The residue then is 820 less the root of 288000. Now 20 roots of 720 equal the root of 288000, the number arising from the product of 400 the square of 20 and 720. Therefore subtract twice the product of ab and ae from the squares on lines ae and ab that is, subtract 20 times the root of 720 from 820. Because line ae was divided into two parts at point b, the squares on lines ae and ab equal twice the product of ab by ae and the square on line eb, as was shown above. For example, let ae be the root of the rational number 720 and ab the number 10. It is the difference between two lines commensurable only in their squares, such as between lines ae and ab. Not to be overlooked is to show how to find the square on line eb called the residue, recisum, or abscissa. It’s from the more obscure De Practica Geometrie.īut is his use of “abscissa” the same as ours? Here’s two excerpts: The use of the word isn’t from his most famous book, Liber Abaci (of the rabbits and the series that bears his name). Also, some dictionaries seem to be picking Leibniz as the first to use abscissa however he was simply the first to popularize it. And a Professor Barney Hughes (from the Pat Ballew entry) claims 1220.įor the later dates, the dictionaries might be aiming for the first use in English, even though the word is identical in Latin. Merriam-Webster claims the first use was in 1694. The Online Etymology Dictionary claims the first use of the word was 1698. In other words: “a line cut off from another line”, rather like the Merriam-Webster picture above. Going deeper, “ab-” means “off” or “away” (as in abnormal) and “scindere” means “to cut” (as in re scind). It’s Latin, from “linea abscissa”, meaning “a line cut off”. None seem to have much of anything to do with the x-axis. There’s also an abscissa of stability and an abscissa mapping and a spectral abscissa. The definition avoids the confusion from the standard dictionaries (and even avoids the Cartesian nitpick), but tosses in an extra use: abscissa as the x-axis itself.įor example, here’s an excerpt from On the Relative Abundance of Bird Species:įor convenience, the abscissa is graduated logarithmically. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the distance along it. The x-(horizontal) coordinate of a point in a two dimensional coordinate system. Just to nitpick, the abscissa also applies to oblique coordinates, not just Cartesian ones.īut that’s not all! Try this version of the definition from MathWorld: The impression is so strong to me I am left wondering if there the word has ever been used historically in such a way. That is, (5,3) would give an abscissa of 5 and (-5,3) would also give an abscissa of 5. The definitions give the impression that the abscissa is the unsigned value of x. Not sure where the confusion is yet? Try this picture from Merriam-Webster: The horizontal coordinate of a point in a plane Cartesian coordinate system obtained by measuring parallel to the x-axis. (in plane Cartesian coordinates) the x-coordinate of a point: its distance from the y-axis measured parallel to the x-axis. Since it’s also in the As (before dictionary writers get tired) there shouldn’t be any ambiguity, issue, or controversy. (The y value is called the ordinate, which in the example would be 5.) * For example, the abscissa of (-3,5) is -3. In a (x,y) coordinate system, the abscissa is the x value.
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