34 ALBERUNTS INDIA.
The ahao-- of Ya'kub Ibn Tarik in the calculation of the universal
given by solar and unardtra days. As he translated from the
T4rik. Indian language a calculation the reasons of which he
did not understand, it would have been his duty to
examine it, and to check the various numbers of it one
by the other. He mentions in his book also the method
of ahargana, i.e. the resolution of years, but his descrip¬
tion is not correct; for he says :—
" Multiply the months of the given number of years
by the number of the adhimdsa months which have
elapsed up to the time in question, according to the
well-known rules of adhimdsa. Divide the product
by the solar months. The quotient is the number of
complete adhimdsa months plus its fractions which
have elapsed up to the date in question."
The mistake is here so evident that even a copyist
would notice it; how much more a mathematician who
makes a computation according to this method; for
he multiplies by the partial adhimdsa instead of the
universal.
A second Bcsides, Ya'kiib mentions in his book another and
given by perfectly correct method of resolution, which is this:
"When you have found the number of months of
the years, multiply them by the number of the lunar
months, and divide the product by the solar months.
The quotient is the number of adhimdsa months to¬
gether with the number of the months of the years in
question.
" This number you multiply by 30, and you add to
the product the days which have elapsed of the current
month. The sum represents the lunar days.
" If, instead of this, the first number of months were
multiplied by 30, and the past portion of the month
were added to the product, the sum would represent
the partial solar days; and if this number were further
computed according to the preceding method, we should
get the adhimdsa, days together with the solar days."
Ya'kub.