Arithmetic, Appendix
An Appendix.
Section 1. Of Exchange of the Coins, Weights, and Meaſures of one Countrey, with the Goins, Weights and Meaſures of another Countrey.
TO perform this work, there is nothing required more then the Golden Rule, if firſt the Rate or Proportion between the Coins, Weights, and Meaſures of any two Countries be known which is beſt obteined by experience, rather then taken upon truſt, all that in this place I ſhall do, is onelyonly to inſtruct the ingenious in the manner of Work, and make uſe of ſuch Rates or Proportions as I find ſet down by Mr. Lewis Roberts Merchant, in his Map of Commerce.
Queſtion 1.
How many Riders (each Rider containing 1 l. 1 s. 2 d. 2 q. Sterling) ſhall I receive for 251 l. 6 s. 4 d. 2 q. Sterling?
Facit 237 Riders.
If 1 l. 1 s. 2½ d. give 1 Rider how many Riders ſhall 251 li. 6 s. 4½ d. give?
Here if you reduce your numbers to their leaſt Denominations, or ſet them down in Decimals, and multiply and divide according to the Golden Rule, you ſhall find in your quotient 237, and ſo many Riders ought to be received for 251 l. 6 s. 4 d. 2 q. Sterling.
Queſtion 2.
How many French Crowns (each French Crown being valued at 6 s. Sterling) ſhall I receive for 492 l. 18 s. Sterling?
Facit 1643 French Crowns.
If 6 s. give 1 F.C. what ſhall 492 li. 18 s. give.
Multiply and divide according to the Golden Rule, and you ſhall have in your quotient 1643, and ſo many French Crowns are to be received for 492 l. 18 s. Sterling.
Queſtion 3.
A Merchant delivered at Paris 1643 Crowns of 6 s. Sterling the piece, how many pounds Sterling ought to be received at London?
Anſwer 492 l. 18 s. Sterling.
If 1 Crown give 6 s. what ſhall 1643 Crowns give?
Multiply and divide, and you ſhall have in your quotient 492 l. 18 s. and ſo much Sterling Money ought to be delivered at London for 1643 French Crowns of 6 s. the Crown Sterling.
Queſtion 4.
If 3 yards at London, be 4 Ells at Antwerpe, how many yards at London make 84 Ells at Antwerpe?
| Ells Antwerp | yards London | Ells Ant. |
| 4 | 3 | 84 |
Facit. 63.
And ſo many yards at London, are equal to 84 Ells at Antwerp.
Queſtion 5.
How many yards of London make 27 Ells of Antwerpe, when 100 Ells of Antwerpe make 60 Ells of Lions, and 20 Ells of Lions make 25 yards of London?
The firſt work.
…
75 facit 75
That is 75 yards of London is equal to 100 Ells of Antwerp.
The ſecond work.
…
Queſtion 6.
If 100 li. Sterling be 104 l. 6 s. 4 d. Flemiſh what is one pound Sterling worth?
…
Facit 322 ponce 36/100 of a peny.
Queſtion 7.
How many Ells of Frankford make 42¼ Ells of Vienna in Auſtria, when 35 Ells of Vienna make 24 at Lions; 3 Ells of Lions, 5 Ells of Antwerp, and 100 Ells of Antwerp, 125 Ells at Frankford.
Firſt work.
| Ells Ant. | Ells Frank. | Ells Ant. | ||
| 100 | 1.25 | 5 | 5 | 625 |
Facit 6.25 or 6 Ells and a quarter of Frankford equal to 3 Ells of Lions.
Second Work.
…
Facit 50 Ells of Frankford, equal to 35 Ells of Vienna.
…
Facit 60.35 or 6 5/14 Ells of Frankford, equal to 35 Ells of Vienna.
Thus have I given you a few Examples of Exchanges, I will now inſert ſome few Tables derived from Mr. Lewis Roberts his Map of Commerce afore-ſaid, of the truth of which, I am not a competent Judge, but ſhall leave that to the ſcrutiny of ſuch as have occaſion to trade into Forreign Countries.
A Table ſhewing what one pound of Avoirdupois weight at London, maketh in divers eminent Cities, and other remarkable places.
