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 firste Chapter of this Addition entreateth of briefe Rules, called Rules of Practize, with diuerse necessarie questions pro∣fitable, not onlie for Merchaunts, but also for all other occu∣piers whatsoeuer.

THe working of Mul∣tiplicatiō in Practize, is no other thing, than a certaine manner of multiplying of one kind by another: wher∣vpon is brougt foorth the product of the pro∣poned number whych is accomplished by the meanes of Diuision in taking the halfe, the third, the fourth, the fifte, or such other parts of the summe whiche is to be multiplyed.

And for the better vnderstanding of suche conuersions: you shall vnderstand that in the manner and vse of these Rules of Practize, you oughte first to knowe the euen or aliquot parts of a shilling, whiche in this Table fol∣lowing doth appeare.

Item d

• 6 is the ½ of a s.
• 4 is the ⅓ of a s.
• 3 is the ¼ of a s.
• 2 is the ••/•• of a s.
• 1 is the ••/12 of a s.

Wherin as you sée according to the order of these rules of Practise at 6 d y^e yeard of a∣ny thing, you must take the ••/2 of your number whiche is to be multiplied, and the product, that commeth thereof shal be shillings, if any vnitie do remaine it is 6 d.

For 4 d take the ½ of the number that is to be multiplied and the product also produ∣ceth shillings if anye vnities doe remaine, ech one shal be worth in valew 4 pence. The like is to be vnderstoode of the other 3 &c.

Example I.

At 6 d the yearde what 379 yeardes 〈 math 〉〈 math 〉

II.

At 4 d the yearde: what are 104 yeardes worth 〈 math 〉〈 math 〉

III.

At 3 pence the yearde 〈 math 〉〈 math 〉:

IIII.

At 2 pence the yearde 〈 math 〉〈 math 〉

V.

At 1 pennie the yearde 〈 math 〉〈 math 〉

Here you may sée in the first example y^e 379 yeards at 6 d the yeard, are worth 189 s 6 d in taking the ½ of 379. And in the seconde ex∣ample the 104 yeardes at 4 d the yeard: are worth 34 shillings 8 d: in taking y^e ⅓ of 104.

Likewise in the third example 5014 yeards at thrée pence the yearde bringeth forth 1253 s 6 d in taking the ¼ of 5014. Also in y^e fourth example at 2 pence the yearde, maketh 88 shillings 8 d.

And lastly in the fifth example: 409 yeards

at 1 d the yeard, amounteth to 34 s and 1 d, in taking the 1/12 of 409: And so is to be done of all other questions the like, when the num∣ber of the pence is anye of the euen or aliquot parts of 12 d.

Item to bring the productes of these shil∣lings and all other the like in poundes is ve∣rie easie in diuiding of it into your minde by 20, for it is to be vnderstoode that as often as 20 is found in that product: So many pounds doth it containe, whiche with facilitie to per∣forme, alwaies strike of the figure to∣warde your right hande, with a right downe dashe of your penne for the 0 that appertay∣to 20: And then beginne at the lefte hand, in taking the ½ of the rest. And if at the laste any vnitie do remaine, the same shall be ioyned with the figure that is cut of, which shall re∣present the odde shillings contained in that worke.

As for example in your third question at 3 d the yearde whiche amounteth to 1253 s. 6 d: the producte whereof maketh 〈 math 〉〈 math 〉 62 lb 13 s 6 d: as here you maye sée is easily performed in the mer∣gent.

Item also for the working of 1 pennie the yearde, it is something harshe and harde to take the 1/12; part of some products: Therefore to ease that hard worke you shall first bryng your deliuered summe into groats, by taking the ¼ part of the product. And if any vnites re∣maine of that ¼ part, as somtimes there may they are pence: and must be signifyed wyth a line from the groates with theyr title of pence: And because that 60 groates ma∣keth a pounde or twentie shillings, strike of the firste figure towarde your righte hande for the 0 that apperteyneth to 60 (as you did euen nowe for the 0 that belongeth to 20:) then in taking the ⅙ of that product, if there do remaine any vnities the same shal you ioyne with the figure that you cut of, estéeming thē as groates: whiche kéepe in your mind. And by taking the ½ part of them, you shall turne into shillings: And so haue you done as for ex∣ample by a question or 2 hereafter proponed shal more plainly by the worke appeare.

