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Re: [EMHL] Forum Geometricorum

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  • Richard Guy
    May I air one of my b^etes noires ? `proven is the past participle of an archaic verb `preve , meaning `to test , certainly not `to prove in the modern
    Message 1 of 476 , May 10, 2001
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      May I air one of my b^etes noires ?

      `proven' is the past participle of an archaic
      verb `preve', meaning `to test', certainly not
      `to prove' in the modern mathematical sense.
      Its etymology (and pronunciation) are clear
      when you compare `woven' and `cloven'.

      It survives in Scottish law as a third possible
      verdict, `Not Proven' and in a few phrases, e.g.
      `a proven remedy' and is connected with the
      `proof' (number of 200ths) of spiritous liquors.

      The p.p. of `to prove' is `proved'. You might
      think that this is just another of my pieces
      of windmill-tilting, but this morning I refereed
      a paper (three, actually) and suggested, amongst
      other things, that `unproven' be changed to
      `unproved'. I'm delighted to say that the
      editor has already emailed me to say that that
      is an editorial change that he/she routinely
      makes. R.
    • forumgeom forumgeom
      The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2013volume13/FG201309ndex.html The editors Forum
      Message 476 of 476 , Apr 16, 2013
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        The following paper has been published in Forum Geometricorum. It can be viewed at

        http://forumgeom.fau.edu/FG2013volume13/FG201309ndex.html

        The editors
        Forum Geometricorum

        Paul Yiu, On the conic through the intercepts of the three lines through the centroid and the intercepts of a given line,
        Forum Geometricorum, 13 (2013) 87--102.

        Abstract. Let L be a line intersecting the sidelines of triangle ABC at X, Y, Z respectively. The lines joining these intercepts to the centroid give rise to six more intercepts on the sidelines which lie on a conic Q(L,G). We show that this conic (i) degenerates in a pair of lines if L is tangent to the Steiner inellipse, (ii) is a parabola if L is tangent to the ellipse containing the trisection points of the sides, (iii) is a rectangular hyperbola if L is tangent to a circle C_G with center G. We give a ruler and compass construction of the circle C_G. Finally, we also construct the two lines each with the property that the conic Q(L,G) is a circle.


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