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several antecedents have to their consequents, the proportaon between the first antecedent end the last consequent is discovered, as well as the proportion between the others in their several respects.

NOTE.-This rule may generally be abridged by cancelling equal quantities, or terms that happen to be the same in both columns: and it may be proved by as many statings in the Single Rule of Three as the nature of the question may require.

CASE I. When it is required to find how many of the first sort of coin, weight or measure, mentioned in the question, are equal to a given quantity of the last.

RULE. Place the numbers alternately, beginning at the left hand, and let the last number stand on the left hand col. umn; then multiply the left hand column continually for a dividend, and the right hand for a divisor, and the quotient will be the answer.

EXAMPLES. 1. II 100 lb. English make 95 lb. Flemish, and 19 The Flemish 25 lb. at Bologna; how many pounds English are equal to 50 lb. at Bologna ? lb.

U. 100 Eng.=95 Flemish. 19 Fle. 25 Bologna ?

50 Bologna. Then 95X25=2375 the divisor. 95000 dividend, and 2875)95000(40 Ans.

2. If 40 lb. at New-York make 48 lb. at Antwerp, and so lb. at Antwerp make 36 lb. at Leghorn ; how many H. at New-York are equal to 144 lb. at Leghorn ?

Ans. 100lb. 3. If 70 braces at Venice be equal to 75 braces at Leg. horn, and 7 braces at Leghorn be equal to 4. Airerican yards ; how many braces at Venice are equal to 64 American yards ?"

Ans. 10445 CASE II. When it is required to find how many of the last sort coin, weight or measure, mentioned in the question, aro nel toa gran quantity of the frete

RULE. Place the numbers alternately, beginning at the left hand, and let the last number stand on the right hand, then multiply the first row for a divisor, and the second for a dividend.

EXAMPLES 1. If 24 lb. at New-London make 20 lb. at Amsterdam, and 50 lb. at Amsterdam 60 lb. at Paris; how many at Paris are equal to 40 at New-London ?

Left. Right.
24 - 20 20 X 60 X 40 = 48000
50 = 60

= 40 Ans. 40 24 x 50 = 1200 2. If 50 lb. at New-York make 45 at Amsterdam, and 80 lb. at Amsterdam make 103 at Dantzic; how many lk. at Dantzic are equal to 240 at N. York: Ans. 2781

3. If 20 braces at Leghorn be equal to 11 vares at Lisbon, and 40 vares at Lisbon to 80 braces at Lucca bow many braces at Lucca are equal to 100 braces at Leghorn

Ans. 110.

EXCHANGE. BY this rule merchants know what sum of money ought to be received in one country, for any sum of different specie paid in another, according to the given course of exchange.

To reduce the monies of foreign nations to that of the United States, you may consult the following

TABLE: Shewing the value of the monies of account, of foreign

nations, estimated in Federal Money.* &cts. Pound Sterling of Great-Britain,

4 44 Pound Sterling of Ireland,

4 10 Livre of France,

0 181 Guilder or Florin of the U. Netherlands, O 39 Mark Banco of Hamburgh, Rix Dollar of Denmark,

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Rial Plato of Spain,

O 10 Milrea of Portugal,

1 24 Tale of China,

1 48 Pagoda of India,

1 94 Rupee of Bengal,

055) I. OF GREAT BRITAIN.

EXAMPLES. t. In 45l. 10s. sterling, how many dollars and cents ?

A pound sterling being=444 cents, Therefore- As ll. : 444cts. : : 45,51. : 20202cts. Ana

2. In 500 dollars how many pounds sterling? Aus 444cts. : 11. : : 50000cts. • 1121. 128. 3d. -- Ans..

II. OF IRELAND.

EXAMPLES. . In 901. 108. 6d. Irish inoney, how many cents :

ll. Irish=410cts.

£. cts. fo. cts. S cta Therefore--As 1 : 410 : : 90,525 : 3711515371, 154

2. In 168 dols. 10 cts. how many pounds Irish ?
As 410cts. : 1l. : : 16810cts. : £41 Irish. Ans.

III. OF FRANCE,
Accounts are kept in livres, sols and deniera.
S 12 deniers, or pence, makc 1 sol, or shilling,
220 sols, or shillings, 1 livre, or pound.

