Rational straight line
idea · 1 work · 6 mentions · 17 anchored passages
rational straight line · rational · AB · D · DE · E · EF · assigned straight line · rational area · rational rectangle
in the texts
Elements
A straight line established as the standard of comparison; lines commensurable with it (in length or square) are termed rational.
Let then the assigned straight line be called rational, and those straight lines which are commensurable with it, whether in length and in square or in square only, rational, but those which are incommensurable with it irrational.
And let the square on the assigned straight line be called rational and those areas which are commensurable with it rational, but those which are incommensurable with it irrational, and the straight lines which produce them irrational, that is, in case the areas are squares, the sides themselves, but in case they are any other rectilineal figures, the straight lines on which are described squares equal to them.
If a rational area be applied to a rational straight line, it produces as breadth a straight line rational and commensurable in length with the straight line to which it is applied.