Bīrūnī, Muḥammad ibn Aḥmad, Alberuni's India (v. 2)

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



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  Page 75  

CHAPTER LV.                               75

the measure of the body would not vary (v. p. 74).
Therefore the commentator Balabhadra holds the same
opinion as Pulisa, viz. that the divisor in this division
should be the true distance reduced (to the measure
of yojctnas).

Brahmagupta gives the following rule for the com- prahma-
putation of the diameter of the shadow, which in our SSifodfor
canones is called the measure of the sphere of the dragon's tation^f^the
head and tail: " Subtract the yojanas of the diameter the^Lrdow.
of the earth, i.e. 1581, from the yojctncts of the diameter
of the sun, i.e. 6522.    There remains 4941, which is
kept in memory to be used as divisor.   It is represented
in the figure by AE.    Further multiply the diameter
of the earth, which is the double sinus totus, by the
yojancts of the true distance of the sun, which is found
by the correction of the sun.    Divide the product by
the divisor kept in memory.    The quotient is the true
distance of the shadow's end.

"Evidently the two triangles AEC and CDH are
similar to each other. However, the normal line OT
does not vary in size, whilst in consequence of the
true distance the ap)pectrctnce of AB varies, though its
size is constantly the same. Now let this distance be
CK. Draw the lines AJ and EV parallel to each other,
and JKV parallel to AB. Then the latter is equal to
the divisor kept in memory.

" Draw the line JCM. Then M is the head of the cone
of the shadow for that time. The relation of JV, the
divisor kept in memory, to KC, the true distance, is
the same as that of CD, the diameter of the earth, to
ML, which he (Brahmagupta) calls a true distance (of Page 240.
the shadow's end), and it is determined by the minutes
of the sine (the earth's radius being the sinus totus).
For KC-------"

Now, however, I suspect that in the following some- Lacuna in

'                       '               -•■                                  _                           '-'                    the manu-

thina: has fallen out in the manuscript, for the author script copy

o                                                                                 ■••              .                               of Brahma-

continues :  " Then multiply it (i.e. the quotient of CK, gupta.
  Page 75