The vvell spryng of sciences whiche teacheth the perfecte woorke and practise of arithmeticke, bothe in whole nombers and fractions, with suche easie and compendious instruction into the said arte, as hath not heretofore been by any sette out nor laboured. Beautified with moste necessary rules and questions, not onely profitable for marchauntes, but also for all artificers, as in the table doeth partlie appere: set forthe by Humfrey Baker citezeine of Lo[n]don.

Numeration. Cap .i.

NUumeration is the art wher∣by to expresse and declare the value of any summe proposed, and is of two kyndes, the one gathe∣reth y^• value of a sum proposed, & the other expresseth anye summe concey∣ued by oue figures and places, for the value is one thinge, and the figures are another thynge: and that cōmeth partlye by the diuersitye of fygures, but chiefelye of the places wherein they be ordeclye sei. And fyrste marke, that there are but ten fygures or cha∣racters whiche are vsed in Arith∣meticke, wherof nine of them are cal∣led signifiynge fygures, and the tenth is called a ciphar, whiche is made lyke an 0. and of it selfe signifi∣eth nothinge, but it beynge ioyned with any of the other figures, encrea∣seth their value, and these be they.

• 1 one.
• 2 two.
• 3 thre.
• 4 four.
• 5 fyue.
• 6 syre.
• 7 seuen.
• 8 eyght.
• 9. nyne.

Also you shal vnderstande that euery one of these fygures hath two values: One is alwaye certaine and hathe his signification of his owne forme, and the other is vncertayne whiche be taketh of his place.

A place is called the scate or roome that a figure standeth in, and howe many fygures so euer are written in one summe, so many places hathe the whole value thereof. And that is called the firste place (whiche nexte is towarde the ryghte hande) of anye summe, and so recknynge by or∣der towarde the lefte hande, so that, that place is laste whiche is nexte the lefte hande. And contrary∣wise, when you expresse the va∣lue of the fygures in anye summe you muste begynne at the lefte hande, and so recken towarde the ryght hande.

Euerye of these nine fygures, (whiche are called signifiynge fy∣gures) hath hys owne simple va∣lew

when he is founde alone, or in the fyrste place of anye sume. In the se∣conde place towarde the lefte hande; he betokeneth his one valewe ten ti∣mes. As. 70. is, seuen times ten: that is to saye seuentie, 80. is viii. times ten: that is to saye eyghtie. In the thirde place euery fygure betokeneth his owne valew a hundreth times. As. 700. in that thirde place betoke∣neth, a hundreth tymes. 7. that is to saye, seuen hundred: In the fourthe place euerye fygure betokeneth hys owne valew a thousande times. As. 7000. is seuen thousande, and 8000. is eyghte thousande. These foure fyrste places muste be had perfectlye in minde, ye and that by harte, for by the knowledge of them you maye expresse all kinde of nombres howe great so euer they be.

In the fyfte place euery figure by tokeneth his owne valewe tenne thousande times. As 70000. is ten tymes seauen thousande, that is to

sayē seauentie thousand: In the sytte place euerye fygure standeth for his owne valew, a hundreth thousande tymes. As 700000, is seauen hun∣dreth thousande. The vii. place a M. M. times, or a million: as 7000000, is vii. M. M. or vii. millions. And the viii. place .x. M. M. times, or ten millions, so that euery place towarde the lefte hande, excedeth the former ten times. But nowe for the easye readynge, and Redye expressynge orderlye of anye summe proposed you shall practise this maner, folowing. And for example I propone this nomber 765432658. in the whiche are nine places. In the fyrste place is 8. and betokeneth, but eyghte, in the seconde place is 5. and betokeneth, x. times fyue that is fyfte, in the thirde place is syxe, and betokeneth a. C. tymes syxe, that is .vi. C. In the forthe place is. 2. and that is twoo. M. And 3. in the fyfte places is x. M. tymes 3. that is xxx. M. So 4. in the syxie

