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The Philosopher's Game -- Rythmomachy
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The Philosopher's GameThis file is a transcription of a 1563
translation by William Fulke (or Fulwood -- the sources disagree)of
Boissiere's 1554/56 description of Rythmomachy. It is entry 15542a
in the Short Title Catalog ofPollard and Redgrave, and on Reel 806
of the corresponding microfilm collection.
Annotation will occur occasionally throughout; they will appear
in square brackets and italics, [like this]. Spelling will be
erratic; I'm transcribing quickly, so I will often be modernizing
the spelling, butwill leave original spelling whenever I consider
there to be doubt about the meaning. I also willsometimes modernize
the punctuation and paragraph breaks in the interests of
readability. This is notintended to serve as a definitive critical
edition, merely a working copy, good enough to understand
thegame.
My thanks to Peter Mebben, who pointed me in the direction of
this source, and provided the first draftof the dedication.
[Title Page]THE MOST NOBLE
ancient, and learned playe, called the Phi-losophers game,
invented for the honest re-
creation of students, and other [sober?] persons, inpassing the
tediousness of time, to the release of
their labours, and the exercise oftheir wittes.
Set forth with such playne precepts, rules and ta-bles, that all
men with ease may understande
it, and most men with pleasure practice it.by Rafe Lever and
augmen-
ted by W. F.[Picture, probably stock, of two men playing at a
game on a square 10x10 board.]
Printed at London by James Rowbothum, and areto be sold at his
shop under Bowchurch
in chepe syde.
[Page]
The Lord Robert Duddedlye.
[Picture of Lord Robert, with the motto "Vulnere virescit
virtus" alongside.]
The Physiognomie here figured, appeares by Paynters Arte:But
valyant are the vertues that, possesse the inward parte.
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Whych in no wise may paynted be, yet playnely so appeare,&
shine abrod in every place with beames most bright & clear.
[Page]
[The Epistle Dedicatory]TO THE RYGHT HO-
norable, the Lord Robert Dudley, Maister of the Queenes
Maiesties horse,Knight of the most honorable order
of the Garter, and one of the Queenesmaiesties privie Counsell,
JAMES
ROUBOTHUM heartelye wisheth long life, withencrease of godly
ho-
nour and eternallfelicitie.
Sith that your honour is full bent,(right honorable lord)To
wisdom & to godlineswith true faithful accord.
Sith that in deed you do delyte,in learning and in skyll:The
show wherof doth well expressea perfect godly wyll.
Sith that also you have in hand,affayres of force and waight:And
study do both day and night,to set all thinges full straight.
[Page]
I thought therfore your honour shouldnot lacke some godly
game:Whereby you might at vacant timesyour self to pastyme
frame.
Whereby I say you might release,such travailes from your
mynde:And in the meane while honest mirthand prudent pastyme
fynde.
Remembring then this auncient play,where wisdome doth
abound:Called the Philosophers game,
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me thinkth I have one found.
Which may your honour recreate,to read and exercise:And which to
you I here submit,in rude and homly wise.
Pithagoras did first invent,this play as it is thought:And
therby after studies great,his receation sought.
[Page]
Yea therby he would well refreshe,his studious wery braine:And
still in knowledge further wadeand plye it to his gaine.
Accompting that a wicked play,wherin a man leudely:Mispendes his
tyme & wit also,and no good getts thereby.
But grevously offendes the Lord,and so in steed of rest:With
trouble and vexation great,on every side is prest.
Most games and playes abused are,and fewe do now remaine:In good
and godly order as,they ought to be certaine.
For why? all games should recreat,the hevy mynde of man:And eke
the body overlayde:with cares and troubles than.
[Page]
But now in stead of pleasant mirth,great passions do arise:In
stead of recreation now,revengings we practise.
In stead of love and amitie,long discords do appeare:In stead of
trueth and quietnes,great othes and lyes we heare.
In stead frendship, falshode now,mixed with cruell hate:We finde
to be in playes & games,which dayly cause debate.
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Pithagoras therfor I saye,to make redresse herein:Invented first
this godly game,therby to flye from sinne.
Since which time it continued hath,in Frenche & Latin
eke:Still exercisde with learned men,their comforts so to
seeke.
[Page]
Wherby without a further prose,all men may be right sure:That
this game unto gravitie,and wisdome doth allure.
Els would not that Philosopher,Pithagoras so wyse:Have laboured
with diligence,this pastime to devyse.
Els would not so well learned men,have amplified the same:From
tyme to tyme with travell great,to bring it into fame.
But let us nerer now proceed,and come we to theffect:And then
shall we assuredly,this pastime not neglect.
For it with pleasure doth asswage,the heavy troubled hart:And
with lyke comforts drives away,all kynde of sourging smart.
[Page]
The mynde it maketh circumspect,and heedfull for to bee;The tyme
that theron is bestowd,is not in vaine trulye.
The body it doth styrre and move,to lightsomnes and ioye:The
sences and the powers all,it no wyse doth annoye.
It practiseth Arithmeticke,and use of number showth:As he that
is conning therein,assuredly well knowth.
In Geometie it truly wades,
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and therein hath to do:A learned play it is doutlesse,none can
say nay thereto.
Proportion also musicall,it ioynes with thother twayne:So that
therin three noble artes,are exercisde certayne.
[Page]
What game therfore lyke unto this,may gotten be or had?There is
not one that I do know,the rest are all to bad.
It causeth no contention this,nor no debate at all,By this no
hatred wrath nor guyle,in any wise doth fall.
It stirreth not such troubles that,our frend becomes our foe:It
moveth not to mischiefe this,as many others do.
Let us avoyde the worst therfore,and cleve we to the best.So
shall we shunne all wickednes,and purchase quiet rest.
So shall we serve the living Lorde,and walke after his will:So
shall we do the thing is good,and flye that which is yll.
[Page]
So shall we live right christianlyke,and do our duties well:So
shall we please both god & prince,none shall us need
compell.
And then the Lord of his mercie,will prosper us alwayes:And
graunt us here to have on earth,full many godly dayes.
Yea then the Lord of his goodnes,and grace celestiall:Will guyde
and governe our affaires,and blesse our doings all.
Which Lord graunt to your honour here,good dayes & long to
have:
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with much encrease of helth & welthand from all hurt you
save.
Your honours most humble,James Roubothum.
[Page]
To the Reader.I Dout not but some man of severe judgement so
soone as he hath one read the title of this boke wylimmediately
sai, that I had more need to exhort men to worke, then to teach
them to play, which censureif it procede not of such a froward
morositie that can be content with nothing but that he doth
himself, Ido not only well admit, but also willingly submit my self
therto. And if I could be persuaded that men atmine exhortation
wold be more diligent to labour, I would not only write a treatise
twise as long as this,but also thynke my whole time wel bestowed,
if I
[Page]
did nothing els, but invent, speake, and write that which might
exhort, move, & persuade them to thefurtherance of the same.
