The Earliest Arithmetics in English

Algorithms; Arithmetic -- Early works to 1900; Mathematics -- History
+---+---+---+-----+---+---+
  |   |   |   |  H. | T.| U.|
  +---+---+---+-----+---+---+
  |   |   |   |     |   | 2 | Difference.
  |   |   |   |     |   | 8 | Divisor.
  +---+---+---+-----+---+---+
  |   |   |   |[4*]9|   |   | +Dividend.+
  |   |   |   |[4*]1| 8 |   | Product of difference by 1st Quotient (9).
  |   |   |   |     | 2 |   | Product of difference by 2nd Quotient (1).
  +---+---+---+-----+---+---+
  |   |   |   |[4*]1|   |   | Sum of 8 and 2.
  |   |   |   |     | 2 |   | Product of difference by 3rd Quotient (1).
  |   |   |   |     |   | 4 | Product of difference by 4th Quot. (2).
  |   |   |   |     |   |   |   +Remainder.+
  +---+---+---+-----+---+---+
  |   |   |   |     |   | 2 | 4th Quotient.
  |   |   |   |     | 1 |   | 3rd Quotient.
  |   |   |   |     | 1 |   | 2nd Quotient.
  |   |   |   |     | 9 |   | 1st Quotient.
  +---+---+---+-----+---+---+
  |   |   |   |  1  | 1 | 2 | +Quotient.+ (+Total of all four.+)
  +---+---+---+-----+---+---+

    [Footnote 4*: These figures are removed at the next step.]

DIVISION. 7800 ÷ 166.

  +---------------+---------------+
  |   Thousands   |               |
  +----+----+-----+-----+----+----+
  | H. | T. |  U. |  H. | T. | U. |
  +----+----+-----+-----+----+----+
  |    |    |     |     |  3 |  4 | Differences (making 200 trial
  |    |    |     |     |    |    |   divisor).
  |    |    |     |   1 |  6 |  6 | Divisors.
  +----+----+-----+-----+----+----+
  |    |    |[4*]7|   8 |    |    | +Dividends.+
  |    |    |   1 |     |    |    | Remainder of greatest dividend.
  |    |    |     |   1 |  2 |    | Product of 1st difference (4)
  |    |    |     |     |    |    |   by 1st Quotient (3).
  |    |    |     |   9 |    |    | Product of 2nd difference (3)
  |    |    |     |     |    |    |   by 1st Quotient (3).
  +----+----+-----+-----+----+----+
  |    |    |[4*]2|   8 |  2 |    | New dividends.
  |    |    |     |   3 |  4 |    | Product of 1st and 2nd difference
  |    |    |     |     |    |    |   by 2nd Quotient (1).
  +----+----+-----+-----+----+----+
  |    |    |[4*]1|   1 |  6 |    | New dividends.
  |    |    |     |     |  2 |    | Product of 1st difference by
  |    |    |     |     |    |    |   3rd Quotient (5).
  |    |    |     |   1 |  5 |    | Product of 2nd difference by
  |    |    |     |     |    |    |   3rd Quotient (5).
  +----+----+-----+-----+----+----+
  |    |    |     |[4*]3|  3 |    | New dividends.
  |    |    |     |   1 |    |    | Remainder of greatest dividend.
  |    |    |     |     |  3 |  4 | Product of 1st and 2nd difference
  |    |    |     |     |    |    |   by 4th Quotient (1).
  +----+----+-----+-----+----+----+
  |    |    |     |   1 |  6 |  4 | +Remainder+ (less than divisor).
  |    |    |     |     |    |  1 | 4th Quotient.
  |    |    |     |     |    |  5 | 3rd Quotient.
  |    |    |     |     |  1 |    | 2nd Quotient.
  |    |    |     |     |  3 |    | 1st Quotient.
  +----+----+-----+-----+----+----+
Public-domain text, read in full here on John Shaqi.
The Earliest Arithmetics in English

No reviews yet
