"The Greeks... were well aware of geometric magnitudes that we call "irrational," but simply did not think of them as numbers. ...a direct result of their unyielding insistence on logical rigor. ...Book X ...devotes 115 propositions... to a comprehensive classification of irrational magnitudes of the forms a \pm \sqrt{b}, \sqrt{a} \pm \sqrt{b}, \sqrt{a \pm \sqrt{b}}, and \sqrt{\sqrt{a} \pm \sqrt{b}}, where a and b are commensurable lengths."
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C. H. Edwards, Jr., The Historical Development of the Calculus (1979)
https://en.wikiquote.org/wiki/Euclid%E2%80%99s_Elements
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Euclid’s Elements
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