Page:The Algebra of Mohammed Ben Musa (1831).djvu/214

 good authority, that Hindu mathematicians and astronomers were among their number.

If we presume that the Arabic word handaseh might, as the Persian hindisah, be taken in the sense of decimal notation, the passage now before us will appear in an entirely new light. The اهل الهندسة, to whom our author ascribes two particular formulas for finding the circumference of a circle from its diameter, will then appear to be the Hindu Mathematicians who had brought the decimal notation with them;—and the اهل النجوم منهم, to whom the second and most accurate of these methods is attributed, will be the Astronomers among these Hindu Mathematicians.

This conjecture is singularly supported by the curious fact, that the two methods here ascribed by Mohammed to the اهل الهندسة actually do occur in ancient Sanskrit mathematical works. The first formula, $$p=\sqrt{10d^2}$$, occurs in the Vijaganita (’s translation, p. 308, 309.); the second, $$p= \tfrac{d \times 62832}{20000}$$, is reducible to $$\tfrac {d \times 3927}{1250}$$, the proportion given in the following stanza of Bhāskara II Lilavati:

व्यासे भनंदाग्निहते विभक्ते
 * खबाणसूर्यैः परिधिस्तु सूक्ष्मः १

द्वाविंशतिघ्ने विहृतेऽथ शैलैः
 * स्थूलेभोऽथवा स्याद्व्यवहारयोग्यः ११

“When the diameter of a circle is multiplied by three