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I would like to know: - who started with calculus-based optimization problems and when it was, - if there is a book focusing on history of ellipses/ conic sections - if someone ever tried to calculate minimum distance between 2 ellipses in 2D back then

Anything related to the abovementioned is welcomed too.

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Probably Fermat –  lhf Sep 12 '12 at 14:20
    
Newton solved the brachistochrone problem. So it seems like the inventor of calculus (along with Leibniz) was himself doing some calculus-based optimization. –  littleO Aug 8 '13 at 5:24

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