# The New Art of Memory/Chapter 8

CHAP. VIII.
Arithmetic.
In this chapter, we have given faithfully the substance of Mr. Feinaigle's Lecture on Arithmetic, without any attempt at illustration; and as this Lecture has been accurately detailed in a recent publication, it is extracted from that work, but without any of the reporter's commentaries and observations.
"We have now to see how our methods will apply to Arithmetic.
"In this subject we think we have, or may have evidence, for every particular proposition. But let us think a little; in many cases we have certainty: but is certainty and evidence the same thing? For instance, we know that 6 multiplied by 6 gives 36: this is certain; but is it evident? All we can say is that we have learned so: but ​Page:The new art of memory (IA artofmemoryfound00fein).pdf/219 ​Page:The new art of memory (IA artofmemoryfound00fein).pdf/220 ​Page:The new art of memory (IA artofmemoryfound00fein).pdf/221 ​perform calculations of which you have no idea. So true is this, that if we were to unknow all that we have learned, and begin from the foundation, it would be better.
" We can go on with the same principles to Mathematics; in them we have three things, weight, measure, and number; but all are reducible to number.
"If we now represent our succession of units thus, and divide ten into two halves, as we have seen that this is necessary for representing two in one. If I ask what is 6 to 8, or give me one half of eight, and one fourth of eight, the child finds this at once, which is sometimes the solution of a difficult problem. If we go on to Addition, and ask what is 7 and 8? the child sees at once that 7 is equal to 5 and 2, and that 8 is equal to 5 and 3; so that 7 and 8 are equal to two fives and five, or one ten and five, or fifteen. In the same manner 6 and 6 are one ten and two, 8 and 8 are one ten and six, &c. &c. so that we see addition is certainly demonstrated thus; and subtraction is as evident.
"Let us go on then to Multiplication. Say that we ask how much is eight taken six times, the answer must be in tens and units, the child sees that and 8 is equal to 5 and 3, and 6 is equal to 5 and 1.
ARITHMETIC,
And
multiplying these he has-
Thus
every
what
it is
member must be
in rapport to
187
-25
considered by 15
10 and 5.
5
3
48 But
let us see if this is
We
have certainly above a and below 6 and c
not in our dots also,
four dots, which arc the tens four,
and above
c
two
above b we have
we have
" In the sam e manner 7 multiplied by tens,
•r 3 units, that
and one multiplied by is
two multiplied by four
give eight for the units, so that
we have 6
48. 9,
3,
63. b-
rr c ​ NEW ART OF MEMORY.
188
And
so 8 multiplied by
9,'
we have
7 tens,
and one multiplied by two units or 72,
and so
every other case; only the rule
in
fr
must be changed when we change the •bject of the question.
So
that
we
see a child has no need of the mul-
tiplication table; it
he burdens not
his
mind with
he sees not only the relation of the different
numbers, but he sees
all
combine with each other the thing
" Let
us
the evidence
now go on to
have to divide 63 by 7
is
how
they affect and
all is in
Division. let
the nature of
before him.
us see
included in the nature of the thing.
Suppose we if this is
We
not
have
7)63( If
we
subtract the 7
from 10,
wet have
3
and ​if we add this to 6, we have 9 the quotient. Divide 54 by 9.
| 1 | | |
| 9 | ) 54 ( | 8 |
Subtracting the 9 from 10, and adding the re- mainder to 5, we have 6 the quotient.
so
| 4 | | |
| 6 | ) 48( | 8 |
| 2 | | |
| 8 | ) 72 ( | 9 |
and so on.
And in cases where the dividend does not exactly contain the devisor, as in
| 1 | | |
| 9 | ) 76 ( | 8 |
we find by multiplication, that 8 multiplied by 9 gives 72, we have then 4 over, which is consequently 4 ninths.
"Thus in every case we have always the answer to the nearest whole number. Here also we have no need of the multiplication table, which, as I said before, is so difficult to learn, as the numbers themselves give us the answer; it is in their nature. You see then how easy it is to advance by our method, and we charge not the memory with what it is so difficult to fix."