Duplicacio{u}n is ag{re}gacion of nombre [to itself] þat me may se the nombre growen. In doublyng{e} ay is but one ordre of figures necessarie. And me most be-gynne w{i}t{h} the lift side, other of the more figure, And after the nombre of the more figure rep{re}sentith{e}. [*Fol. 51.] In the other .3. before we begynne all{e} way fro the right side and fro the lasse nombre, In this spice and in all{e} other folowyng we wolle begynne fro the lift side, ffor and me bigon th{e} double fro the first, omwhile me myght double oo thynge twyes. And how be it that me myght double fro the right, that wold{e} be harder in techyng and in workyng. Therfor yf thow wolt double any nombre, write that nombre by his differences, and double the last. And of that doubly{n}g other growith{e} a nombre digital, article, or componed{e}. [If it be a digit, write it in the place of the first digit.] If it be article, write in his place a cifre and transferre the article toward{e} the lift, as thus:-- +------------------+----+ | double | 10 | +------------------+----+ | to be doubled{e} | 5 | +------------------+----+ And yf the nombre be componed{e}, write a digital that is part of his composicio{u}n, and sette the article to the lift hand{e}, as thus:-- +------------------+----+ | doubled{e} | 16 | +------------------+----+ | to be doubled{e} | 8 | +------------------+----+ That done, me most double the last save one, and what groweth{e} þ{er}of me most worche as before. And yf a cifre be, touch{e} it not. But yf any nombre shall{e} be added{e} to the cifre, in þe place of þe figure wiped{e} out me most write the nombre to be added{e}, as thus:-- +------------------+---+---+---+ | doubled{e} | 6 | 0 | 6 | +------------------+---+---+---+ | to be doubled{e} | 3 | 0 | 3 | +------------------+---+---+---+ [Sidenote: How to prove your answer.] In the same wise me shall{e} wirch{e} of all{e} others. And this p{ro}bacio{u}n: If thow truly double the halfis, and truly half the doubles, the same nombre and figure shall{e} mete, such{e} as thow labo{ur}ed{e} vpon{e} first, And of the contrarie. +------------------+---+---+---+ | Doubled{e} | 6 | 1 | 8 | +------------------+---+---+---+ | to be doubled{e} | 3 | 0 | 9 | +------------------+---+---+---+ [Headnote: Chapter VI. Multiplication.] [Sidenote: Definition of Multiplication. Multiplier. Multiplicand. Product.]