416 
**It would be impossible, with the few materials yet 
brought to light, to conjecture with any great probability 
how far these Boetian contractions may have influenced the 
introduction, or cooperated with the Arabic system to the 
formation of our present numerical notation. It appears to 
me highly probable that the two systems became united, 
because the middle age forms of the figure five coincide 
with the Boetian mark for the same numeral, and those of 
two others are very similar. The idea of local position, 
again, may have had an independent European origin; the 
inconveniences of the abacus on paper would have suggested 
it by destroying the distinguishing boundaries, and invent- 
ing an arbitrary hieroglyphic for the representation of an 
empty square.”—Rara Mathematica, p. 111. 
Now, from the Mentz MS. in the Arundel Collection, it is 
very evident that their mode of operation with the abacus 
had received one great improvement on the Greek and 
Roman system, the abolishing the necessity of motion, and 
only using the table cum pulvere, as a means for distinguish- 
ing position. Thus, in the following addition sum, using the 
names instead of the cabalistic characters, we have an ex- 
ample of their method of proceeding:— 
Andras Igin | Calcis Andras 
Tenis Arbas Ormis Celentis 
Celentis Calcis Igin 
Thus making a total of — celentis, calcis, zero, igin. Now, it 
is evident, that in order to do away with the necessity of 
this table, supposing the contractive marks again substituted 
for the latter words, we have only to imagine an arbitrary 
character for the deficiency under the ormis, and the modus 
operandi is synonymous with our own present form. 
OE ee 
