This may serve likewise for Amsterdam, Hamburgh, and Venice; but you must take half of the deniers lubs, which are given at Hamburgh for a ducat, and instead of Paris, you must read from Venice.

But if the change from Lisbon on Lyons exceed 567 reis, take instead of, and the fixed number will be 3479.

That is, whatever French Livres are given or received for a pistole of Spain must be reduced into sols, and the quarter part taken.

There might be chosen many other places, but to be short, we have taken no more than two particular cases, which we have in the 7th and 8th propositions.

Genoa, Venice, Florence, Leghorn, Novi, Milan, Amsterdam, and London.

For the provision at per cent. the fixed number is 144; and at per cent. 214.

No. II. is for London; No. III. is for Hamburgh; if the exchange is found in the 8ths and 16ths: No. I. is for all other places; and for Hamburgh when the exchange

is in shillings, shillings, and shillings. No. IV. serves to shew the numbers that must be added together, viz. all those that are found on the same side.

The 5th and 6th are for profit and loss. If it is found that the sum of the addition of the side in which to find that given is less than the other sum of the side where what is received is, it must be sought for in the table of profit, No. V. and when there is a loss, in that of No. VI. And that the use which may be made of these tables may the easier be comprehended, I shall here add some examples.

First Example.

A. of Amsterdam remits on London to B. at 34s. 5 groots, what B. remits for the account of A. to Cadiz at 49 d. sterling per dollar. If the merchant at Cadiz remits the produce on Amsterdam at 1214 grts. of Holland per ducat of 375 maravedis; it is demanded how much A. hath gained or lost exclusive of the charges?

Now the 2d and 3d terms multiplied, and divided by the first in the order they now stand, will be expressed as follows:

Now the difference between 34s. 5 gts. † and 425 gts. is 11 gts. therefore

111 gts.

34s. 5 gts.

23

8
X100=22×100=2 nearly.

827

You may now express the last three terms divided by the first two thus.

240 × 243 × 272x4

199 × 375×2

425, as before.

Second Example.

A. of Amsterdam remits to B. of Dantzic, gross, the which B. remits on Hamburgh at burgh remits what it amounts to, to A. at 33 is demanded how much per cent. A. has gained or lost, omitting the charges.

at 276 gross of Poland, for one livre of 1154 gross for 48 shillings lubs; if Hamstivers per daalder of two marks lubs: it

This ordered according to the foregoing example will produce 118 stivers, which taken from the 120 stivers first given, there remains 1

stivers, therefore

By the Double Rule of Three.

Gross
276

Stivers of Amsterd.

33+

S. L.

48

The fractional terms being reduced into improper fractions, as these in the first example, the operation then will be entirely similar to the last in the said example, and gives 118 stivers, as before.

VOL. I,

4 N

Third Example.

Two persons A. and B. at Paris, have occasion for money at Cadiz; A. remits directly, and gives 18 livres 3 sols per Spanish pistole; B. chuses the way of Holland, and orders to be remitted him from Amsterdam at 1214 groots for a ducat of 375 maravedis; Amsterdam reckons per cent. charges, and draws for his reimbursement at the rate of 56 groots per French crown of 60 sols; it is demanded which of the two methods proved most advantageous.

Answer; his who remitted directly.

-60,

By reflecting on the nature of the question, it appears, that what Amsterdam reckons for charges may be considered to increase the number of sols so much more than B. would otherwise have paid for the 375 maravedis; therefore first say, if 100or if 106, or if 5-10 -3 must give, which B. must pay at Amsterdam for his charges for every 60 sols in the value of the 375 maravedis. But instead of finding the sols B. must pay, excluding the charges, and then computing the charges, and adding them to the sols last found for B.'s whole payment, you may by parity of reason

say,

Groots
As 56

Sols 603

Groots

121 to 129 sols paid by B. for the maravedis in a pistole Sols

a ducat. Lastly, to compare whether A. or B. has succeeded best, say,

£. s.

If 18-3

-1088

-129% will give 389 maravedis, which B. would have got instead of 375, had he changed as A. did; therefore it is manifest, that in receiving only 375 he had less than A. for the same sum of Paris money by 14 maravedis; and to make a calculate per cent. it will

Mar.

be as 2375

Mar. -to 14

Fourth Example.

100 to 3, the answer.

A merchant of Hamburgh orders us to draw for his account on Dantzic, at 270 gross of Poland for 1 livre de gross, and to remit the amount on London at 35 schillings per pound sterling, or at other rates' which may be more advantageous for him, provided he can draw on Dantzic at 261 gross of Poland; it is demanded at how much he ought to remit to follow the last order? Answer, at 36 schillings 24 groots.