The merchants mappe of commerce wherein, the universall manner and matter of trade, is compendiously handled. The standerd and currant coines of sundry princes, observed. The reall and imaginary coines of accompts and exchanges, expressed. The naturall and artificiall commodities of all countries for transportation declared. The weights and measures of all eminent cities and tovvnes of traffique, collected and reduced one into another; and all to the meridian of commerce practised in the famous citie of London. By Lewes Roberts, merchant. Necessary for all such as shall be imployed in the publique affaires of princes in forreigne parts; for all gentlemen and others that travell abroad for delight or pleasure, and for all merchants or their factors that exercise the art of merchandizing in any part of the habitable world.

CAHP. CCCCL.

Of the abreviation of Division and Multiplication af∣ter the Italian and forraine manner and methode.

FOr as much as I have in many parts of this particular Tract of Exchanges followed the arithmeticall me∣thod * 1.1 & manner of those rules practised in the calcula∣tion of these exchanges by the Bankers and Exchan∣gers of Italy, it will be here needfull for the better in∣lightning of the same, & the easier casting up & calculation thereof, that I shew how the Italian Brokers and Exchangers do abreviate their labour, and shorten their taske therein, and the rather I have presumed to adde the same here, and in this place, partly in regard that I have not found it published by any of our English Arethme∣ticians, but principally to shew the learner the wayes how the same are there wrought and arethmetically calculated.

It is generally confest by all Arethmetictans that the whole art of Arethmetick depends upon five principall rules, now common∣ly in all countries received and taught, that is, by Numeration, Ad∣dition, Subtraction, Multiplication, and Division, and that no one proposed question in Arethmetick can be perfected without the help of some of these, for the three former I find not any disagree∣ment in the common received manner by them and us, and there∣fore I will omitt to speak any thing thereof; but of the two later, whereby is observed that most rules and questions of all exchanges are perfected and performed, I will here insist upon, induced princi∣pally as I sayd before to inlighten thereby the preceding examples that I have handled in the calculatians of the exchanges before mentioned.

I will then in the first place contrary to the custome of our Eng∣lish Masters in this Science, begin with that part of Arethmetick which wee call Division, and by an example or two of the working thereof explaine the same to such as either shall bee desirous to

learne it, or such as shall desire to make use of these before menti∣oned tables.

A certaine marchant then bought 46 clothes, which cost him 673 l. and desireth by a briefe way to know what one cloth doth * 1.2 stand him in, to do which I dispose of the question after the man∣ner of the rule of three, and say, If 46 Clothes cost 673 l. how much doth the Cloth cost.

Now for as much as it would prove to be too difficult, at first sight after the cōmon manner, to find how often 46 the divisor is found in 673, it will be more facile and commodious, to take it after their method thus, take then the first figure which is 4 and see how often the same is included in the figure 6 which is once, the which 1 I write then under the 〈◊〉〈◊〉 drawing a line between them, & then multiply it by the whole divisor 〈◊〉〈◊〉, beginning at 6, saying once 6 is 6, & next comming to the sum that is to be divided 673 I chuse the second figure 7 from whence I take 6 and there remaines one, which I place under the said 7, and returning againe to the divisor, I multiply 1 by 4 which giveth 4, which I deduct from the other figure 6, of the summe to be divided, and there remaines 2, the which I write under the 6, so that 46 taken by this meanes out of 67 there 〈◊〉〈◊〉 •…•…1, from whence I proceed and put this before the figure 3 remayning, which thereby makes 213, for the summe that now remaynes to be divided by 46, saying in 21 how many times 4, which cannot be but 4 times, for in taking 5 there will remaine but 〈◊〉〈◊〉 which with the following figure doth make 13, (the which number cannot pay 5 times 6, and for this cause I can take but 4,) multiplying the divisor as at first, saying (beginning alwayes by the last figure of the divisor) 4 times 6 is 22, and taking the last figure 3 from the summe to be divided 213, the which for payment of 24 I borrow 3 tenns, which I beare in mind, and say 24 from 33 there •…•…sts 9 the which I place under the 3 and then come to multiply the other figure 4 of the divisor by 4 and it makes 16, which with the 3 tenns borne in minde, makes 19 which must be deducted from the sume to be divided 21 so there will rest 2 the which I place un∣•…•…der 1 as by the example appeareth more at large.

