Algorithms; Arithmetic -- Early works to 1900; Mathematics -- History
So y^t yf I subtracte 2892 fro{m} 8746, the remayner wyll be 5854,
[*117b] And that this is truely wrought, you maye proue by Addition: for
yf you adde to this remayner the same su{m}me that you dyd subtracte,
then wyll the formar su{m}me 8746 amount agayne.
_S._ That wyll I proue: and fyrst I set the su{m}me that was subtracted,
which was 2892, {and} the{n} the remayner 5854, thus.
--------------+--------------
| o
-||--o-o------+--------------
o | o
-----o-o-o----+--o-o-o-------
o | o
-----o-o-o-o--+--------------
|
-----o-o------+--o-o-o-o-----
Then do I adde fyrst y^e 2 to 4, whiche maketh 6, so take I vp 5 of
those counters, and in theyr stede I sette 1 in the space, as here
appereth.
--------------+------------
| o
-||--o-o------+------------
o | o
-----o-o-o----+--o-o-o-----
o | o
-----o-o-o-o--+------------
| o
--------------+--o---------
[*118a] Then do I adde the 90 nexte aboue to the 50, and it maketh 140,
therfore I take vp those 6 counters, and for them I sette 1 to the
hundredes in y^e thyrde lyne, {and} 4 in y^e second lyne, thus.
------------+--------------
| o
-||--o-o----+--------------
o | o
-----o-o-o--+--o-o-o-o-----
|
------------+--o-o-o-o-----
| o
------------+----o---------
Then do I come to the hundredes, of whiche I fynde 8 in the fyrst summe,
and 9 in y^e second, that maketh 1700, therfore I take vp those 9
counters, and in theyr stede I sette 1 in the .iiii. lyne, and 1 in the
space nexte beneth, and 2 in the thyrde lyne, as you se here.
----------+--------------
| o
-||--o-o--+--o-----------
| o
----------+--o-o---------
|
----------+--o-o-o-o-----
| o
----------+--o-----------
Then is there lefte in the fyrste summe but only 2000, whiche I shall
take vp from thence, and set [*118b] in the same lyne in y^e second
su{m}me, to y^e one y^t is there all redy: {and} then wyll the hole
su{m}me appere (as you may wel se) to be 8746, which was y^e fyrst
grosse summe, {and} therfore I do perceaue, that I hadde well subtracted
before. And thus you may se how Subtraction maye be tryed by Addition.
----+--------------
| o
-X--+--o-o-o-------
| o
----+--o-o---------
|
----+--o-o-o-o-----
| o
----+----o---------
_S._ I perceaue the same order here w^t cou{n}ters, y^t I lerned before
in figures.
_M._ Then let me se howe can you trye Addition by Subtraction.
_S._ Fyrste I wyl set forth this exa{m}ple of Additio{n} where I haue
added 2189 to 4988, and the hole su{m}me appereth to be 7177,
Public-domain text, read in full here on John Shaqi.
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