Again, we have five fingers and five toes on each hand and foot, and we have, also, five senses, as before mentioned:—We find, that the ancients counted by tally on wood, the same as the returns of our elections are made out on paper by FIVES, and, the North American Indians count, by holding up their hands, so, that, nature has furnished, the great and universal standard, of addition by 5.

ADDITION is the first step to Mathematical knowledge, and is founded, on the first axiom, in Euclid, viz: the the whole is equal to its parts.

The learned instructer may use his own discretion, on

the subject of proposing questions.

Q. Why do we carry, 1 for every 10 in addition?

A. The reason is manifest, from numeration, we find, that numbers increase in a ten fold ratio.

Example. Gave $26 for a cow, and $9 for a load of hay, what did I give for both? Ans. $35 00,

Operation,

tens.

units.

26

Here 9 and 6 added together make 9 15, which is 5 above 10.

I set down 5, in the units place, and carry 1 to 2 which make 3, which I set down in the ten's place and find the sum is 35.

DEFINITION. To add, is to collect together, to make greater,

DIVERTING EXERCISES IN ADDITION, calculated to instruct and amuse the learner.

Elucidation of the foregoing Table.

On the foregoing page you see, that 1, 2, 4, 8, 16 and 32 are in the 1st horizontal row and no where else; but 1+2=3, shews that 3 is to be found in the 1st and 2nd columns, because it requires 1 and 2 to make 3. If it requires three or more of the top numbers to make one of the numbers in the table, as 1+2+4+8=15, the number 15 is to be found in all the columns in which 1, 2, &c. are found at top; and so it is with all the other numbers, which are generated in the same way. The horizontal rank of numbers, 1, 2, 4, 8, &c. are in geometrical ratio, and the perpendicular rank on the left in arithmetical ratio; both together the abscisae and ordinates of the Logarithmic curve. The rank of geometricals at the top viz: 1, 2, 4, &c., afford such combinations as make up all other numbers, in whatever column any number stands, the sum of the geometricals which stand over such a number is equal to it, and the reason, why one can guess any number thought on, is, the sum of the numbers which stand over it, in the first horizontal row, makes it, and no other exactly. Suppose for example, I fix upon the number 50, and ask you to tell, which number I thought on, you would ask me in which of the columns, and how many does it stand in? I would say in the second and two last columns, you would then put 2+16+32=50, and tell me to a certainty; because 50 is no where else, but in the second and two last columns. Whatever number you guess upon, if only, in the first, second, third, fourth, fifth, or sixth columns, the numbers must be 1, 2, 4, 8, 16 or 32, because each of them are found but once. But where it takes two or more of the figures in the horizontal row of geometricals, to make the one you think on, the number is to be found in all the columns, exactly under the geometricals, which compose it, and no where else, hence it is easy to understand the diverting exercises, if another column was added its head number would be 64, from