The Hindu-Arabic Numerals | Page 5

FORMS WITH NO PLACE VALUE
While it is generally conceded that the scientific development of astronomy among the Hindus towards the beginning of the Christian era rested upon Greek[42] or Chinese[43] sources, yet their ancient literature testifies to a high state of civilization, and to a considerable advance in sciences, in philosophy, and along literary lines, long before the golden age of Greece. From the earliest times even up to the present day the Hindu has been wont to put his thought into rhythmic form. The first of this poetry--it well deserves this name, being also worthy from a metaphysical point of view[44]--consists of the Vedas, hymns of praise and poems of worship, collected during the Vedic period which dates from approximately 2000 B.C. to 1400 B.C.[45] Following this work, or possibly contemporary with it, is the Brahmanic literature, which is partly ritualistic (the Br[=a]hma[n.]as), and partly philosophical (the Upanishads). Our especial interest is {13} in the S[=u]tras, versified abridgments of the ritual and of ceremonial rules, which contain considerable geometric material used in connection with altar construction, and also numerous examples of rational numbers the sum of whose squares is also a square, i.e. "Pythagorean numbers," although this was long before Pythagoras lived. Whitney[46] places the whole of the Veda literature, including the Vedas, the Br[=a]hma[n.]as, and the S[=u]tras, between 1500 B.C. and 800 B.C., thus agreeing with Bürk[47] who holds that the knowledge of the Pythagorean theorem revealed in the S[=u]tras goes back to the eighth century B.C.
The importance of the S[=u]tras as showing an independent origin of Hindu geometry, contrary to the opinion long held by Cantor[48] of a Greek origin, has been repeatedly emphasized in recent literature,[49] especially since the appearance of the important work of Von Schroeder.[50] Further fundamental mathematical notions such as the conception of irrationals and the use of gnomons, as well as the philosophical doctrine of the transmigration of souls,--all of these having long been attributed to the Greeks,--are shown in these works to be native to India. Although this discussion does not bear directly upon the {14} origin of our numerals, yet it is highly pertinent as showing the aptitude of the Hindu for mathematical and mental work, a fact further attested by the independent development of the drama and of epic and lyric poetry.
It should be stated definitely at the outset, however, that we are not at all sure that the most ancient forms of the numerals commonly known as Arabic had their origin in India. As will presently be seen, their forms may have been suggested by those used in Egypt, or in Eastern Persia, or in China, or on the plains of Mesopotamia. We are quite in the dark as to these early steps; but as to their development in India, the approximate period of the rise of their essential feature of place value, their introduction into the Arab civilization, and their spread to the West, we have more or less definite information. When, therefore, we consider the rise of the numerals in the land of the Sindhu,[51] it must be understood that it is only the large movement that is meant, and that there must further be considered the numerous possible sources outside of India itself and long anterior to the first prominent appearance of the number symbols.
No one attempts to examine any detail in the history of ancient India without being struck with the great dearth of reliable material.[52] So little sympathy have the people with any save those of their own caste that a general literature is wholly lacking, and it is only in the observations of strangers that any all-round view of scientific progress is to be found. There is evidence that primary schools {15} existed in earliest times, and of the seventy-two recognized sciences writing and arithmetic were the most prized.[53] In the Vedic period, say from 2000 to 1400 B.C., there was the same attention to astronomy that was found in the earlier civilizations of Babylon, China, and Egypt, a fact attested by the Vedas themselves.[54] Such advance in science presupposes a fair knowledge of calculation, but of the manner of calculating we are quite ignorant and probably always shall be. One of the Buddhist sacred books, the Lalitavistara, relates that when the B[=o]dhisattva[55] was of age to marry, the father of Gopa, his intended bride, demanded an examination of the five hundred suitors, the subjects including arithmetic, writing, the lute, and archery. Having vanquished his rivals in all else, he is matched against Arjuna the great arithmetician and is asked to express numbers greater than 100 kotis.[56] In reply he gave a scheme of number names as high as 10^{53}, adding that he could proceed as far as 10^{421},[57] all of which suggests the system of Archimedes and the unsettled question of