This 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 of Pollard 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, but will leave original spelling whenever I consider there to be doubt about the meaning. I also will sometimes modernize the punctuation and paragraph breaks in the interests of readability. This is not intended to serve as a definitive critical edition, merely a working copy, good enough to understand the game.
My thanks to Peter Mebben, who pointed me in the direction of this source, and provided the first draft of the dedication.
[Picture, probably stock, of two men playing at a game on a square 10x10 board.]
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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.
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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Sith that your honour is full bent,
(right honorable lord)
To wisdom & to godlines
with true faithful accord.
Sith that in deed you do delyte,
in learning and in skyll:
The show wherof doth well expresse
a 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 should
not lacke some godly game:
Whereby you might at vacant times
your self to pastyme frame.
Whereby I say you might release,
such travailes from your mynde:
And in the meane while honest mirth
and prudent pastyme fynde.
Remembring then this auncient play,
where wisdome doth abound:
Called the Philosophers game,
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 wade
and 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.
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,
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:
with much encrease of helth & welth
and from all hurt you save.
Your honours most humble,
James Roubothum.
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I Dout not but some man of severe judgement so soone as he hath one read the title of this boke wyl immediately sai, that I had more need to exhort men to worke, then to teach them to play, which censure if it procede not of such a froward morositie that can be content with nothing but that he doth himself, I do not only well admit, but also willingly submit my self therto. And if I could be persuaded that men at mine 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 the furtherance of the same. But if after honest labour and travell recreation be requisit, (and that nede no further probation because we favour the cause wel inough) I had rather teach men so to play, as both honestye may be reserved, their wittes exercised, they them selves refreshed, and some profit also attayned, then for lacke of exercise to see them either passe the tyme in idlenes, or els to have pleasure in thyngs fruitles and uncomely. And if great Emperours and mighty Monarches of the world have not bene 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 of defence, to teache the game, which so wyse men have invented, so learned men frequented, and no good man 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, they have filled this game with much diversitie. In which as I could perceive the most differens of playing to consist in thre kindes, so have I playnly and briefly set them forth in Englishe not as though there might not 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, from playe & game, to fall to earnest contention, if any man in this doing or any part thereof shall think I have done amisse, and will do better himself, so far am I from envying his good proceding, that I wil be right glad, and geve him heartye thankes therefore.
All things belonging to this game
for reason you may bye:
At the bookeshop under Bochurch
in Chepesyde redilye.
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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:
Interpone tuis interdum gaudia curis:
Yt possis animo quemuis sufferre laborem.
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That 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 even parte is against the odde, either parte havinge a kyng, whych being taken of the adversaryes part, and a triumphe celebrated within his campe, the game is ended.
Amonge the dyverse kyndes of playing thys game, we shall sette forth three sortes, of which the reader maye 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.
He that wyll learne thys game, any of the three waies, muste first be enstructed of these sixe partes.
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The table muste be a playne borde conteynynge .128. squares that is .8. in breadth and .16. in length sette forthe in two dyverse collours. Or for a plainer understandynge, the table is a doble chesse bord, as it were two chessebordes joyned together, the length of twoo, the breadth of one, whereof thys is an example.
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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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The men be in number .48. Wherof .24. be of one side & must be knowen by one colour, and .24. on the other syde, whyche also must be marked with a contrarye colour, as White and Blacke, Blew and Redde, or what colours els you lyke best. But in the colering there .3. thinges must be observed, the bottome or lower part of every man (excepte the two kinges) muste by marked wyth his adversaries colour, 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 showing roundes, triangles, squares].
The kynges because they consist of all three sortes, as it is knowen by the learned speculation of the numbers, beare
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the fashion of all thre kindes, his foundations are two squares, on which are sette, two triangles & upon them rounds. But this difference is betwene the kinges, the king of the even numbers, hath a pointed toppe, the king of the odde numbers is not pointed, the cause dependeth upon the consideration of these numbers by which they arise into piramidall fashion. The third thing considered in the men, is the number that must be written or graven upon them which to learne plainely for practise marke these short rules.
