Thus 162 l. 18 s.

3258 s. and 4 s. 6 d. = 54 d. Then 54 13258: 724 the Answer.

:

Quest. 2. How many Saragofa Ducats, of 5 s. 6 d. the Ducat, may be had for 275 Bergonia Ducats, at 4 s. 4 d. the Piece? Answer 216 and 3 s. 8 d. over.

Thus 5 s. 6 d. 66 d. and 4 s. 4 d. 52 d.

Then 275 × 52 = 14300 d. 275 Ducats.

Confequently 66) 14300 (2163 the Anfwer required.

Queft. 3. A Traveller would change 233 l. 16 s. 8 d. Sterling Money; for Venice Ducats at 4 s. 9 1⁄2 d. per Ducat; How many Ducats must he have? Answer 976 Ducats. Thus 4 s. 9 d. 57,5 d. and 233. 16 s. 8 d. Then 57,5 d.) 56120 d. (976 the Answer required.

56120 d.

6 d.

Quest. 4. A Cashier hath received 759 Ducats, at 7 s. per Ducat; And 579 Dollars at 4 s. 8 d. per Dollar: Which he would exchange for Flemish Marks at 14 s. 3 d. per Piece: How many ought he to have?

Answer 589 Marks, and 15 d. over.

For 7 s. 6 d. 90 d. and 4 s. 8 d. 56 d.

=

Then {759x90=68310 d. the Value of the Ducats. 579 × 5632424 d. the Value of the Dollars. their Sum

And 14 s. 3 d.

100734 d.

171 d. the Flemish Mark in Pence. Confequently 171) 100734 (589 &c. the Anfwer required.

Queft. 5. A Bill of Exchange was accepted at London for the Payment of 400 1. Sterling, for the like Value delivered in Amfterdam, at 11. 13 s. 6 d. for 1 l. Sterling; How much Money was delivered at Amfterdam?

Anfwer 670 1. Flemish.

For 1 l. 240 d. and 1 l. 13 s. 6 d. = 402 d.

Then 240 402 :: 400: 670 the Answer required.

Queft. 6. When the Exchange from Antwerp to London'is at 11. 4 s. 7 d. Flemish, for 11. Sterling; How many Pounds Sterling must be paid at London; to ballance 2361. Flemish at Antwerp.

Answer 1921. Sterling.

Thus II. 4 s. 7 d. 295 d. and I = 240 d.
Then 295: 240:: 236: 192 the Answer.

P 2

Queft.

Queft. 7. A Merchant delivered at London 120 l. Sterling to receive 1471. Flemish in Amfterdam; How much was 1 1, Sterling valued at, in Flemish Money.

Answer 11. 4 s. 6 d.

Thus 120: 147 :: 240 d. : 294 d. = 1 l. 4 s. 6 d. &c.

Quest. 8. A Factor hath fold Goods at Cadiz for 1468 Pieces of Eight, valued at 4 s. 6d. Sterling per Piece; How much Sterling Money do thofe Pieces of Eight amount to?

Answer 3334. 7 s. 2 d.

Thus, if 154,5 d. then 1468 x 54,5 83006 d. &c.

Quest. 9. A Traveller would have an equal Number of Crowns at 5 s. 6 d. per Crown; and Dollars at 4 s. 5 d. per Piece; How many of each fort may he have for 309 1. 8s.?

Thus 309 1.8s.=74256 d.

And 5 s. 6d. + 4 s. 5 d. 119 d.

Anfwer 624 of each.

Then 119) 74256 (624 the Anfwer required.

Quest. 10. Suppose I would exchange 527. 17 s. 6 d. for Dollars at 4 s. 6d. a Piece, Ducats at 5 s. 8 d. a Piece, and Crowns at 6s. 1 d. a Piece; and would have 2 Dollars for I Ducat, and Dollars for 2 Crowns. How many of each fort muft I have?

3

Answer 927 Dollars, 463 Ducats, and 618 Crowns.

And 126690 d. — 527 l. 17 s. 6 d.

Now if the Crowns, Dollars, and Ducats were to be equal in Number; then 73+54+68 muft have been the Divifor, by which 126690' muft have been divided, and the Quotient would have been, the Anfwer to the Queftion. As in the laft Example.

But here inftead of their Sum, fuch Parts of them must be taken as are affigned or limited by the Queftion; that fo the Number of fome one of them may be found,

2 Dollars for 1 Ducat, and

And because there must be {3 Dollars for 2 Crowns,

Therefore it will be of a Ducat for one Dollar, and of a

Crown for one Dollar,

Confequently,

Confequently, 54+ : +3 of 73=1363, or 4 will be the Divifor to find the Number of Dollars.

Thus) 126690 (927 the Number of Dollars.
Then of 927463 is the Number of Ducats.
And of 927 618 is the Number of Crowns.

=

Or if you pleafe you may form Divifors to find either the Ducats or Crowns firft: For if it be 2 Dollars for I Ducat, and 3 Dollars for 2 Crowns, as before;

Then will 6 Dollars be for 3 Ducats, and 6 Dollars for 4 Crowns.

