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    Re: Snellius Construction questions
    From: Herbert Prinz
    Date: 2009 Jan 05, 22:18 -0500

    The construction is based on the fact that
    
    1. Periphery angles over the same arc are equal
    
    and
    
    2. The central angle is twice as large as the periphery angle.
    
    Therefore, for any given chord, the locus of all points from which that 
    chord is seen under a given angle is a circle. The center of that circle 
    is on the bisector of the chord, exactly in the place from which that 
    chord is seen at twice the given angle.
    
    Of course, said circle is a LOP. (The claim on the referred website that 
    a position can be derived without LOPs is misleading.) In order to get a 
    position, one must combine this circle with any other suitable LOP, 
    which may or may not be obtained in the same way.
    
    The horizontal angle between the two chosen landmarks can be measured 
    directly with a sextant or as the difference of two compass bearings. 
    The former has the advantage of increased accuracy (minutes of arcs 
    instead of degrees). I believe there is a plotting tool specially 
    designed to assist with the method. I have never seen one in natura, but 
    it's some kind of a rule-plus-protractor with three arms that can be set 
    to the given angles.
    
    Herbert Prinz
    
    
    
    
    NavList---.com wrote:
    
    >
    >I have found an intriguing example of triangulation from a 16th century 
    mathematician, Willebrord 
    Snellius(http://www.sailingissues.com/navcourse4.html). I have searched other 
    web sources on the web and so far, have had no success in finding a straight 
    forward explanation of how this method of triangulation works. Have any of 
    you actually used the "Snellius Construction" technique, and could you help 
    me understand it as a practical navigation application?
    >
    >Thank you,
    >
    >Todd Frye
    >
    >-----------------------------------------------
    >[Sent from archive by: fryefamily-AT-sisna.com]
    >
    >
    >>
    >
    >  
    >
    
    
    
    
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