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, and then 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 a round 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 triangles together, 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 after adding 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 even syde .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. Except one of the kynges, which must with the whole number of their pyramid, be marked, onely on the bottome. Because the sydes muste have other numbers, namely the highest point of the even kyng, must have .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 odde upon his head, whiche is a rounde, not pointed hath .16. upon his first triangle .25. on the second triangle .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 may you take one for another, as 6 the even round & 9 the odde rounde, may be taken one for another with oute this lyne or some suche marke, lykewise 6 and 9 Tryangles bothe of one syde. And this sufficient for the men, the fashion, colours and numbers.
For them that seke the speculation of these numbers, rather then the practise for playing, and have some sight in the sciens of Arithmetike, some thyng must be sayde of proportion. For this purpose there be three kyndes of proportion. Multiplex, superparticuler, and superpartiens.
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MULTIPLEX proportion, is when a great number conteyneth a lesse number manye tymes, and leaveth nothing, as .8. conteyneth .2. fower tymes and nothing remaineth .16. conteyneth .4. &, this proportion semeth best to agree with roundes because the one number conteyneth the other and nothynge remaineeth as the fyrste order of roundes be.
[The following table shows the white (even) and black (odd) rounds.]
| 2 | 4 | 6 | 8 |
| 3 | 5 | 7 | 9 |
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[This table shows the first and second orders of rounds for both sides.]
| double. | quadruple. | sextuple. | occuple. | |
| 2 | 4 | 6 | 8 | |
| 4 | 16 | 36 | 64 | proportion. |
| triple. | quintuple. | septupl. | nonuple | |
| 3 | 5 | 7 | 9 | |
| 9 | 25 | 49 | 81 |
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Superparticuler proportion is when a greater number contayneth a lesser with one part of it, which may measure 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 a trianguler forme, whyche hathe fewest lynes and angles next unto a circle. For the manner of thys proportion 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. I believe the rows of base numbers are wrong -- the first set should be the evens (2, 4, 6, 8), and the second the odds (3, 5, 7, 9). That would make each Latin header match the number below it, the first row of triangles would be the superparticulates for that base number, and the second row would be the second order of triangles for that base number, which is (x+1)2.]
| sesquialter. | sesquiquart | sesqui.sext | sesqu.oct. |
| 3 | 5 | 7 | 9 |
| 6 | 20 | 42 | 72 |
| 9 | 25 | 49 | 91 |
| sesquiter. | sesquiquint. | sesquisept. | sesquinona. |
| 4 | 6 | 8 | 10 |
| 12 | 30 | 56 | 90 |
| 16 | 36 | 64 | 100 |
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The superpartiens proportion is when the greater number conteyneth the lesser and mo partes of it then one 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 wel figured in the square, which also conteyneth more corners and sides. For the maner of their proportion consyder thys table.
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[The following table contains the two rows of triangles, with the corresponding square beneath.]
| 6 | 20 | 42 | 72 | supparticulares added |
| 9 | 25 | 49 | 91 | |
| 15 | 45 | 91 | 153 | being the squares. |
| 12 | 30 | 56 | 90 | |
| 16 | 36 | 64 | 100 | |
| 28 | 66 | 120 | 190 |
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| third | fyft | seventh | ninth | |
| 5. | 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 | tenth | |
| 7. | 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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[Image of the two kings. Each is a pyramid of numbered pieces, with two squares, two triangles, and a round; one has a little triangular "cap" on top. The images make it look like higher-numbered pieces are actually larger -- I wonder if this is true...]
The kinges conteine in them suche numbers, as beyng all added together, make the whole piramidall number, the lowest square of the even is .36. which riseth of the multiplying of .6. in it selfe. The next square 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 maner consisteth 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 beene sayde before.To retorne againe to the plaine and easye playing of this game, next to the armie & their armour, follow ether the order of their battel or encamping. Which because it is more playne and easely seen which the eye, then learned by the eare, I referre thee unto the table where the battell is appoynted in suche order as thys 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 into square braces, triangles into angle brackets, and rounds into parentheses. Kings are signified with an asterisk. Note that the top half, the evens, should be upside-down.]
| [25] | [81] | [169] | [289] | |||||
| [15] | [45] | <25> | <20> | <42> | <49> | [91]* | [153] | |
| <9> | <6> | (4) | (16) | (36) | (64) | <72> | <81> | |
| (2) | (4) | (6) | (8) | |||||
| (9) | (7) | (5) | (3) | |||||
| <100> | <90> | (81) | (49) | (25) | (9) | <12> | <16> | [Error in original: 2 instead of 12] |
| [190]* | [120] | <64> | <56> | <36> | <30> | [66] | [28] | |
| [361] | [225] | [121] | [49] | |||||
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The battell beyng duely placed, it followeth next, to know the maner of marching & removing, for every kynd of men, hath their proper kynde of motion, and fyrste we muste speake of the roundes.
