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Chapter 6, ‘How to Teach It: Finding the Right Direction’, offers a reappraisal of the foundation of mining academies. Subterranean geometry merges here with broader questions about technical education in the eighteenth century. Early attempts to replace the guild-like training and to establish brick-and-mortar institutions prompt a familiar debate between professors and practitioners. Who could best formalize and improve a century-old corpus? Moreover, what was the right way to teach it? Major mining centres, I argue, offered varied solutions to improve theoretical teaching, of which mining academies were but the ultimate step. I focus here on the biography of Johann Andreas Scheidhauer (1718–1784), mining master and autodidact mathematician. His vast geometrical production – unpublished and long forgotten – looms large in the early projects of mining academies, not least through the influence of his student Johann Friedrich Lempe (1757–1801), emblematic professor of the Bergakademie Freiberg.
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