But if after honest labour and travell recreation be requisit, (and
that nede nofurther probation because we favour the cause wel
inough) I had rather teach men so to play, as bothhonestye may be
reserved, their wittes exercised, they them selves refreshed, and
some profit alsoattayned, then for lacke of exercise to see them
either passe the tyme in idlenes, or els to have pleasure inthyngs
fruitles and uncomely. And if great Emperours and mighty Monarches
of the world have notbene ashamed by writing bookes to teaches the
art of Dyce
[Page]
playing, of all good men abhorred, and by all good lawes
condemned: have I not some colour ofdefence, to teache the game,
which so wyse men have invented, so learned men frequented, and no
goodman hath ever condemned.
The invention is ascribed to Pythagoras, it beareth the name of
Philosophers, prudent men do practise it& godly men do praise
it. But because many herein (as in a play) have challenged much
authoritie, theyhave filled this game with much diversitie. In
which as I could perceive the most differens of playing toconsist
in thre kindes, so have I playnly and briefly set them forth in
Englishe not as though there mightnot more diversities be espied,
but
[Page]
that I thought these to them whom I have written to be
sufficient. yet for that I woulde be lothe, fromplaye & game,
to fall to earnest contention, if any man in this doing or any part
thereof shall think I havedone amisse, and will do better himself,
so far am I from envying his good proceding, that I wil be
rightglad, and geve him heartye thankes therefore.
All things belonging to this gamefor reason you may bye:At the
bookeshop under Bochurchin Chepesyde redilye.
[Page]
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The bookes verdicte.Wanting I have bene long truly,In english
language many a day:Lo yet at last now here am I,Your labours great
for to delay,And pleasant pastime you to showe,Mynding your wits to
move I trowe.
For though to mirth I do provoke,Unto Wisdome yet move I
more:Laying on them a pleasant yoke,Wisdom I meane, which is the
dore,Of all good things and commendable:Dout this I thinke no man
is able:
CATO
Interpone tuis interdum gaudia curis:Yt possis animo quemuis
sufferre laborem.
[Page]
The diffinitionThat moste auncient and learned playe, called the
Philosophers game, beinge in Greeke termed [...], is as much to
saye in Englishe, as the battell of numbers. Numbers be either even
or odde, wherefore the evenparte is against the odde, either parte
havinge a kyng, whych being taken of the adversaryes part, and
atriumphe celebrated within his campe, the game is ended.
Of diverse kyndes of playinge.Amonge the dyverse kyndes of
playing thys game, we shall sette forth three sortes, of which the
readermaye chose whether of them he lyketh beste. And of all those
three, we shall
[Page]
gyve suche shorte and easye rules, that no man (althoughe he
were altogether ignoraunt in Arithmetike)shall fynde the game so
hard, but that he may learne to playe it.
Of the partes of thys Game.He that wyll learne thys game, any of
the three waies, muste first be enstructed of these sixe
partes.
The table as the fielde.2. the menne and the numbers of them as
the hoste.3. the placynge of them, as the encampynge.4. the order
of playe and removynge the men, as the marchynge and fyghtynge.5.
the manner and lawes of conqueryng and taking.6. and last of al the
triumphe after the victorye.
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Of these partes in the fyrst kynd of playng.[Page]
The table muste be a playne borde conteynynge .128. squares that
is .8. in breadth and .16. in lengthsette forthe in two dyverse
collours. Or for a plainer understandynge, the table is a doble
chesse bord, asit were two chessebordes joyned together, the length
of twoo, the breadth of one, whereof thys is anexample.
[Page]
[Complex picture, showing a 16x8 checkerboard, with various
letter and symbols on various parts.This can't be fully represented
in text, so I won't try to show the whole thing now. The middle
section --rows 6 through 12 -- have letters on them, and look
somewhat like this:]
K L M X F Z B S C R H Y A T I N E V D W G Q P O
[Later sections will refer back to this table frequently, to
describe movement.]
[Page]
Of the men.The men be in number .48. Wherof .24. be of one side
& must be knowen by one colour, and .24. onthe other syde,
whyche also must be marked with a contrarye colour, as White and
Blacke, Blew andRedde, or what colours els you lyke best. But in
the colering there .3. thinges must be observed, thebottome or
lower part of every man (excepte the two kinges) muste by marked
wyth his adversariescolour, that when he is taken, he maye chaunge
his coate and serve him unto whome he is prisoner.
The seconde thinge considered in the men, is their fashion: for
of euther syde .8. are rounds, other .8.are triangles & .7.
(the king making .8.) are squares. There fashion is such [small
inset showingroundes, triangles, squares].
The kynges because they consist of all three sortes, as it is
knowen by the learned speculation of thenumbers, beare
[Page]
the fashion of all thre kindes, his foundations are two squares,
on which are sette, two triangles & uponthem rounds. But this
difference is betwene the kinges, the king of the even numbers,
hath a pointedtoppe, the king of the odde numbers is not pointed,
the cause dependeth upon the consideration of thesenumbers by which
they arise into piramidall fashion. The third thing considered in
the men, is thenumber that must be written or graven upon them
which to learne plainely for practise marke these shortrules.
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There be of eche kynde of men, two rankes or orders.
The first ranke or order of roundes be the digites even or odde
namely of the even .2.4.6.8. of the odde.3.5.7.9.
The second order of rounds are found by multiplyinge these
digites by themselves as .2. times .2. is.4.3. times .3. is .9. Of
the even they be .4.16.36.64. of the odde they be .9.25.49.81.
The first order of the triangles are found by addinge two of the
roundes together
[Page]
one of the firste order and another of the seconde order, as .2.
and .4. make sixe .3. and .9. make twelve,on the even syde they are
these .6.20.42.72. on the odde syde .12.30.56.90.
The second order of triangles be made by addynge one to every
one of the first order of roundes, andthen multiplying that number
in hym selfe: as .2. is one of the firste order of roundes, thereto
adde one,that is .3. then .3. tymes .3. is .9. a triangle of the
seconde order, on the even syde. Likewise to thre around on the
odde side, adde .1. so it is .4. then .4. tymes .4. is .16. On the
even parte, they be.9.25.49.81. on the odde parte
.16.36.64.100.
The first order of squares (in whyche are contayned the kynges)
be made by addynge two trianglestogether, one of the fyrste order,
and another of the secondes, as .6. and .9. make .15. likewyse .12.
and.16. make .28. Amonge the even they be .15.45. and .91. the
kynge .153. amonge the odde they be.28.66.120. and .190. the
kynge.
[Page]
The last order of squares be found, by dobling of every one of
the firste order of roundes, and afteradding one, last of all be
multiplying that number in itself, as twise .2. is .4. and .1.
added is .5. so .5.times .5. is .25. likewyse twyse .3. is .6.1.
added is .7. then .7. tymes .7. is .49. These be on the evensyde
.25.81.169.289. And of the odde syde .49.121.225.361.
These numbers must be sette uppon the men both on the upper
side, & also on the nether side. Exceptone of the kynges, which
must with the whole number of their pyramid, be marked, onely on
thebottome. Because the sydes muste have other numbers, namely the
highest point of the even kyng, musthave .1. the rounde next under
him marke with .4. the uppermost triangle with .9. the nethermost
with.16. The uppermost square muste have .25. The nethermost square
shall have .36. The king of the oddeupon his head, whiche is a
rounde, not pointed hath .16. upon his first triangle .25. on the
secondtriangle .36. uppon the fyrste square .49. upon the lowest
square .64.