The roundes muste move into the space that is next unto them cornerwyse, as in the table, from the space .A. to any of these .B.C.D. or .E.
[Yes, this is clearly saying that rounds only move diagonally.]
The triangles passe three spaces counting that in which they stande for one, and that into whych they do remove 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 the motion of the triangle in marchying or takyng. But in flying he maye remove the knyghtes draught of the chesse, as from .A. into .X. or .W. &c.
The Squares remove into the fourth place from them, that is leaping over two, right forwarde or sydelong, as from the place of .A. to any of these spaces .L.N.P.R. flyinge they maye remove after the knyghts draught, but that they must passe foure spaces, as from .P. to .Y. or .T. &c. And this for the marchinge 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.
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, and into the fourth with the square, and finally in all poyntes lyke the Queene at the Chesse, saving that he can not passe above foure spaces at the most.
The men may be taken sixe wayes, namely by Equalitie, Oblivion, Addition, Subtraction, Multiplication and Division, and also if you wyll, and so agree by
| / | Arithmeticall. | |
| Proportion | < | Geometricall. |
| \ | Musicall. |
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By equality men may be taken, when one man after hys motion, seeth hys enemye beyng of the same number that he is, standing in such place as he may remove into, then maye he take awaye hys enemye and 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. the triangle, espye nine the rounde, before he remove, standing in his draught, he maye take hym up and remove 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 hys adversaries colloure, may serve his enemye on whose syde he is taken, there maye yet be taken by equalitie .4. and .6.
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By oblivion anye man maye be taken even the kinge him selfe, if he be so compassed with .4. men, that hys lawfull draught be hindered, as for example the round standing in the place of .1. and .4. men of what kynd it skylleth not, occupying the places of .2.3.4.5. after have set your last man in hys place may be taken by, also if a triangle be enclosed, as in .a. with any foure men standing in .b.c.d.e. he may be takenm even so may a square be taken. Also Triangles and squares may be beseged, if al the foure men or any of them, the rest standyng nearer, doe standes in the thyrde or fourth space from them so that they have no waye to remove, as a triangle or square standing in .A. may be beseged by .4. men or anye of them (the reste standynge nearer) in .F.G.H.I. Also a square standyng in .A. maye be taken by oblivion, 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 for Oblivion, by which every man may be taken in maner and forme as it hath bene taught.
When two numbers are so brought that they fynde one of theyr enemies, which is as muche as bothe they beyng added together, standing in such place as bothe they might remove into, they shall take hym up, without removing into his place, so soone as the latter of those two is set downe, but if the adversaries men be in their daunger before they remove, one of them whether the player lyst, shalbe removed 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 the sayde square .169. by Addition.
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 in his place, he may take awaye the adversarie, not removing into his place, unlesse he finde him so before he 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.
When two numbers stande so, that being multiplied one by the other, the producte is all one with their adversaryes 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 his place that is taken, as in example. The rounde .3. standeth in .D. and .5. standeth in .C. these two shal take 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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By division a manne maye be taken, when twoo of hys enemyes doe so stand, that one of them beyng devided by the other, the product is the same that their enemye is, standynge in their draught, immediatly after 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. maye take their enemye .6. standynge in .A. for .5. in .30. is conteyned .6. tymes.
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The game is never wonne, untyll the king be taken. The kings (as hath bene sayde) may remove anye way, so they passe not the fourth space. They can not be taken by equalitie. But by oblivion the whole kyng maye be taken away. Also his whole number at ones, that is .91. or .190. by Addition, by Subtraction, by Multiplication, or by Division. Also he maye be taken by partes, when any of hys syde numbers maye be taken then [loseth?] he that draughte, as when anye of hys square numbers is gone he can not remove the square draughtm and so of the rest, tyl nothyng of him be left, then muste he be taken away, and the triumph prepared.
