Algorithms; Arithmetic -- Early works to 1900; Mathematics -- History
[{20}]To draw a rote of the nombre quadrat it is What-eu{er} nombre be
p{ro}posed{e} to fynde his rote and to se yf it be quadrat. And yf it be
not quadrat the rote of the most quadrat fynde out, vnder the nombre
p{ro}posed{e}. Therfor yf thow wilt the rote of any quadrat nombre draw
out, write the nombre by his differences, and compt the nombre of the
figures, and wete yf it be od{e} or even. And yf it be even, than most
thow begynne worche vnder the last save one. And yf it be od{e} w{i}t{h}
the last; and forto sey it shortly, al-weyes fro the last od{e} me
shall{e} begynne. Therfor vnder the last in an od place sette, me most
fynd{e} a digit, the which{e} lad{e} in hym-self{e} it puttith{e} away
that, þat is ou{er} his hede, oþ{er} as neigh{e} as me may: suche a
digit found{e} and w{i}t{h}draw fro his ou{er}er, me most double that
digit and sette the double vnder the next figure toward{e} the right
hond{e}, and his vnder double vnder hym. That done, than me most
fy{n}d{e} a-noþ{er} digit vnder the next figure bifore the doubled{e},
the which{e} [*Fol. 54b] brought in double setteth{e} a-way all{e} that
is ou{er} his hede as to reward{e} of the doubled{e}: Than brought into
hym-self settith{e} all away in respect of hym-self, Other do it as nye
as it may be do: other me may w{i}t{h}-draw the digit [{21}][last]
found{e}, and lede hym in double or double hym, and after in
hym-self{e}; Than Ioyne to-geder the p{ro}duccion{e} of them bothe, So
that the first figure of the last p{ro}duct be added{e} before the first
of the first p{ro}duct{es}, the second{e} of the first, {et}c. and so
forth{e}, subtrahe fro the totall{e} nombre in respect of þe digit.
[Sidenote: Examples.]
+------------------+-+-+-+-+-++-+-+-+-+-++---+-+---+-+---+-+-+
| The residue | | | | | || | | | | || | | |5| 4 |3|2|
+------------------+-+-+-+-+-++-+-+-+-+-++---+-+---+-+---+-+-+
| To be quadred{e} |4|1|2|0|9||1|5|1|3|9|| 9 |0| 0 |5| 4 |3|2|
+------------------+-+-+-+-+-++-+-+-+-+-++---+-+---+-+---+-+-+
| The double | |4|0| | || |2| |4| || |6| |0| | |0|
+------------------+-+-+-+-+-++-+-+-+-+-++---+-+---+-+---+-+-+
| The vnder double |2| |0| |3||1| |2| |3||[3]| |[0]| |[0]| |0|
+------------------+-+-+-+-+-++-+-+-+-+-++---+-+---+-+---+-+-+
[Sidenote: Special cases. The residue.]
Public-domain text, read in full here on John Shaqi.
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