Algorithms; Arithmetic -- Early works to 1900; Mathematics -- History
Wherby you se, that 1542 (which is the nomber of yeares syth Ch[r]ystes
incarnation) beyng multyplyed by 365 (which is the nomber of dayes in
one yeare) dothe amounte vnto 562830, which declareth y^e no{m}ber of
daies sith Chrystes incarnatio{n} vnto the ende of 1542[{1}] yeares.
(besyde 385 dayes and 12 houres for lepe yeares).
_S._ Now wyll I proue by an other exa{m}ple, as this: 40 labourers
(after 6 d. y^e day for eche man) haue wrought 28 dayes, I wold [*125a]
know what theyr wages doth amou{n}t vnto: In this case muste I worke
doublely: fyrst I must multyplye the nomber of the labourers by y^e
wages of a man for one day, so wyll y^e charge of one daye amount: then
secondarely shall I multyply that charge of one daye, by the hole nomber
of dayes, {and} so wyll the hole summe appeare: fyrst therefore I shall
set the su{m}mes thus.
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|
------+--o-o-o-o-----
o |
--o---+--------------
Where in the fyrste space is the multyplyer (y^t is one dayes wages for
one man) {and} in the second space is set the nomber of the worke men to
be multyplyed: the{n} saye I, 6 tymes 4 (reckenynge that second lyne as
the lyne of vnites) maketh 24, for whiche summe I shulde set 2 counters
in the thyrde lyne, and 4 in the seconde, therfore do I set 2 in the
thyrde lyne, and let the 4 stand styll in the seconde lyne, thus.[*125b]
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-----+--o-o---------
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So apwereth the hole dayes wages to be 240d’. that is 20 s. Then do I
multiply agayn the same summe by the no{m}ber of dayes and fyrste I
sette the nombers, thus.
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---------+--------------
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---------+--o-o---------
|
--o-o----+--o-o-o-o-----
o |
--o-o-o--+-------------
The{n} bycause there are counters in dyuers lynes, I shall begynne with
the hyghest, and take them vp, settynge for them the multyplyer so many
tymes, as I toke vp counters, y^t is twyse, then wyll y^e su{m}me stande
thus.
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| o
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| o
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Then come I to y^e seconde lyne, and take vp those 4 cou{n}ters,
settynge for them the multiplyer foure tymes, so wyll the hole summe
appeare thus.[*126a]
-----+----------
| o
-----+--o-------
| o
-----+--o-o-----
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-----+--o-o-----
|
-----+----------
So is the hole wages of 40 workeme{n}, for 28 dayes (after 6d’. eche
daye for a man) 6720d’. that is 560 s. or 28 l’i.
[Headnote: Division on the Counting Board.]
[Sidenote: Diuision.]
Public-domain text, read in full here on John Shaqi.
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