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/sci/ - Science & Math

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14623512 No.14623512 [Reply] [Original]

Has anyone heard of or seen a proof of the property in Lemma 1.3?

The only thing I worked through in appolonius resembling it is proposition 14 in heath's translation.

>> No.14623519
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14623519

>>14623512
Also the book I'm pulling that image from is "Second year Calculus" by David M bressoud.

Proposition 14 from heath is pic related.

>> No.14623743

>>14623512
Let R be the intersection point of the lin QG and the tangent at P. Then, QOPR is similar to GMPR, and so
(1) QO/GM = OP/MP.
Also, since QQ' and PP' are conjugate, we have
(2) P'O = OP.
Are (1) and (2) enough to obtain the formula?

>> No.14623945
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14623945

>>14623743
Using your technique again for another point R', I obtain the ratio
QO:GM = PO : P'M
Multiplying the ratio you gave and this one gives the desired result.

If thats correct, thanks alot for the answer. I like your geometric solution.