At 1 d the yearde 〈 math 〉〈 math 〉

Here in taking the ⅙ part of 1359: in com∣ming to the last work the ⅙ part of 39 being taken, the remainer is 3 whiche ioined with the 2 that was cutte off, maketh 32 groates: which conuerted into shillings by taking the ⅓ part: maketh as appeareth 10 s 8 d: Many other wayes there are, but none more apter for a yong learner to vnderstande than this: wherfore this one way wel impressed in me∣morie is better thā 20 waies doubtfully vn∣derstoode.

At 1 d the yeard, what 4533 yeards 〈 math 〉〈 math 〉

At 1 d the yeard what 64768 yeardes 〈 math 〉〈 math 〉

Nowe followeth also to be vnderstood y^t if the number of pence be not an aliquot part of 12, you must reduce them into some aliquot part of 12. And after the aforesaid maner, you shall make of them 2 or 3 products as néede shal require: And adde them togither into one sum: And here for thy furtherance appeareth a note of the order of their partes, as they are to be taken.

For pence

• 5. take. 3 & 2 or 4 and 1
• 7. take. 4 & 3 or 6 and 1
• 8. take. 4 & 4 or 6 and 2
• 9. take. 6 & 3 or 4.4 & 1
• 10 take. 6 & 4 or 4.4 & 2
• 11 take. 6▪ 4 & 1 or 4.4 & 3

Here in the firste note of this table at 5 d, you shall first take for 3 d the ¼ of the num∣ber that is to be multiplied: And likewise for 2 d: the ⅙ of the same number, adding togi∣ther both the products. But if you wil worke by 4 and 1 you must for 4 d firste take the ⅓ of the number that is to be multiplied: And for 1 d take the 1/12 of the whole summe or ra∣ther, which is more better for 1 d. you maye take the ¼ of the producte whiche did come of y^e 4 d: Bicause y^e 1 d is y^e ¼ of 4 d: The total sums of these two nūbers shall be the soluti∣on to the question. And in like maner is to be done of all others: As by these examples fol∣lowing shal appeare.

I.

At 5 pence the yearde What will —758 yeards amount to 〈 math 〉〈 math 〉

Otherwise.

At 5 d y^e yard what are 758 yeardes worth 〈 math 〉〈 math 〉

II.

At 7 d the ell what 562 elles 〈 math 〉〈 math 〉

III.

At 8 d the lb what 112 pounds 〈 math 〉〈 math 〉

Otherwise.

What coms — 112 pound at 8 d the pound 〈 math 〉〈 math 〉

IIII.

At 9 d the Ell What coms — 356 elles to 〈 math 〉〈 math 〉

V.

At 10 d the péece What coms — 795 péeces to 〈 math 〉〈 math 〉

VI.

At 11 d the pound What — 757•• pound 〈 math 〉〈 math 〉 maketh 〈 math 〉〈 math 〉

Here in this first exāple where it is demā∣maunded (at 5 d the yeard) what will 758 cost: First for 3 d I take the ¼ of 758: And thereof commeth 18•• s — 6 d: Then for 2 d I take the ⅙ of the same product whi∣che amounteth to 126 s 4 d: these two sum∣mes added togither do make 315 s 10 d: And so much are the 758 yards worth at 5 d the yard.

Item also for the same again: First for 4 d I take the ½ of 758: and thereof commeth 252 s —8 d: then for 1 penny I take the ¼ of the same product, that is to say of 252 s — 8 d, and it yéeldeth me 63 s 2 d: whiche both added togither make 315 s — 10 d, as before.

Item, for 7 d there is take then ½ and the 1/•• of the whole summe: which is to be multi∣plyed,

and adde them togither, that is to say, first, for 4 d there is taken the ⅓ of 563: whi∣che coms to 187 s -8 d as appeareth by the worke: and for 3 d there is taken the 1/•••• of the whole sum which amounteth to 140 s -9 d. Both which products added togither maketh 328 s—5 d: And so much coms 563 elles to at 7 d the Ell.

Item, for the first 8 d there is taken for 4 d the ⅛ of the whole summe: and an other ⅓ for the other 4 d, which added togither as in the example doth euidently appeare, amoū∣teth to 74 s — 8 d.

Againe, for the second work of 112 lb, there is taken first the ½ of the whole summe for 6 d, whiche coms to 56 s: then for the 2 d you haue to take ⅙ of the whole summe, or if you will the ½ part of the product that came of 6 d either which maketh 18 s 8 d. These two sommes being added togither doe make 74 s 8 d: as in the third example appeareth.

