On a cloudy day in 1413, architect and engineer Filippo Brunelleschi stood at the entrance to the Cathedral of Florence, and—using a painting and a mirror—proved that the world and everything in it was governed by geometry. Surveying the intervening 600 years, Amir Alexander offers an illustrated overview of how our societies, politics, and ideals have been shaped by a geometric view of provable truths. From the terraces of Versailles to the broad avenues of Washington, D.C., and the boulevards of New Delhi and Manila, the geometry that began with Euclid has been carved into the landscape of the modern world as kings, empire-builders, and even revolutionaries all rushed to cast their rule as the apex of universal order.