a and in India is hardly
more surprising than that it signified ten at one time in Babylon.[124] It
is therefore quite probable that an extraneous origin cannot be found for
the very sufficient reason that none exists.

Of absolute nonsense about the origin of the symbols which we use much has
been written. Conjectures, {36} however, without any historical evidence
for support, have no place in a serious discussion of the gradual evolution
of the present numeral forms.[125]

TABLE OF CERTAIN EASTERN SYSTEMS
Siam [Illustration: numerals]
Burma[126] [Illustration: numerals]
Malabar[127] [Illustration: numerals]
Tibet[128] [Illustration: numerals]
Ceylon[129] [Illustration: numerals]
Malayalam[129] [Illustration: numerals]

{37}

We may summarize this chapter by saying that no one knows what suggested
certain of the early numeral forms used in India. The origin of some is
evident, but the origin of others will probably never be known. There is no
reason why they should not have been invented by some priest or teacher or
guild, by the order of some king, or as part of the mysticism of some
temple. Whatever the origin, they were no better than scores of other
ancient systems and no better than the present Chinese system when written
without the zero, and there would never have been any chance of their
triumphal progress westward had it not been for this relatively late
symbol. There could hardly be demanded a stronger proof of the Hindu origin
of the character for zero than this, and to it further reference will be
made in Chapter IV.

* * * * *

{38}

CHAPTER III

LATER HINDU FORMS, WITH A PLACE VALUE

Before speaking of the perfected Hindu numerals with the zero and the place
value, it is necessary to consider the third system mentioned on page
19,--the word and letter forms. The use of words with place value began at
least as early as the 6th century of the Christian era. In many of the
manuals of astronomy and mathematics, and often in other works in
mentioning dates, numbers are represented by the names of certain objects
or ideas. For example, zero is represented by "the void" (_['s][=u]nya_),
or "heaven-space" (_ambara [=a]k[=a]['s]a_); one by "stick" (_rupa_),
"moon" (_indu ['s]a['s]in_), "earth" (_bh[=u]_), "beginning" (_[=a]di_),
"Brahma," or, in general, by anything markedly unique; two by "the twins"
(_yama_), "hands" (_kara