We should not believe... that commensurability is a quality of every magnitude as of all the numbers; and whoever has not investigated this subject, … - William Rowan Hamilton

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We should not believe... that commensurability is a quality of every magnitude as of all the numbers; and whoever has not investigated this subject, shows a gross and unseemly ignorance of what the Athenian Stranger says in the seventh treatise of the Book of the Laws, [namely], "And besides there is found in every man an ignorance, shameful in its nature and ludicrous, concerning everything which has the dimensions, length, breadth, and depth; and it is clear that mathematics can free them from this ignorance. For I hold that this [ignorance] is a brutish and not a human state, and I am verily ashamed, not for myself only, but for all Greeks, of the opinion of those men who prefer to believe what this whole generation believes, [namely], that commensurability is necessarily a quality of all magnitudes. For everyone of them says: "We conceive that those things are essentially the same, some of which can measure the others in some way or other. But the fact is that only some of them are measured by common measures, whereas others cannot be measured at all".