s, he states that traces are found from 590 A.D. on. "That
the system now in use by all civilized nations is of Hindu origin cannot be
doubted; no other nation has any claim upon its discovery, especially since
the references to the origin of the system which are found in the nations
of western Asia point unanimously towards India."[169]

The testimony and opinions of men like Buehler, Kielhorn, V. A. Smith,
Bhandarkar, and Thibaut are entitled to the most serious consideration. As
authorities on ancient Indian epigraphy no others rank higher. Their work
is accepted by Indian scholars the world over, and their united judgment as
to the rise of the system with a place value--that it took place in India
as early as the {48} sixth century A.D.--must stand unless new evidence of
great weight can be submitted to the contrary.

Many early writers remarked upon the diversity of Indian numeral forms.
Al-B[=i]r[=u]n[=i] was probably the first; noteworthy is also Johannes
Hispalensis,[170] who gives the variant forms for seven and four. We insert
on p. 49 a table of numerals used with place value. While the chief
authority for this is Buehler,[171] several specimens are given which are
not found in his work and which are of unusual interest.

The ['S][=a]rad[=a] forms given in the table use the circle as a symbol for
1 and the dot for zero. They are taken from the paging and text of _The
Kashmirian Atharva-Veda_[172], of which the manuscript used is certainly
four hundred years old. Similar forms are found in a manuscript belonging
to the University of Tuebingen. Two other series presented are from Tibetan
books in the library of one of the authors.

For purposes of comparison the modern Sanskrit and Arabic numeral forms are
added.

Sanskrit, [Illustration]
Arabic, [Illustration]

{49}

NUMERALS USED WITH PLACE VALUE

1 2 3 4 5 6 7 8 9 0
a[173] [Illustration]
b[174] [Illustration]
c[175] [Illustration]
d[176] [Illustration]
e[177] [Illustration]
f[178] [Illustration]
g[179] [Illustration]
h[180] [Illustration]
i[180] [Illustration]
j[181] [Illustration]
k[181] [Illustration]
l[182] [Illustration]
m[183] [Illustration]
n[184] [Illustration]

* * * * *

{51}

CHAPTER IV

THE SYMBOL ZERO

What has been said of the improved Hindu system with a place value does not
touch directly the origin of a symbol for zero, although it assume