One pound of Avoirdupois weight at London, makes at
ANtwerpe .9615 lb.
Amſterdam .9 lb.
Abbeville .91 lb.
Ancona 1.282 lb.
Avignon 1.12 lb.
Burdeaux .91 lb.
Burgoyne .91 lb.
Bollonia 1.25 lb.
Bridges .98 lb.
Calabria 1.3698 lb.
Callais 1.07 lb.
Conſtantinople .8474 lb.
Conſtantinople Loder; lb.
Deepe .91 lb.
Danſick 1.16 lb.
Ferrara 1.3333 lb.
Florence 1.282 lb.
Flanders in general 1.06 lb.
Geneva .9345 lb.
Genoa 1.4084 ſuttle lb.
Genoa 1.4285 groſſe lb.
Hamburg .92 lb.
Holland .95 lb.
Lixborne .881 lb.
Lions 1.07 common weight lb.
Lions .98 ſilke weight lb.
Lions .9 cuſtomers weight lb.
Legorn 1.3333 lb.
Millan 1.4285 lb.
Mirandola 1.3333 lb.
Norimberg .88 lb.
Naples 1.4084 lb.
Paris .89 lb.
Prague .83 lb.
Placentia 1.3888 lb.
Rochell 1.12 lb.
Rome 1.27 lb.
Rovan .875 by Vicont lb.
Rovan .9017 common weight lb.
Sivill 1.08 lb.
Tholouſa 1.12 lb.
Turin 1.2195 lb.
Venetia 1.5625 ſuttle lb.
Venetia .9433 groſſe lb.
Vienna .813 lb.
The uſe of the preceding Table.
How much weight at Bollonia, will 655 l. Avoirdupois make?
Look in the Table for Bollonia, and right againſt it you ſhall find 1.25, which ſheweth that one pound Avoirdupois at London is equal to 1.25 l. at Bollonia, Therefore ſay by the Rule of Three:
If 1 l. Avoirdupois give 1.25 l. at Bollonia, what ſhall 655 li. Avoirdupois give? Anſwer 818.75. As by the operation following doth appear.
…
A Table ſhewing what one pound Weight in divers forreign Cities, and remarkable places, maketh at London of Avoirdupois Weight.
One pound weight in ANt werpe makes at London of Avoirdupois weight. 1.04 lb.
One pound weight in Amſterdam makes at London of Avoirdupois weight. 1.1111 lb.
One pound weight in Abbeville makes at London of Avoirdupois weight. 1.0989 lb.
One pound weight in Ancona makes at London of Avoirdupois weight. .78 lb.
One pound weight in Avignon makes at London of Avoirdupois weight. 8928 lb.
One pound weight in Burdeaux makes at London of Avoirdupois weight. 1.0989 lb.
One pound weight in Burgoyne makes at London of Avoirdupois weight. 1.0980 lb.
One pound weight in Bollonia makes at London of Avoirdupois weight. .8 lb.
One pound weight in Bridges makes at London of Avoirdupois weight. 1.0204 lb.
One pound weight in Calabria makes at London of Avoirdupois weight. .73 lb.
One pound weight in Calais makes at London of Avoirdupois weight. .9345 lb.
One pound weight in Deepe makes at London of Avoirdupois weight. 1.0989 lb.
One pound weight in Danſick makes at London of Avoirdupois weight. .862 lb.
One pound weight in Ferrara makes at London of Avoirdupois weight. .75 lb.
One pound weight in Florence makes at London of Avoirdupois weight. .78 lb.
One pound weight in Flanders in general makes at London of Avoirdupois weight. .9433 lb.
One pound weight in Geneva makes at London of Avoirdupois weight. 1.07 lb.
One pound weight in Genoa ſuttle makes at London of Avoirdupois weight. .71 lb.
One pound weight in Genoa groſſe makes at London of Avoirdupois weight. .7 lb.
One pound weight in Hamburg makes at London of Avoirdupois weight. 1.0865 lb.
One pound weight in Holland makes at London of Avoirdupois weight. 1.0526 lb.
One pound weight in Lixborne makes at London of Avoirdupois weight. 1.135 lb.
One pound weight in Lions common weight makes at London of Avoirdupois weight. .9345 lb.
