Explanation.

I divide the given quantity by 40, which denominates the part which ôd. is of a pound, and thereby get the pounds, and by dividing the remainder by the part. which 6d. is of Is. I find the shillings and pence, if any, viz. 410 dividing 1755 the quotient is 43 and the remainder 35; I say 35s. is 17s..and 1 remains, which I multiply by 12 makes 12d. the whereof is 6d. And so I find the answer 437 17s. 6d.

After this manner let the Examples be wrought.

Case III. Of the Complements.

I. When the price is the complement of an aliquot part of 11.

Rule.

Find the amount of the aliquot part whereof it is the complement (last) and subtract the same from the quantity taken as so many pounds, the remainder is the

answer.

Application.

42. Let it be required to find the price of 713. at 13s. 4d. p.?

43. At 15s. Cwt. what cost 336C. of logwood? Answ. 2521..

44. How much cost 194 yards of broad cloth, at 16s. 8d. yard? Answ. 1611. 13s. 4d.

45. What cost 479 yards of velvet at 173. 6d. yard? Answ. 4191. 2 6d.

46. At 18s 4d.

Answ. 871. 1s. 8d.

Cu t. what cost 95 Cwt. of rice ?

P 2

47. At

47. At 19s. Cwt. what come 317 C. of butter to? Answ. 3011, 38. Od.

The Complement of the Aliquot part of a Shilling. 48. At 9d. b. what cost 1784 of tobacco?

Here 9d. is the complement of is. I take out of 1784 taken as shillings, then the remainder is 1338s. &c.

d.

1784

49. At 10d. p yard, what cost 540 yards of flannel?

Answ. 221. 10s. Od.

50. How much cost 7644b. at 101d. Hb.?

Answ. 3341. Ss. 6d.

51. What is the price of 5649 of pepper at 11d. th.? Answ. 2587. 18s. 3d.

III. Of 2 Shillings.

First find the amount of the quantity at 2s. ' and the said amount divide by the denominator of the aliquot part, the quotient must be subtracted from the amount at 2s. and the remainder is the answer.

52. What cost 524 yards of linen at 1s. 4d. No yard ?

1. S.

53. What cost 1648h of hops, at 1s. 6d. b.? Answ. 1231. 12s.

54. At Is. 9d. ell, what cost 729 ells of dowlass? Answ. 631. 15s. 9d.

55. What is the price of 1733 gallons of cyder, at 13. 10d. gallon? Answ. 1591, 6s. 4d.

Case

Case IV. Of Aliquot Parts, into Complements. Any aliquot part (of a pound or shilling) may be di-vided into several aliquot parts thus. Take the greatest aliquot part, less than the given aliquant part, out of the said aliquant part, then if the remainder be likewise an aliquot part, the thing proposed is manifestly effected: So if 5d. be the aliquant part of a shilling, given to be divided into aliquot parts, I know, (from the Table) that 4d.s. is the greatest aliquot part less than 5d. and 1d. remains, which is likewise an aliquot part, viz. z; So 7d. may be divided into 6-s. and 1d.-; 7d. into 6—4s. and 14d.—1$. &c. In like manner we may divide 7s. 6d. ino 5s.-4. and 2s. 6d —; 12s. 6d, into 10s. - and 2s. 6d.-1; 11s. 8d. into 10s.. and 1s. 8d-11. &c.

But if the remainder be not an aliquot part, then take again the greatest aliquot part (less than it out of the remainder, and so on, and thus at last we shall divide the given aliquant part into several aliquot parts, whose sum shall be equal to the said aliquant part: Thus we may divide..

Thus it is shewn how to divide any aliquant part into But as the least parts may sometimes,

aliquot parts of the whole.

*In some cases it may be more convenient to take a lesser aliquot part rather than the greatest (in the reina.nder,) as if 4s. 6d. were to be divided into aliquot parts of 1. the greatest aliquot part less than 4s. 6d. is 3s. 4d. and it will by the rule be divided into

Note Expertness in the most commodious division iss attained by Practice.

sometimes have denominators greater than 12, (which should be avoided that the division may be performed) we may observe that the lesser aliquot parts of the whole, are often likewise aliquot parts of some greater aliquot part before taken, and by considering them in this light we shall generlaly avoid large divisors: Thus may the foregoing aliquant parts be divided and considered as follow eth;

I. When the price is an aliquant part of a pound. First divide the given price into aliquot parts of a pound; then divide the given quantity by the denominator of each aliquot part successively; Thirdly, add all the quotients into one sum, and that sum is the answer required.

Application.

Let it be required to find the price of 198 yards of broad-cloth, at 14s. 6d. d yard.

S. d. 1.

198

When a lesser part is an aliquot part of a greater taken before, divide the amount or quotient of the greater, by te denominator of the less, and so will the same quotient be found as by dividing the quantity as

last. Application.

57. How much is the amount of 4563 cobbs, at 4s. 9d. piece? Answ. 1083l. 148. 3d.

58. What must I give for 127 yards of cloth, at 99. Bld.? · Answ. 617. 12s. 114d

63. At 19s. 112d. Cut. what cost 95Cwt. ?

Answ. 941. 18s. 04d. =

64. At 2s. 8

piece. what come 1784 to?

Answ. 2411, 11s. 8d.

2. Of a Shilling.

Divide the aliquant parts into several aliquot parts and proceed as before; only the sum will be shillings, &c. which must there fore be div.ded by 20 to give the answer in pounds.