[The numbers in the next paragraph are in circles and triangles,
to illustrate.]
Finally it shalbe good for the avoydance of confusion, to drawe
a line under every number. Ells mayyou take one for another, as 6
the even round & 9 the odde rounde, may be taken one for
another withoute this lyne or some suche marke, lykewise 6 and 9
Tryangles bothe of one syde. And this sufficientfor the men, the
fashion, colours and numbers.
The reason of these numbers and the knowledge of
theirproportione.For them that seke the speculation of these
numbers, rather then the practise for playing, and have somesight
in the sciens of Arithmetike, some thyng must be sayde of
proportion. For this purpose there be
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three kyndes of proportion. Multiplex, superparticuler, and
superpartiens.
[Page]
Of multiplex.MULTIPLEX proportion, is when a great number
conteyneth a lesse number manye tymes, and leavethnothing, as .8.
conteyneth .2. fower tymes and nothing remaineth .16. conteyneth
.4. &, this proportionsemeth best to agree with roundes because
the one number conteyneth the other and nothyngeremaineeth as the
fyrste order of roundes be.
[The following table shows the white (even) and black (odd)
rounds.]
2 4 6 83 5 7 9
[Page]
The second order be these.[This table shows the first and second
orders of rounds for both sides.]
double. quadruple. sextuple. occuple.2 4 6 84 16 36 64
proportion.triple. quintuple. septupl. nonuple3 5 7 99 25 49 81
[Page]
Of superparticuler proportion.Superparticuler proportion is when
a greater number contayneth a lesser with one part of it, which
maymeasure the whole, as .12. contayneth .9. and .3. whiche is a
thyrde parte of nine .6. contayneth .4. and.2. that is one halfe to
.4. Thys proportion beinge the cheife, next unto multiplex, is
beste figured by atrianguler forme, whyche hathe fewest lynes and
angles next unto a circle. For the manner of thysproportion
consider thys figure.
[Page]
[This table shows each base number above two rows of triangles,
and appears to be badly fouled up. Ibelieve the rows of base
numbers are wrong -- the first set should be the evens (2, 4, 6,
8), and thesecond the odds (3, 5, 7, 9). That would make each Latin
header match the number below it, the firstrow of triangles would
be the superparticulates for that base number, and the second row
would be thesecond order of triangles for that base number, which
is (x+1)2.]
sesquialter. sesquiquart sesqui.sext sesqu.oct.
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3 5 7 96 20 42 729 25 49 91sesquiter. sesquiquint. sesquisept.
sesquinona.4 6 8 1012 30 56 9016 36 64 100
[Page]
Superpartiens proportion.The superpartiens proportion is when
the greater number conteyneth the lesser and mo partes of it
thenone as .15. conteyneth .9. and .6. whiche is two thirdes of .9.
lyke wyse .28. conteyneth .16. and .12.that is 3/4 of .16. This
proportion conteineth divers parts beside the whole number therfore
is welfigured in the square, which also conteyneth more corners and
sides. For the maner of their proportionconsyder thys table.
[Page]
The first order of squares.[The following table contains the two
rows of triangles, with the corresponding square beneath.]
6 20 42 72 supparticulares added9 25 49 9115 45 91 153 being the
squares.12 30 56 9016 36 64 10028 66 120 190
[Page]
The second order followeth.third fyft seventh ninth5. 9. 13. 17.
These two rows are
just plain numbers.10. 36. 78. 136.15 43 91 153 These two rows
are the
two white orders of squares.25 81 169 289
superbipartiens tertias
supquadrupartiens quintas
supsextupartiens septimas
supoctupartiens nonas
[Page]
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fourth sixth eight tenth7. 11. 15. 19. These two rows are
just
plain numbers.21. 55. 105. 171.28 66 120 190 These two rows are
the
two black orders of squares.49 121 225 361
supertripartiens quartas
supquinpartiens sextas
supseptupartiens octavas
supnonpartiens decimas
[Page]
Of the kings.[Image of the two kings. Each is a pyramid of
numbered pieces, with two squares, two triangles, and around; one
has a little triangular "cap" on top. The images make it look like
higher-numbered piecesare actually larger -- I wonder if this is
true...]
The kinges conteine in them suche numbers, as beyng all added
together, make the whole piramidallnumber, the lowest square of the
even is .36. which riseth of the multiplying of .6. in it selfe.
The nextsquare that must be lesse, is .25. arisinge by the
multiplyinge of fyve in it self and so followeth .16. of.4. then
.9. of .3. laste .4. of .2. and single .1. all these added together
make up .91. After the same manerconsisteth the king of adde. The
lowest square is .64. arisinge of .8. multiplied in himselfe. The
next .49.of
[Page]
.7. times .7. then .36. of .6., .25. of .5. and .16. of .4.
these numbers make the whole pyramidall number
.190. which because it riseth not to the poynct of one, oughte
not to be sharpe poyncted, as hathe beenesayde before.
Of the placing, encamping or setting in araie.To retorne againe
to the plaine and easye playing of this game, next to the armie
& their armour, followether the order of their battel or
encamping. Which because it is more playne and easely seen which
theeye, then learned by the eare, I referre thee unto the table
where the battell is appoynted in suche order asthys kynde of playe
requireth.
[Page]
[The table below shows the layout of the board. To illustrate
this through text, I put squares intosquare braces, triangles into
angle brackets, and rounds into parentheses. Kings are signified
with anasterisk. Note that the top half, the evens, should be
upside-down.]
[25] [81] [169] [289][15] [45] [91]* [153] (4) (16) (36)
(64)
(2) (4) (6) (8)
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(9) (7) (5) (3)
(81) (49) (25) (9) [Error in original: 2 instead of 12][190]*
[120] [66] [28][361] [225] [121] [49]
[Page]
Of the marchinge or removing of the men.The battell beyng duely
placed, it followeth next, to know the maner of marching &
removing, for everykynd of men, hath their proper kynde of motion,
and fyrste we muste speake of the roundes.
The motyon of the roundes.The roundes muste move into the space
that is next unto them cornerwyse, as in the table, from thespace
.A. to any of these .B.C.D. or .E.
[Yes, this is clearly saying that rounds only move
diagonally.]
Of the triangles.The triangles passe three spaces counting that
in which they stande for one, and that into whych they doremove for
another, that is leaping over
[Page]
one space. As from the space .A. he maye remove into any of
these space .F.G.H. or .I. this is themotion of the triangle in
marchying or takyng. But in flying he maye remove the knyghtes
draught of thechesse, as from .A. into .X. or .W. &c.
Of the Squares.The Squares remove into the fourth place from
them, that is leaping over two, right forwarde orsydelong, as from
the place of .A. to any of these spaces .L.N.P.R. flyinge they maye
remove after theknyghts draught, but that they must passe foure
spaces, as from .P. to .Y. or .T. &c. And this for themarchinge
and removyng of the men, where note, that with theyr flying
draughte they can take no man,but if needed by helpe to besiege a
man.
Of the kynge marching.
