of Lemniscate

Literary usage of Lemniscate

Below you will find example usage of this term as found in modern and/or classical literature:

1. An Elementary Treatise on Cubic and Quartic Curves by Alfred Barnard Basset (1901)
"The lemniscate also possesses the double property of being the inverse and also the pedal of a rectangular hyperbola with respect to its centre. ..."

2. An Elementary Course in Analytic Geometry by John Henry Tanner, Joseph Allen (1898)
"The lemniscate of Bernouilli.* The lemniscate may be defined as follows : let ... the locus of P as T moves along the hyperbola is called the lemniscate. ..."

3. Mathematical Questions and Solutions by W. J. C. Miller (1866)
"SP : PO = sp : so, FP : PO =fp :fO •, hence the lemniscate is the locus of the ... if through the origin and any point P in the lemniscate two circles be ..."

4. The Oxford, Cambridge, and Dublin Messenger of Mathematics (1868)
"The locus of p is a lemniscate, which is at once the first pedal and the inverse of the rectangular hyperbola with respect to the centre. ..."

5. Newton's Principia, First Book, Sections I., II., III.: With Notes and by Isaac Newton, Percival Frost (1878)
"THE lemniscate. 137. PEP. The lemniscate is the locus of the feet of the perpendiculars drawn from the centre of ,a rectangular hyperbola upon the tangent. ..."

6. Elements of Analytic Geometry by Joseph Johnston Hardy (1897)
"The lemniscate 334. The lemniscate.—If from the center of an equilateral hyperbola a perpendicular be drawn to a tangent to the hyperbola, and the point of ..."

7. Geometrical Analysis: Or the Construction and Solution of Various by Benjamin Hallowell (1872)
"To construct the lemniscate from the equation a?y2 = Analysis.—When x = 0, y = 0. Hence the curve passes through the origin O. If y = 0, we have a;2 = a2 or ..."

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