SUMMARY

Chapter 3: Round and Square (100 Years: A Crescent Phase, ca. 750–850) turns to the subject of geometry, the earliest subject transmitted to and through Islamic lands, and continues with the message that besides roots through ancient Greek sources like Euclid’s Elements, and routes through classical languages like Arabic, another component critical to developments and outcomes is ‘rules’. In this chapter, rules are highlighted in the form of political rules, here early ʿAbbasid patrons, as well as geometrical rules like laws of proportion. Sources, figures, developments and outcomes are all from the first century of scientific translations and transmissions, here termed a ‘Crescent Phase.’