Item, for 9 d there is taken for 6 d, the ½ of the whole summe: and the ¼ of the whole summe for 3 d, or otherwise for the 3 d you may take the ••/2 of y^e product that came of 6 d, bicause 3 d is the ½ of 6 d: which added togi∣ther as plainly appéereth in the fourth exam∣ple,

amounteth to 267 s—0 d.

Item, for 10 d, first there is takē for 6 d the ½ of the whole summe, which amounteth to 397 s—6 d. Then for 4 d there is foūd 265 s: bothe whiche added togither maketh 662 s—6 d as appeareth in the fift exam∣ple: it may also be wrought, as appeareth by the second note in the table by 4 d twice ta∣ken, and the ½ of the product of 4 d: or els by the ⅙ of the whole summe, &c.

Item, for 11 d, there is first taken the ½ for 6 d: then the ⅓ of the whole summe for 4 d: lastly, the ¼ of the last producte for 1 d: All which 3 summes added togither maketh in s 6947-5 d, & in pounds 347-7 s—5 d.

Item, likewise by the same reason, when you will multiply (by shillings) any number that is vnder 20 s you shal haue in the pro∣duct pounds, if you know the euen or aliquot partes of 20, which are here in this little ta∣ble set downe to sight.

Item s

• 10 is the 1/•• of one lb
• 5 is the 1/•• of one lb
• 4 is the ••1/5 of one lb
• 2 is the 1/10 of one lb
• 1 is the ••/20 of one lb

So that for 10 s which is the ½ of a poūd you may take the ½ of the number whiche is to be multiplyed: and you shal haue in your product pounds: if a vnitie do remaine, it shal be worth 10 s.

Likewise for 5 s you must take the ¼ of the number whiche is to be multiplyed: And if there doe remaine any Vnities, they shall be fourth partes of a pound, euery Vnitie being in valewe 5 s.

For 4 s take the ⅕ of the number which is to be multiplied: And if there doe remaine anye Vnities, they shall be fifte partes of a pound, eche vnitie being worth 4 s.

For 2 s you must take the 1/10 of the num∣ber to be multiplied: wherefore to take the 1/10 of any number: you must cut off the laste figure of the same number (whiche is nearest your right hand) from all the other figures with a small right downe line or dash with a pen, and so haue you done: for all the other figures which do remaine toward your lefte hand from the same figure that you doe sepa∣rate shal be the saide 1/10 of a pound: And that figure so separated towards your right hand shall be so manye péeces of 2 s the péece: the whiche figure you muste double to make

therof the true number of s, as by the exam∣ple shall appeare.

Finally, for 1 s, néedeth smal worke, for it is so many shillings as be proponed in the summe, whiche to bring into poundes hathe bene already taught in the firste Rule.

Example.

At 10 s the péece 〈 math 〉〈 math 〉

At 5 s the Ell 〈 math 〉〈 math 〉

At 4 s the yarde 〈 math 〉〈 math 〉

At 2 s the pound waight 〈 math 〉〈 math 〉

At 1 s the péece 〈 math 〉〈 math 〉

Nextly, nowe followeth in order to bée vnderstoode, that if the number of shillings be not some euen, or aliquot parte of 20, you must then conuerte the same number of shil∣lings into the aliquot parts of 20: And ther∣of make two or thrée products, as néede shall require: which done, adde them togither, and bring them into poundes. And here for thy furtherance I haue set down a note of the or∣der of their parts, as they are to be taken.

s					s
3	of	2 & 1	or		13	of	10.2 & 1
6	4 & 2	5. & 1	14	10. & 4
7	5 & 2		15	10. & 5
8	4 & 4	5.2.1	16	10.5.1
9	5 & 4	4.4.1	17	10.5.2
11	10 & 1		18	10.4.4
12	10 & 2		19	10.5.4

For 3 s according to the tenor that you sée is expressed in the Table, you muste firste take for 2 s the 1/1•• of the number that is to be multiplied: Then for 1 s you muste take the ½ of the product which didde come of the same 1/20 parte, and adde those two sums ad∣ded

ther, produceth the effecte desired.

Item, for 6 s according to the note set forth in the table, first for 4 s I take the ⅕ of the number that is to be multiplied: Then for 2 s the ½ of the product that came of 4 s, and adde them togither.

Or else, as appeareth also in the table, for 5 s you may take the ¼ and the 2/•• parte of the product that came of 5 s, and adde them togi∣ther.

Item, for 7 s, firste take for 5 s the 1/•• of the producte, that is to be multiplied, then for 2 s, take the 1/•• of the number that is to be multiplied, and adde them togither, &c.