EXAM"LES. 1. In 250 livres, 8 sols, how many dollars and cents:

1 livre of France=183 cts. 'or 185 mills. £. m. £. m. $. ets. m. As 1 : 185 : : 250,4 : 46324=46, 32 4 Ans. 2. Reduce 87 dols. 45 cts. 7 m. into livres of France

mills. biv. mills. liv. so. den. As 185 :1: : 87457 : 472 14 9+ Ans.

IV. OF THE V. NETHERLANDS Accounts are kept here in guilders, stivers, groate and phennings.

s 8 phennings make 1 groat.
3 2 groats - 1 stiver.
( 20 stivers - 1 guilder, or florin.
A guilder is 39 sents, or 390 mille.

EXAMPLES.
Reduce 12A guilders, 14 stivers, into federal money.

Guil. cts. Guil. $ d. c. m. "
As 1 : 39 : : 124,7 : 48, 6 3 S Ans.

mills. G. mills. G.
As 390 : 1 :: 48633 : 124,7 Proof

V. OF HAMBURGH, IN GERMANY. Accounts are kept in Hamburgh in marks, sous and deniers-lubs, and by some in rix dollars.

( 12 deniers-lubs make 1 sous-lubs. 3 16 sous-lubs,

1 mark-lubs. [3 mark-lubs, - 1 rix-dollar. Note.-A mark is = S3} cts. or just of a dollar.

RULE.
Divide the marks by 3, the quotient will be dollars.

EXAMPLES.
Reduce 641 marks, 8 sous, to tederal money.

3)641,5

8213,853 Ans. But to reduce Federal Money into Marks, multiply the given sum by 3, &c.

EXAMPLES
Reduce 121 dollars, 90 cts. into marks banco.

121,90

365,70=365 marks 11 sous, 2,4 den. Ans.

VI. OF SPAIN.
Accounts are kept in Spain in piastres, rials and marvadies.

$ 34 marvadies of plate make 1 rial of plate.
? 8 rials ot plate - 1 piastre or piece of E.

To reduce rials of plate to Federal Money. Since a rial of plate is = 10 cents, or 1 dime, you need only call tne rials so many dimes, and it is done.

EXAMPLES. 485 rials=485 dimes -48 dols. 50 cts. &e..

But to reduce cents into rials of plate, divide by 10'Thus, 845 cents +10=84,5=84 rials, 17 marvadies, &

VII. OF PORTUGAL Accounts are kept throughout this kingdom in mihreas, ind reas, reckoning 1000 reas to a milrea.

Note.--A miirea is = 124 cents; therefore to reluce nilreas into Federal Money, multiply by 124, and the product will be cents, and decimals of a cent.

EXAMPLES.
L In 340 milreas how many cents ?

340x124342160 cents,=8421, 60cts, Ans. 2. In 211 milreas, 48 rcas, how many cents ? Note. When the reas are less than 100, place a cy: wher before them.-Thus 211,048 x 12426169,952cts. or 261 dols. 69 cts. 9 mills. + Ans.

But to reduce cents into milreas, divide them by 184, and if decimals arise you must carry on the quotient as far as three decimal places; then the whole numbers thereof will be the milreas, and the decimals will be the reas.

EXAMPLES. 1. În 4195 cents, how many milreas ?

4195--124=33,830+or 33 milreas, 330 reas. Ans. 2. In 24 dols. 92 cts. how many milreas of Portugali

Ans. 20 milreas, 096 reas.
VIII. EAST-INDIA MONEY.
To reduce India Money to Federa, vize
rTales of China, multiply with 148
Pagodas of India,

194
(Rupee of Bengal,

EXAMPLES. 1, 17641 Tales of China, how many conts ?

Ars. 94868 2. In 50 Pagodas of Indid, how many cents ?

ins. 9700 3. In 98 Rupeos of Bengal, how many cents ?

Ang. 1189.

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