When any is taken captive, he must be tourned with his conquerers collor upward & placed in the hindermost space of his victors campe, and from thens being removed must fight against his conquerours enemies, and serve him also to make his triumphe.
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[In the original, this table is four columns up; in the interests of typing, I am simply leaving it as flat text. I will do the same for all the ensuing tables of numbers.]
Addition & Subtraction.
1 1 2 3 1 3 4 1 4 5 1 5 6 1 6 7 1 7 8 1 8 9 1 15 16 1 120 121 ------------------- 2 2 3 5 2 4 6 2 5 7 2 6 8 2 7 9 2 28 30 2 64 66 ------------------- 3 3 4 7 3 5 8 3 6 9 3 9 12 3 12 15 3 42 45 ------------------- 4 4 4 8 4 5 9 4 8 12 4 12 16 4 16 20 4 45 49 ------------------- 5 5 7 12 5 15 20 5 20 25 5 25 30 ------------------- 6 6 6 12 6 9 15 6 30 36 6 36 42 6 66 72 ------------------- 7 7 8 15 7 9 16 7 42 49 7 49 56 ------------------- 8 8 12 20 8 20 28 8 28 36 8 56 64 ------------------- 9 9 36 45 9 72 81 9 81 90 9 91 100 ------------------- 12 12 16 28 12 30 42 ------------------- 15 15 30 45 15 49 64 15 66 81 ------------------- 16 16 20 36 16 56 72 16 153 169 ------------------- 20 20 25 45 20 36 56 20 100 120 ------------------- 25 25 56 81 25 66 91 ------------------- 28 28 36 64 28 72 100 ------------------- 30 30 36 66 30 42 72 30 90 120 30 91 121 ------------------- 36 36 36 72 36 45 81 36 64 100 ------------------- 42 42 49 91 ------------------- 45 45 noth. ------------------- 49 49 72 121 49 120 169 ------------------- 56 56 64 120 56 169 225 ------------------- 64 64 225 289 ------------------- 72 72 81 153 72 153 225 72 28 361 [sic -- 28 should be 289] ------------------- 81 nothing
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90 90 100 190 ------------------- 91 91 nothing ------------------- 100 100 nothing ------------------- 120 120 169 289 ------------------- 121 121 169 190 ------------------- 153 169 190 noth. 225 289 361
Multiplication & Division
2 2 3 6 2 4 8 2 6 12 2 8 16 2 15 30 2 28 56 2 36 72 2 45 90 ------------------ 3 3 4 12 3 5 15 3 12 36 3 15 45 3 30 90 ------------------- 4 4 4 16 4 5 20 4 7 28 4 9 36 4 16 64 4 25 100 4 30 120 ------------------- 5 5 6 30 5 9 45 5 20 100 5 45 125 [sic -- should be 225] ------------------- 6 6 6 36 6 7 42 6 12 72 6 15 90 6 20 120 ------------------- 7 7 8 56 ------------------- 8 8 9 72 8 15 120 ------------------- 9 9 9 81 9 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 this game, and in playinge learne some parte of Arithmeticke.
If the Gamesters be disposed, they maye take men also by proportion, Arithmeticall, Geometricall, or Musicall. But because it is not necessarily required that they should so do, I wyll fyrst prosecute the maner of triumph, in which also they maye learne to take by proportion, as afterwarde shalbe seene. For when they can joyne two or three of their men to one of their adversaries men in such order as the triumph is set, so that those three or foure numbers have anye of these three proportions they maye take their adversaries man.
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When the king is taken, the triumph must be prepared to be set in the adversaries campe. The adversaries campe is called al the space, that is betweene the first front of his men, as they were first placed, unto the neither ende of the table, conteyning .40. spaces or as some wil .48. When you entend to make a triumph you 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 for the 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 proportion Arithmeticall, Geometricall, or Musicall, as wel of your owne men, as of your enemyes men that be taken, 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 foure numbers, they maye be set lyke a square two agaynst two, as in .E.B.D.C. or .2.3.4.5. and after the same maner muste you set them so that your adversaries man make the thyrde or fourth, when you take by proportion.
There be thre kyndes of triumphes a great triumphe, a greater triumph, and the greatest and moste noble of all.
The great triumph standeth in proportion, eyther Arithmeticall, Geometrical, or Musical onely.