Item, for 8 s, according to reason, and the intent of the Table, for the firste 4 s take the ⅕ of the product, and the same number a∣gaine for the other 4 s: and adde them togi∣ther.

Item, for 9 s: firste for 5 s take the 1/••: then for 4 s take the ⅕: and adde them togi∣ther.

Otherwise as you sée by the intente of the table, work twice for 4 s, as was taught euē now for 8: and then take the ¼ of the last pro∣duct

for the 1 s: But 5 and 4 is the shorter.

Itē, for 11 s: first dispatch 10 s: for which you must take the ½ of the product: then last∣ly for 1 s take the 1/10 parte of the summe pro∣duced of the ½ of the product and adde them to¦gither.

Item, for 12 s where I will end wyth the firste part of my Table: First take the ½ for 10 s: And then for 2 s take the ⅕ of the sum that came of 10 s, and adde them togither: or else, if you please for 2 s you may take the ½ of the whole giuen number.

To write more of the maner of taking the true parts, I thinke superfluous. The desi∣rous practitioner will (no doubt) conceiue it. Also the Table is some aide to helpe the vn∣perfect: wherevpon by & by I will set downe thrée or foure of these notes in examples: and the rest I wil leaue to thine own industrie & practise to labour vpon.

This is the order most commonly vsed in Practise when the number of the s is not an aliquot part of a pound. But louing Reader) after I haue touched the euē or aliquot parts of a lb that falleth out in d and s, I will deli∣uer 2 new Rules that shal drowne this com∣mon order quite and cleane: wherein shal be

comprehended in one line, or working bothe euen and odde part of s vnder ••0: without regard whether it be an aliquot or not an ali∣quot parte: which 2 Rules, when they come in place, I committe to thy friendly iudge∣ment in working: Nowe followeth the ex∣amples vpon the notes before saide.

At 6 s the yard 〈 math 〉〈 math 〉

Otherwise by multiplication of 6: 〈 math 〉〈 math 〉

At 7 s the Ell 〈 math 〉〈 math 〉

Otherwise by multiplication of 7: 〈 math 〉〈 math 〉

At 8 s y^e péece what 7563 péeces 〈 math 〉〈 math 〉

Otherwise by Multiplication.

〈 math 〉〈 math 〉

At 13 s y^t péece what 401 péeces 〈 math 〉〈 math 〉

Otherwise by Multiplication.

〈 math 〉〈 math 〉

These & such like questions of Compound numbers, which I haue here in this fourth rule for orders sake set down, I count but as superfluous. For, in the seconde parte of my new promised Rules shall appeare, that the giuen price of any odde nūber of Shillings, either vnder or aboue 20: shall bee wrought at two wor-kings at the moste howe diffi∣cult so euer the question be.

Item, there resteth yet a kind of Practize, howe to bring pence into poundes at the first working: wherevpon you must vnderstand, that 240 pence maketh one pound, or 20 s, I cutte off the laste figure or 0: and there re∣maineth but 24 (of whiche 24) 8 d is the ⅓ parte thereof: 6 d is the ¼ parte, 4 d the ⅙ parte: and 2 d is the 1/12 parte thereof.

Wherevpon if it were demaunded what 1486 yeardes or poundes of any thing com∣meth to: at 8 d the yeard, in pricking or cut∣ting off the firste figure towardes your right hande: for the 0 that appertaineth to 240: There is remaining of the saide summe 148: whereout I take the ⅓ parte: and it cōmeth to 49 lb: and there resteth one: which 1 I putte to the 6: that I pricke or cutte off, and it maketh 16 péeces of 8 pence, whiche I

double to make into groates and they make 32. whereof the •• part maketh 10 s and ther remaineth •• s: which is 8 pence, whereby it followeth, that the 1486 yeardes at 8 pence the yeard, maketh 49 lb 10 s 8 d: as by the example shall appeare.

Item for •• pence, take the 1/•• parte of the number from the prickt figure: And if any v∣nities do remaine, they are so many sixepen∣ces, whereof taking the 1/••, they are shillings, if there do remaine yet one, it is in valewe 6 pence.

Item for 4 pence, take the ⅙ parte of the number from the prickte figure: If any vni∣ties remaine, they are so many groates, whi∣che to conuert into shillings, take the ⅓ part: And if any thing yet remaine, they are thirds of shillings, echcone in valewe being worth 4 pence.

Item, for 3 pence, take the •• parte from the prickt figure, if any vnities remayne, they are so many péeces of •• pence wherof in taking the 1/•• part, maketh shillings: If anye thing yet remaine, they are fourth partes of shillings, echone being in valewe 3 pence.

