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Area Mathematics - General concepts and linear algebra / Geometry

IEV ref102-04-22

en
abscissa, <along a curve>
for a given point of an oriented curve with an origin point, real number, the absolute value of which is the length of the curve between the origin and the given point, and the sign is positive or negative depending on whether the path from the origin to the given point is consistent or not with the orientation of the curve

Note 1 to entry: For a curve defined by the position vector r=f(u) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahkhacqGH9aqpca WHMbGaaiikaiaadwhacaGGPaaaaa@3E10@ as a function of the parameter u, with an origin O corresponding to u=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadwhacqGH9aqpju gibiaaicdaaaa@3C16@ , the abscissa of the point M corresponding to u = uM is the line integral O M | dr| = 0 u M | df du |du MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaapehabaWaaqWaae aajugibiGacsgakiaahkhaaiaawEa7caGLiWoaaSqaaiaab+eaaeaa caqGnbaaniabgUIiYdGccqGH9aqpnmaapehakeaadaabdaqaamaala aabaqcLbsaciGGKbGccaWHMbaabaqcLbsaciGGKbGccaWG1baaaaGa ay5bSlaawIa7aKqzGeGaciizaOGaamyDaaqaaiaabcdaaeaacaWG1b WaaSbaaSqaaKqzGdGaaeytaaWcbeaaaKqzakGaey4kIipaaaa@5202@ .

Note 2 to entry: In the usual geometrical space, the abscissa along a curve is a quantity of the dimension length.


fr
abscisse, <le long d'une courbe> f
pour un point donné d'une courbe orientée munie d'un point origine, nombre réel dont la valeur absolue est la longueur de la courbe entre l'origine et le point donné et dont le signe est positif ou négatif selon que le parcours de l'origine au point donné est compatible ou non avec l'orientation de la courbe

Note 1 à l'article: Pour une courbe définie par le rayon vecteur r=f(u) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahkhacqGH9aqpca WHMbGaaiikaiaadwhacaGGPaaaaa@3E10@ en fonction du paramètre u et munie d'une origine O correspondant à u=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadwhacqGH9aqpju gibiaaicdaaaa@3C16@ , l'abscisse du point M correspondant à u = uM est l'intégrale curviligne O M | dr| = 0 u M | df du |du MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaapehabaWaaqWaae aajugibiGacsgakiaahkhaaiaawEa7caGLiWoaaSqaaiaab+eaaeaa caqGnbaaniabgUIiYdGccqGH9aqpnmaapehakeaadaabdaqaamaala aabaqcLbsaciGGKbGccaWHMbaabaqcLbsaciGGKbGccaWG1baaaaGa ay5bSlaawIa7aKqzGeGaciizaOGaamyDaaqaaiaabcdaaeaacaWG1b WaaSbaaSqaaKqzGdGaaeytaaWcbeaaaKqzakGaey4kIipaaaa@5202@ .

Note 2 à l'article: Dans l'espace géométrique usuel, l'abscisse le long d'une courbe est une grandeur ayant la dimension d'une longueur.


de
Abszisse (entlang einer Kurve), f

es
abscisa (a lo largo de una curva)

ja
横座標, <曲線に沿った>
横軸

pl
odcięta (wzdłuż krzywej)

pt
abcissa (ao longo de uma curva)

sr
апсциса, <дуж криве> ж јд

sv
abskissa

zh
坐标, <沿曲线的>

Publication date: 2008-08
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