Commensurability
idea · 1 work · 3 mentions · 11 anchored passages
commensurable · commensurable in length · incommensurable · commensurable in square · commensurable in square only
in the texts
Elements
The relation between magnitudes that share a common measure (in length or in square), central to Book X's classification of rational and irrational lines.
18] it follows, as regards medials, that a straight line commensurable in length with a medial straight line is called medial and commensurable with it not only in length but in square also, since, in general, straight lines commensurable in length are always commensurable in square also.
But, if any straight line be commensurable in square with a medial straight line, then, if it is also commensurable in length with it, the straight lines are called, in this case too, medial and commensurable in length and in square, but, if in square only, they are called medial straight lines commensurable in square only.
But ED is rational and incommensurable in length with DC;