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Arithmeticall proportion, is when the mydle number differeth as much from the first, as from the thyrde, that is to saye, when the thyrde hath so many more, from the seconde as the seconde hath from the firste, as .2.4.6. Here, two, is the distans, for .4. excedeth .2. by two, & .6. is more then foure by .2.
When you have the first and the last if you would finde out the midle in proportion. Adde the first & the last 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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2 3 4 2 4 6 2 5 8 2 7 12 2 9 16 2 15 28 2 16 30 3 4 5 3 5 7 3 6 9 3 9 15 4 5 6 4 6 8 4 8 12 4 12 20 4 20 36 4 30 56 5 6 7 5 7 9 5 15 25 5 25 45 6 7 8 6 9 12 6 36 66 7 8 9 7 16 25 7 64 121 9 12 15 9 45 81 9 81 153 12 16 20 12 20 28 12 42 72 12 66 120 15 20 25 15 30 45 15 120 225 16 36 56 20 25 30 20 28 36 20 42 64 28 42 56 28 64 100 30 36 42 42 49 56 42 66 90 49 169 289 56 64 72 72 81 90 49.
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Geometricall proportion, is when the seconde hath that proportion to the first that the thyrde hath to the seconde, as .2.4.8. as .4. excedeth .2. by .2. so .8. excedeth .4. by .4.
Multiplie the first by the thyrde, and of the product fynde out the roote square, for that is the midle, if the numbers 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 and the 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 yf you lyste not to take suche paynes, here is a Table that maye serve your tourne for Geometricall proportion to be used in this game.
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2 4 8 2 12 72 3 6 12 4 6 9 4 8 16 4 12 36 4 16 64 4 20 100 5 15 45 9 12 16 9 15 25 9 45 225 16 20 25 16 28 49 16 36 81 20 30 45 25 30 36 25 45 81 36 42 49 36 66 121 36 90 225 49 56 64 49 91 169 64 72 81 64 120 225 81 90 100 81 153 289 27.
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Musicall proportion is when the differences of the first and last from the middes, are the same, that is betwene the first and the last, as .3.4.6., betwene .3. and .4. is .1. betwene .4. and .6. is .2. the whole difference is .3. which is the difference betwene .6. and .3. the first and the last.
Multiplie the seconde by the thyrd, devide the products by the distans and the thyrde number, and the quotient is the first, as havynge .6. and .12. I would fynde the first, .6. tymes .12. is .72. the difference betwene .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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2 3 6 3 4 6 3 15 16 4 6 12 4 7 28 5 8 20 5 9 45 6 8 12 7 12 42 8 15 120 9 15 45 9 16 72 12 15 20 15 20 30 5 45 225 [sic -- the 5 should be a 25] 30 36 45 30 45 49 72 90 120 17.
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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 and Musicall. Of these three conjunctions the greater triumph consisteth, of the which the table below foloweth.
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2 3 4 8 2 4 6 8 2 4 6 9 2 4 5 8 2 7 12 72 2 9 12 16 2 12 42 72 3 6 9 12 3 4 6 9 3 9 15 25 4 5 6 9 4 6 8 9 4 6 9 12 4 6 8 16 4 12 20 36 4 8 12 16 4 8 12 36 4 8 16 28 4 12 20 100 4 16 28 49 4 16 28 64 4 20 36 100 5 9 15 25 5 15 25 45 5 25 45 81 6 9 12 16 7 16 20 25 7 49 91 169 8 9 12 16 8 64 120 225 9 12 15 16 9 12 15 25 9 12 16 20 9 45 81 225 9 25 45 81 9 12 16 20 9 15 20 25 9 8 153 289 12 16 20 25 15 16 20 25 15 20 30 45 16 20 25 30 16 36 56 81 20 25 30 45 30 36 42 49 36 42 40 56 42 49 56 64 49 56 64 72 49 91 169 289 56 64 72 81 64 72 81 90 72 81 90 100 52.
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3 4 5 6 3 4 5 15 3 4 6 9 3 5 7 25 3 5 9 15 3 9 15 45 3 4 6 8 4 5 6 12 4 6 12 15 4 6 12 20 4 12 15 20 5 7 9 45 6 7 8 12 8 15 120 225 9 12 15 45 9 12 15 20 9 15 30 45 9 15 45 81 12 15 20 25 15 20 25 30 15 20 30 45 15 30 36 45 15 30 45 90 36 36 42 45 72 81 90 120 25.
