The Philosopher's Game -- Rythmomachy - Wm. Fulke

The Philosopher's Game -- Rythmomachy http://jducoeur.org/game-hist/fulke.html

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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.

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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.

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[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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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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

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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

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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.

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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.

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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

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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.

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[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.]

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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

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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

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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.

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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.

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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

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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

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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.

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[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

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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.

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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

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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

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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

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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

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.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.

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[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]

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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

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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

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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.

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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

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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

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.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.

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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.

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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.

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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

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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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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.

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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

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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[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.

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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})

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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.

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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.

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[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.

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[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.

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[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]

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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.

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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

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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.

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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}

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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.

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[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]

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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.

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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

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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

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(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.

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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.

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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.

Documents

The Philosopher's Game -- Rythmomachy - Wm. Fulke