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The kings because thei beare the forme of al the thre kynds, may
remove any
[Page]
of all theyr draughts when they list, into the nexte with the
rounde, into the thyrde with the triangle, andinto the fourth with
the square, and finally in all poyntes lyke the Queene at the
Chesse, saving that hecan not passe above foure spaces at the
most.
Of the maner of taking.The men may be taken sixe wayes, namely
by Equalitie, Oblivion, Addition, Subtraction, Multiplicationand
Division, and also if you wyll, and so agree by
/ Arithmeticall.Proportion < Geometricall.
\ Musicall.
Of Equalitie.[Page]
By equality men may be taken, when one man after hys motion,
seeth hys enemye beyng of the samenumber that he is, standing in
such place as he may remove into, then maye he take awaye hys
enemyeand not remove into hys place, as in this example .9. a
triangle of the even army, after he hath removed,espyeth .9. a
rounde of the odde armye, hym may he take up and not remove into
his place. But if .9. thetriangle, espye nine the rounde, before he
remove, standing in his draught, he maye take hym up andremove into
his place.
These men may be taken by equalitie .9.16.25.36.49.64.81.
because they are found in both the armies,and in asmuch as anye man
taken beinge torned wyth hys bottome upward, &that beareth
hysadversaries colloure, may serve his enemye on whose syde he is
taken, there maye yet be taken byequalitie .4. and .6.
[Page]
Of taking by oblivion.By oblivion anye man maye be taken even
the kinge him selfe, if he be so compassed with .4. men, thathys
lawfull draught be hindered, as for example the round standing in
the place of .1. and .4. men ofwhat kynd it skylleth not, occupying
the places of .2.3.4.5. after have set your last man in hys place
maybe taken by, also if a triangle be enclosed, as in .a. with any
foure men standing in .b.c.d.e. he may betakenm even so may a
square be taken. Also Triangles and squares may be beseged, if al
the foure menor any of them, the rest standyng nearer, doe standes
in the thyrde or fourth space from them so thatthey have no waye to
remove, as a triangle or square standing in .A. may be beseged by
.4. men or anyeof them (the reste standynge nearer) in .F.G.H.I.
Also a square standyng in .A. maye be taken byoblivion, yf the
fower
[Page]
men or some of them (the rest standing nearer) doe stande in
.L.N.P.R. And this is sufficient forOblivion, by which every man
may be taken in maner and forme as it hath bene taught.
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Of taking by Addition.When two numbers are so brought that they
fynde one of theyr enemies, which is as muche as bothethey beyng
added together, standing in such place as bothe they might remove
into, they shall take hymup, without removing into his place, so
soone as the latter of those two is set downe, but if
theadversaries men be in their daunger before they remove, one of
them whether the player lyst, shalberemoved into the place of that
man which is taken by Addition. As for example .12. the triangle is
in .A.if you can bring sixe the round, to stande in .B. and .6. the
triangle to stande in .G. because .6. and .6.being added make .12.
and bothe maye remove to .A. you maye take up the triangle
[Page]
.12. by addition. Also .120. the square standing in .P. and .49.
the rounde standing in .B. or elles .49.the square standing in .L.
which being added together make .69. [sic] which standeth in .A.
shal take thesayde square .169. by Addition.
Of taking by Subtraction.When two men do so stande, that the
lesser beyng subtracted out of the greater, the number remaining,is
all one with the adversaries man that standeth in both their
draughtes, so soone as the latter is set inhis place, he may take
awaye the adversarie, not removing into his place, unlesse he finde
him so beforehe remove: as for as example, .2. the rounde standing
in .B. & .9. the triangle standing in .6. [sic -- I believe it
means .G.] shall take theyr adversarie .7. standynge in .A. for .2.
out of .9. remayneth .7.Another example.
[Page]
The rounde .2. standyng in .A. maye be taken by .30. the
Triangle standynge in .H. and the square .28.standynge in .P. for
take .28. out of .30. and their remaineth .2.
Of takynge by multiplycation.When two numbers stande so, that
being multiplied one by the other, the producte is all one with
theiradversaryes man standynge in both their draughts, they may
take that man so sone as the latter is placed.And if they lye so
before thei remove, being so left of the adversarie, one of them
shal succede in hisplace that is taken, as in example. The rounde
.3. standeth in .D. and .5. standeth in .C. these two shaltake the
square .15. standynge in .A. because three tymes fyve is .15.
another example. The rounde .2.standing in .B. and the triangle .6.
standynge in .I. shall take their enemye the triangle .12. standing
in.A. by multiplycation for .2. tymes .6. is .12.
[Page]
Of takyng by division.By division a manne maye be taken, when
twoo of hys enemyes doe so stand, that one of them beyngdevided by
the other, the product is the same that their enemye is, standynge
in their draught, immediatlyafter the latter is placed, the enemye
may be removed. If he were left in their daunger before
removyng,one of them may remove into his place, an example. The
round .4. standyng in .D. and the triangle .20.standing in .F. may
take the adversarie .5. standing in .A. by division, bycause .4. in
.20. is conteyned.5. tymes. Another example, the round .5. standyng
in .B. and the triangle .30. standynge in .F. mayetake their enemye
.6. standynge in .A. for .5. in .30. is conteyned .6. tymes.
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Of the takynge of the kynges.[Page]
The game is never wonne, untyll the king be taken. The kings (as
hath bene sayde) may remove anyeway, so they passe not the fourth
space. They can not be taken by equalitie. But by oblivion the
wholekyng maye be taken away. Also his whole number at ones, that
is .91. or .190. by Addition, bySubtraction, by Multiplication, or
by Division. Also he maye be taken by partes, when any of hys
sydenumbers maye be taken then [loseth?] he that draughte, as when
anye of hys square numbers is gone hecan not remove the square
draughtm and so of the rest, tyl nothyng of him be left, then muste
he betaken away, and the triumph prepared.
The lawe of prisoners.When any is taken captive, he must be
tourned with his conquerers collor upward & placed in
thehindermost space of his victors campe, and from thens being
removed must fight against hisconquerours enemies, and serve him
also to make his triumphe.
[Page]
A Table to take any of the men, by addition,
subtraction,multiplication or division.[In the original, this table
is four columns up; in the interests of typing, I am simply leaving
it as flattext. I will do the same for all the ensuing tables of
numbers.]
Addition & Subtraction.
