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§ 38.-1. Combinations by 8.-The right-hand figure of any number consisting of two figures becomes less by 2, whenever that number is increased by 8, unless the righthand figure be 1 which then becomes 9; while if any change take place in the left-hand figure, it becomes greater by 1.

2. A change always does take place in the left-hand figure whenever the right-hand figure is greater than 1.

38. When a number consisting of two figures is increased by 8, what change takes place in the right-hand figure? What in the left? When does a change take place in the left-hand figure?

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§ 39.-1. Combinations by numbers less than 8 are perhaps undesirable. The following, however, consisting of numbers above 10, are worthy of attention.

2. Combinations by 11.-Each of the figures of any number of two figures, is made larger by 1, when that number is increased by 11, except when the right-hand figure is 9 in which case, the 9 becomes 0 and the left-hand figure is increased by 2.

39. How is each figure of any number of two figures affected when increased by 11? What exception? How then affected?

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§ 40. Combinations by 12.—When any number of two figures is increased by 12, the left-hand figure is increased by 1, and the right-hand one by 2. The only exceptions are, when the right-hand figure is 8, or 9, in which case this figure becomes 0 or 1, while the left-hand figure is increased by 2.

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number is increased by 12?

40. How is the left-hand figure of any number affected when that

How the right-hand? What excep

tions. How is it then?

§ 41. Combinations by 8s, 9s, and 10s. It will be observed that in all these combinations the figures taken by couplets amount to one of these numbers. (See § 36, 37,

38.)

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§ 42. Combinations by 9s, 10s, and 11s.-Let the work be strictly performed by combinations. (See § 36, 37, 39.)

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