⋆
Pappus: Given four lines in a plane, find the locus of a point that moves so that the
product of the distances from two fixed lines (along specified directions) is propor
tional to the square of the distance from the third line [threeline locus problem],
or proportional to the product of the distances from the other lines [fourline locus
problem].
⋆
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 persons
who boast that they know everything would not miss the opportunity of saying that I
have written nothing that they did not already know, were I to make myself sufficiently
intelligible for them to understand me.”
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 Fall '10
 wen
 Conic Sections, Descartes, Conic section, threeline locus problem

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