The grounde of artes teaching the perfect vvorke and practise of arithmetike, both in whole nu[m]bers and fractions, after a more easie ane exact sort, than hitherto hath bene set forth. Made by M. Robert Recorde, D. in Physick, and afterwards augmented by M. Iohn Dee. And now lately diligently corrected, [and] beautified with some new rules and necessarie additions: and further endowed with a thirde part, of rules of practize, abridged into a briefer methode than hitherto hath bene published: with diverse such necessary rules, as are incident to the trade of merchandize. Whereunto are also added diuers tables [and] instructions ... By Iohn Mellis of Southwark, scholemaster.

The fifteenth Chapter entreateth of the saide 6 Rules of breuitie, and of valuation of English, Flemish, and French money, and how ech of them may easilie bee brought to others value.

How brieflie to reduce lb, s, and d Fle∣mish, into lb, s, and d Englishe, Sterling.

IT is to be noted, that 7 pound Flemish maketh but 6 lb. sterling, 7 s Flemishe, maketh 6 s sterl. and 7 d flem. 6 d sterl. So that 7 yéeldeth but 6. Wherin is euidēt, that there is lost 1/7, (if it may be so called) when it is reduced into English money. Wherefore to know how much 233 lb. 13 s, 4 d, flemish maketh English, you must subtract from it 1/7, beginning with the pounds, &c. and that whi∣che resteth after this subtraction is the sum required: so that 233 lb, 13 s, 3 d flem. ma∣keth 200 lb, 5 s, 8 4/7 d. sterling.

Example. 〈 math 〉〈 math 〉

An other Example. 〈 math 〉〈 math 〉

To reduce lb s. and d. ster. into lb s d flem.

Note that a lb sterling, maketh 1 lb, 3 s, 4 d flem. that is 1 lb ⅙: 1 s ster. maketh 1 s ⅙ flem. and 1 ster. maketh 1 ⅙ Flem. So that there is gained (if it may so be called) ⅙ of the summe being thus reduced to Flem. For of 6/6 is made 7/6▪ which is 1 whole, and ⅙. Then to knowe how much 237 lb 7 s 6 d ster. ma∣keth Flem. subtract from your ster. the ⅙ of the whole summe. and adde it to the same summe, and it maketh 276 lb 18 s 9 d, whi∣che is the summe required.

Example. 〈 math 〉〈 math 〉

An other example. 〈 math 〉〈 math 〉

Ye shal note, that the equalitie of Flemish and French mony is this, that is to say, the lb

Flemish, maketh 7 lb ⅕ French or Turnois 1 s Flemish maketh 7 s ⅕ French, & a great Flemish, maketh 7 d ⅕ French.

Wherefore to knowe howe muche 143 lb 4 s 9 d Flemish maketh French. Ye must multiplie the whole number twice by 6, be∣ginning at d, and so forwarde: and the pro∣duct of your second multiplication, diuide by 5, so that worke is finished. Or multiplie the saide summe by 7, and take out of it ⅕ adding it to the producte of your multiplication by 7, and that is your number required. So that as well by the one, as by the other, 143 lb 4 s 9 d Flemish, maketh 1031 lb 6 s 2 d ⅖ French or Tournois.

Example. 〈 math 〉〈 math 〉

An other Example. 〈 math 〉〈 math 〉

Another example. 〈 math 〉〈 math 〉 or thus. 〈 math 〉〈 math 〉

A briefe Reduction of lb s and d French, into lb s and d Flemish.

Multiply 233 lb, 8 s, 4 d, fr. by 5, and diuide the product twice by 6, that is the saide num∣ber by 6, and the product againe by 6: and the quotient of this seconde diuision is the thing required. So that 233 lb, 8 s, 4 d, fren. ma∣keth 32 lb, 8 s, 4 d, 5/9 flemish.

Example. 〈 math 〉〈 math 〉

Another. 〈 math 〉〈 math 〉

To reduce lb, s and d Sterling, into lb s and d French or Tournois.

The lb ster. maketh 8 lb, 8 s french, that is to say, 8 lb ⅖: the s maketh 8 s ⅖, and the pe∣ny 8 d ⅖ frenche. Wherefore to know what 231 lb, 13 s, 4 d ster. maketh french, ye must multiply your whole sum by 42, that is by 7, and the product of it by 6, and diuide thys se∣cond product by 5, and that is the sum requi∣red.

Otherwise multiply the sum ster. by 8, and adde twice to the product ⅖, and it shall pro∣duce the sum required. So that both waies, 231 lb, 13 s, 4 d ster. maketh 1946 lb french. As here vnder followeth.

The same otherwise. 〈 math 〉〈 math 〉

An other Example. 〈 math 〉〈 math 〉

The same. 〈 math 〉〈 math 〉

To reduce lb s and d fren. into lb s d ster.

To know how much 1256 lb 12 s 6 d fren. maketh in sterling money, multiplie the sum by 5, and diuide the producte by 7 and 6 at twice, and the last quotient shal be the thing required that is to say, 1256 lb 12 s 6 d ma∣keth 149 lb 11 s 11 d 4/7 sterling.

Example. 〈 math 〉〈 math 〉

An other Example. 〈 math 〉〈 math 〉

Note, that when any money is giuen by exchange at London for Roan at 71 d ½: or ra∣ther 71 1/7, for the crown of 50 s french, there is neyther gaine nor losse, for it is one mony for an other, accompting 8 lb 8 s French for 1 lb sterling So the Gyuer loseth the time of payment which is about 15 dayes, & hée that taketh it, hath gaine of the same.

They of Rean that putte sorth, or take mo∣ney by exchange for London, ought to haue like consideration.

Item, when any man giueth at London 64 d ⅓, or rather 64 d 2/7, to haue at one of the Faires of Lions a crowne de Marc, he that so giueth his mony, loseth the time, and he that taketh it, gaineth the same: for 62 d 2/7 is e∣quall in value to 45 s French. He that put∣teth or taketh money at Lions for London, ought to consider the same.

Item, when anye deliuer in Antwerpe 75 d, to receiue at Lions a crown of Marcke, hée that putteth it foorth, looseth the tyme, and hée that taketh it, gaineth the same: For 75 groates Flemish is equall in valewe to 45 s French.

Thus for this time I make an ende of the practise of exchaunge and the enstructions therevnto belonging, and according to my promise gratify such as are desirous to know the common coynes vsed for traffique a∣mong Merchauntes in these Cities follow∣ing: Here followeth a briefe declaration of their monies and y^e recknings and accompts of them.