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 ninth Chapter treateth of lengthes and breadthes of Arras, and other clothes with o∣ther questions incident vnto length and breadth.

IF a péece of Arras be 7 els and ¼ long: & 5 els and ⅖ broad: how many els square doth the same péece containe?

Answer. Multiply the length by the bredth that is to say 7 ¼ by 5 ⅔: And therof wil come 4•• 11/12 elles: so manye elles square doeth the same péece containe.

Item more a péece of Arras doeth con∣taine 22 elles square, And y^e same being in length 3 1/•• elles I demaunde how manye elles in bredth the same péece doth cōtaine?

Answer Diuide 22 elles by 2 1/•• and therof commeth 6 10/13: So many elles doth y^e same containe in bredth

Item more a Merchant hath 3 ¼ elles of Arras, at 1 ⅔ elles broade which he wyll chaunge with another man for a péece of Arras, that is 7/8 el square. The question is howe manye elles of that squarenesse ought the first Merchant is to haue.

Answere. Multiplie the first Merchantes péece his length by his breadth, and you shall find it containeth 5 5/12 elles, which 5 5/12 elles you shall diuide by ⅞ and you shall finde 6 4/21 elles: and so many elles of that squarenesse, ought the latter Merchant to giue the first.

Item, a student hath bought 3 ••/2 yards of broade Cloth, at 7 quarters broade, to make a Gowne: and should line the same throughout with Lambe, at a foote square eche skin: the question is now how many skinnes he ought to haue?

Answeare. Séeke firste the number of yards square that his cloth containeth, which to doe, multiplie 3 ½ his length, by 1 ¾ hys breadth, and you shal find 6 ⅛ yeards square: then say by the rule of thrée: if 1 yeard square giue 9 foote, what shal 6 ⅛? worke, and you shall finde 55 ⅛ skinnes.

Item more, a Lawier hath a rich péece of séeling come home which is 34 foote, and thrée inches long: and 7 foote and 2 ½ inches high: the Ioiner is to be paide by the yard square: the question is, how many yeards

this péece containeth?

Answere. Multiplie his length by hys breadth, that is to wit, 24 ¼ foote by 7 5/24 foote and you shall finde 174 77/96 foote square, which 174 you shall diuide by 9 (for so many foote make a yeard square) and you shall finde 19 yeardes, 3 foote, and 77/96 of a foote: and so ma∣ny yeards doth this péece holde.

Item, bought a péece of Hollande Cloth containing 36 elles ⅓ Flemmishe: The question is, how many Elles Englishe it makes?

Answere. You muste note, that 5 Elles Flemmish do make but 3 Elles Englishe: Therfore say by the Rule of thrée: if 5 elles Flēmish make but 3 elles english, how ma∣ny Elles Englishe will 36 ⅓ Elles Flēmish make? Multiplie and diuide, and you shall finde 21 ⅘: and so many Elles English doth 36 ⅓ Elles Flemmish containe. The like is to be done of all others.

Item more, I haue bought 342 Elles Flemmish, of Arras worke at two Elles broade, Flemmish, and I woulde line the same with Ell broad Canuas of English

measure: The question is, howe many•• Elles English will serue my turne?

Answere. For as much, as 3 elles En∣glish are worth 5 elles Flemmish: therfore put 3 elles English into his square: in mul∣tiplying 3 by himselfe, whiche maketh 9: Likewise multiplie the English ell which is 5 quarters euery way into himself squarely, and you shal finde 25: Then multiplie 342 whiche is the length of the péece, by 2 whiche is the breadth, and thereof commeth 684: then say by the rule of 3, as before: if 25 elles square of Flemmishe measure be worth 9 elles square of Englishe measure, what are 684 of Flemmish measure? multiply and di∣uide, and you shal find 246 6/25 elles English.

The same is also wrought by the backer Rule of 3, in séeking the squares contained in the Flemmish ell of 2 elles broade (which are 18): and also in séeking the squares con∣teined in the English ell (which are 25:) then say by the Rule of 3 backward: if 18 quar∣ters require 34 elles, what shal 25 quarters giue? Multiply, & diuide by y^e Rule of 3: Re∣uerse, & you shal finde as before 246 6/25 elles Englishe.

Item more, at 3 s 4 d the Flemmishe Ell what is the Englishe Ell worth after the rate?

Answere. Say, if 5 Elles Flemmish be worth 3 Elles Englishe, what is one Ell Flemmish worth? Multiplie, and diuide, and you shall finde ⅗ of an Englishe Ell: Then say by the Rule of thrée, if ⅗ of an Ell bée worth 3 ½ s, what is one ell English worth? multiplie and diuide, and you shall finde 5 s 6 4/9 d?

Item more, at 8 s 4 d the Flemmish El square, what is the English El worth after that rate.

Answere. Say by the aforesaide reason: if 25 Elles Flemmish square be worth 9 els square Englishe, what is one Ell square Flēmish worth? work, & you shal find 9/25 of a an Ell square English: Then saye, if 9/25 of an Englishe Ell be worth 8 ½ s, what is 1 square Ell worth? Multiplie and diuide, & you shall finde 2•• s—1 7/9 d: and so much is the Englishe Ell worth.

Itē, more at 6 s 8 d y^e Ell square, what shall a peece of cloth cost that is 7 ½ Elles long, and 3 ¼ Elles broade?

Answere. Multiplie the breadth by the length, and you shall finde 24 ⅜ elles square: Thē say by the Rule of thrée: if 1 Ell square costa 6 ⅔ s what 24 ••/8? Multiplie and diuide and you shal finde: 8 lb— 2 s6 d: and so muche the same péece of cloth shall coste.

Item more, a Mercer solde 2 péeces of silke. To wit, 24 ¼, 24 ⅓, and 25 yeards at 9 ¾ s the yeard: and was glad to receiue in parte of payment againe, a Cloth con∣taining 34 ½ yeardes at 7 ⅔ s the yeard: The question is now, what the Debitor is in the Creditors debt: Worke, and you shall finde, he oweth the Mercer 22 lb— 3 s— 2 ¼ d.