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Topic: [HM] Pascal theorem query
Replies: 4   Last Post: Dec 7, 2005 8:43 PM

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Dick Tahta

Posts: 30
Registered: 12/3/04
[HM] Pascal theorem query
Posted: Dec 1, 2005 10:03 AM
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Two queries about Pascal's (inscribed hexagon) theorem

1) My understanding is that Pascal announced the theorem at Mersenne's
seminar in terms of a circle. I suppose everyone there knew that this would
carry over to conics. Did they realise the link with Pappus at the time?
What evidence is there for who first did this and when?

2) There is a famous neat proof by algebraic geometry using single letters
for the linear expressions of lines ( abc ­ k.pqr = 0 is cubic curve passing
through meets of opposite sides a,p etc ......) Coolidge gives this but
says he can't recall where he might seen it (and adds that it may even be
his own). I assume he would have said if it was in say Plucker. Kirkman
gives it at the start of an 1849 paper on inscribed conic. Had anyone given
this proof before?

All this may be well- known, but I don't where to look ....

Dick Tahta





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