2 3 6 12 3 4 6 9 3 4 6 12 3 6 8 12 4 6 12 36 4 7 28 49 5 9 15 45 5 9 45 225 5 9 45 81 9 12 16 72 9 15 25 45 9 15 45 225 9 25 45 225 15 20 30 45 20 30 36 45 25 45 81 225 16.
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The greatest triumph is of Arithmeticall, Geometricall, and Musicall proportions all joyned together.
2 3 4 6 2 3 6 9 2 4 6 12 2 5 8 20 2 7 12 42 2 9 16 72 3 4 6 8 3 4 6 9 3 5 9 15 3 5 15 25 3 9 15 45 4 6 8 12 4 6 9 12 4 7 16 28 4 7 28 49 5 6 25 45 5 9 45 81 5 25 45 225 5 15 25 45 6 8 9 12 6 8 12 16 6 12 15 20 7 12 42 72 8 15 64 120 8 15 120 225 12 15 16 20 12 15 20 25 15 20 36 45 15 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 you would learne to play conningly, you must use to playe often, so shall you learne better then by anye preceptes or rules.
There is in this kynde of playing to be considered, the table, the men, the marking of them, the setting of them in araye, their marching, their lawed of taking, and the maner of triumphynge.
The Table is the same that was first described, namely a double chessbord.
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The men be as before in number .48.23. on a syde, and two contrarye kynges of even and of odde. They must 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 men taken, may serve onely to celebrate a triumphe, but not to fight on his syde that taketh them.
They be marked with the same numbers, that have bene shewed
before and therefore so are to be founde out as is taught before.
But they be marked besyde their numbers, with cossicall signes,
which be signes used in the rule called regula cossa,
or algebra, betokening rootes, quadrats, cubes,
fouresquared quadrats, 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 use textual representations. In the interests of my modern mind, I am using "r" to represent the root, or by the 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. The quadrat 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 a qradrate 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 a cube, as .2. times .32. is .64. which is a quadrat of a cube. So have you the roote, quadrat, cube, quadrat of 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 the roote of a fouresquared quadrate, .2. referred to .32. is the roote of a sursolide, .2. referred to .64. is the roote of a quadrate of a cube. These numbers muste have the proper cossicall signes.
Also one number having divers relations, may have divers cossicall signes, as .9. referred to .81. being roote, hathe the signe of a roote {r}, but beyng referred to .3. it hath the signe of a quadrate, for it is a quadrate 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 a root and a quadrat.]
The first order of roundes in bothe numbers, must have the signe of the roote upon them al after this maner.
[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 adversaries men 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 the cossicall signes, except onely .6. which is signed with the roote.
| <72> | <42> | <20> | <6{r}> |
| <81> | <56> | <30> | <12> |
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The seconde order of triangles, have all excepts one (whiche is the number of .100.) their cossicall signes, 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 foure squared quadrate.
| <81{24}> | <49{2}> | <25{2}> | <9{r2}> |
| <100> | <64{236}> | <36{2}> | <16{24}> |
In the first order of squares, onely .15. is marked with the roote, all the rest doe want theyr cossicall sygnes in thys game.
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[A rather odd little illustration here, showing the two kings in some detail, with each constituent pieces marked both with its number and the square root of that number, and the complete number of the king on 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 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. wyth the 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 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 in length, 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] | ||||
| <100> | <64> | <36> | <16> | ||||
| <90> | <56> | <30> | <12> | ||||
| (81) | (49) | (25) | (9) | ||||
| (9) | (7) | (5) | (3) | ||||
| (2) | (4) | (6) | (8) | ||||
| (4) | (16) | (36) | (64) | ||||
| <6> | <20> | <42> | <72> | ||||
| <9> | <25> | <49> | <81> | ||||
| [15] | [45] | King | [153] | ||||
| [25] | [81] | [169] | [289] |
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The men maye remove every way, into voyde places, forwarde, backewarde, towarde both sydes, direct or cornerwyse. So that the rounde men remove into the next space, the triangles into the third place, and the 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, may remove the knights draught in chesse, but neither take anye man (except it be by siege) nor erect a triumphe by suche motions. The kynges move even as squares, but that they have not the flyinge draughte.
