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    Re: Certain Errors in "Certaine Errors".
    From: George Huxtable
    Date: 2007 Dec 12, 00:42 -0000

    Thanks to Herbert Prinz for trying to drive home the explanation of Wright's
    to dimwits such as me. However, He has failed to do so, in my case; not his
    fault, surely, but mine.
    
    I will insert my own comments into what he wrote to show where I still have
    problems.
    
    | Garry and George have been puzzling over the inner workings of Wright's
    | geometrical method for finding GCD. It's based on an analemma, whereby
    | various orthogonal projections are sitting on top of each other. To add
    | a little confusion, some lines are shifted around, other ones are reused
    | for more than one purpose, all in an effort to minimize the effort of
    | plotting.
    |
    | E is London, N is Jerusalem, F and O are the projections of these places
    | onto the equatorial plane. FO can be constructed from the known
    | latitudes and longitudes by means of projections into the respective
    | meridional planes.
    
    OK so far. I see that most of the labelled points and lines are in the plane
    of the equator, but not points E and N, which stand up from the equator at
    the end of vertical stalks NO and EF, which correspond to the sines of the
    two latitudes.
    
    | In trapezoid FONE, EN is the chord of the required
    | distance.
    
    Yes, I think I've got that, after a bit of a struggle with the
    three-dimensional picture.
    
    | EF and NO are parallel to each other and perpendicular to FO.
    | FE = sin(Lat(London)) and NO = sin(Lat(Jerusalem)).
    
    OK so far. But from now on, I start to get lost. Where has the point N*
    appeared from?
    
    | The trapezoid FONE
    | can thus be broken down into a rectangle FONN* and a right triangle NN*E
    | with the right angle at N*. The rectangle is of no interest, only the
    | triangle gets drawn as PFQ, with right angle at F.
    |
    | The recipe is actually explained for "him who desireth a
    | demonstration",  but there are two small errors in the example for
    | London and Jerusalem, which may confuse the issue:
    |
    | 1. Read "[make] EQ equal to NO" instead of "PQ equal to NO". (This is
    | mentioned in the errata.)
    | 2. In the corresponding diagram, the point Q is supposed to be a member
    | of the line EF; not of FO, as it is drawn. The line from P to Q should
    | thus meet the line EF in Q. (This is not mentioned in the errata. It may
    | be just a flaw in the printing of the copy at hand.)
    |
    | I hope everything falls into place now.
    
    Afraid not, in my case. No doubt, it's one of those three-dimensional
    pictures that suddenly switches from being quite inscrutable to blindingly
    obvious.
    
    | If not, I may try to come up
    | with a 3-dimensional diagram of what's going on.
    
    Yes, please Herbert, if you don't mind trying. Really, in NavList we need
    the facility to send each other, not just plane attachments, but solid
    three-dimensional models. Unfortunately, that inability to "teleport" solid
    objects, as in Starquest, is one of the internet's little shortcomings.
    
    ==================
    
    It's interesting that the sort of accuracy that Wright was indicating from
    his graphical technique for great-circle distances corresponded rather
    closely with the accuracy of the measuring instruments of his time; the
    astrolabe and the cross-staff. And that within the limits imposed by those
    instruments, Wright had the necessary tools to determine intercepts by the
    St Hilaire method, if only he had thought about it, as early as 1600!
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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