Elementary arithmetic, with brief notices of its history... by Robert Potts.

MLet it be required to find the product of 5342 by 4.
Hlere 5342 = 5000 + 300 + 40 + 2.
And 4 times 5000 = 20000.
4 times 400 = 1600.
4 times 40 = 160.
4 times 2 8.
The sum of the partial products is 21368, the product of 5342 by 4.
In practice, the process is thus exhibited, omitting the ciphers5342
4
21368
The addition and multiplication are performed at each step of the
process, in this manner:
First. 4 times 2 is 8; write 8 under the place of units.
Secondly. 4 times 4 is 16; write 6 in the place of tens, and reserve
the 1.
Thirdly. 4 times 3 is 12, and adding the 1 reserved make 13; write
-3 in the third place, and reserve the 1.
Fourthly. 4 times 5 is 20, and adding the 1 reserved make 21,
which write in the next place, and the product is 21368.
4. PROB. To find the product of any two numbers.'
1 The following method of multiplication is found in the commentary of Gancsa
un the Lilavati, and was the method adopted by the Arabians, by whom it seems to
have been preferred. It was also adopted by the Persians with some slight modifi-,cation, and, lastly, by the Italians.
Form a parallelogram whose length and breadth respectively contain as many
'units as there are digits in the multiplicand and multiplier, and draw parallel lines
through the points of division, thus dividing the figure into equal squares, and
ilastly, let diagonals be drawn in the same direction in these squares.
Write the digits of the multiplicand and multiplier along the length and breadth
of the parallelogram, placing each digit opposite to a square beginning with the.highest places from the same angle.
Multiply the digts of the multiplicand and multiplier, and place the units of each
product in the lower, and the tens in the upper half of the square which is common
to the two figures which are multiplied together.
Ex. Multiply 5342 by 324.
5 3 4 2
2 1/!l/ 7 2
3 5 9 /6 3
1 7 3 0 8 0 8=1730808, the product.
The operation could be performed from left to right instead of from right to
left, as the products of every two figures of the multiplicand and multiplier would:still occupy the same places.