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    Re: Certain Errors in "Certaine Errors".
    From: Gary LaPook
    Date: 2007 Dec 11, 15:25 -0800

    Gary writes:
    
    
    Did you mean "planisphere" and not "analemma"? All I can find about
    analemmas is that they relate to sundials.
    
    
    gl
    
    On Dec 10, 7:35 am, Herbert Prinz  wrote:
    > 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. In trapezoid FONE, EN is the chord of the required
    > distance. EF and NO are parallel to each other and perpendicular to FO.
    > FE = sin(Lat(London)) and NO = sin(Lat(Jerusalem)). 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. If not, I may try to come up
    > with a 3-dimensional diagram of what's going on.
    >
    > Analemmata have been employed since antiquity to solve problems in
    > spherical astronomy. They are orthographic projections. Their purpose
    > was to convert problems of spherical trigonometry into ones of plane
    > trig. The latter could be solved numerically by means of proportions.
    > For a long time, this was the only way of expressing trigonometric
    > equations. The analemma also found direct use in geometrical
    > construction, e.g. of sun dials.
    >
    > Lacaille proposed a graphical method applying an analemma for the the
    > reduction of time sights and lunar distances as late as 1761. At that
    > time the moon predictions were still the limiting factor of accuracy in
    > solving the longitude problem. After the introduction of Mayer's tables,
    > graphical reduction was no longer adequate. I would not say that it
    > disappeared. It pops up now and then in lifeboat navigation and the
    > like. Other projections (e.g. stereographic) have been suggested since
    > for graphical or mechanical methods with little success.
    >
    > Herbert Prinz
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