Mediacio{u}n is the fyndyng of the halfyng of eu{er}y nombre, that it may be seyn{e} what and how moch{e} is eu{er}y half{e}. In halfyng ay oo order of figures and oo nombre is necessary, that is to sey the nombre to be halfed{e}. Therfor yf thow wilt half any nombre, write that nombre by his differences, and begynne at the right, that is to sey, fro the first figure to the right side, so that it be signyficatif{e} other rep{re}sent vnyte or eny other digitall{e} nombre. If it be vnyte write in his place a cifre for the figures folowyng, [lest they signify less], and write that vnyte w{i}t{h}out in the table, other resolue it in .60. mynvt{es} and sette a-side half of tho m{inutes} so, and reserve the remen{au}nt w{i}t{h}out in the table, as thus .30.; other sette w{i}t{h}out thus .{dī}: that kepeth{e} none ordre of place, Nathelesse it hath{e} signyficacio{u}n. And yf the other figure signyfie any other digital nombre fro vnyte forth{e}, oþ{er} the nombre is od{e} or even{e}. If it be even, write this half in this wise:-- +-----------------+---+---+ | Halfed{e} | 2 | 2 | +-----------------+----+--+ | to be halfed{e} | 4 | 4 | +-----------------+---+---+ And if it be odde, Take the next even vndre hym conteyned{e}, and put his half in the place of that odde, and of þe vnyte that remayneth{e} to be halfed{e} do thus:-- +-----------------+---+---+ | halfed{e} | 2 | 3 | [di] +-----------------+---+---+ | To be halfed{e} | 4 | 7 | +-----------------+---+---+ [Sidenote: Then halve the second figure. If it is odd, add 5 to the figure before.] This done, the second{e} is to be halfed{e}, yf it be a cifre put it be-side, and yf it be significatif{e}, other it is even or od{e}: If it be even, write in the place of þe nombres wiped{e} out the half{e}; yf it be od{e}, take the next even vnder it co{n}tenyth{e}, and in the place of the Impar sette a-side put half of the even: The vnyte that remayneth{e} to be halfed{e}, respect had{e} to them before, is worth{e} .10. Dyvide that .10. in .2., 5. is, and sette a-side that one, and adde that other to the next figure p{re}cedent as here:-- +-----------------+---+---+---+ | Halfed{e} | | | | +-----------------+---+---+---+ | to be halfed{e} | | | | +-----------------+---+---+---+ And yf þe addicio{u}n shold{e} be made to a cifre, sette it a-side, and write in his place .5. And vnder this fo{ur}me me shall{e} write and worch{e}, till{e} the totall{e} nombre be halfed{e}. +------------------+---+---+---+---+---+----+----+---+ | doubled{e} | 2 | 6 | 8 | 9 | 0 | 10 | 17 | 4 | +------------------+---+---+---+---+---+----+----+---+ | to be doubled{e} | 1 | 3 | 4 | 4 | 5 | 5 | 8 | 7 | +------------------+---+---+---+---+---+----+----+---+ [Headnote: Chapter V. Duplation.] [Sidenote: Definition of Duplation. Where to begin. Why. What to do with the result.]