SCALES OF NOTATION 47

For some reasons it would be better if we reverst the order
of the numbers and wrote the expression @@ *** @n_1@n.
We, who write from left to right, set figures down in the same
visual order as the Arabs, from whom we got this notation
and who write from right to left.

Thus 139 = 1024 (radix 5)
= 256 (radix 7)

108. When the radix ten is understood, as is usually the
case, the number is said to be written in the Hindu-Arabic
notation, called by this name because the Arabs apparently
got the notation from the Hindus.

Thus, above, 139 was used for 139 (radix ten),
or 1 X (ten)? 4+ 3 X (ten) + 9.

109. We see then that ten is not the only possible base.
We may use any primary number greater than 1.

If 2 is used as the base, the number represented is said to be
written in the binary notation, or binary system, or binary scale.

Similarly we have the

ternary () scale, in which the radix is three
quaternary il 6l [ e 6 é fOur
quinary [ ‘6 é ¢ ‘° [ five
senary six
septenary seven
octary, octonary, or octimal : eight
nonary nine
decimal, or denary ten
undecimal, or undenary eleven
duodecimal, duodenary, or duodenal (?) twelv
sexadecimal, sexadenary, or sexidenal sixteen
vigesimal, or vicenary twenty
sexagesimal, or sexagenary sixty

(1) See D. O’Sullivan, The Principles of Arithmetic, 16th ed., p. 415,
Dublin, M. H. Gill and Son.

(2) See John W. Nystrom, On the French metric system . . . and on
the duodenal arithmetics and metrology, Philadelphia, J. Penington & Son,
1876.