Bīrūnī, Muḥammad ibn Aḥmad, Alberuni's India (v. 1)

(London :  Kegan Paul, Trench, Trübner & Co.,  1910.)



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  Page 315  

CHAPTER XXXI.                           315

on the circle of latitude, whilst the roughly calculcded
number is the distance between the two places in

This method of calculation is found in the astrono- The author


mical handbooks of the Hindus in conformity with the this method.
account of Alfazari, save in one particular.    The here-
mentioned portio is the root of the difference between
the squares of the sines of the two latitudes, not the
sum of the squares of the sines of the two latitudes.

But whatever this method may be, it does not hit the
right mark. We have fully explained it in several of
our publications specially devoted to this subject, and
there we have shown that it is impossible to determine
the distance between two places and the difference of
longitude between them by means of their latitudes
alone, and that only in case one of these two things is
known (the distance between two places or the differ¬
ence between the longitudes of them), by this and
by means of the two latitudes, the third value can be

Based on the same principle, the following calcula- Another
tion has been found, there being no indication by whom of the

,,               .             .    -,                                                                                                         desdntara.

it was invented :—

" Multiply the yojanas of the distance between two
places by 9, and divide the product by (lacuna) ; the
root of the difference between its square and the square
of the difference of the two latitudes. Divide this
number by 6. Then you get as quotient the number
of day-minutes of the difference of the two longi¬

It is clear that the author of this calculation first
takes the distance (between the two places), then he
reduces it to the measure of the circumference of the
circle. However, if we invert the calculation and re¬
duce the parts (or degrees) of the great circle to yojanas
according to his method, we get the number 3200, i.e.
100 yojanas less than we have given on the authority of
  Page 315