It is compted lawefull amonge suche as wyll to agree, that the Triangles and Squares, maye remove into voyde places, thoughe the spaces betwene be occupyed of other men.
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The men may be taken seven ways by Oblivion, by Equalitie, by Addition, by Subtraction, by Multiplication, by Division, and by Cossicall Sygnes.
All men maye be taken by Oblivion when by foure men they be letted of theyr ordinarie draughte, as hath bene taught before.
By Equalitie maye these men take or be taken, as hathe bene sayde before, .9.16.25.36.49.64.81., as yf after 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 standing in your draught before you playe, then muste you take him up and remove into his place.
The takyng by Addition is all one with the first kynde of play, in all respectes, saving that some require the men that shoulde take by Addition to stande in the next spaces to him that is taken, either directly, or cornerwyse, but the former waye is better.
That whiche was sayde in the first kinde of subtraction and that whiche was last sayde of Addition may be 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 onelye in the nexte spaces to him that is taken.
Takyng by multiplication doth differ. For in this kynde of playng, it is thus. When your man standeth so, that beyng lesser than your adversaries man, you may multiplie your man by the voyde spaces betwene them, and the product is all one with the adversarye, you maye take hym upm not removynge into his place, except you espye hym so, before you remove your man.
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Lykewise by Division, yf your man beyng greater then the adversarye, stande so, that beyng devyded by the voyde spaces, the quotient is all one with the adversarye, you maye take hym up, not removyng into hys place, unlesse you see hym so standynge before you drawe.
By Cossicall sygnes anye man that hath these signes, {2}.{3}.{4}.{6}. meeting with his roote in his ordinary draught that hath this signe {r} taketh him up, or elles is taken of him, without removing into his place, except he maye take him before he remove.
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The king of the even must be foursquare, havyng sixe steppes, every one lesser then other, on one syde he muste have on him these rootes .1.2.3.4.5.6. on the other syde the quadrates arising of these rots, that is .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 can not ende in .1. The quadrates of hys rootes by these .16.25.36.49.64. These muste be so set on, that the least must be hyghest and the greatest lowest.
The kinges be taken by Oblivion, or yf theyr Pyramidall number, be taken by anye of the aforesayde meanes. Also yf by suche meanes you can take all his quadrates one after another.
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If anye of the kynges quadrates be taken, he maye redeme it by anye of his men having the same number, and muste remove into his place, whiche redemed hym. But yf he have none of the same number, he maye redeme hym for anye man of hys, that his adversarye wyll chuse, and lykewyse remove into his place by whome he is redemed.
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Even against odd
spaces
6 2 12
8 2 16
15 2 30
45 2 90
4 3 12
4 4 16
9 4 36
16 4 64
6 5 30
20 5 100
2 6 12
15 6 90
20 6 120
4 7 28
8 7 56
2 8 16
8 8 64
4 9 36
9 9 81
25 9 225
9 10 90
21.
odd against even
spaces
3 2 6
36 2 72
3 3 9
5 3 15
12 3 36
5 4 20
9 4 36
16 4 64
3 5 15
5 5 25
9 5 45
12 6 72
7 7 49
5 9 45
9 9 81
3 12 36
3 14 42
17.
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even against odd
spaces
6 2 3
72 2 36
15 3 5
36 3 12
9 3 3
20 4 5
36 4 9
64 4 16
15 5 3
25 5 5
45 5 9
42 6 7
72 6 12
49 7 7
72 7 9
45 9 5
81 9 9
36 12 3
91 13 7
42 14 3
20.
odd against even
spaces
12 2 6
16 2 8
30 2 15
90 2 45
12 3 4
16 4 4
36 4 9
64 4 16
100 4 25
22 5 45 [sic -- 22 should be 225]
30 5 6
100 5 20
12 6 2
36 6 6
90 6 15
120 6 20
28 7 4
56 7 8
16 8 2
64 8 8
120 8 15
3 9 4 [sic -- 3 should be 36]
81 9 9
225 9 25
90 10 9
66 11 6
28 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}
15 225{2}
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The triumph is after the Kynge be cleane taken away, to be create in the adversaries campe, as well of your owne men as of your adversaries men that be taken, or of both in proportion as hath bene shewed before, and proclaimed that those men ons placed, may not be taken, as it was declared sufficiently, and no 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.