So that 673 l. divided by 46 Clothes, the quotient giveth 14 l. and the rest is 29 l. which now is to be devided by 46, which cannot be done, and therefore the same to be reduced to shillings which mul∣tiplied by 20 comes to 5•…•…0 sh: which must now be divided by 46 in the manner before shewed, saying how many times 4, in 5 which is once, the which I write in the quotient at the side of 14 l. pro∣ceeding from the first divison, multiplying it by 6 and it giveth 6, which taken from 8 the rest is 2, which I put under the 8, and mul∣tiply the other figure of the divisor 4 by 1 which giveth 4 taken from 5 there rests 1, then 46 substracted from 58 there rests 12, right with which I put the other figure 0 resting of the summe to

be divided and returne to say, how many times 4 in 12, the which I can take but 2 and I place it in the quotient and multiply 〈◊〉〈◊〉 by the last figure of the devisor, saying 2 times 6 is 12 which I deduct from 120, the which to do I say (borrowing 2 tenns which I bare in mind) 12 from 20 rests 8 which I place under the 0 and multiply the other figure of the divisor 4 by 〈◊〉〈◊〉 making 8 with the 2 borne in mind, comes to be 10, taken from 12 there rests 2, so that •…•…0 sh. divided by 46 the product is 12 shill. and there remayneth yet 28 shill. which must be brought into 〈◊〉〈◊〉, multiplyed by 12 and it makes 336 the which must be divided by 46, saying in 33 how ma∣ny times 4, which is 7 times, the which I place in the quotient by the shillings, multiplying 7 by 〈◊〉〈◊〉, which makes 42 from 46 there rests 4, the which I place under the 6, and keepe 4 in mind borrowed ad∣ding them with 4 times 7 they make 32, which deducted from 33, there rests 1, the which I place under the 3, so that 336 divided by 46 the perduct giveth 7 and there rests 14 d. to divide which is a thing of a small valew.

So that if 46 peeces of cloth cost 673 l. the one will cost 14. l. 12. shill. 7. d. as may be seene by the example here under wrought. 〈 math 〉〈 math 〉

To shew the brevity of this manner of dividing, I will shew * 1.3 here another example, which cannot without much difficulty be performed by the common manner of divison in cancelling the figures, and yet is very easily and compendiously performed •…•…is way, by observing the order which is before prescribed, and there∣fore to avoyd prolixity I shall not need here to put downe any particular explication, the example shall be thus then to, divide 19999100007 by 99999, which by the product doth give 199993 without any remaynder as shall appeare by the working here un∣derneath. 〈 math 〉〈 math 〉

Division which is wrought by the rule of practise, is done in this manner by the help of the parts found therein, as for example, if 72 * 1.4 peeces of sarges cost 169. l. 12 shil. how much will the peece stand in, then dividing by 72 I find first the parts thereof, and observe that 8 times 9 makes 72, I take then the 〈◊〉〈◊〉 of the summe to be divided, saying the eighth part of 16 is 2, which I place under a line drawne, and the 〈◊〉〈◊〉 of 9 is 1, there remains one pound which is 20 shil. which with the 12 makes 32, the 〈◊〉〈◊〉 whereof is 4, so that the eighth of the said 169 l. 12 shil. is 21 l. 4 shil. of which number I take the 1/9 (which shall be the price of the peece) in this manner, saying, the 1/9 of 21 is 2, the rest is 3 l. which is 60 shil. and with the 4 maketh 64 shil. of which the 1/9 is 7, then there rests 1, which is 12 pence, and the 1/9 of 12 is 1, so that the ninth part of 21 l. 4 shil. is 2 l. 7 shil. 1 d. the price of the peece as by this example is shewed, 〈 math 〉〈 math 〉