11 2 31 3 41 4 51 5 61 6 71 7 81 8 91 15 161 120
121------------------- 22 3 52 4 62 5 72 6 82 7 92 28 302 64
66------------------- 33 4 73 5 83 6 93 9 123 12 15
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3 42 45------------------- 44 4 84 5 94 8 124 12 164 16 204 45
49------------------- 55 7 125 15 205 20 255 25
30------------------- 66 6 126 9 156 30 366 36 426 66
72------------------- 77 8 157 9 167 42 497 49
56------------------- 88 12 208 20 288 28 368 56
64------------------- 99 36 459 72 819 81 909 91
100------------------- 1212 16 2812 30 42------------------- 1515
30 4515 49 6415 66 81------------------- 1616 20 3616 56 7216 153
169------------------- 2020 25 4520 36 5620 100
120-------------------
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2525 56 8125 66 91------------------- 2828 36 6428 72
100------------------- 3030 36 6630 42 7230 90 12030 91
121------------------- 3636 36 7236 45 8136 64
100------------------- 4242 49 91------------------- 4545
noth.------------------- 4949 72 12149 120 169-------------------
5656 64 12056 169 225------------------- 6464 225
289------------------- 7272 81 15372 153 22572 28 361 [sic -- 28
should be 289]-------------------81 nothing
[Page]
9090 100 190------------------- 9191 nothing-------------------
100100 nothing------------------- 120120 169 289-------------------
121121 169 190
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-------------------153169190 noth.225289361
Multiplication & Division
22 3 62 4 82 6 122 8 162 15 302 28 562 36 722 45
90------------------ 33 4 123 5 153 12 363 15 453 30
90------------------- 44 4 164 5 204 7 284 9 364 16 644 25 1004 30
120------------------- 55 6 305 9 455 20 1005 45 125 [sic -- should
be 225]------------------- 66 6 366 7 426 12 726 15 906 20
120------------------- 77 8 56------------------- 88 9 728 15
120------------------- 99 9 819 25 225
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[Page]
By this Table, any man though he have small or no skyll in
Arithmeticke, maye learne to playe at thisgame, and in playinge
learne some parte of Arithmeticke.
Of takynge by proportion.If the Gamesters be disposed, they maye
take men also by proportion, Arithmeticall, Geometricall,
orMusicall. But because it is not necessarily required that they
should so do, I wyll fyrst prosecute themaner of triumph, in which
also they maye learne to take by proportion, as afterwarde shalbe
seene. Forwhen they can joyne two or three of their men to one of
their adversaries men in such order as thetriumph is set, so that
those three or foure numbers have anye of these three proportions
they maye taketheir adversaries man.
[Page]
Of the triumphe.When the king is taken, the triumph must be
prepared to be set in the adversaries campe. The adversariescampe
is called al the space, that is betweene the first front of his
men, as they were first placed, unto theneither ende of the table,
conteyning .40. spaces or as some wil .48. When you entend to make
a triumphyou must proclaime it, admonishing your adversarie, that
he medle not with anye man to take hym,whiche you have placed for
youre triumphe. Furthermore, you must bryng all your men that serve
forthe triumph in their direct motions, and not in theyr flying
draughtes.
To triumphe therefore, is to place three or foure men within the
adversaries campe, in proportionArithmeticall, Geometricall, or
Musicall, as wel of your owne men, as of your enemyes men that
betaken, standing in a right
[Page]
lyne, direct or crosse, as in .D.A.B. or els .5.1.3. if it
consist of three numbers, but if it stande of fourenumbers, they
maye be set lyke a square two agaynst two, as in .E.B.D.C. or
.2.3.4.5. and after the samemaner muste you set them so that your
adversaries man make the thyrde or fourth, when you take
byproportion.
Of dyvers kyndes of triumphes.There be thre kyndes of triumphes
a great triumphe, a greater triumph, and the greatest and moste
nobleof all.
Of the great triumph.The great triumph standeth in proportion,
eyther Arithmeticall, Geometrical, or Musical onely.
[Page]
Of Arithmeticall proportion.Arithmeticall proportion, is when
the mydle number differeth as much from the first, as from the
thyrde,
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that is to saye, when the thyrde hath so many more, from the
seconde as the seconde hath from thefirste, as .2.4.6. Here, two,
is the distans, for .4. excedeth .2. by two, & .6. is more then
foure by .2.
A rule to fynde out Arithmeticall proportion between the
firsteand the last.When you have the first and the last if you
would finde out the midle in proportion. Adde the first &
thelast together, and devide the whole into .2. for the halfe is
the midle in proportion
[Page]
as I would knowe what is the midle number in proportion betwene
.5. and .25. first I adde .5. to .20.[sic] that is .30. the half of
thirtie is .15. whiche is midle in proportion betwene .5. and .30.
[sic] so have I .5.15.35. [sic] in Arithmeticall proportion.
[Page]
A table of al the Arithmetical proportions that be in this
game.2 3 42 4 62 5 82 7 122 9 162 15 282 16 303 4 53 5 73 6 93 9
154 5 64 6 84 8 124 12 204 20 364 30 565 6 75 7 95 15 255 25 456 7
86 9 126 36 667 8 97 16 257 64 1219 12 159 45 819 81 15312 16 2012
20 2812 42 7212 66 12015 20 2515 30 45
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15 120 22516 36 5620 25 3020 28 3620 42 6428 42 5628 64 10030 36
4242 49 5642 66 9049 169 28956 64 7272 81 90 49.
[Page]
Of Geometricall proportion.Geometricall proportion, is when the
seconde hath that proportion to the first that the thyrde hath to
theseconde, as .2.4.8. as .4. excedeth .2. by .2. so .8. excedeth
.4. by .4.
A rule to fynde the mydle number in Geometricall
proportion.Multiplie the first by the thyrde, and of the product
fynde out the roote square, for that is the midle, if thenumbers
have anye roote square in whole numbers. The roote square is a
number multiplied in it selfe,wherefore you muste seeke such a
number, as multiplied in it selfe, maketh the producte of the fyrst
andthe thyrde number multiplied one by the other.
[Page]
As .20. multiplied by .45. is .900. the roote is .30. square,
whych multiplyed in is selfe is .900. But yfyou lyste not to take
suche paynes, here is a Table that maye serve your tourne for
Geometricallproportion to be used in this game.
[Page]
A table for Geometricall proportion.2 4 82 12 723 6 124 6 94 8
164 12 364 16 644 20 1005 15 459 12 169 15 259 45 22516 20 2516 28
4916 36 81
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20 30 4525 30 3625 45 8136 42 4936 66 12136 90 22549 56 6449 91
16964 72 8164 120 22581 90 10081 153 289 27.
[Page]
Of Musicall proportion.Musicall proportion is when the
differences of the first and last from the middes, are the same,
that isbetwene the first and the last, as .3.4.6., betwene .3. and
.4. is .1. betwene .4. and .6. is .2. the wholedifference is .3.
which is the difference betwene .6. and .3. the first and the
last.
A rule to fynde the first, when you have the two last.Multiplie
the seconde by the thyrd, devide the products by the distans and
the thyrde number, and thequotient is the first, as havynge .6. and
.12. I would fynde the first, .6. tymes .12. is .72. the
differencebetwene .6. and .12. is .6. whiche added to .12. is .18.,
devide .72. by .18. the quotient is .4. so have you.4.6.12. in
Musicall proportion.
[Page]
A table of Musicall proportion.2 3 63 4 63 15 164 6 124 7 285 8
205 9 456 8 127 12 428 15 1209 15 459 16 7212 15 2015 20 305 45 225
[sic -- the 5 should be a 25]30 36 4530 45 4972 90 120 17.
[Page]
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Of the greater triumphe.The greater victorie is, when foure
numbers be broughte together, whiche agree in two
proportions,either Arithmeticall and Geometricall, or elles
Arithmeticall and Musicall, or elles Geometricall andMusicall. Of
these three conjunctions the greater triumph consisteth, of the
which the table belowfoloweth.
