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

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

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150
 

ALBERUNPS INDIA.
 

keep their original places, and then  exchange them
with each other :—
 

II.
 

III.
 

4
 

i6
 

4
 

4
 

15
 

5
 

4
 

14
 

6
 

4
 

13
 

7 &c.
 

4
 

i6
 

4
 

5
 

15
 

4
 

6
 

14
 

4
 

7
 

13
 

4 &c.
 

" IV.-V. The right-side number is placed to the left,
and the other two numbers first keep their original
places, and then exchange them with each other:—
 

IV.
 

V.
 

i6
 

4
 

4
 

IS
 

4
 

5
 

14
 

4
 

. 6
 

13
 

4
 

7 &c.
 

i6
 

4
 

4
 

15
 

5
 

4
 

14
 

6
 

4
 

13
 

7
 

4 &c.
 

"Because, further, the numbers of the syllables of a
pdda rise like the square of 2, for after 4 follows 8, we
may represent the syllables of the three pddas in this
way: 8 + 8 + 8 (=4+4+16). However, their arith¬
metical peculiarities follow another rule. The four-
pcida metre follows the analogy of the three-pdda
metre."

Of the above-mentioned treatise of Brahmagupta I
have only seen a single leaf: it contains, no doubt,
important elements of arithmetic.    God  affords   help
  Page 150