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

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



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2,6                           ALBERUNTS INDIA.

and the number they get is subtracted from the num¬
ber written down in the middle place. The double of
the remainder they divide by 65. Then the quotient
represents the partial adhimdsa months. This number
they add to that one which is written down in the
uppermost place. They multiply the sum by 30, and
add to the product the days which have elapsed of the
current month. The sum represents the partial solar
days. This number is written down in two different
places, one under the other. They multiply the lower
number by ii, and write the product under it. Then
they divide it by 403,963, and add the quotient to the
middle number. They divide the sum by 703, and
the quotient represents the partial dnccrdtrct days. This
number they subtract from the number written in the
uppermost place, and the remainder is the number of
civil days which we want to find."
Explication The rationale of this computation is the following:—
method. If WO divide the universal solar months by the uni¬
versal adhimdsa months, we get as the measure of one
adhimdsa month Z'^^i'^'^ii solar months. The double
of this is 65Yy-9%% solar months. If we divide by this
number the double of the months of the given years, the
quotient is the.number of the partial ctdhimdsas. How¬
ever, if we divide by wholes plus a fraction, and want
to subtract from the number which is divided a certain
portion, the remainder being divided by the wholes
only, and the two subtracted portions being equal por¬
tions of the wholes to which they belong, the whole
divisor stands in the same relation to its fraction as
the divided number to the subtracted portion.
The latter If wc make this computation for our gauge-year, we
^piiedto    get the fraction of T,irVV/tfo^"o> ^.nd dividing both num-

the gauge-      -,          -,         _                i.       n i

year.          bcTS by 15, wc get WtW-

It would also be possible here to reckon by single
adhimdsas instead of double ones, and in that case it
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