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What advances in geometry, beyond the basic results found in the Elements, are due to Archimedes?

1. Given that we have no documents from the time of Greek mathematics—the earliest manuscripts we have are medieval—how can we be sure that the texts we have are actually what the authors wrote? Were the copyists who wrote the early medieval manuscripts simply concerned with reproducing the text faithfully, or is it possible that […]

What were the two similar and the two different factors between the crisis in the 1st century BCE that undermined the Roman Republic and the crisis in the 3rd century CE that undermined the Principate?

What were the two similar and the two different factors between the crisis in the 1st century BCE that undermined the Roman Republic and the crisis in the 3rd century CE that undermined the Principate?

Compare and contrast the 1) economies, 2) social structures, and/or 3) political institutions/policies that have organized life in California across three of the following four periods of California history: 1) Pre-Columbian California (circa 40,000 BCE – 1542 CE); 2) Spanish California (1542-1821); 3) Mexican California (1821-1848.)

Compare and contrast the 1) economies, 2) social structures, and/or 3) political institutions/policies that have organized life in California across three of the following four periods of California history: 1) Pre-Columbian California (circa 40,000 BCE – 1542 CE); 2) Spanish California (1542-1821); 3) Mexican California (1821-1848); Your response should be specific and analyze precise evidence/examples […]

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