place is a C. thousand times. 4. that is .iiii. C. M. then fyue in the seuenth place is a. M. M. times 5. that is v. M. or rather 5. millyons. And 6. in the viii. place is .vi. times x. millions, that is lx. millions. And laste of all .vii. in the. ix place, is vii. C. millions now fo∣loweth the practise. Fyrste put a prick ouer the fourthe fygure, and so o∣uer the seuenthe, and lykewyse o∣uer the tenthe. And also ouer the 13, 16. or 19 if you had so many, and so stil leauinge twoo fygures betwene euerye twoo prickes and those roo∣mes from one pricke to an other are called ternaries, then you muste pronounce euery three fygures from one pricke to an other as though they were written alone from the reste. And at the ende of theyr valewe, adde so manye tymes thousande, as your nomber hathe prickes (that is to saye, yf there be but 1. pricke, it is but one M. yf two prickes a M. M. or els a mil∣lion yt 3. prickes a. M. M. M. or a M.

million, and so consequentlye of all other fygures folowynge.) Then come lykewyse to the nexte three fy∣gures, and sounde them as yf they were aparte from the reste, and adde to their valewe so manye times thou∣sandes as there are pryckes betwene them and the fyrst place of your whole nomber. And so do by they next three fygures folowyng and of all the reste likewise as in exāple. 451234678567. The fyrste pricke is ouer. 8. in the fourth place, whiche is the place of a. M. the Seconde pricke is ouer 4. in the vii. place, whiche is the place of a M. M. or one million, the third pricke is ouer the .x. place whiche is the place of a M. M. M. or of a M. million, as in the former example. Then for the expressynge of this nomber by the valewe of euerye fygure, accordynge to the place wherin they stande••, you shall fyrste begynne at the laste prycke ouer one, and take yt and the other twoo fygures. 5. and. 4.

whiche do folowe him & valew them alone and they are iiij. C li. MMM. or els CCCC li. M. millions. Then take the other iij. fygures from one to the nerte pricke, and valewe them as if they were a parte from the o∣ther, and they are. 234. which are. CCxxxiiij. million, or 234. MM. Then come to the thyrde pricke ouer 8. and take the other ii. fygures be∣hinde it, and recken them lykewyse as yf they were alone, and they are vi C lxxviii. M. And laste of all come to the other twoo fygures whiche remaine, that is. 567. and they are fyue Clxvii. Thus the whole sume of these fygures, is iiii. Cli. M. ii Cxxxiiii. Millions, viC .lxxviii. M. vClxvii, as before.

Note also that whole nomber is de∣uided * 1.1 into three kindes, that is to saye, diget nomber, article, and mixte or compounde nomber. The dyget nomber, is all maner of nom∣bres * 1.2 vnder. 10. whiche are these. 9.

fygures 123456789. of the whiche I haue spoken before. The Article nom¦ber * 1.3 is anye kinde whiche beginneth wyth a cyphar as this. 0. and they maye euer be deuided Iuste by. 10. without anye remayne as these. 10. 20. 30. 40. 50. 100. and all other su∣che like. The mixte, or compounde * 1.4 nomber, conteineth diuers and ma∣ny articles, or at the lest one article, and a diget, as. 11. 12. 16. 19. 22. 38. 108. 1007. and so forthe. And as any article nomber maye be made a compounde, by puttynge ther∣to a diget, euen so lykewise euery compounde nom∣ber, may be made an article nomber by addinge ther∣vnto a 0.

¶ And here foloweth a briefe reher∣sall of the order and Denomina∣tours of the places. And this shalbe sufficient for Numera∣tion.

The denominatours. of the places.		The order of the places.
M. of Millions.	4	Tenth.
C. of Millions.	3	Nyneth.
X. of Millions.	2	Eyghteth.
Millions.	1	Seuenth.
C. of Thousandes.	0	Sixte.
X. Thousandes.	1	Fyfthe.
Thousandes.	8	Fourth.
Hundrethes.	3	Thyrde.
Tenthes.	4	Seconde.
Vnities.	5	Fyrste.

Notes

• * 1.1

  〈…〉〈…〉 of 〈…〉〈…〉
• * 1.2

  〈…〉〈…〉
• * 1.3

  Article.
• * 1.4

  Mixte or com∣pounde.