And if it hap þ{a}t no digit may be found{e}, Than sette a cifre vndre a cifre, and cesse not till{e} thow fynde a digit; and whan thow hast founde it to double it, neþ{er} to sette the doubled{e} forward{e} nether the vnder doubled{e}, Till thow fynde vndre the first figure a digit, the which{e} lad{e} in all{e} double, settyng away all{e} that is ou{er} hym in respect of the doubled{e}: Than lede hym into hym-self{e}, and put a-way all{e} in regard{e} of hym, other as nygh{e} as thow maist. That done, other ought or nought wolle be the residue. If nought, than it shewith{e} that a nombre componed{e} was the quadrat, and his rote a digit last found{e} w{i}t{h} vnder{e}-double other vndirdoubles, so that it be sette be-fore: And yf ought[{22}] remayn{e}, that shew{i}t{h} that the nombre p{ro}posed{e} was not quadrat,[{23}] [[wher-vpon{e} se the table in the next side of the next leef{e}.]] but a digit [last found with the subduple or subduples is] [Sidenote: This table is constructed for use in cube root sums, giving the value of ab.^2] +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 2 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 3 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 4 | 32 | 48 | 64 | 80 | 96 |112[{24}]| 128 | 144 | +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 5 | 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 6 | 72 | 108 | 144 | 180 | 216 | 252 | 288 | 324 | +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 7 | 98 | 147 | 196 | 245 | 294 | 343 | 393 | 441 | +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 8 | 128 | 192 | 256 | 320 | 384 | 448 | 512 | 576 | +---+-----+-----+-----+-----+-----+---------+-----+---------+ | 9 | 168 | 243 | 324 | 405 | 486 | 567 | 648 |729[{25}]| +---+-----+-----+-----+-----+-----+---------+-----+---------+ [Sidenote: How to prove the square root without or with a remainder.] The rote of the most quadrat conteyned{e} vndre the nombre p{ro}posed{e}. Therfor yf thow wilt p{ro}ve yf thow have wele do or no, Multiplie the digit last found{e} w{i}t{h} the vnder-double oþ{er} vnder-doublis, and thow shalt fynde the same figures that thow haddest before; And so that nought be the [*Fol. 55.] residue. And yf thow have any residue, than w{i}t{h} the addicio{u}n þ{er}of that is res{er}ued{e} w{i}t{h}-out in thy table, thow shalt fynd{e} thi first figures as thow haddest them before, {et}c. [Headnote: Chapter XI. Extraction of Cube Root.]