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

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as a multiplier with the former will give a product composed entirely
of the repetition of any one of the nine digits. Ex. Find numbers
which, when multiplied by 13, shall produce a series of products, which
respectively shall consist of repetitions of each of the nine digits.
8. If the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, be prefixed respectively to the figure 9 successively repeated, and these numbers so
formed be each divided by 13; then (1) the quotients will consist of
ten periods, each of six repeating figures: (2) the last three figures of
each period will be the difference between 999 and the first three:
and (3) the sums of the first and tenth periods, the second and ninth,
the third and eighth, the fourth and seventh, and the fifth and sixth,
will be respectively equal to one another. Shew the truth of these
statements by performing the operations.
9. There are four prime numbers; the product of the first three is
2431; of the last three, 4199; of the first, second, and fourth, 2717;
and of the first, third, and fourth, 3553; determine the four numbers.
10. There are three numbers of which the least common multiple
of the first and second is 1125, of the first and third 1625, and of the
second and third 2025; determine the three numbers.
YIII.
1. Find the least number of ounces of standard gold which can be
coined into an exact number of half-sovereigns, if gold be worth
~3 17s. 10-d. per ounce.
2. Find the least number of pounds which can be paid in either
half-crowns or guineas.
3. Find the least sum which can be paid in an integral number of
francs and roubles, if a rouble be worth 3s. 4-d., and a franc 9|d.
4. If an American dollar is 4s. 3-d., or 5- francs; what is the
smallest sum which can be paid in either shillings, dollars, or francs?
IX.
1. What number of grains will be the least and the greatest
common measure of 4oz. l0dwts. 12grs., and lOoz. lldwts. 4grs. Troy?
2. Find the greatest common measure of 3cwts. 2qrs. 41bs., and
3cwts. 3qrs. 12lbs.
3. What is the greatest number of ounces Avoirdupois that will
exactly measure 15cwts. lqr. 271bs. lOoz., and 21cwts. 2qrs. 211bs.
14oz.
4. If the pound Avoirdupois contain 7,000 grains, find tlie
greatest weight which will measure both a pound Troy and a pound
Avoirdupois; and the least weight which can be expressed without,
fractions in both pounds Troy and pounds Avoirdupois.
5. A cask is required which can be filled exactly by any one of the
following measures, taken any number of times exactly: half a pint,
half a gallon, three gallons, five gallons, and nine gallons; find the
smallest cask for this purpose.