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

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

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274
 

ALBERUNPS INDIA.
 

Calculation
on the ex¬
tent of
human
vision on
the earth.
 

Further, the remark of Balabhadra (v. p, 273),
that man, on account of the smallness of his stature,
cannot observe the rotundity of the earth, is not true ;
because even if the human stature were as tall as the
plumb-line of the highest mountain, if he were to make
his observation only from one single point without
going to other places, and without reasoning about the
observations made at the different places, even such a
height would be of no avail to him, and he would not be
able to perceive the rotundity of the earth and its nature.
What, however, is the connection of this remark
with the popular theory ? If he had concluded from
analogy that that side of the earth which is opposed
to the round one—I mean the lower half—was also
round, and if he then had given his theory about the
extent of the power of human vision as a result of
reflection, not as a result of the perception of the
senses, his theory would seem to have a certain foun¬
dation.

With regard to Balabhadra's definition of the extent
which may be reached by the human eye, we propose
the following calculation :—

Let A B round the centre II represent the globe of
the earth. B is the standing-
point of the observer ; his
stature is B C. Further, we
draw the line C A, so that it
touches the earth.

Now it is evident that the
field of vision is B A, which
we suppose to be equal to
-Jg- of the circle,-i.e. 3f degrees,
if we divide the circle into
360 degrees.

According to the method
followed in the calculation of the mountain Meru (in
chap, xxiii.), we divide the square of T A, i.e. 50,625, by
  Page 274