; 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 Buerk[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