But when it happens that any broken numbers fall in the divisor, the divisor and the summe to be divided, must then be reduced to * 1.5 one and the selfe same denominator, as for example, If 13 〈◊〉〈◊〉 peeces should cast 264 l. 17 shil. 6 d. what would the peece stand in? to doe which I reduce into halfes the peeces 13 〈◊〉〈◊〉 multiplying the same by 2 making 27 halfes, doing the same with the summe to be divided, multiplying it by 2 which comes to be l. 529. 15, which to be divi∣ded by 27, must be considered that 3 times 9 is 27, therefore must be taken 〈◊〉〈◊〉 and 1/9 of the said third in this manner saying 〈◊〉〈◊〉 of 5 is 1, of 22 is 7 and of 19 is 6, and there remaines 1 pound which is 20 shil. which with the 15 makes 35, the 〈◊〉〈◊〉 of which is 11 and there rests 2 shil. which are 24 pence, the 〈◊〉〈◊〉 whereof is 8, and afterward taking the of 〈◊〉〈◊〉 the said 〈◊〉〈◊〉 saying, the 〈◊〉〈◊〉 of 17 is 1, and of 86 is 9, and there •…•…s 5 l. which with the 11 shil. is 111 shil. the 1/9 whereof is 12, then rests 3 shil. which with the 8 d remaining is 44 d, the 〈◊〉〈◊〉 whereof is 4, so that the product of the said 1/9 giveth 19 l. 12 shil. 4 d, the value of the said peece, as by example, 〈 math 〉〈 math 〉

Againe, at 34 l. 16 shil. the 21 〈◊〉〈◊〉 yards, how much will the yard amount unto, doe this as the preceding rule, putting the yard into * 1.6 thirds, in multiplying them by 3 they make 64 for divisor to 34 l. 16

also multiplied by 3 which make 104 l. 8 shil. which to divide by 64, is to be considered that 8 times 8 is 64, and therefore the ⅛ of an eight is the price of a yard, as example, 〈 math 〉〈 math 〉

Many other divisions are resolved in the same manner as the pre∣ceding, which I willingly here omit, and referre them to the oc∣currences of traffique that shall happen herein, and now I will pro∣ceed to Multiplication abreviated, by which two rules both the golden Rule of three, and many other in Arithmetique are wrought and performed, commodious and necessary to this Tract of Exchan∣ges and this Map of Commerce, as being indeed the proper rules, by which the Exchanges in this book are cast up and calculated.

The method that hath beene shewed in the former Division, may in some sort serve also in multiplication in this manner, suppose you * 1.7 were to multiply 56 yards by 4 l. 18 shil. 9 d. you must consider that 56 is composed of 7 times 8, and therefore you must multiply the said 4. 18. 9. by 7, and its product by 8, beginning with the pence, and saying 7 times 9 is 63, I write 3 pence, and retaine 5 shill. which I ad with 7 times 8 which make 61, write then 1 and retain 6 which added to 1 times 7 makes 13 which is 6 l. 10 shil. and following the common method of addition, I put downe one ten, and retaine 6 l. which I add with 4 times 7, and they make 34 l. the which product I multiply againe by 8, beginning to multiply by the pence which are with the pounds, and then by the shil. calculating for 12 d, one shill. and for 20 shill. 1 pound they then make 276 l. 10 shil. for the value of 56 yards as shall be more plainly demonstrated by this Example following. 〈 math 〉〈 math 〉

Many other questions may be answered as the above sayd, but yet note, that to multiply by an uneven number, such as is 31, 43, * 1.8 and the like, then do in this manner, posito I demand at 5l. 9. sh. 3. d. the yard, what will 43 yards come unto, now for as much as 43, hath no dividable parts I take 42, multiplying it by 6 and by 7, as hath beene shewed, and for the yard that doth remaine I adde to the last multiplication 5. l. 9. 3. d. which is the cost of 1 yard and it makes 234 l. 17. 9. d. the cost of 43 yards as may be observed by the following example. 〈 math 〉〈 math 〉

But when there is any broken number in the yards or peeces, doc * 1.9 thus by example, at l. 7. 14. 6 the peece, what will 81½ cost, then for 81 I multiply by 9 the cost of the peece, and its product againe by 9 because that 9 times 9 is 81 and I find l. 625. 14. 6 for the va∣lew of the said 81 peeces, and for the ½ peece I take the 〈◊〉〈◊〉 of 7. l. 14. 6. d. and adding it thereto the same comes to be l. 629. 11. sh. 9. d. and so much the 81½ cost, example. 〈 math 〉〈 math 〉

