On Arithmetical Complements. 211 
‘The arithmetical complement of any number is what that number 
wants of another number, which has unity for the left hand figure 
followed by as many ciphers as are digits in the proposed number, 
This is equivalent to the usual definition ; but in my opinion it is 
incorrect, and not congenial to any good principle of explaining 
this kind of practice. Authors usually direct to subtract every 
digit from 9, except the last, which must be subtracted from 10. 
But as to this, the reader may put in practice which method he 
thinks proper. 
As my principal object is only to change such numbers as are 
put in opposition to affirmative numbers, and properly indicated 
by the sign —; and in doing this I only find equivalent numbers, 
each composed of a negative and an affirmative part; thisis there- . 
fore not a complement, it will thus be inconsistent to em- 
ploy the term arithmetical complement ; but as some term must. 
be used in order to be understood, I shall therefore call the one 
number the reciprocal equivalent of the number proposed, as by 
the same operation the one may be converted to the other by 
observing the proper change of the signs. 
I shall here present the reader with a few examples on this 
species of arithmetic. 
ADDITION. 
To add numbers which have different signs together. 
Rule. 
Find the reciprocal equivalents of the negative numbers: then 
add these equivalents and the affirmative numbers into one sum, 
and deduct the negative units that. may be in any column from 
the sum of the column. 
Example. 
Add 7854, 31416, —734, 65321, —2965. 
Common Method. 
7854 7854 
31416 734 381416 
65321 2965 1266 
104591 3699 65321 
. : 17035 
ae 104591 prema 
3699 ! 100892 
100892 
SUBTRACTION. 
Add the reciprocal equivalent of the number to be taken away — 
to the number which is required to be reduced, and the suin is 
the remainder. 
Examples are unnecessary. 
MULTI- 
