Re: [EMHL] Forum Geometricorum
- 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
- The following paper has been published in Forum Geometricorum. It can be viewed at
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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