At First Glance – 2400 Year Old Problem UnSolvable: Philo’s Line Construction With Unmarked Straightedge and a Compass

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It looks like Philo’s Line cannot be drawn, using only a straightedge and a compass, by virtue of knowing NordaVinci’s Formula for the Area of a Right Triangle, which can be used to show that the two tangent points 1) the inscribed circle tangent point to the hypotenuse, and 2) the escribed circle tangent point to the hypotenuse, are equidistant from the endpoints of the hypotenuse on each end.

3 thoughts on “At First Glance – 2400 Year Old Problem UnSolvable: Philo’s Line Construction With Unmarked Straightedge and a Compass”

  3. PHD Thesis on IMPOSSIBILITY RESULTS: FROM GEOMETRY TO
    ANALYSIS by Davide Crippa

    Davide Crippa. IMPOSSIBILITY RESULTS: FROM GEOMETRY TO ANALYSIS : A study in early modern conceptions of impossibility. History, Philosophy and Sociology of Sciences. Univeristé Paris, Diderot Paris 7, 2014. English. fftel-01098493

    HAL Id: tel-01098493
    https://hal.archives-ouvertes.fr/tel-01098493
    Submitted on 25 Dec 2014

    https://hal.archives-ouvertes.fr/tel-01098493/file/phdNovember.pdf

    Reply

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