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For any point, the abscissa is the first value (x coordinate), and the ordinate is the second value (y coordinate). In mathematics, the abscissa (/ æ b ˈ s ɪ s. 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]
The first and second coordinates are called the abscissa and the ordinate of P, respectively; and the point where the axes meet is called the origin of the coordinate system. The coordinates are usually written as two numbers in parentheses, in that order, separated by a comma, as in (3, −10.5) .
When the abscissa and ordinate are on the same scale, the identity line forms a 45° angle with the abscissa, and is thus also, informally, called the 45° line. [5] The line is often used as a reference in a 2-dimensional scatter plot comparing two sets of data expected to be identical under ideal conditions. When the corresponding data points ...
The abscissa and ordinate (,) of each point on the circle are the magnitudes of the normal stress and shear stress components, respectively, acting on the rotated coordinate system. In other words, the circle is the locus of points that represent the state of stress on individual planes at all their orientations, where the axes represent the ...
Gottfried Wilhelm Leibniz (or Leibnitz; [a] 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics.
The equation of a line on a linear–log plot, where the abscissa axis is scaled logarithmically (with a logarithmic base of n), would be = +. The equation for a line on a log–linear plot, with an ordinate axis logarithmically scaled (with a logarithmic base of n), would be:
The entire point of referring to these axes as "abscissa and ordinate" is for free yourself from a specific reference. Yes, it is usual -- in cartesian coordinates -- that the abscissa is x and the ordinate is y, but that's not *always* the case (consider for example action occurring in the y-z plane or the z-x plane).
With this simple definition of a curvilinear coordinate system, all the results that follow below are simply applications of standard theorems in differential topology. The transformation functions are such that there's a one-to-one relationship between points in the "old" and "new" coordinates, that is, those functions are bijections , and ...