There must also in this thyrd kynde be considered the table, the men, their markyng, the order of theyr battell, 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 at the lest is must conteyne .10. squares in length and alwayes .8. in breadth. The longest is best.
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.
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The fasion is as hath bene last declared both of the men, and of the kynges, the inscription of numbers the same, but without cossical signes.
The order of battell is after the firste maner, but not so farre from the bordes end, namely the .4. squares standynge in the plattes nearest to the bordes end the rest accordingly joined to them, as in the first kynde of playing.
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[Note that, in this diagram, the odds are colored black. Also, it actually shows the odds and evens on reverse ends from this textual representation; I'm not redoing the whole thing right now...]
| [25] | [81] | [169] | [289] | ||||
| [15] | [45] | <25> | <20> | <42> | <49> | [91]* | [153] |
| <9> | <6> | (4) | (16) | (36) | (64) | <72> | <81> |
| (2) | (4) | (6) | (8) | ||||
| (9) | (7) | (5) | (3) | ||||
| <100> | <90> | (81) | (49) | (25) | (9) | <12> | <16> |
| [190]* | [120] | <64> | <56> | <36> | <30> | [66] | [28] |
| [361] | [225] | [121] | [49] |
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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 the squares into the fourth, the kyngs move as squares. And these be their ordinary draughts in marching.
They are taken by encountering, bu eruption, by laying wayght, and by Oblivion.
To take by encountering is to take by Equalitie, as hath bene twyse before declared.
To take by eruption is when a lesse number beyng multiplied by the spaces that are betwene him & hys adversary, the product is asmuch as his adversary, he may take his enemie awaye whether he stand directly 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 kynd of playing.
To take by deceypt or lying weight, is to take by addition, not as before when the adversary standeth within 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 in the table that was set forth for takyng by addition in the first kynde of playinge.
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 not remove 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 foure muste 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 him that is taken, but when he maye be taken before we drawe, then shall we remove our man into his place.
The king standeth for so many men as he hath steppes, that is the even for .6. the odde for .5. if anye of these
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(except the lowest and greatest) be taken the king may redeme hym, by any man of his that is of the same number. If he have none of the same number, he maye redeme him be any of his men that hys adversary wyll chuse. But if his lowest square be taken, no ransom will delyver him. Also if the whole kyng at ons that is the whole number of Pyramis be taken, he can not be redemed.
To take awaye the tediousnes of long play from them that be yonge beginners, wryters of this game have 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 set forth in the first kind of playing.
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 is only to take a certain number of men, as if the gamesters agree, that he which first taketh .4. or .5. or .6. or .10. men &c, shall wyn the game.
Victorie of goods, is to take a certain number without respect of the men. As if it be covenanted, that he which first taketh men amounting to the number of .100. or .200. shall have the victorie.
Victorie of quarell is when neither the men, nor the number, but the characters of the number be considered. As if it be determined that he which first taketh .100. in .8. characters not regarding in how many men they standes, shall winne. As .2.4.5.8.24.64. so you have .100. in .8. characters it skilleth not, although there be more then .100. as in this example there is more then .100. by .4.
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Victorie of honour, is whe a determined number is made in a determined number of men, as if it be determined 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.
The victorie of honour and quarell, is when one obteyneth the decreed number, in the decreed number of men and the decreed number of characters: as let .100. be the decreed number .8. the determined number of men, and .9. the determined number of characters. He that obteyneth .2.4.6.8.4.6.9.64. obteineth the victorie 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 in the victorie before.
They have invented another victorie, that is of standerdes, by counterfeyting two armies, one of the Christians, 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 let them devide the whole armye into .10. standerds so every standerd shall have .130. men, besyde the two captaines 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 every standerd .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 and forth of the rest.
If the odde armye wynne .260. they wyn two standerds .390. three standerds and so of the rest.
You maye use anye of these syxe kyndes of common victorie, in every one of the three kyndes of playing.
Prynted at London by Rouland Hall,
for James Rowbothum, and are to
be solde at his shoppe in
chepeside under Bowe
churche.
1563.