And me shall{e} not cesse fro such{e} settyng of fig{ur}es forward{e}, nether of settyng{e} of þe quocient into the dyviser, neþ{er} of subt{ra}ccio{u}n of the dyvyser, till{e} the first of the dyvyser be w{i}t{h}-draw fro þe first to be divided{e}. The which{e} don{e}, or ought,[{17}] oþ{er} nought shall{e} remayne: and yf it be ought,[{17}] kepe it in the tables, And eu{er} vny it to þe diviser. And yf þ{o}u wilt wete how many vnytees of þe divisio{u}n [*Fol. 53^3.] wol growe to the nombre of the diviser{e}, the nombre quocient wol shewe it: and whan such{e} divisio{u}n is made, and þ{o}u lust p{ro}ve yf thow have wele done or no, Multiplie the quocient by the diviser, And the same fig{ur}es wolle come ayene that thow haddest bifore and none other. And yf ought be residue, than w{i}t{h} addicio{u}n therof shall{e} come the same figures: And so multiplicacio{u}n p{ro}vith{e} divisio{u}n, and dyvisio{u}n multiplicacio{u}n: as thus, yf multiplicacio{u}n be made, divide it by the multipliant, and the nombre quocient wol shewe the nombre that was to be multiplied{e}, {et}c. [Headnote: Chapter VIII. Progression.] [Sidenote: Definition of Progression. Natural Progression. Broken Progression. The 1st rule for Natural Progression. The second rule. The first rule of Broken Progression. The second rule.] Progressio{u}n is of nombre after egall{e} excesse fro oone or tweyn{e} take ag{r}egacio{u}n. of p{ro}gressio{u}n one is naturell{e} or co{n}tynuell{e}, þ{a}t oþ{er} broken and discontynuell{e}. Naturell{e} it is, whan me begynneth{e} w{i}t{h} one, and kepeth{e} ordure ou{er}lepyng one; as .1. 2. 3. 4. 5. 6., {et}c., so þ{a}t the nombre folowyng{e} passith{e} the other be-fore in one. Broken it is, whan me lepith{e} fro o nombre till{e} another, and kepith{e} not the contynuel ordir{e}; as 1. 3. 5. 7. 9, {et}c. Ay me may begynne w{i}t{h} .2., as þus; .2. 4. 6. 8., {et}c., and the nombre folowyng passeth{e} the others by-fore by .2. And note wele, that naturell{e} p{ro}gressio{u}n ay begynneth{e} w{i}t{h} one, and Int{er}cise or broken p{ro}gressio{u}n, omwhile begynnyth{e} w{i}th one, omwhile w{i}t{h} twayn{e}. Of p{ro}gressio{u}n naturell .2. rules ther be yove, of the which{e} the first is this; whan the p{ro}gressio{u}n naturell{e} endith{e} in even nombre, by the half therof multiplie þe next totall{e} ou{er}er{e} nombre; Example of grace: .1. 2. 3. 4. Multiplie .5. by .2. and so .10. cometh{e} of, that is the totall{e} nombre þ{er}of. The second{e} rule is such{e}, whan the p{ro}gressio{u}n naturell{e} endith{e} in nombre od{e}. Take the more porcio{u}n of the oddes, and multiplie therby the totall{e} nombre. Example of grace 1. 2. 3. 4. 5., multiplie .5. by .3, and thryes .5. shall{e} be resultant. so the nombre totall{e} is .15. Of p{ro}gresio{u}n int{er}cise, ther ben also .2.[{18}] rules; and þe first is þis: Whan the Int{er}cise p{ro}gression endith{e} in even nombre by