One pound weight in Lions ſilk weight makes at London of Avoirdupois weight. 1.0204 lb.
One pound weight in Lions cuſtom weight makes at London of Avoirdupois weight. 1.1111 lb.
One pound weight in Legorne makes at London of Avoirdupois weight. .75 lb.
One pound weight in Millan makes at London of Avoirdupois weight. .7 lb.
One pound weight in Mirandola makes at London of Avoirdupois weight. .75 lb.
One pound weight in Norimberg makes at London of Avoirdupois weight. 1.136 lb.
One pound weight in Naples makes at London of Avoirdupois weight. .71 lb.
One pound weight in Paris makes at London of Avoirdupois weight. 1.1235 lb.
One pound weight in Prague makes at London of Avoirdupois weight. 1.2048 lb.
One pound weight in Placentia makes at London of Avoirdupois weight. .72 lb.
One pound weight in Rotchel makes at London of Avoirdupois weight. .8928 lb.
One pound weight in Rome makes at London of Avoirdupois weight. .7874 lb.
One pound weight in Rovan by Vicont, makes at London of Avoirdupois weight. 1.1428 lb.
One pound weight in Rovan common weight makes at London of Avoirdupois weight. 1.1089 lb.
One pound weight in Sivil makes at London of Avoirdupois weight. .9259 lb.
One pound weight in Tholouſa makes at London of Avoirdupois weight. .8928 lb.
One pound weight in Turin makes at London of Avoirdupois weight. .82 lb.
One pound weight in Venetia ſuttle, makes at London of Avoirdupois weight. .64 lb.
One pound weight in Venetia groſſe: makes at London of Avoirdupois weight. 1.06 lb.
One pound weight in Vienna makes at London of Avoirdupois weight. 1.23 lb.
The uſe of the foregoing Table.
In 7652 li. weight at Mirandola, how many pound Weight at Avoirdupois.
Look in the Table for Mirandola, and right againſt it you ſhall find .75, which ſheweth that one pound Avoirdupois is equal to the 75 or ¾ of a pound at Mirandola, wherefore ſay by the Rule of Three.
If 1 l. at Mirandola, gives .75 or ¾ of a pound Avoirdupois, what ſhall 7652 l. of Mirandola give? Anſwer 5739, as by the operation doth appear.
…
A Table reducing Engliſh Ells to the Meaſures of divers forreign Cities and remarkable places.
One Ell at London makes at AMſterdam 1.6949 Ells
One Ell at London makes at Antwerpe 1.6666 Ells
One Ell at London makes at Bridges 1.64 Ells
One Ell at London makes at Arras 1.65 Ells
One Ell at London makes at Norimberg 1.74 Ells
One Ell at London makes at Colen 2.08 Ells
One Ell at London makes at Liſle 1.66 Ells
One Ell at London makes at Maſtrich 1.57 Ells
One Ell at London makes at Frankford 2.0866 Ells
One Ell at London makes at Danſick 1.3833 Ells
One Ell at London makes at Vienna 1.45 Aulns
One Ell at London makes at Paris .95 Aulns
One Ell at London makes at Rovan 1.03 Aulns
One Ell at London makes at Lions 1.0166 Aulns
One Ell at London makes at Callais 1.57 Aulns
One Ell at London makes at Venice linnen 1.8 Braces
One Ell at London makes at Venice ſilke 1.96 Braces
One Ell at London makes at Lucques 2. Braces
One Ell at London makes at Florence 2.04 Braces
One Ell at London makes at Milan 2.3 Braces
One Ell at London makes at Legorn 2. Braces
One Ell at London makes at Madera 1.0328 Braces
One Ell at London makes at Iſles 1.0328 Braces
One Ell at London makes at Sivill 1.35 Vares
One Ell at London makes at Lisbone 1. Vares
One Ell at London makes at Caſtillia 1.3875 Vares
One Ell at London makes at Andoluzia 1.4625 Vares
One Ell at London makes at Granado 1.3625 Vares
One Ell at London makes at Genoa 4.8083 Palmes
One Ell at London makes at Saragoſa .55 Canes
One Ell at London makes at Rome .56 Canes
One Ell at London makes at Barſelona .7125 Canes
One Ell at London makes at Valentia 1.2125 Canes
The uſe of this Table.
