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In mathematics, the abscissa (Template:IPAc-en; plural abscissae or abscissas) and the ordinate are respectively the first and second coordinate of a point in a Cartesian coordinate system:<ref name="WolframAlpha" /><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
- abscissa <math>\equiv x</math>-axis (horizontal) coordinate
- ordinate <math>\equiv y</math>-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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
EtymologyEdit
Though the word "abscissa" (Template:Ety) 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).<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Historically, the term was used in the more general sense of a 'distance'.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
In his 1892 work {{#invoke:Lang|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 {{#invoke:Lang|lang}}.
The use of the word ordinate is related to the Latin phrase linea ordinata appliicata 'line applied parallel'.
In parametric equationsEdit
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.<ref name="WolframAlpha">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> 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 alsoEdit
ReferencesEdit
de:Kartesisches Koordinatensystem#Das Koordinatensystem im zweidimensionalen Raum pl:Układ współrzędnych kartezjańskich#Współrzędne