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L’Hospital (1696): vive la différence!

This figure appears in Analyse des infiniment petits, pour l'intelligence des lignes courbes by Guillaume-François-Antoine de L'Hospital (1661-1704), Fig 1 (with explanation p. 2). In the first textbook on ‘the calculus’, L’Hospital defines difference (or differential) in the geometrical Leibnizian tradition. If m is close to M, so too will p be close to P, and MAm will be a small triangle (almost). The points m, M & B are dynamic. L’Hospital’s work is in the collection of Marsh’s Library, Dublin.