abscissum

Abscissum is a rarely used mathematical term that refers to the sum of the abscissae, or x-coordinates, of a set of points in the Cartesian plane. Given a finite collection of points (x1, y1), (x2, y2), ..., (xn, yn), the abscissum A is defined as A = x1 + x2 + ... + xn. When the points are the vertices of a polygon, the abscissum is simply the sum of the x-coordinates of those vertices. The term is uncommon in modern texts; most authors instead speak of the sum of the x-coordinates or the sum of the abscissae.

Basic properties follow from the definition. The abscissum is additive with respect to the included points: adding a point with x-coordinate x increases A by x. The centroid of the set of points has x-coordinate equal to A/n, where n is the number of points. If all points lie on a vertical line x = c, then A = n·c. If the points are symmetrically distributed about a vertical line x = m, then A = n·m.

In practice, abscissum is a descriptive shorthand rather than a formal prerequisite concept. It can be useful in quick computations of averages or moments along the x-axis. When more formal language is preferred, one speaks of the sum of the x-coordinates, or of the first moment about the y-axis, rather than using the term abscissum.

See also: abscissa, ordinate, centroid, moments of area, first moment.