[Page]
A table of Arithmeticall, and Geometricall proportion.2 3 4 82 4
6 82 4 6 92 4 5 82 7 12 722 9 12 162 12 42 723 6 9 123 4 6 93 9 15
254 5 6 94 6 8 94 6 9 124 6 8 164 12 20 364 8 12 164 8 12 364 8 16
284 12 20 1004 16 28 494 16 28 644 20 36 1005 9 15 255 15 25 455 25
45 816 9 12 167 16 20 257 49 91 1698 9 12 168 64 120 2259 12 15 169
12 15 259 12 16 209 45 81 2259 25 45 819 12 16 209 15 20 259 8 153
28912 16 20 2515 16 20 2515 20 30 4516 20 25 3016 36 56 8120 25 30
4530 36 42 4936 42 40 56
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42 49 56 6449 56 64 7249 91 169 28956 64 72 8164 72 81 9072 81
90 100 52.
[Page]
Arithmeticall and musicall proportion.3 4 5 63 4 5 153 4 6 93 5
7 253 5 9 153 9 15 453 4 6 84 5 6 124 6 12 154 6 12 204 12 15 205 7
9 456 7 8 128 15 120 2259 12 15 459 12 15 209 15 30 459 15 45 8112
15 20 2515 20 25 3015 20 30 4515 30 36 4515 30 45 9036 36 42 4572
81 90 120 25.
Geometricall and musicall proportion together.2 3 6 123 4 6 93 4
6 123 6 8 124 6 12 364 7 28 495 9 15 455 9 45 2255 9 45 819 12 16
729 15 25 459 15 45 2259 25 45 22515 20 30 4520 30 36 4525 45 81
225
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16.
[Page]
Of the greatest triumph.The greatest triumph is of
Arithmeticall, Geometricall, and Musicall proportions all joyned
together.
Arithmeticall, Geometricall, and Musicall proportions,
alltogether.2 3 4 62 3 6 92 4 6 122 5 8 202 7 12 422 9 16 723 4 6
83 4 6 93 5 9 153 5 15 253 9 15 454 6 8 124 6 9 124 7 16 284 7 28
495 6 25 455 9 45 815 25 45 2255 15 25 456 8 9 126 8 12 166 12 15
207 12 42 728 15 64 1208 15 120 22512 15 16 2012 15 20 2515 20 36
4515 30 45 90 30.
[Page]
And thus is the first kynd of playing at an end. And this is
sufficient to teach you to play, but if youwould learne to play
conningly, you must use to playe often, so shall you learne better
then by anyepreceptes or rules.
Of the seconde kynde of playinge at the Philosophers game.There
is in this kynde of playing to be considered, the table, the men,
the marking of them, the setting ofthem in araye, their marching,
their lawed of taking, and the maner of triumphynge.
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Of the Table.The Table is the same that was first described,
namely a double chessbord.
Of the men.[Page]
The men be as before in number .48.23. on a syde, and two
contrarye kynges of even and of odde. Theymust be of divers
colours, as hath bene sayde, the bottome of every one must have his
enemies colour,and his owne mark of number, differing in this
poinct from the former playing, that the enemies mentaken, may
serve onely to celebrate a triumphe, but not to fight on his syde
that taketh them.
Of the markyng of the men.They be marked with the same numbers,
that have bene shewed before and therefore so are to be foundeout
as is taught before. But they be marked besyde their numbers, with
cossicall signes, which be signesused in the rule called regula
cossa, or algebra, betokening rootes, quadrats, cubes,
fouresquaredquadrats, sursolides, & quadrates of cubes. All
these .6. signes must be conteyned in thys game.
[Page]
[Following is a chart giving the six signs. Since I can't
reproduce these in the text easily, I will usetextual
representations. In the interests of my modern mind, I am using "r"
to represent the root, or bythe power the root is being raised
to.]
The signe
of the roote -- {r}of the quadrate -- {2}of the cube, or solide
quadrat -- {3}of the fouresquared quadrat -- {4}of the sursolide --
{5}of the squared cube -- {6}
Every number maye be taken for a roote, as .2. this number
multiplyed in it self is a square as .4. Thequadrat or square
multiplied by the roote geveth a cube or solide square, as .4.
multiplied by .2. geveth.8. that is a cube.
Multiplie the cube by the roote, so have you a squared quadrat,
as .8. by .2. geveth .16. which is aqradrate of a a quadrate.
Multiplie the square or quadrat of quadrat by the roote, and the
product is the sursolide, as .2. tymes .16.is .32. whiche is a
sursolide. Multiplie the sursolide by the roote, and the product is
the quadrate of acube, as .2. times .32. is .64. which is a quadrat
of a cube. So have you the roote, quadrat, cube, quadratof quadrat,
sursolide, quadrat of cube .2.4.8.16.32.64.
[Page]
So .2. referred to .4. is a roote of a square, referred to .8.
it is a roote of a cube, .2. referred to .16. is theroote of a
fouresquared quadrate, .2. referred to .32. is the roote of a
sursolide, .2. referred to .64. is theroote of a quadrate of a
cube. These numbers muste have the proper cossicall signes.
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Also one number having divers relations, may have divers
cossicall signes, as .9. referred to .81. beingroote, hathe the
signe of a roote {r}, but beyng referred to .3. it hath the signe
of a quadrate, for it is aquadrate of .3. and is thus signed {2},
and so of the rest that have like relation.
[When necessary, I will include multiple characters, so the 9
above would be {r2}, since it is both aroot and a quadrat.]
The marking of the men.The first order of roundes in bothe
numbers, must have the signe of the roote upon them al after
thismaner.
[First of several illustrations of the pieces. I will use the
same visuals that I have been using.]
(8{r}) (6{r}) (4{r}) (2{r})(9{r}) (7{r}) (5{r}) (3{r})
[Page]
The second order of roundes founde out as before, be not all
marked with cossicall signes, but onely .4.and .9. with the roote,
and .81. with the quadrate. The rest have none because amonge their
adversariesmen there is none that can be cossicall roote to them in
such maner as this game requireth.
(64) (36) (16) (4{r})(81{2}) (49) (25) (9{r})
The first order of triangles (havyng the same numbers that have
bene taught before) do all lack thecossicall signes, except onely
.6. which is signed with the roote.
[Page]
The seconde order of triangles, have all excepts one (whiche is
the number of .100.) their cossicallsignes, as .9. bothe of the
roote and of the quadrate, .25.36. and .49. have the signe of the
quadrate .64.of the quadrate and the cube, and also the quadrat of
the cube .16. and .81. of the quadrate, and the fouresquared
quadrate.
In the first order of squares, onely .15. is marked with the
roote, all the rest doe want theyr cossicallsygnes in thys
game.
[Page]
[A rather odd little illustration here, showing the two kings in
some detail, with each constituent piecesmarked both with its
number and the square root of that number, and the complete number
of the kingon the top. Also, a couple of odd little images of a
round and a square with a peculiar symbol on top;this symbol may be
peculiar to king components. Note also that, in the table of
squares below, the 91
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and 190 have a picture of the king on them.]