Item, for 3 pence, as appeareth also by the table, take the 1/12 parte of the number from

the prickt figure: If any thing remaine, they are so many peeces of 2 pence: whiche by ta∣king the ⅛ parte, you shall turne into shil∣lings: and if any vnities remaine, they are so many sixte parte of shillings, or péeces of 2 pence, whether you will.

If one pound cost — 8 d 〈 math 〉〈 math 〉

If one cost 6 d 〈 math 〉〈 math 〉

If one yeard cost 4 d 〈 math 〉〈 math 〉

At 3 d the yeard 〈 math 〉〈 math 〉

At 2 d the ell what 7894 〈 math 〉〈 math 〉

But if your number of pence be not an ali∣quot or euen part of 24: then must you bring them into the aliquot partes of 24, and make thereof diuers products, which must be added togither, as by the questions hereafter follo∣wing shall appeare.

Item, for 5 d, first take for 3 d, then for 2 d: and adde them togither according to the instruction of the second Rule: Or else firste take for 4 d, then for 1 d.

Item for 7 d, first take for 4 d: then for 3 d and adde them togither.

Item, for 9, first take for 6 d: then for 3 d, and adde them togither.

Item, for 10 d, firste take for 6 d: then for 4 d, and adde them togither.

Item for 11 d firste take for 8 d then for 3 d and adde them togither: as by these ex∣amples folowing doth appeare.

Examples.

If one yearde cost 5 d what 7596 〈 math 〉〈 math 〉

Otherwise.

〈 math 〉〈 math 〉

If one cost 7 pence what 987 〈 math 〉〈 math 〉

Otherwise.

〈 math 〉〈 math 〉

If one cost 9 pence what 987 〈 math 〉〈 math 〉

Otherwise.

〈 math 〉〈 math 〉

If one yearde cost 10 d what 987 〈 math 〉〈 math 〉

If one cost 11 pence what 987 〈 math 〉〈 math 〉

But if you haue any shillings, & pence to be multiplied togither: Then are you to take for the shillings according to the enstruction of the third Rule: And for the pēce according to the first Rule before mentioned: vnlesse

you can spie the aduauntage therof: and ther∣by helpe your selfe: as appeareth in this se∣conde example, where first I worke for 6 d: which is to be rebated out of the giuen num∣ber, and I haue 719 lb 11 s my desire.

At 10 s 6 d: the yearde What 738 yeardes 〈 math 〉〈 math 〉

The like againe is done by rebating as by these 2 examples appeareth:

Item, 418 elles at 18 s 〈 math 〉〈 math 〉

Item 517. at 16 s 〈 math 〉〈 math 〉

And now I wil touch a little the euen parts of a pound that falleth out in pence and shil∣lings, wherof for those partes you shall take such like part of the giuen number that is to be multiplied, as the price of that giuen nū∣ber beareth in proportion to a pound whiche also for thy better aide is here set down.

• 1 s. 8 d is the 1/12 of the lb.
• 2. 6 is the ⅛ of a lb.
• 3. 4 is the ⅙ of a lb.
• 6. 8 is the ⅓ of a lb.

Item first for 1 s 8 d take the 1/12 parte of the giuen number & if any thing do remaine, they are twelue parts of a pounde, eache one being in value 1 s 8 d.

Item for 2 s 6 d take the ⅛ part of the nū∣ber that is to be multiplied. And if any thing do remaine they are eight parts of a pounde each one being in value 2 s 6 d.

Item for 3 s 4 d as appeareth by the ta∣ble, you must take the ⅙ part of the giuen nū∣ber. And if anye thing do remaine they are 6 parts of a lb: each one being in value 3 s 4 d.

Item for 6 s 8 pence take the ⅓ part of the number that is to be multiplied: And if anye vnities do remaine, they are thirds of a pound euerie one being worth 6 s 8 pence.

Other infinite numbers there are, that may be reduced by abbreuiation into the proporti∣onate parts of a pounde: as 16 s 8 pence ma∣keth ⅙: whiche 16 s 8 d is easilie reduced into groates by multiplying 16 by 3: & ther∣to adde 2: which maketh 50 groates: Then set 60 the groates of a pounde vnder 50, cut∣ting of the 2 Ciphers, as is here 〈 math 〉〈 math 〉 performed in the margent. And then haue you broughte 16 s 8 pence into the knowen partes of a lb which maketh ⅚.