In 632 Ells at London, how many Braces at Florence?
Look in the Table for Florence, and right againſt it you ſhall find 2.04, which ſheweth that one Ell at London, maketh at Florence 2.204 Braces, wherefore ſay by the Rule of Three.
If one Ell at London, give 2.04 Braces at Florence, how many Braces ſhall 632 Ells give? Anſwer 1289.28, as by the operation following doth appear.
…
A Table reducing the Meaſures of divers forreign Cities and remarkable places, to Engliſh Ells.
One Ell at AMſterdam makes at London .59 Ells
One Ell at Antwerp makes at London .6 Ells
One Ell at Bridges makes at London .6097 Ells
One Ell at Arras makes at London .606 Ells
One Ell at Norimberg makes at London .5474 Ells
One Ell at Colen makes at London .4807 Ells
One Ell at Liſle makes at London .6024 Ells
One Ell at Maſtright makes at London .6369 Ells
One Ell at Frankford makes at London .4792 Ells
One Ell at Danſick makes at London .7228 Ells
One Ell at Vienna makes at London .9896 Ells
One Auln at Paris makes at London 1.0526 Ells
One Auln at Rovan makes at London .9708 Ells
One Auln at Lions makes at London .9836 Ells
One Auln at Callais makes at London .6369 Ells
One Brace at Venice linnen makes at London .5555 Ells
One Brace at Venice ſilke makes at London .5102 Ells
One Brace at Lucques makes at London .5 Ells
One Brace at Florence makes at London .4901 Ells
One Brace at Millan makes at London .4347 Ells
One Brace at Leghorn makes at London .5 Ells
One Brace at Madera Iſles makes at London .9681 Ells
One Vare at Sivil makes at London .7409
One Vare at Lisbone makes at London 1.
One Vare at Caſtilia makes at London .7207
One Vare at Andoluſia makes at London .7339
One Vare at Granado makes at London .7339
One Palm at Genoa makes at London .2079
One Cane at Saragoſa makes at London 1.8181
One Cane at Rome makes at London 1.7857
One Cane at Barſelona makes at London 1.4035
One Cane at Valentia makes at London .8247
The uſe of this Table.
In 5727 Braces at Ligorn, how many Ells Engliſh.
Look in the Table for Ligorn, and right againſt it you ſhall find .5, which ſheweth that one Brace at Ligorn maketh at London. or half an Ell, wherefore ſay by the Rule of Three.
If one Brace at Ligorn give .5 Ells at London, what ſhall 5727 Braces give? Anſwer 2863.5, as by the work appeareth.
…
Section 2. Concerning Intereſt and Annuities.
The firſt Table ſhewing what one pound being forborn any number of years under 31, will amount unto, accounting intereſt upon intereſt, after the rate of 6 per cent.
| Y. | 6 per cent. |
| 1 | 1,06 |
| 2 | 1,1236 |
| 3 | 1,19101 |
| 4 | 1,26247 |
| 5 | 1,33822 |
| 6 | 1,41851 |
| 7 | 1,50363 |
| 8 | 1,59384 |
| 9 | 1,68947 |
| 10 | 1,79084 |
| 11 | 1,89829 |
| 12 | 2,01219 |
| 13 | 2,13292 |
| 14 | 2,26090 |
| 15 | 2,39655 |
| 16 | 2,54035 |
| 17 | 2,69277 |
| 18 | 2,85433 |
| 19 | 3,02559 |
| 20 | 3,20713 |
| 21 | 3,29056 |
| 22 | 3,60353 |
| 23 | 4,81975 |
| 24 | 4,04893 |
| 25 | 4,29187 |
| 26 | 4,54938 |
| 27 | 4,82234 |
| 28 | 5,11168 |
| 29 | 5,41838 |
| 30 | 5,74349 |
The firſt Column of this Table having Y at the top thereof, beginning at 1, and ſo proceeding to 30, ſignifie years, and the number in the next Column anſwering thereunto do ſhew what one pound is worth, being forborn any number of years under 31, which Table is made according to this proportion.
