WordNet

the value of a coordinate on the horizontal axis

PrepTutorEJDIC

横座標

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/01/02 17:56:23」(JST)

wiki en

[Wiki en表示]

Illustration of a Cartesian coordinate plane. The first value in each ordered pair is the abscissa of the corresponding point.

In mathematics, an abscissa (/æbˈsɪs.ə/; plural abscissae or abscissæ or abscissas) is the perpendicular distance of a point from the vertical axis. Usually this is the horizontal coordinate of a point in a two-dimensional rectangular Cartesian coordinate system. The term can also refer to the horizontal axis (typically x-axis) of a two-dimensional graph (because that axis is used to define and measure the horizontal coordinates of points in the space). An ordered pair consists of two terms—the abscissa (horizontal, usually x) and the ordinate (vertical, usually y)—which define the location of a point in two-dimensional rectangular space.

Etymology

Though the word "abscissa" (Latin; "linea abscissa", "a line cut off") has been used at least since De Practica Geometrie published in 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 of 1659.^[1]

In his 1892 work Vorlesungen über Geschichte der Mathematik, Volume 2, ("Lectures on history of mathematics") German historian of mathematics Moritz Cantor writes

"Wir kennen keine ältere Benutzung des Wortes Abssisse in lateinischen Originalschriften [than degli Angeli's]. Vielleicht kommt das Wort in Übersetzungen der Apollonischen Kegelschnitte vor, wo Buch I Satz 20 von ἀποτεμνομέναις die Rede ist, wofür es kaum ein entsprechenderes lateinisches Wort als abscissa geben möchte."^[2]

"We know no earlier use of the word abscissa in Latin originals [than degli Angeli's]. Maybe the word descends from translations of the Apollonian conics, where in Book I, Chapter 20 there appears ἀποτεμνομέναις, for which there would hardly be as an appropriate Latin word as abscissa."

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.^[3] 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).

Examples

For the point (2, 3), 2 is called the abscissa and 3 the ordinate.
For the point (−1.5, −2.5), −1.5 is called the abscissa and −2.5 the ordinate.

References

^ Dyer, Jason (March 8, 2009). "On the Word "Abscissa"". https://numberwarrior.wordpress.com. The number Warrior. Retrieved September 10, 2015. line feed character in |publisher= at position 5 (help); External link in |website= (help)
^ Cantor, Moritz (1900). Vorlesungen über Geschichte der Mathematik, Volume 2. Leipzig: B.G. Teubner. p. 898. Retrieved 10 September 2015.
^ Hedegaard, Rasmus; Weisstein, Eric W. "Abscissa". MathWorld. Retrieved 14 July 2013.

This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.

External links

The dictionary definition of abscissa at Wiktionary

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

1. 血清クレアチニン濃度と慢性腎疾患の関係 reciprocal serum creatinine concentration and chronic kidney disease

English Journal

Upper-extremity H-reflex measurement post-stroke: reliability and inter-limb differences.

Phadke CP, Robertson CT, Condliffe EG, Patten C.SourceNeural Control of Movement Laboratory - Brain Rehabilitation Research Center of Excellence, Malcom Randall VA Medical Center, Gainesville, FL 32608, USA.
Clinical neurophysiology : official journal of the International Federation of Clinical Neurophysiology.Clin Neurophysiol.2012 Aug;123(8):1606-15. Epub 2012 Jan 23.
OBJECTIVE: To establish test-retest reliability of flexor carpi radialis (FCR) H-reflexes in non-disabled and stroke participants. We also investigated inter-limb differences and effects of chronicity post-stroke compared to non-disabled group and age-related effects in the non-disabled group.METHOD
PMID 22277759

Effect of the Leaving Group and Solvent Combination on the LFER Reaction Constants.

Matić M, Jurić S, Denegri B, Kronja O.SourceFaculty of Pharmacy and Biochemistry, University of Zagreb, 10000 Zagreb, Ante Kovačića 1, Croatia; E-Mails: mmatic@pharma.hr (M.M.); sjuric@pharma.hr (S.J.).
International journal of molecular sciences.Int J Mol Sci.2012;13(2):2012-24. Epub 2012 Feb 13.
Fine effects that influence the variations of the reaction constants s(f) in LFER log k = s(f)(N(f) + E(f)) have been summarized here. Increasing solvent polarity in the series of binary mixtures increases the solvolysis rates for the same factor for all benzhydryl derivatives in which the solvation
PMID 22408434

Japanese Journal

Ability of Water-Soluble Biosubstances to Eliminate Hydroxyl and Superoxide Radicals Examined by Spin-Trapping ESR Measurements : Two-Dimensional Presentation of Antioxidative Ability

NAKAJIMA Akira,SAKURAI Yasuhiro,MATSUDA Emiko [他],MASUDA Yukari,NAGANOBU Yoshiko,TAJIMA Kunihiko,SAMESHIMA Hiroshi,IKENOUE Tsuyomu
Bioscience, biotechnology, and biochemistry 77(2), 324-331, 2013-02-23
… The obtained results are depicted two-dimensionally, taking idh50 (mg/mL) as the abscissa and ids50 (mg/mL) as the ordinate in the ROS inhibitory diagram. …
NAID 10031164736

表計算ソフトウェアMicrosoft Office Excelを用いた心拍─運動リズム間の同期現象の解析方法

竹内真太,西田裕介,美津島隆
理学療法科学 27(5), 609-616, 2012
〔目的〕運動中に観測される心拍リズムと運動リズム間の同期現象の解析を簡便なものにするため，表計算ソフトウェアMicrosoft Office Excelを用いた解析方法を紹介する．〔方法〕解析には歩行中の健常男性のデータを例として使用する．心電図とフットスイッチから，R波と踵接地の発生時刻を示した時系列データを抽出し，相対位相を算出する．次に，相対位相を縦軸，時間軸を横軸にした散布図（位相同期図） …
NAID 130004874837

社会空間と学力の階層差

近藤博之
教育社会学研究 90(0), 101-121, 2012
　学力に階層差のあることは広く知られているが，マクロな社会の変化とともにそれがどう変容していくかについては，必ずしも明確な展望が描けていない。本稿では，OECD の PISA 調査データ（2009）に多次元階層分析を適用し，国際比較の観点からこの問題に取り組んでいる。まず，生徒の家庭背景について，多重対応分析からブルデュー流の社会空間を構築し，経済発展により階層の多次元化が進むかどうかを検討した。 …
NAID 130003379345