[153] [91] [45] [15{r}][190] [120] [66] [28]
The seconde order of squares hath .3. numbers marked with
cossicall signes, that is .25. and .225. wyththe signe of the
quadrate .81. is marked with the sygne of the quadrate and the
fouresquared quadrate.
[Page]
[289] [169] [81{24}] [25{2}][361] [225{2}] [121] [49]
And thys have you all the men that be marked with cossicall
sygnes.
The setting in aray.The teachers of this kynde of playing, doe
not so well allowe, the former kynde of placing or any other,as the
naturall placing of every man under him of whome he aryseth. So
thei conteyne .6. ranks inlength, extending to the furthermoste
edge of the Table after this sorte.
[Page]
[Note that, in this table, the odds are colored black, while the
evens are left white.]
[361] [225] [121] [49] King [120] [66] [28] (81) (49) (25) (9)
(9) (7) (5) (3) (2) (4) (6) (8) (4) (16) (36) (64) [15] [45] King
[153] [25] [81] [169] [289]
[Page]
The marching or moving.
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The men maye remove every way, into voyde places, forwarde,
backewarde, towarde both sydes, director cornerwyse. So that the
rounde men remove into the next space, the triangles into the third
place, andthe squares into the fourth place, accompting that place
in which they stande for one.
Also every man savyng the two kynges to besiege his enemie, or
to flye from the siege himself, mayremove the knights draught in
chesse, but neither take anye man (except it be by siege) nor erect
atriumphe by suche motions. The kynges move even as squares, but
that they have not the flyingedraughte.
It is compted lawefull amonge suche as wyll to agree, that the
Triangles and Squares, maye remove intovoyde places, thoughe the
spaces betwene be occupyed of other men.
[Page]
The maner of taking.The men may be taken seven ways by Oblivion,
by Equalitie, by Addition, by Subtraction, byMultiplication, by
Division, and by Cossicall Sygnes.
Of takynge by Oblivion.All men maye be taken by Oblivion when by
foure men they be letted of theyr ordinarie draughte, ashath bene
taught before.
Of takynge by Equalitie.By Equalitie maye these men take or be
taken, as hathe bene sayde before, .9.16.25.36.49.64.81., as
yfafter you have played your .9. stande in
[Page]
your mans draught, you may take him by not removing into his
place, unlesse you espye him standingin your draught before you
playe, then muste you take him up and remove into his place.
Of takynge by Addition.The takyng by Addition is all one with
the first kynde of play, in all respectes, saving that some
requirethe men that shoulde take by Addition to stande in the next
spaces to him that is taken, either directly, orcornerwyse, but the
former waye is better.
Of taking by Subtraction.That whiche was sayde in the first
kinde of subtraction and that whiche was last sayde of Addition
maybe bothe referred together. For this subtraction
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differeth not from the former, but for the opinion of them, that
would have the two takers stande onelyein the nexte spaces to him
that is taken.
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Of takyng by Multiplication.Takyng by multiplication doth
differ. For in this kynde of playng, it is thus. When your man
standethso, that beyng lesser than your adversaries man, you may
multiplie your man by the voyde spacesbetwene them, and the product
is all one with the adversarye, you maye take hym upm not
removyngeinto his place, except you espye hym so, before you remove
your man.
Of takynge by Division.[Page]
Lykewise by Division, yf your man beyng greater then the
adversarye, stande so, that beyng devydedby the voyde spaces, the
quotient is all one with the adversarye, you maye take hym up, not
removynginto hys place, unlesse you see hym so standynge before you
drawe.
Of taking by Cossicall signes.By Cossicall sygnes anye man that
hath these signes, {2}.{3}.{4}.{6}. meeting with his roote in
hisordinary draught that hath this signe {r} taketh him up, or
elles is taken of him, without removing intohis place, except he
maye take him before he remove.
Of the kynges, and their taking.[Page]
The king of the even must be foursquare, havyng sixe steppes,
every one lesser then other, on one sydehe muste have on him these
rootes .1.2.3.4.5.6. on the other syde the quadrates arising of
these rots, thatis .1.4.9.16.25.36.
The king of the odde men, muste have but fyve steppes, that is
.4.5.6.7.8. lackyng the rootes that he cannot ende in .1. The
quadrates of hys rootes by these .16.25.36.49.64. These muste be so
set on, that theleast must be hyghest and the greatest lowest.
The kinges be taken by Oblivion, or yf theyr Pyramidall number,
be taken by anye of the aforesaydemeanes. Also yf by suche meanes
you can take all his quadrates one after another.
The privilege of the king.[Page]
If anye of the kynges quadrates be taken, he maye redeme it by
anye of his men having the samenumber, and muste remove into his
place, whiche redemed hym. But yf he have none of the samenumber,
he maye redeme hym for anye man of hys, that his adversarye wyll
chuse, and lykewyseremove into his place by whome he is
redemed.
[Page]
A table to take the men by Multiplication and Division.
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Even against odd spaces6 2 128 2 1615 2 3045 2 904 3 124 4 169 4
3616 4 646 5 3020 5 1002 6 1215 6 9020 6 1204 7 288 7 562 8 168 8
644 9 369 9 8125 9 2259 10 90 21.
odd against even spaces3 2 636 2 723 3 95 3 1512 3 365 4 209 4
3616 4 643 5 155 5 259 5 4512 6 727 7 495 9 459 9 813 12 363 14 42
17.
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For Division.even against odd spaces6 2 372 2 3615 3 536 3 129 3
320 4 5
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36 4 964 4 1615 5 325 5 545 5 942 6 772 6 1249 7 772 7 945 9 581
9 936 12 391 13 742 14 3 20.
odd against even spaces12 2 616 2 830 2 1590 2 4512 3 416 4 436
4 964 4 16100 4 2522 5 45 [sic -- 22 should be 225]30 5 6100 5 2012
6 236 6 690 6 15120 6 2028 7 456 7 816 8 264 8 8120 8 153 9 4 [sic
-- 3 should be 36]81 9 9225 9 2590 10 966 11 628 14 2 27.
To take by cossicall signes
2 16{4}2 64{6}3 81{4}3 9{2}4 16{2}4 64{3}5 25{2}6 36{2}7 49{2}8
64{2}9 81{2}
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15 225{2}
[Page]
Of the triumph.The triumph is after the Kynge be cleane taken
away, to be create in the adversaries campe, as well ofyour owne
men as of your adversaries men that be taken, or of both in
proportion as hath bene shewedbefore, and proclaimed that those men
ons placed, may not be taken, as it was declared sufficiently,
andno difference betwene the triumphes, savyng that some wyll not
alowe a triumphe but of foure numbers,and two proportions at the
lest. All three for the greater victorie, makynge but two kyndes of
triumphes.
Here foloweth the thyrd kynde of playing at the
Philosophersgame.There must also in this thyrd kynde be considered
the table, the men, their markyng, the order of theyrbattell, the
motions, their taking, and last of all theyr triumphing.
The table is the same that hath bene twyse already discribed.
Yet some wyll not have it so longe, but atthe lest is must conteyne
.10. squares in length and alwayes .8. in breadth. The longest is
best.
