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    Re: W.H. Simms Math Question
    From: Alexander Castro
    Date: 2011 Nov 6, 11:50 -0800
    Thanks for the welcome and the information Frank!

    I'm going through all of the derivations of this book because it is only one I've come across explaining the sextant in any analytical detail.

    If anyone is interested I'll start posting my step by step notes on the derivations.

    Regards,

    Alexander Castro

    Sent from my iPhone

    On Nov 5, 2011, at 11:05 PM, "Frank Reed" <FrankReed@HistoricalAtlas.com> wrote:

    Hello Alexander.

    Welcome aboard!

    In many nineteenth century treatments of trigonometry you'll find that sin(1") factor inserted in various formulae. It is indeed related to the small angle approximation, but I would say that it was really their way in that era of saying "in radians". In modern mathematical notation, we would say:
    sin(x) = x (for x small enough),
    but they would say:
    sin(x) = sin(1")*x.
    The sine of one second of arc is extremely close to (2*pi)/(360*3600), differing at the twelfth decimal point (if I remember correctly), so it works well. You can easily convert to modern trigometric fashion by dropping sin(1") wherever you come across it in those older works.

    -FER


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