Abscissa and ordinate
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In mathematics, the abscissa (/æbˈsɪs.ə/; plural abscissae or abscissas) and the ordinate are respectively the first and second coordinate of a point in a Cartesian coordinate system:[1][2]
- abscissa -axis (horizontal) coordinate
- ordinate -axis (vertical) coordinate
Together they form an ordered pair which defines the location of a point in two-dimensional rectangular space.
More technically, the abscissa of a point is the signed measure of its projection on the primary axis. Its absolute value is the distance between the projection and the origin of the axis, and its sign is given by the location on the projection relative to the origin (before: negative; after: positive). Similarly, the ordinate of a point is the signed measure of its projection on the secondary axis. In three dimensions, the third direction is sometimes referred to as the applicate.[3]
Etymology
Though the word "abscissa" (Script error: No such module "params".) has been used at least since De Practica Geometrie (1220) by Fibonacci (Leonardo of Pisa), its use in its modern sense may be due to Venetian mathematician Stefano degli Angeli in his work Miscellaneum Hyperbolicum, et Parabolicum (1659).[4] Historically, the term was used in the more general sense of a 'distance'.[5]
In his 1892 work Script error: No such module "Lang". ("Lectures on history of mathematics"), volume 2, German historian of mathematics Moritz Cantor writes:
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At the same time it was presumably by [Stefano degli Angeli] that a word was introduced into the mathematical vocabulary for which especially in analytic geometry the future proved to have much in store. […] We know of no earlier use of the word abscissa in Latin original texts. Maybe the word appears in translations of the Apollonian conics, where [in] Book I, Chapter 20 there is mention of ἀποτεμνομέναις, for which there would hardly be a more appropriate Latin word than Script error: No such module "Lang"..
The use of the word ordinate is related to the Latin phrase linea ordinata appliicata 'line applied parallel'.
In parametric equations
In a somewhat obsolete variant usage, the abscissa of a point may also refer to any number that describes the point's location along some path, e.g. the parameter of a parametric equation.[1] Used in this way, the abscissa can be thought of as a coordinate-geometry analog to the independent variable in a mathematical model or experiment (with any ordinates filling a role analogous to dependent variables).
See also
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References
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- ^ a b Page Module:Citation/CS1/styles.css has no content.Hedegaard, Rasmus; Weisstein, Eric W. "Abscissa". MathWorld. Retrieved 14 July 2013.
- ^ Page Module:Citation/CS1/styles.css has no content.Hedegaard, Rasmus; Weisstein, Eric W. "Ordinate". MathWorld. Retrieved 14 July 2013.
- ^ Page Module:Citation/CS1/styles.css has no content."Cartesian coordinates". PlanetMath. Archived from the original on 2025-02-21. Retrieved 2025-04-02.
'applicate' is rare in English, but its [equivalents] in continental European, [such as] 'die Applikate' in German and 'aplikaat' in Estonian, are more known.
- ^ Page Module:Citation/CS1/styles.css has no content.Dyer, Jason (March 8, 2009). "On the Word "Abscissa"". numberwarrior.wordpress.com. The number Warrior. Retrieved September 10, 2015.
- ^ Page Module:Citation/CS1/styles.css has no content.Miller, Jeff (June 24, 2017). "Earliest Known Uses of Some of the Words of Mathematics". MacTutor. University of St. Andrews, Scotland. Retrieved 2025-01-06.
- ^ Page Module:Citation/CS1/styles.css has no content.Cantor, Moritz (1900). Vorlesungen über Geschichte der Mathematik (in Deutsch). Vol. 2 (2nd ed.). Leipzig: B.G. Teubner. p. 898. Retrieved 10 September 2015.
