"[605]

It would seem that a system that was thus used for dating documents, coins,
and monuments, would have been generally adopted much earlier than it was,
particularly in those countries north of Italy where it did not come into
general use until the sixteenth century. This, however, has been the fate
of many inventions, as witness our neglect of logarithms and of contracted
processes to-day.

As to Germany, the fifteenth century saw the rise of the new symbolism; the
sixteenth century saw it slowly {150} gain the mastery; the seventeenth
century saw it finally conquer the system that for two thousand years had
dominated the arithmetic of business. Not a little of the success of the
new plan was due to Luther's demand that all learning should go into the
vernacular.[606]

During the transition period from the Roman to the Arabic numerals, various
anomalous forms found place. For example, we have in the fourteenth century
c[alpha] for 104;[607] 1000. 300. 80 et 4 for 1384;[608] and in a
manuscript of the fifteenth century 12901 for 1291.[609] In the same
century m. cccc. 8II appears for 1482,[610] while M^oCCCC^o50 (1450) and
MCCCCXL6 (1446) are used by Theodoricus Ruffi about the same time.[611] To
the next century belongs the form 1vojj for 1502. Even in Sfortunati's
_Nuovo lume_[612] the use of ordinals is quite confused, the propositions
on a single page being numbered "tertia," "4," and "V."

Although not connected with the Arabic numerals in any direct way, the
medieval astrological numerals may here be mentioned. These are given by
several early writers, but notably by Noviomagus (1539),[613] as
follows[614]:

[Illustration]

{151}

Thus we find the numerals gradually replacing the Roman forms all over
Europe, from the time of Leonardo of Pisa until the seventeenth century.
But in the Far East to-day they are quite unknown in many countries, and
they still have their way to make. In many parts of India, among the common
people of Japan and China, in Siam and generally about the Malay Peninsula,
in Tibet, and among the East India islands, the natives still adhere to
their own numeral forms. Only as Western civilization is making its way
into the commercial life of the East do the numerals as used by us find
place, save as the Sanskrit forms appear in parts of India. It is therefore
with surprise that the student of mathematics comes to realize how modern
are these forms so common in the West, how limite