+----------------+--+-+-+-+-+-+---++--+-+-+-+-+--++----+-+--+-+--+ | Residuu{ m} | | | | | | | 5 || | | | | | 4|| 1|0|1 |9| | +----------------+--+-+-+-+-+-+---++--+-+-+-+-+--++----+-+--+-+--+ | Cubicandu{ s} | 8|3|6|5|4|3| 2 || 3|0|0|7|6| 7|| 1 1|6|6 |7| | +----------------+--+-+-+-+-+-+---++--+-+-+-+-+--++----+-+--+-+--+ | Triplum | | |6|0| | | || | | |1|8| || | |4 | | | +----------------+--+-+-+-+-+-+---++--+-+-+---+--++----+-+--+-+--+ | Subt{ r}iplu{ m} | 2| | |0| | |[3]|| | |6| | | 7|| 2| | |2| | +----------------+--+-+-+-+-+-+---++--+-+-+-+-+--++----+-+--+-+--+
[Sidenote: Continue this process till the first figure is reached. Examples. The residue. Special cases. Special case.]
Nother me shall{ e} not cesse of the fyndyng{ e} of that digit, neither of his triplacio{ u}n, neþ{ er} of the triplat-is [{ 29}]anteriorac{ i}o{ u}n, that is to sey, settyng forward{ e} by .2. differences, Ne therof the vndre-triple to be put vndre the triple, Nether of the multiplicacio{ u}n þ{ er}of, Neither of the subtraccio{ u}n, till{ e} it come to the first figure, vnder the which{ e} is a digitall{ e} nombre to be found{ e}, the which{ e} with{ e} his vndre-treblis most be had{ e} in tribles, After-ward{ e} w{ i}t{ h}out vnder-treblis to be had{ e} into produccio{ u}n, settyng away all{ e} that is ou{ er} the hed{ e} of the triplat nombre, After had into hymself{ e} cubikly, and sette all{ e}-way that is ou{ er} hym.
+------------------+---+---+---+---++---+---+---+---+---+ | To be cubiced{ e} | 1 | 7 | 2 | 8 || 3 | 2 | 7 | 6 | 8 | +------------------+---+---+---+---++---+---+---+---+---+ | The triple | | | 3 | 2 || | | | 9 | | +------------------+---+---+---+---++---+---+---+---+---+ | The vnder triple | | | 1 | 2 || |[3]| | 3 | 3 | +------------------+---+---+---+---++---+---+---+---+---+
Also note wele that the p{ ro}ducc{ i}on comyng{ e} of the ledyng of a digite found{ e}[{ 30}] [[w{ i}t{ h} an vndre-triple / other of an vndre-triple in a triple or triplat is And after-ward{ e} w{ i}t{ h} out vndre-triple other vndre-triplis in the p{ ro}duct and ayene that p{ ro}duct that cometh{ e} of the ledyng{ e} of a digit found{ e} in hym-self{ e} cubicall{ e}]] me may adde to, and also w{ i}t{ h}-draw fro of the totall{ e} nombre sette above that digit so found{ e}.[{ 31}] [[as ther had be a divisio{ u}n made as it is opened{ e} before]] That done ought or nought most be the residue. If it be nought, It is open that the nombre p{ ro}posed{ e} was a cubik{ e} nombre, And his rote a digit founde last w{ i}t{ h} the vnder-triples: If the rote therof wex bad{ e} in hym-self{ e}, and afterward{ e} p{ ro}duct they shall{ e} make the first fig{ ur}es. And yf ought be in residue, kepe that w{ i}t{ h}out in the table; and it is open{ e} that the nombre was not a cubik{ e}. but a digit last founde w{ i}t{ h} the vndirtriplis is rote of the most cubik{ e} vndre the nombre p{ ro}posed{ e} conteyned{ e}, the which{ e} rote yf it be had{ e} in hym-self{ e}, And aft{ er}ward{ e} in a p{ ro}duct of that shall{ e} growe the most cubik{ e} vndre the nombre p{ ro}posed{ e} conteyned{ e}, And yf that be added{ e} to a cubik{ e} the residue res{ er}ued{ e} in the table, woll{ e} make the same figures that ye had{ e} first. [*Fol. 56.] And yf no digit after the anterioracio{ u}n[{ 32}] may not be found{ e}, than put ther{ e} a cifre vndre a cifre vndir the third{ e} figure, And put forward{ e} þe fig{ ur}es. Note also wele that yf in the nombre p{ ro}posed{ e} ther ben no place of thowsand{ es}, me most begynne vnder the first figure in the extraccio{ u}n of the rote. some vsen forto distingue the nombre by threes, and ay begynne forto wirch{ e} vndre the first of the last t{ er}nary other unco{ m}plete nombre, the which{ e} maner of op{ er}acio{ u}n accordeth{ e} w{ i}t{ h} that before. And this at this tyme suffiseth{ e} in extraccio{ u}n of nombres quadrat or cubik{ es} { et}c.