The Hindu-Arabic Numerals | Page 5

text of the first few lines is as
follows:
"Hec algorism' ars p'sens dicit' in qua Talib; indor[um] fruim bis quinq;
figuris.[41]
"This boke is called the boke of algorim or augrym after lewder use.
And this boke tretys of the Craft of Nombryng, the quych crafte is
called also Algorym. Ther was a kyng of Inde the quich heyth Algor &
he made this craft.... Algorisms, in the quych we use teen figurys of
Inde."
* * * * *
{12}
CHAPTER II
EARLY HINDU 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