lly used our present form[596] with the closed top [Symbol], the open
top used in writing ( [Symbol]) being {147} purely modern. The following
are other forms of the four, from various manuscripts:[597]

[Illustration]

5. "Five" also varied greatly before the time of printing. The following
are some of the forms:[598]

[Illustration]

6. "Six" has changed rather less than most of the others. The chief
variation has been in the slope of the top, as will be seen in the
following:[599]

[Illustration]

7. "Seven," like "four," has assumed its present erect form only since the
fifteenth century. In medieval times it appeared as follows:[600]

[Illustration]

{148}

8. "Eight," like "six," has changed but little. In medieval times there are
a few variants of interest as follows:[601]

[Illustration]

In the sixteenth century, however, there was manifested a tendency to write
it [Symbol].[602]

9. "Nine" has not varied as much as most of the others. Among the medieval
forms are the following:[603]

[Illustration]

0. The shape of the zero also had a varied history. The following are
common medieval forms:[604]

[Illustration]

The explanation of the place value was a serious matter to most of the
early writers. If they had been using an abacus constructed like the
Russian chotue, and had placed this before all learners of the positional
system, there would have been little trouble. But the medieval {149}
line-reckoning, where the lines stood for powers of 10 and the spaces for
half of such powers, did not lend itself to this comparison. Accordingly we
find such labored explanations as the following, from _The Crafte of
Nombrynge_:

"Euery of these figuris bitokens hym selfe & no more, yf he stonde in the
first place of the rewele....

"If it stonde in the secunde place of the rewle, he betokens ten tymes hym
selfe, as this figure 2 here 20 tokens ten tyme hym selfe, that is twenty,
for he hym selfe betokens tweyne, & ten tymes twene is twenty. And for he
stondis on the lyft side & in the secunde place, he betokens ten tyme hym
selfe. And so go forth....

"Nil cifra significat sed dat signare sequenti. Expone this verse. A cifre
tokens no[gh]t, bot he makes the figure to betoken that comes after hym
more than he shuld & he were away, as thus 10. here the figure of one
tokens ten, & yf the cifre were away & no figure byfore hym he schuld token
bot one, for than he schuld stonde in the first place....