⋆Pappus: Given four lines in a plane, find the locus of a point that moves so that theproduct of the distances from two fixed lines (along specified directions) is propor-tional to the square of the distance from the third line [three-line locus problem],or proportional to the product of the distances from the other lines [four-line locusproblem].⋆Pappus stated without proof that the locus was a conic section.⋆Descartes showed this algebraically.·Descartes: “[S]ince so many lines are confusing, I may simplify matters by consid-ering one of the given lines and one of those to be drawn . . . as the principal lines,to which I shall try to refer all the others.”⋆Newton later showed it geometrically.◦Descartes “I have omitted nothing inadvertently but I have foreseen that certain personswho boast that they know everything would not miss the opportunity of saying that Ihave written nothing that they did not already know, were I to make myself sufficientlyintelligible for them to understand me.”
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