As 100 to 106, ſo is 1 to 1.06 and again, As 100 — 106 — 106 — 1.1236 and thirdly. As 100 — 106 — 1.1236 — 1.19101 Et ſic ad infinitum.
The uſe of this Table.
What 136 l. 15 s. 6 d. amount unto, being forborn 20 years, after the rate of 6 per centum, intereſt upon entereſt.
Look in the Table for 20 years, and right againſt in the broader Column, you ſhall find 2.20713, which ſhewes that one pound being forborn 20 years will be augmented to 3.20713. Then if you reduce your 136 li. 15 s. 6 d. into a Decimal, either by the Tables in the Second Part, or by the Scales in the Third Part of this Book, you ſhall find it to be 136.775. Wherefore ſay by the Rule of Three Direct.
If one pound being forborn 20 years will be augmented to 3.20713, to how much will 136.775 li. be augmented to in the ſame time. Anſwer, to 438 li. 13 s. 1 d. 1 q. as by the operation following doth appear.
… Or 438 li. 13 s. 1 d. 1 q.
The Second Table, ſheweth what one pound Annuity will amount unto, being forborn any number of years under 31, at 6 per cent. intereſt upon intereſt, the Annuity being to be paid yearly.
| Y. | 6 per cent. |
| 1 | 1,00000 |
| 2 | 2,06000 |
| 3 | 3,18360 |
| 4 | 4,37461 |
| 5 | 5,63709 |
| 6 | 6,97531 |
| 7 | 8,39383 |
| 8 | 9,89746 |
| 9 | 11,49131 |
| 10 | 13,18079 |
| 11 | 14,97164 |
| 12 | 16,86994 |
| 13 | 18,88213 |
| 14 | 21,01506 |
| 15 | 23,27596 |
| 16 | 25,67252 |
| 17 | 28,21287 |
| 18 | 30,90565 |
| 19 | 33,75999 |
| 20 | 36,78559 |
| 21 | 39,99272 |
| 22 | 43,39228 |
| 23 | 46,99582 |
| 24 | 50,81557 |
| 25 | 54,86451 |
| 26 | 59,15638 |
| 27 | 63,70576 |
| 28 | 68,52810 |
| 29 | 73,63979 |
| 30 | 79,05818 |
The uſe of this Table.
What will an Annuity of 20 li. payable yearly, be augmented unto in 12 years, being all that time forborn accounting intereſt upon intereſt at 6 per cent. per annum.
Look in the firſt column of the Table for 12 years, and right againſt it in the next column you ſhall find 16,86994, which ſhewes that 1 li. Annuity payable yearly, being forborn 12 years will amount unto 16.86994, wherefore ſay by the Rule of Three Direct.
If 1 pound Annuity forborn 12 years give 16.86994 what ſhall an Annuity of 20 pound a year give? being forborn the ſame term of 12 years? Anſwer 337 li. 7 s. 11 d. 3 q. fere, as in the operation doth appear.
…or 337 l. 7 s. 11 d. 3 q. ferè.
The third Table ſheweth what one pound being forborn any number of years under 31 is worth in ready money, rebating yearly, after the rate of 6 per cent. intereſt upon intereſt.
| Y | 6 per cent. |
| 1 | ,943396 |
| 2 | ,809996 |
| 3 | ,839619 |
| 4 | ,792093 |
| 5 | ,747258 |
| 6 | ,704960 |
| 7 | ,665057 |
| 8 | ,627412 |
| 9 | ,591898 |
| 10 | ,558394 |
| 11 | ,526787 |
| 12 | ,496989 |
| 13 | ,468839 |
| 14 | ,442300 |
| 15 | ,417263 |
| 16 | ,393646 |
| 17 | ,370364 |
| 18 | ,351343 |
| 19 | ,330512 |
| 20 | ,311804 |
| 21 | ,294155 |
| 22 | ,277505 |
| 23 | ,261797 |
| 24 | ,246978 |
| 25 | ,232998 |
| 26 | ,219810 |
| 27 | ,207367 |
| 28 | ,195630 |
| 29 | ,184536 |
| 30 | ,174110 |
The making of the Table.
