In XVIII and XIX centuries all the complex calculations, particularly those
astronomical, were made using logarithms.
For this reason, astronomers and mathematicians tried and invented formulas
containing only products and divisions, without addition and subtraction.

In particular in spherical trigonometry  where calculations were often very
long and repetitive.
In these formulas appeared often (if not always) sin (a / 2), cos (a / 2) or
tan (a / 2).



These formulas today can only be found in old texts and to us, accustomed to
calculators and PCs, seem strange and difficult: on the contrary until about
a century ago they were very useful and led to great savings in the computation
time.

For example Gauss invented some formulas (that have his name) for the
search of the elements of a spherical triangle.
If a, b, c are the sides and A, B, C the angles of the triangle ,  one of
the formulas of Gauss is
sin (A / 2). sin [(b + c) / 2] = sin (a / 2). sin [(B-C) / 2]

See  the excellent volume* F. Brunnow Spherical Astronomy-1865* (that can
be downloaded free)


Best regards
Gianni Ferrari


2013/6/12 dharani <[email protected]>

> Roger and Gianni, Thank you for you kind replies.
>
> I am not even close to being a mathematician so it is a bit difficult to
> read math formulas, not to speak of understanding what I read. Is it the
> same thing you both said? If so then what was the practical use of these
> values? Were they used for sundial making?
>
> I took a closer look at the dial and plate and it seems to me these do not
> come from the same period (the numerals used on them are different), hense
> originally they were not parts of one set. What do you think about this
> supposition?
>
> Roger: no, there is no nodus and the values arround the gnomon are not
> EoT. I believe Gianni explained it right.
>
> --
> Best regards
> Darek Oczki
> 52N 21E
> Warsaw, Poland
>
> GNOMONIKA.pl
> Sundials in Poland
> http://gnomonika.pl
> ---------------------------------------------------
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>


-- 

---------------------
Ing. Gianni Ferrari
Lat.    44;38,18.5N
Long. 10;56,05.3E
[email protected]
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