This section is from the book "The Engineer's And Mechanic's Encyclopaedia", by Luke Hebert. Also available from Amazon: Engineer's And Mechanic's Encyclopaedia.

**Duodecimals**, or Cross Multiplication, is a rule used by workmen and artificers in computing their work. Dimensions are usually taken in feet, inches, and parts, omitting all those which are less than one quarter of an inch as of no consequence. Rule: - Set down the two dimensions to be multiplied togetber one under the other, in such manner, that feet shall stand under feet, inches under inches, and parts under parts; then multiply each term in the multiplicand, beginning with the lowest, by the feet in the multiplier, and set the result of each directly under its respective term, observing to carry one for every 12 from the parts to the inches, and from the inches to the feet. In like manner multiply all the multiplicand by the inches and parts of the multiplier, and set the result of each in one place, removed to the right hand of those in the multiplicand, and the sum of these successive products will be the answer.

Example. Multiply 6 feet 4 inches 3 parts by 10 feet 3 inches 9 parts.

ft. | in. | pts. | |||

6 | 4 | 3 | |||

10 | 3 | 9 | |||

63 | 6 | 6 | |||

1 | 7 | 0 | 9 | ||

4 | 9 | 2 | 3 | ||

Answer . . | 65 | 6 | 3 |

It should be observed, that the feet in the answer are square feet, but the numbers standing in the place of inches are not square inches, as might at first be supposed, but twelfth parts of square feet, each part being equal to twelve square inches. In like manner the number standing in the place of parts, or in the third place of figures, are so many parts of the preceding denomination; these, therefore, are square inches.

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