But for as much as this may seeme difficult, I will here note an∣other * 1.10 way of Multiplication abreviated, serving as well in exchan∣ges or in marchandising posito; I would know what comes 154 yards unto, at 56 shillings the yard, to do this multiply the sayd yards, by the halfe of the sayd mony which is 28 sh. and in adding its pro∣duct, double the last figure taking that for so many shill. and the rest for pounds as doth appeare by this example following, which I adde in this manner, saying 2. 4. and 9 make 15, and after the ordinary manner, you must set downe 5, and beare 1 ten, but in this me∣thode,

you must double it, setting downe 10 for 5. the which doub∣led you must hold as so many shillings and so proceeding in the ad∣dition of the rest, and adding the tenth borne of 15, it will come to l. 431. 4. sh. the valew of 154 yards, and this note is to be obser∣ved in all other questions of this nature, as by example doth ap∣peare. 〈 math 〉〈 math 〉

There is yet another briefe way of Multiplication, used in France * 1.11 and many parts beyond the seas, which is done by taking the parts of 10 or of 100 in this manner, I would multiply 113 yards by 1¼ I note what part 1¼ is in 10 and find it to be ⅛ therefore is 113 yards to be multiplyed by 10, or else more briefe by adding an 0 and in taking the 〈◊〉〈◊〉 which shall be the valew of the said 113 yards, and for to multiply by 1 〈◊〉〈◊〉 you must take the 〈◊〉〈◊〉 of the summe to be mul∣tiplyed, after you have added thereunto an o because that 1 〈◊〉〈◊〉 is the 〈◊〉〈◊〉 of 10, and for to multiply by 3 〈◊〉〈◊〉 you must adde an o and take 〈◊〉〈◊〉 because that 3⅓ is the 〈◊〉〈◊〉 of 10 and so in many others, in taking alwayes the parts of 10, and note that the same may bee done in taking the parts of 100, as to multiply 137 yards by 8 〈◊〉〈◊〉 you must adde two oo to the summe, then take 〈◊〉〈◊〉, because that 8 〈◊〉〈◊〉 is the 〈◊〉〈◊〉, part of 100 and for to multiply by 12 〈◊〉〈◊〉, you must adde two oo and take the ⅛ because that the 〈◊〉〈◊〉 of 100 is 12 〈◊〉〈◊〉 as may be seene by these following examples. 〈 math 〉〈 math 〉

Againe at 3 shill: the pound, what will the 100 l. come unto? to * 1.12 doe this in briefe a cipher is to be added to the cost of the pound

which is 3 sh. and it makes 30 of which summe take the ½ and it makes 15 l. which makes the cost of the hundred, and so for others by these examples following. 〈 math 〉〈 math 〉

Againe at 3 d. the pound, I would know how much 100 l. comes * 1.13 unto, multiply the pence (which the pound is worth) by 5, and out of its product take 1/12 which shall be the cost of the quintall and to find the cost of the pound, you must multiply the valew of the hun∣dred by 12, and the ⅕ of the product is the cost of the pound as fol∣loweth by these examples. 〈 math 〉〈 math 〉

But I have wandred too farre, and proceeded farther in this subject than I intended, therefore here will conclude both the cal∣culations of Exchanges and these methods of abroviating the rules of Division and Multiplication, referring what is here by me omitted in both the sayd subjects to the ingenuous hand and head of the mysterious Exchanger.

Notes

• * 1.1

  Of Division and Multi∣plication abreviated after the I∣talian man∣ner.
• * 1.2

  Division a∣breviated in calculations of accounts.
• * 1.3

  Another ex∣ample.
• * 1.4

  Another method of dividing by rule of pra∣ctise.
• * 1.5

  Note ano∣ther ex∣ample.
• * 1.6

  Another.
• * 1.7

  Multiplica∣tion abrevi∣ated.
• * 1.8

  Another Example.
• * 1.9

  Another Ex-ample.
• * 1.10

  Another way of Mul∣tiplication abreviated.
• * 1.11

  Another way of abre∣viated Mul∣tiplication.
• * 1.12

  Another ex∣ample.
• * 1.13

  Another.