As — 106 — 100 — .943396 — 889996 and again, As 106 — 100 — .889996 — 839619
Et ſic ad infinitum.
If 356 l. be payable at the end of 7 years, what is it worth in ready money, diſcounting or rebating after the rate of 6 per cent. intereſt upon intereſt.
Look in the Table for 7 years, and againſt it you ſhall find .665057, being the ready money which 1 l. is worth payable at 7 years end, wherefore ſay by the Rule of Three.
If 1 l. in 7 years rebate or decreaſe to .665057, to what will 356 l. rebate or decreaſe in the ſame time? Anſwer to 170 l. 5 s. 1 d. as by the operation doth appear.
…
The fourth Table ſheweth the preſent worth of one pound Annuity; to continue any number of years under 31, and payable yearly after the rate of 6 per cent. intereſt upon interſt.
| Y. | 6 per cent. |
| 1 | 0,94339 |
| 2 | 1,83339 |
| 3 | 2,67301 |
| 4 | 3,46510 |
| 5 | 4,21236 |
| 6 | 4,91732 |
| 7 | 5,58238 |
| 8 | 6,20979 |
| 9 | 6,80169 |
| 10 | 736008 |
| 21 | 7,88687 |
| 22 | 8,38384 |
| 23 | 8,85268 |
| 24 | 9,29498 |
| 25 | 9,71224 |
| 26 | 10,10589 |
| 27 | 10,47725 |
| 28 | 10,82760 |
| 29 | 11,15811 |
| 30 | 11,469…2 |
| 21 | 11,76305 |
| 22 | 12,04158 |
| 23 | 12,30337 |
| 24 | 12,55035 |
| 25 | 12,78335 |
| 26 | 13,00316 |
| 27 | 13,01053 |
| 28 | 13,40616 |
| 29 | 13,59071 |
| 30 | 13,76482 |
The uſe of this Table.
What is the preſent Rent or Annuity of 25 pound per annum worth payable yearly, for 21 years, accounting Intereſt upon Intereſt at 6 per centum.
Look in the Table for 21 years, and right againſt it you ſhall find 11.76407, which is the preſent worth of one pound Annuity, for 21 years, wherefore ſay by the Rule of Three.
If an Annuity of 1 l. per annum for 21 years be worth 11.76407 ready money, what is an Annuity of 25 li. per annum worth in ready money for the ſame time? Anſwer 294 l. 2 s. 0 d. 1 q. as by the operation following doth appear.
… or 294 l. 2 s. 0 d. 1 q.
The fifth Table ſheweth what Annuity payable yearly, one pound will purchaſe for any number of years under 31, after the rate of 6 per cent. compound intereſt.
| Y | 6 per cent. |
| 1 | 1.06000 |
| 2 | .54363 |
| 3 | .37411 |
| 4 | .28859 |
| 5 | .23739 |
| 6 | .20336 |
| 7 | .17913 |
| 8 | .16103 |
| 9 | .14702 |
| 10 | .13586 |
| 11 | .12679 |
| 12 | .11926 |
| 13 | .10297 |
| 14 | .10758 |
| 15 | .10296 |
| 16 | .09895 |
| 17 | .09544 |
| 18 | .09235 |
| 19 | .08962 |
| 20 | .08718 |
| 21 | .08500 |
| 22 | .08304 |
| 23 | .08127 |
| 24 | .07967 |
| 25 | .07822 |
| 26 | .07690 |
| 27 | .07569 |
| 28 | .07459 |
| 29 | .07357 |
| 30 | .07264 |
The uſe of this Table.
What Annuity to begin preſently and to continue 28 years, payable at yearly payments, will 640 l. purchaſe, accounting compound Intereſt after the rate of 6 per cent.
Look in your Table for 28 years, and right againſt it in the next column you ſhall find .07459, which ſhewes that one pound ready money will purchaſe an annuity worth .07459, and to continue 28 years, wherefore ſay by the Rule of three.
If one pound ready money, will purchaſe an Annuity worth .07459 to continue 28 years, what Annuity ſhall I purchaſe for the ſame time, paying 640 l. ready money? Anſwer 47 l. 14 s. 9 d. as by the operation doth appear.
…
FINIS.