Therefore, {

Confequently,

2 of a Dollar

of a Ducat

} will be for

will be for 1 Crown.

of 54: + of 68:+73 Divifor to find the Crowns firft, &c.

205 will be the

Queft. 11. A Cashier is to receive 500 l. He is offered Crowns at 6 s. 1 d. per Crown, which are worth but 6.s.. Or he may have Dollars at 4 s.,5 d. the Piece, which are worth but 4 s. 4 d. Which of these fhall he receive to have the leaft Lofs? And how much will he lose in the Payment?

SI I Crown=72 d. according to the true Values.
Dollard.according

I

{

I Crown = 73,5 d.
I Dollar 53,0 d.

}

the advanced Values.

Now to find which will be the leaft Lofs; find what the advanced Value of a Dollar ought to be in Proportion to that of I Crown.

Thus 72: 73,5:52:53,083 &c. But he may have Dollars at 53 d. per Piece, therefore the Payment in Dollars will be the leaft Lofs; viz. 53 is less than 53,083 &c.

Next, to find what the whole Lofs will be by receiving Dollars. Because the 500 1.120000 d. is advanced as much above the true Value, as 53 d. is above 52 d. therefore fay, If 53 d. advance 1 d. 53 d.-52 d.; what will 120000 d. advance? i. e.

=

53 d. 1 d. :: 120000 d.: 2264 d. = 9 1. 8 s. 4 d. the Lofs.

Quest. 12. Suppofe I exchange 41 10s. 10 d. for 11 Crowns and 7 Dollars; and at another Time I have 4 Crowns and 3 Dollars for 1. 15 s. each being of the fame Value with the firft. What is the Value of a Crown, and of a Dollar?

First 11 Crowns +7 Dollars
Second 2 Crowns + 3 Dollars

1090 d.

}

420 d. by the Queftion.

Then in order to find the Value of 1 Crown, you must cast off of the fame Number; Thus,

the Dollars by making them 33 Crowns+21 Dollars 28 Crowns +21 Dollars Then 5 Crowns

3270 d. the first multipl. with 3.
2940 d. the second multipl. with 7.
330 d. being the Difference.
s. 6 d. is the Value of 1 Crown.

264 d. = 156 d.

4 s. 4 d. the Value of 1 Dollar.

WE

CHAP IX.

of Alligation.

HEN it is required to mix feveral Sorts of Ingredients together; as different Sorts of Corn, Wines, Wool, Spices, or Metals; or to compofe Medicines, &c. the Method of proportioning fuch Mixtures, is called the Rule of Ailigation; and is divided into two Parts or Branches; called Medial and Alternate.

Sect. 1. Of Alligation Medial.

•ALligation Medial, is that by which the Mean Rate or Price

of any Mixture is found, when the particular Quantities of the Mixtures and Rates are given; and is thus performed." Firft find the Sum of all the Quantities propofed to be mixed ? And alfo the Sum of all their particular Rates.

Rule.

Then the Proportion will be,

As the Sum of all the Quantities: Is to the Sum of all their
Rates: So is any Part of the Mixture: To the Mean
Rate or Price of that Part.

Queft. 1. Suppofe 15 Bufhels of Wheat at 5 s. the Bufhel, and 12 Bushels of Rye at 3 s. 6 d. the Bushel, were mixed together;

What

What is the Mean Rate or Price, it may be fold for a Bufhel, without Lofs or Gain?

This Queftion prepared as directed above will stand

Thus

15 Bufhels of Wheat at 5 s. per Bushel, comes to 900 d. 12 Bushels of Rye at 3 s. 6 d. each, comes to 504 d. 27= their Sum. And their total Value 1404 d. Then 27 Bufhels: 1404 d. :: 1 Bufhel: 52 d. 4 s, 4 d. the Answer required.

Quest. 2. A Grocer mixeth 36 Pounds of Tobacco, worth 1's. 6 d. a Pound, with 12 Pounds of another Sort at 2 s. a Pound, and 12 Pounds of a third Sort at I s. 10 d. the Pound. How may he fell the Mixture per Pound?

Then 60 lb 1200 d.: 1 lb: 20 d. = 1 s. 8 d. the Anfwer required.

Queft. 3. A Vintner mixeth 31 Gallons and a half of Malaga Sack worth 7 s. 6 d. the Gallon; with 18 Gallons of Canary at 6 s. 9 d. the Gallon; 13 Gallons and a half of Sherry at 5 s. the Gallon; and 27 Gallons of White Wine at 4 s. 3 d. the Gallon It is required to find what one Gallon of this Mixture is worth.

90=the Number of Gal. Their Value = 6480 Then 90: 6480:: 1 : 72 d. 6 s. the Rate or Price of one Gallon, as was required.

The Proof of all Operations in thefe Sorts of Mixtures, is done by comparing the Value of all the Mixture (being fold at the Mean Rate) with the total Value of all the particular Quantities, fuppofing they had been fold at their respective Rates unmixed; if thofe Sums are equal, e Work is true.

Sect.