But yet gentle Reader, for thy further enstruction, I haue herevnto annexed in a table, howe pence and shillings beareth pro∣portion to a lb: which I cōmitte to thy friend∣lie beneuolence, it will be some aide vnto the vngrounded practitioner: but I counte him the best workeman that can presentlie reduce his giuen price vnto the knowen and proportionate parts of a lb.

s	d	lb
0	2	1/120
0	3	1/80
0	4	1/60
0	6	1/40
0	8	1/••0
1	0	1/20
1	3	1/16
1	8	1/12
2	0	1/10
2	6	⅛
3	0	3/20
3	4	⅙
3	9	2/••6
4	0	⅕
5		¼
6		1/10
6	3	20/16
6	8	⅓
7		7/20
7	6	⅜
8		⅖
8	4	5/12
8	9	7/16
9		9/20
10		½
11		11/2••
11	3	7/16
11	8	7/12
12		⅗
13		1••/2••
13	4	⅔
13	9	1/1
14		7/1
15		¾
16		4/5
16	8	⅚
17		••7/2••
17	6	⅞
18		9/10
18	4	11/12
18	9	15/16
19	19	19/20

Here followeth 4 examples vpon the 4 notes deliuered.

At 1 s 8 pence the yearde What 3884 yeardes 〈 math 〉〈 math 〉

At 2 s 6 pence the yearde What 4562 yeardes 〈 math 〉〈 math 〉

At 3 s 4 pence the yearde What 583•• yeardes 〈 math 〉〈 math 〉

At 6 s 8 pence the yearde What 7562 yeardes 〈 math 〉〈 math 〉

Nowe by custome you are able to worke by all sortes of summmes, being deliuered in shillings & pence, as 1 s 1 pennie: •• s •• pence 3 s 3 pence, and so of all other: wishing you to haue some considerations of your questi∣ons, when they are set downe, for there are many subtill abbreuiations, and great aduā∣tages to be gotten, and easilie to be perceiued

• As •• s. 8 d of 2 s & 1 lb 8 d.
• 4 s •• d: of •• s 4 d: and 10 d whiche 10: is ••/4 of 3 s 4 d
• 5 s 8 d. of 4 s: and 1 s. 8 d.
• 5 s. 10 d, of 5 s and 10 d: whiche 10 d is ⅙ of 5 s·

And by this meane when you haue taken one product, you maye oftentimes vppon the same take an other more briefelie then vpon the sum which is to be multiplied &c.

Nowe gentle Reader that you haue séene the vertue of the euen or aliquot partes of a lb: in shillings alone, And also in the aliquot parts of shillings and pence: according to my promise hereafter followeth a briefer and ea∣sier method for any euen number of shillings either vnder or aboue 20, then euer yet hath bene published: Notwithstanding Maister Humfrey Baker, whose trauel is worthie cō∣mendation, And whom for knowledge sake I reuerence hath in some part touched thys first parte: though not in this method: The worke of the Rule is both pleasante, readie and briefe. As by the varietie of the exam∣ples deliuered therevpon shall appeare. And first I wil set forth a question: Thereby the better to expresse or teach you the order ther∣of: which is this.

If one yearde cost 6 s what 8574 〈 math 〉〈 math 〉

To the vnderstanding of this exāple, after you haue set down your giuen nūber in form of the rule of 3, with a line drawen vnder it: you shal presētly set a prick vnder your first fi∣gure 4, towards your right hād, drawing frō the pricke as heretofore hath bene practised, a little short line, thereto sette downe the shil∣lings anone, which done, multiplie the first fi∣gure 4 by 6. the value of your price, (whyche here you sée standeth in sight aboue the line.) it maketh 24: which is 1 lb 4 s. The 1 lb kéep to carrie to the next place, & the 4 s set downe at the end of the prescribed line towards your right hande: Thus haue you done nowe with 6 aboue the line, and also with 4 in the firste place (for the pricke vnder the 4. doeth repre∣sent that 4 hath done his office.) Then secō∣darily for a general rule take but the ½ of the giuen price whiche here is ••, which 3, is the number that shal now continue the reste of y^e multiplication and end the worke, whervpon I multiply 3 into 7 standing in the seconde place it maketh 21, and with the 1 lb I kept in minde 22, set downe 2 & kéepe 3 in minde working according to the rule of multiplica∣tion, deliuering the tens in mind in their due place, which done, the product from the pricke

to your left hand representeth the pounds and the other at the ende of the line the shillings: as appeareth by the examples.

