Algorithms; Arithmetic -- Early works to 1900; Mathematics -- History
[*121b.] and then is there 80, as well w^t those 4 counters, as yf I had
set downe y^e other 4 also. Now do I take the 200 in the fyrste su{m}me,
and adde them to the 400 in the seconde summe, and it maketh 600,
therfore I take vp the 2 counters in the fyrste summe, and 3 of them in
the seconde summe, and for them 5 I set 1 in y^e space aboue, thus.
-----------|------------
| o
-----------|--o---------
| o
-X--o-o-o--|------------
| o
-----------|--o---------
| o
-----------|--o-o-o-----
|
-----------|--o---------
Then I take y^e 3000 in y^e fyrste su{m}me, vnto whiche there are none
in the second summe agreynge, therfore I do onely remoue those 3
counters from the fyrste summe into the seconde, as here doth appere.
----|-------------
| o
----|---o---------
| o
-X--|---o-o-o-----
| o
----|-o-----------
| o
----|---o-o-o-----
|
----|---o---------
[*122a.] And so you see the hole su{m}me, that amou{n}teth of the
addytio{n} of 65436 with 3245 to be 6868[1]. And yf you haue marked
these two exa{m}ples well, you nede no farther enstructio{n} in Addition
of 2 only summes: but yf you haue more then two summes to adde, you may
adde them thus. Fyrst adde two of them, and then adde the thyrde, and
y^e fourth, or more yf there be so many: as yf I wolde adde 2679 with
4286 and 1391. Fyrste I adde the two fyrste summes thus.
-------------|-----------|--------------
| | o
-X--o-o------|--o-o-o-o--|--o-----------
o | | o
----o--------|--o-o------|--o-o-o-o-----
o | o | o
----o-o------|--o-o-o----|--o-----------
o | o | o
----o-o-o-o--|--o--------|--------------
[*122b.] And then I adde the thyrde thereto thus. And so of more yf you
haue them.
-------------|-----------|------------
| o | o
-X--o--------|--o--------|--o-o-o-----
| o |
----o-o-o----|--o-o-o-o--|--o-o-o-----
o | o | o
----o-o-o-o--|----o------|------------
| o | o
----o--------|-----------|--o---------
[Headnote: Subtraction on the Counting Board.]
[Sidenote: Subtraction.]
_S._ Nowe I thynke beste that you passe forth to Subtraction, except
there be any wayes to examyn this maner of Addition, then I thynke that
were good to be knowen nexte.
_M._ There is the same profe here that is in the other Addition by the
penne, I meane Subtraction, for that onely is a sure waye: but
consyderynge that Subtraction must be fyrste knowen, I wyl fyrste teache
you the arte of Subtraction, and that by this example: I wolde subtracte
2892 out of 8746. These summes must I set downe as I dyd in Addition:
but here it is best [*116a (_sic_).] to set the lesser no{m}ber fyrste,
thus.
Public-domain text, read in full here on John Shaqi.
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