Chapter VII. Division.
Definition of division. For to dyvyde oo nombre by a-nother, it is of .2. nombres proposede, It is forto depart the [moder] nombre into as many partis as ben of vnytees in the lasse nombre. And note wele that in makynge of dyvysioun ther ben .3. nombres necessary: Dividend, Divisor, Quotient. that is to sey, the nombre to be dyvydede; the nombre dyvydyng and the nombre [exeant], [other] how oft, or quocient. Ay shalle the nombre that is to be dyvydede be more, other at the [lest] evene with the nombre the dyvysere, yf the nombre shalle be made by hole nombres. How to set down your Sum. Therfor yf thow wolt any nombre dyvyde, write the nombre to be dyvydede in þe ouerer [bordure] by his differences, the dyvisere in the lower ordure by his differences, so that the last of the dyviser be vnder the last of the nombre to be dyvyde, the next last vnder the next last, and so of the others, yf it may competently be done; An example. as here:—
| The residue | 2 | 7 | |
| The quotient | 5 | ||
| To be dyvydede | 3 | 4 | 2 |
| The dyvyser | 6 | 3 |
| Residuum | 8 | 2 | 7 | 2 | 6 | ||||||
| Quociens | 2 | 1 | 2 | 2 | 5 | 9 | |||||
| Diuidendus | 6 | 8 | 0 | 6 | 6 | 3 | 4 | 2 | 3 | 3 | 2 |
| Diuiser | 3 | 2 | 3 | 6 | 3 | 3 | 4 |
When the last of the divisor must not be set below the last of the dividend. And ther ben .2. causes whan the last figure may not be sette vnder the last, other that the last of the lower nombre may not be with-draw of the last of the ouerer nombre for it is lasse than the lower, other [how be it, that] it myght be with-draw as for hym-self fro the ouerer the remenaunt may not so oft of them above, other yf þe last of the lower be even to the figure above his hede, and þe next last oþer the figure be-fore þat be more þan the figure above sette. Fol. 532. *These so ordeynede, me most wirche from the last figure of þe nombre of the dyvyser, and se how oft it may be with-draw of How to begin. and fro the figure aboue his hede, namly so that the remenaunt may be take of so oft, and to se the residue as here:—
| The residue | 2 | 6 | |
| The quocient | 9 | ||
| To be dyvydede | 3 | 3 | 2 |
| The dyvyser | 3 | 4 |
An example. And note wele that me may not withe-draw more than .9. tymes nether lasse than ones. Therfor se how oft þe figures of the lower ordre may be with-draw fro the figures of the ouerer, and the nombre that shewith þe quocient most be writ ouer the hede of þat figure, vnder the whiche the first figure is, of the dyviser; Where to set the quotiente And by that figure me most withe-draw alle oþer figures of the lower ordir and that of the figures aboue thaire hedis. This so done, me most sette forwarde þe figures of the diuiser by o difference towardes the right honde and worche as before; and thus:— Examples.
| Residuum | . | 1 | 2 | ||||||||||
| quociens | 6 | 5 | 4 | 2 | 0 | 0 | 4 | ||||||
| Diuidendus | 3 | 5 | 5 | 1 | 2 | 2 | 8 | 8 | 6 | 3 | 7 | 0 | 4 |
| Diuisor | 5 | 4 | 3 | 4 | 4 | 2 | 3 |
| The quocient | 6 | 5 | 4 | |||
| To be dyvydede | 3 | 5 | 5 | 1 | 2 | 2 |
| The dyvyser | 5 | 4 | 3 |
A special case. And yf it happe after þe settyng forwarde of the figures þat þe last of the divisor may not so oft be withdraw of the figure above his hede, above þat figure vnder the whiche the first of the diuiser is writ me most sette a cifre in ordre of the nombre quocient, and sette the figures forwarde as be-fore be o difference alone, and so me shalle do in alle nombres to be dyvidede, for where the dyviser may not be with-draw me most sette there a cifre, and sette forwarde the figures; as here:—