 “A distance on a line is a one-one relation whose converse domain (and its domain too) is the whole line. If we call two such distances \(R\) and \(S\), we may say that they have the ratio \(\mu / \nu\) if, starting from some point \(x\) , \(\nu\) repetitions of \(R\) take us to the same point \(y\) as we reach by \(\mu \;\)repetitions of \(S\), i.e., if \(xR^{\nu} y \: . \: x S^{\mu} y\).” (PM III, 260)