If one yearde cost 2 s what 7536 〈 math 〉〈 math 〉

If one yearde cost 4 s what 8792 〈 math 〉〈 math 〉

If one péece cost 6 s what 9537 〈 math 〉〈 math 〉

If one cost 8 s what 7509 〈 math 〉〈 math 〉

If one cost 12 what 5794 〈 math 〉〈 math 〉

If one cost 14 s what 3705 〈 math 〉〈 math 〉

If one cost 18 s what 5703 〈 math 〉〈 math 〉

If one cost 22 s what 953 〈 math 〉〈 math 〉

Let these suffise gentle reader for an en∣treance into euen numbers: And now I wyll shew the like rule for any od or vneuen parts of a pound.

To help you to the vnderstanding of these other questions y^t hereafter followeth: where in my first example the giuen nūber is 6487. At 3 s the yeard: I multiply 3 aboue the line into 7. it maketh 21: The 1 shilling I set down & the 1 lb I kéepe: Nowe am I to take the ½ of 3: which because it is an odde number I cannot. Therefore I shal kéepe and conti∣nue my multiplication by 3 stil: And worke by the ½ of the rest of the giuen figures or nū∣bers: To wit 648: And first the ½ of 8 whiche is 4 multiplied into •• maketh 12 therto ioine y^e 1 lb in minde, it maketh 1••: set down •• kepe one. Then againe multiply by 2 the ½ of 4 it maketh 6, and with 1 in minde it maketh 7. Then lastly take the ½ of 6 which is 3, saying 3 times 3, is 9: whiche 9 set downe and so is the question aunswered as appeareth by the practise, and the examples following.

At 3 s the yearde what 6487 〈 math 〉〈 math 〉

If one yearde cost 5 s what 4769 〈 math 〉〈 math 〉

At 7 s the elle what 6489 〈 math 〉〈 math 〉

If one elle cost 9 s what 2807 〈 math 〉〈 math 〉

At 11 s the pistolet what 8263 〈 math 〉〈 math 〉

If one piece cost 13 s what 4629 〈 math 〉〈 math 〉

But nowe note gentle Reader, when the giuen price falleth vppon anye odde number. As 3.5.7.9.11.13. &c: Then it is to be pre∣supposed, that the giuen summe to be multi∣plied muste be a summe made of euen num∣bers, as 2.4.6.8.0 &c. else can not that questi∣on be wrought at one line or working.

Prouiding alwayes that it maye beare an odde figure in the firste place towardes your righte hand: as appeareth in these 6 Exam∣ples which last were wrought, and such like &c. which may beare an odde number for the price, and be done at one line or working ve∣ry wel.

But if the giuen price be an odde number, and the summe to be multiplyed odde num∣bers also: Thē can it not be done at one wor∣king, but requireth the aide of 2 workings: for odde with odde will not agrée, which not∣withstanding to bring to passe. Take this for a general rule: First work for the euen num∣ber, contained in that question, or giuen price, according as you haue learned, And thē afterwards for the one odde shilling, take the ½ of the summe giuen to be multiplied, o∣mitting the first prickt place, As was taught for y^e working of one shilling in my first rule of practise, And adde those two togither. And you shal haue your desire.

Example.

At 3 s the yearde what 7539 〈 math 〉〈 math 〉

At 7 s the ell what 7539 〈 math 〉〈 math 〉

At 13 s the yearde what 7534 〈 math 〉〈 math 〉

And thus haue I abbridged into these two Rules how to bring any number of s: what∣soeuer they be into pounds, w^t a brieffer me∣thod, then euer yet hath bene published, whi∣che I commende vnto thy friendlye censure and iudgements in the vse of practise there∣of.

If one cost 6 s 5 d what 1231 〈 math 〉〈 math 〉

At 14 s 2, d what 2825 〈 math 〉〈 math 〉

At 16 s 4 d what 2531 〈 math 〉〈 math 〉

At 3 s the Pistolet what 8325 〈 math 〉〈 math 〉

At 7 s the crowne what 6529 〈 math 〉〈 math 〉

At 9 s the péece what 6567 〈 math 〉〈 math 〉

These thrée last questions may séeme some thing harde, yet are they easie ynough, if you marke them well, if I should explaine them, then are they too easie: therfore I leaue them to whet the minds of the desirous.

Item, when any one of the summes whi∣che is to be multiplied, is composed of manye Denominations: and the giuen number but of one figure alone: Then shall you multi∣plye all the denominations of the other sum, by the same one figure, beginning first with that summe which is least in valew towards your right hande, and bring the producte of those d into s, and the producte of the s into lb▪ as by this example doth appeare.

