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FIrst set downe the diuisor, for feare of forgetting, and thē set the nūber that shal be diuided, at the right side, so farre from the Diuisor, that the quotient may be set betwéene them: as for example.
If 225 shéepe cost 45 lb. what did euerye
shéepe cost? To know this, I shoulde diuide the whole summe that is 45 lb, by 225, but that cannot be: therefore must I firste reduce that 45 lb into a lesser denomination, as into shillinges, then I multiplie 45 by 20, and it is 900: that summe shall I diuide by the number of sheepe, which is 225, these two numbers therefore I set thus.
Then begin I at the highest lyne of the di∣uident, and séeke how often I maye haue the diuisour therein, and that maye I doe foure times: then saye I, foure times 2 are 8, whi∣the if I take from 9, there resteth but 1, thus.
And because I founde the diuisor 4 times in the diuident, I haue set as you sée, 4 in the middle roome, which is the place of the quotient: but now must I take the rest of ye diuisour as often out of the remayner, there∣fore come I to the seconde line of the diuisor, saying: 2 foure times make 8, take 8 from 10, and there resteth 2, thus.
Then come I to the lowest number which is 5, and multiplie it 4 times, so is it 20, that take I from 20, & there remayneth nothing,* 1.1 so that I sée my quotient to be 4, which are in valewe shillings, for so was the diuident: and therby I know yt if 225 Shéepe did cost 45 lb, euery shéepe cost 4 s.
This can I doe,* 1.2 as you shall per∣ceiue by this exāple. If 100 soldiours do spēd euery moneth 68 lb, what spendeth ech man?
First because I cannot diuide the 68, by 160, therefore I will turne the lb into pen∣nies
by multiplicatiō, so shal there be 16320 d. Now must I diuide this summe by the number of souldiors, therefore I set them in order thus.
Then beginne I at the highest place of the diuidend, séeking my Diuisor there, which I finde once, therefore sette I 1 in the nether line.
Not in the nether line of the whole summe, but in the nether lyne of that worke which is the third line.
So standeth it with reason.
Then thus doe they stand.
Then séeke I agayne the rest, how often I may finde my diuisour: and I sée that in the 300 I mighte finde 100 thrée tymes, but then the 60 will not be so often found in ••0, therefore I take 2 for my quotient: thē take I 100 twice frō 300, and there resteth 100, out of which with the 20 (that maketh 120) I may take 60 also twice, and then standeth the numbers thus.
Where I haue set the quotient 2 in the lowest line: So is euery Souldiors portion 102 d that is 8 s, 6 d.
But yet because you shall iustlye perceiue the reason of Diuision, it shall bée good that you doe set your diuisor stil agaynst those numbers from which you doe take it, as by this example I will declare.
If the purchase of 20 acres of ground did cost 290 pound, what did one acre cost?* 1.3
First will I turne the poundes into pen∣nies,
so will there be 69600 pence. Then in setting down these numbers, I shal do thus. First set the diuidend on the right hand as it ought, and then the diuisor on the lefte hande agaynst those numbers from which I intend to take him firste as here you sée, where I haue set the diuisor two lines higher than is his owne place.
This is like the order of Diuision by the pen.
Truth you say, and now must I sette the quotient of this worke in the thirde line, for that is the lyne of vnits in respecte to the diuisor in this worke.
Then I séeke how often the diuisor maye be found in the diuident, and that I fynd 3 tymes, then set I 3 in the third lyne for the quotient and take awaye that 60000 from the diuidend, and farther I do set the diuisor
one line lower, as you see here.
And then séeke I howe often the diuisor will be taken from the number agaynste it, which will be 4 times and 1 remaining.
But what if it chaunce that when the diuisor is so remoued, it cannot be ones taken out of the diuident against it?
Then muste the diuisour be set in an other line lower.
So was it in diuision by the pen, and therefore was there a cipher set in the quoti∣ent: but how shall that be noted here?
Here néedeth no token, for the lines doe represent the places: onely looke that you set your quotient in that place whiche stan∣deth for vnits in respect of ye diuisor: but now to returne to the example. I finde the diuisor 4 times in the diuident, and 1 remaining, for 4 times 2 make 8, which I take frō 9, & there
resteth 1, as this figure following sheweth; and in the middle space for the quotient I set 4 in the second line 〈◊〉〈◊〉 he is in this worke the place of vnits.
Then remoue I the diuisour to the next lo∣wer line, & seeke how often I may haue it in the diuident, which I may doe here 8 tymes iust, and nothing remain, as in this fourme.
Where you may sée, that the whole quoti∣ent is 348 d, that is 29 s, whereby I knowe that so much cost the purchase of one acre.
Now resteth the proues of Multiplica∣tion, and also of Diuision.
Their best proues are eche one by the other: for multiplication is prooued by Di∣uision, and Diuision by Multiplication, as in the worke by the pen you learned.
If that be all, you shall not néede to re∣peate agayn that that was sufficiētly taught alreadie: and except you will teache me any other feate, here maye you make an ende of this art, I suppose.
So will I doe as touching whole number: and as for brokē number, I will not trouble your wit with it, till you haue pra∣ctised this so well, that you be full perfect, so that you néede not to doubt in any point that I haue taught you, and then maye I boldlye instruct you in the arte of Fractions or Bro∣ken number: wherein I will also shew you the reasons of al that you haue now learned. But yet before I make an end, I will shew you the order of common casting, wherin are both pennies, shillings, and poundes, procée∣ding by no grounded reason, but onelye by a receyued forme, and that diuerslye of diuerse men: for the Marchantes vse one forme, and Auditours an other.
Example of vvages
Example of purchase.