Of the men.The men be .48. as it hath bene told of two contrary
collor, the head and bottom all of one collor,because men ons taken
be no more occupyed in thys kynde of playing.
The inscription and fashion.[Page]
The fasion is as hath bene last declared both of the men, and of
the kynges, the inscription of numbersthe same, but without
cossical signes.
Of the order of the battell.The order of battell is after the
firste maner, but not so farre from the bordes end, namely the .4.
squaresstandynge in the plattes nearest to the bordes end the rest
accordingly joined to them, as in the firstkynde of playing.
[Page]
[Note that, in this diagram, the odds are colored black. Also,
it actually shows the odds and evens onreverse ends from this
textual representation; I'm not redoing the whole thing right
now...]
[25] [81] [169] [289][15] [45] [91]* [153] (4) (16) (36)
(64)
(2) (4) (6) (8)
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(9) (7) (5) (3)
(81) (49) (25) (9) [190]* [120] [66] [28][361] [225] [121]
[49]
[Page]
Of their motions.The men move frowarde and backward, to the
right hand, and to the left hande, but not cornerwise,except the
gamesters so agree, the rounds into the next space, the triangles
into the thyrde, and thesquares into the fourth, the kyngs move as
squares. And these be their ordinary draughts in marching.
Of their taking.They are taken by encountering, bu eruption, by
laying wayght, and by Oblivion.
Of takyng by encountering.To take by encountering is to take by
Equalitie, as hath bene twyse before declared.
Of taking by eruption.To take by eruption is when a lesse number
beyng multiplied by the spaces that are betwene him &
hysadversary, the product is asmuch as his adversary, he may take
his enemie awaye whether he standdirectly from him or
cornerwise.
[Page]
For men that may be taken by eruption looke in the table of
takyng by multiplication in the second kyndof playing.
Of takyng by deceypt or lying weyght.To take by deceypt or lying
weight, is to take by addition, not as before when the adversary
standethwithin the draught of two men which being added make the
juste number of the adversary, but when the.2. numbers that are to
be added, stande in the next spaces to the adversarie. For to take
by deceipt, looke
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in the table that was set forth for takyng by addition in the
first kynde of playinge.
Of taking by Oblivion.By Oblivion all men may be taken, when
foure men besiege the adversarye, standynge in the foure nexte
[Page]
spaces about him directly, or cornerwise, the man so besieged
can not escape, because he can notremove cornerwyse, therefore maye
be taken up, so soone as the last of the foure is set in his
place.
In all three kyndes of playing no Oblivion can be of any man
with some of his fellowes, but all fouremuste be hys
adversaries.
In this thyrde kynde, these men can be none otherwyse taken but
by Oblivion. Namely amonge the even.2.4.4.135. among the odde
.3.5.7.190.
In all maner of taking this is to be noted, that we muste not
place the man which taketh in place of himthat is taken, but when
he maye be taken before we drawe, then shall we remove our man into
his place.
The privilege of the king.The king standeth for so many men as
he hath steppes, that is the even for .6. the odde for .5. if anye
ofthese
[Page]
(except the lowest and greatest) be taken the king may redeme
hym, by any man of his that is of thesame number. If he have none
of the same number, he maye redeme him be any of his men that
hysadversary wyll chuse. But if his lowest square be taken, no
ransom will delyver him. Also if the wholekyng at ons that is the
whole number of Pyramis be taken, he can not be redemed.
Of the triumphe.To take awaye the tediousnes of long play from
them that be yonge beginners, wryters of this gamehave invented
divers kyndes of shorte victories, wherefore they devide victory
into proper and common.Of the proper victory need nothing here be
spoken, for all things thereto belonging are sufficientlu setforth
in the first kind of playing.
Of the common victory.The common victorie (they say) is after
fyve maners, for men contende either for bodies, goods,quarrelles,
honour, or els for both quarels & honor.
[Page]
Victory of bodies.Victory of bodies is only to take a certain
number of men, as if the gamesters agree, that he which firsttaketh
.4. or .5. or .6. or .10. men &c, shall wyn the game.
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Victorye of goods.Victorie of goods, is to take a certain number
without respect of the men. As if it be covenanted, that hewhich
first taketh men amounting to the number of .100. or .200. shall
have the victorie.
Victory of quarell.Victorie of quarell is when neither the men,
nor the number, but the characters of the number beconsidered. As
if it be determined that he which first taketh .100. in .8.
characters not regarding in howmany men they standes, shall winne.
As .2.4.5.8.24.64. so you have .100. in .8. characters it
skillethnot, although there be more then .100. as in this example
there is more then .100. by .4.
[Page]
Victorie of honour.Victorie of honour, is whe a determined
number is made in a determined number of men, as if it bedetermined
that he whiche first cometh to .100. in .8. men, shall winne the
game. As in these.2.4.6.8.4.16.45.15. And though there were
somewhat more then .100. so it be in .8. men, it skilleth not.
Of victorie of honour and quarell.The victorie of honour and
quarell, is when one obteyneth the decreed number, in the decreed
number ofmen and the decreed number of characters: as let .100. be
the decreed number .8. the determined numberof men, and .9. the
determined number of characters. He that obteyneth
.2.4.6.8.4.6.9.64. obteineth thevictorie of honour and quarell. It
shalbe no hinderance though .8.
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men and .9. characters conteyne somwhat more then .100. so that
there be not .100. upon one man, as inthe victorie before.
Victorie of standers.They have invented another victorie, that
is of standerdes, by counterfeyting two armies, one of
theChristians, another of the Turkes. The whyte men, that is the
even hoste, conteyneth .1312. footemen(not compting the rootes of
squares expressed in the kynges) let the first and last be
captaines and letthem devide the whole armye into .10. standerds so
every standerd shall have .130. men, besyde the twocaptaines and
the ten standard bearers. The black men, that is the odde armie
(except the kings rootes) be.1752. The two captaynes and ten
standerd bearers taken out, there remayneth .1740. souldyers, to
everystanderd .174. He that wynneth more standers have the
victorye. If the even hoste
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wyne .348. men he hath obtayned two standerds if he wynne .522.
he hath gotten thre standerds andforth of the rest.
If the odde armye wynne .260. they wyn two standerds .390. three
standerds and so of the rest.
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Table of the victorye of standerds.One standerd of the even,
conteyneth 130.Two standerds. 260.Three standerds. 390.Foure
standerds. 520.Fyve standerds. 650.Sixe standerds. 780.Seven
standerds. 910.Eyght standerds. 1040.Nyne standerds. 1170.Tenne
standerds. 1300.One standerd of the odde, conteyneth 174.Two
standers. 348.Three standerds. 522.Foure standerds. 696.Fyve
standerds. 870.Sixe standerds. 1044.Seven standerds. 1218.Eyght
standerds. 1392.Nyne standerds. 1566.Tenne standerds. 1740.
You maye use anye of these syxe kyndes of common victorie, in
every one of the three kyndes ofplaying.
FINISPrynted at London by Rouland Hall,for James Rowbothum, and
are to
be solde at his shoppe inchepeside under Bowe
churche.1563.