〈 math 〉〈 math 〉

But if in any of the summes that are to be multiplied ther be a broken number: First worke for the whole according to the instru∣ctions that you haue learned: and then take suche part of the giuen price: as that broken number beareth in proportion to the price, as in the example: after you haue wrought, for 3 s and for 6 d: then are you to take the ••/•• of 36 d for the ½ yeard: and adde that to the summe: So adding all 3 productes togither which maketh 43 lb — 2 s — 11 d the iuste price of 246 ½ Els: and thus muste you do of all other.

At 3 s 6 d the Ell what 246 ½ 〈 math 〉〈 math 〉

At 16 s 4 d the péece What 〈 math 〉〈 math 〉

If one péece coste 〈 math 〉〈 math 〉 What 〈 math 〉〈 math 〉

The Proofe.

If 12 peces cost 50 lb· 2 s· 6 d what one pece 〈 math 〉〈 math 〉

Item, touching the manner howe to vn∣derstande the order of this proofe, and others the like: first seeke howe many times 12 is contained in 50: maketh 4: resteth 2 lb whi∣che conuerted into shillings, and ioined with the other 2 s, maketh 42 s: wherein is foūd 12 thrée times: resteth 6 s which turned in∣to pence, putting thereto the 6 d in the firste place, it maketh 76: wherein 12 is founde 6 times, resteth 6 d, which containeth 12 but ½ a time, put that ½ to the 6 d: And then the solution is 4 lb — 3 s —6 ½ as appeareth by the practise thereof.

Item, the like is to be done of any thing that is bought or solde after 5 score to the hundreth, or the Quintall: As for exam∣ple.

If 100 lb cost 27 lb — 13 s — 4 d What one pound.

〈 math 〉〈 math 〉

I haue wrought this at lēgth for y^e aide of y^e yōg learner, bicause he should vnderstād how al y^e Mul∣tiplication is set downe.

〈 math 〉〈 math 〉

But to works it more neatly, it is by a little vn∣derstanding en∣ded thus.

Item to the vnderstanding of this and suche like questions, the right downe line is all the guide, which is pulled down close by 20, as you sée in the example, where 27 lb — 13 s is reduced all into s: maketh 552.

The 5 towards your lefte hād being sepa∣ted

with the hanging or right downe line, is the iust number of shillings: that aunswea∣reth to the question: Nextly, 53 s is multipli∣ed by 12 to reduce them to pence, putting to the 4 d: it yéeldeth for the multiplication of the first figure two: 1 10: the one beyond the line towards the left hande: is 1 penny to∣wardes the reste of the price: then 53 also multiplied by 1 yéeldeth 53: but the 5 be∣hinde the line towards the left hande, is also 5 d more, towards the price, which 1 and 5: I adde togither vnder the line: it maketh 6 d: So is there found nowe as appeareth by the Titles of s and d: 5 s 6 d.

Finally, I come nowe on this side the line, towards the right hand: and vnder 12: I find first 10: and then 3: whiche added to∣gither maketh 40: vnder whiche 40, you muste putte the 100: and it maketh— 40/1••0 which abbreuiated commeth to ⅖: So the iuste price of one pounde after 5 score to the hundreth, maketh — 5 s — 6 ⅖ d.

One example more, and so will I leaue this rule.

If 100 cost 10 ¾ d What 〈 math 〉〈 math 〉

Also the like maye be done of our vsuall waightes here in England (whiche is 112 lb for euery hūdreth waight) in case you know the Aliquot parts of a hundreth waight, whi∣che are these, 56 lb, 28 lb, 14 lb, and 7 lb: For 56 lb is the ½ of 112 lb, 28 lb is the ¼ of 112 lb, 14 lb is the ⅛, and 7 lb is the 1/16.

Therfore for 56 lb, take the ½ of the summe of mony that 112 lb waight is worth.

For 28 lb take the ¼ of the summe of mo∣ney that 112 lb waight is worth.

For 14 lb, take the ⅛ of the summe that 112 lb is worth.

And for 7 lb, the 1/16 of the summe of mo∣ney that C. is worth.

As for example: at 17 lb — 19 s the hun∣dreth poundes waight, that is to saye, the 112 lb, what shall thrée quarterus and 7 lb coste?

〈 math 〉〈 math 〉

Notes

• 2. Rule.
• 3. Rule▪
• 4. Rule.
• 6. Rule.
• 7. Rules
• 8. Rule.
• Note. A general rule.
• 9 Rule.
• A general rule.
• ••0. Rule.
• 11. Rule.
• 12. Rule.
• 13. Rule.