The theorike and practike of moderne vvarres discoursed in dialogue vvise. VVherein is declared the neglect of martiall discipline: the inconuenience thereof: the imperfections of manie training captaines: a redresse by due regard had: the fittest weapons for our moderne vvarre: the vse of the same: the parts of a perfect souldier in generall and in particular: the officers in degrees, with their seuerall duties: the imbattailing of men in formes now most in vse: with figures and tables to the same: with sundrie other martiall points. VVritten by Robert Barret. Comprehended in sixe bookes.
Barret, Robert, fl. 1600.

The first Dialogue:

VVherein is briefly touched of the orders of our now vsed fights: the great com∣modity of due and skilfull trayning: the tables for the embattailing of men in graund square of men: and into battallions of the same kind: with pro∣portioned figures to the same: and arithmeticall rules to the working there∣of: and a declaration of euery the sayd tables.

Gentleman.

WEll (Captaine) sith you haue in your former fiue bookes at large discoursed touching most martiall pointes; as well of souldiers, offices, officers, and Commanders, as also of most sorts of imbattailing of men, now most in vse; wherein you haue satisfied vs wonderfull well: yet, I pray (according to your promise) will you now describe vnto vs their seuerall tables,* and figures to the same: whereby we (which are not skilled) may reape some knowledge from thence: and so shall haue good cause to yeelde you thankes for your great paines.

Capt.

Although that I haue in our former discourses, declared (at large) of most sorts of imbattailing, both auncient and moderne; yet for better declaration and vnderstanding of the tables following, I must of necessity repeate a great part thereof againe.* Touching errors found in battels (according to mine opinion) by reason of sundry compound weapons within the body of the same, I haue spoken already.* Wherefore now let vs consider, and declare, what kind of battels (by rea∣son) may bee held for good and firme, considering our now vsed fights, and the weapons most befitting the same, & suted in so good sort as may become able to abide or performe a victory, whereunto they are appointed. Principally therfore if you will rest vpon one sole and entire battell, whether the same be square of mē, or square of ground,* or any other proportion, or forme, as hearst, crosse battell, or tryangle: the which two first (as I haue erst before sayd) do at this present day re∣maine chiefly in vse among vs: or deuide your army into many battallions of that kind, which your graund battell shall be formed of: then set your squadron of bat∣tell or battallions round about vnder the guard of the pikes, with such number of shot, as shall be best fitting vnto the proportion of the same, according to the Ser∣geant Maior his appointment; either by 3, 5, or 7 shot in a ranke: and the rest to be reparted into many small troupes, of 30, 40, or 50 in a troupe; trouping round a∣bout Page  182 the battel, with a reasonable distance from the same, to maintaine skirmish, which way soeuer the enemie approcheth. Prouiding that the same troupes be still maintained, one to second another, that the battell may be by them shadow∣ed, to the end that the enemies troupes or skirmishers may not haue that aduan∣tage to discharge vpon the body of your battell.

*Now among these your troupes of shot, it shall be very behouefull to mingle some of your short weapons, as halbards, bils, swords and targets, halfe pikes, and such like: for there shall your short weapon do best seruice, mixed with your na∣ked shot, to backe them, if they should happen to be distressed by the enemy.

Your battell thus framed, girdled, and enuironed with shot in troupes, the which troupes,* seconding one another, shall still keepe your battell shadowed, as in the figures of all their kinds, set downe before their seuerall tables, shall plainely appeare: alwayes regarding that your girdling shot do neuer discharge vntill the enemy commeth within 20,* or 30, pases of them at the least; and then to discharge roundly vpon the face and body of the enemy. The which being performed, if they be encountred with foote, they are speedily to retire vnto either flanke of the battell, or sleeued in betwixt the pikes, or if encountred with horse, to bend downe vpon one knee, vnder the guard and succour of the pike.

*Now hauing deepely considered the rare victories and great conquests of the auncient Romaines, atchieued (in mine opinion) by their due obseruing of true martiall discipline, and great readinesse in their politike and suddaine alterations of their proportions, wherewith to encounter their enemies, I find therein a most notable patterne of a right excellent Chiefetaine. The very circumspection of whom, by a most wonderfull regard, was cause vnto them, of so many, and such honourable victories:* wherein the continuall readinesse of their souldiers and people of war, to be transported (with all facilitie) into euerie forme, vpon anie oc∣casion: and the skilfull direction of their Captaines was such therin, as to so victo∣rious a people seemed to be most correspondent and conuenient. The which true discipline, obedience, skill, and readinesse, were it vsed (and more then it is) in this our age, I thinke warres would carry a farre better conduction then they now do.

*This kind of readinesse in souldiers, and the indeuour of a continuall vse vnto them in the same, especially in the time of their trainings (the which I could wish to be put in practise with vs by skilfull trainers) vpon what chaunce soeuer shold happen, hath no doubt, seemed vnto many, to be of no small importance and force; and the rather do I so iudge, for that hauing sounded the depth and com∣modity thereof, I find the contrary negligence to beare with it a note of most great imperfection. The disposition whereof, leauing vnto the knowledge and regard of euery good and expert Captaine,* and for that I haue at large discoursed thereof already in my third booke of these military discourses, I will at this pre∣sent content my selfe, to shew vnto you the seuerall tables and figures of all these battels and battallions, with the arithmeticall rules to frame the same; and how that out of the grand square of men, may all these battallions and battels be re∣duced, and that without any great confusion. The practike rules whereof I haue, as I sayd, at large set downe in these our former discourses, as in the third booke may appeare:* moreouer I haue in sundry other places particularly declared and Page  183 the orders of the embattailing of men now most in vse, with their order of impa∣ling with armed pikes, their diuisions into Maniples, and the ready reframing of them againe into their grand square, as at large in the sayd third booke appeareth in many and diuerse places.

Finally in the aforesaid third booke, in folio 89, and 90, and in the fourth booke in folio 99, I haue described the order to draw your army through straights, and difficult passages, by quartering the same into such proportions as the straights will permit: especially if the enemy do constraine you to fight in the same, as most commonly it falleth out:* also in the fift booke, in folio 157 is dessigned a plat of encampement, with the arithmeticall rules of the same: in the consideration of all which, the value, and waight of this readinesse, may vnto the diligent re∣garders (perchance) in their seuerall descriptions, giue some manifest appearāce.

A declaration of the tables of battels and battallions with the arith∣meticall rules to worke the same.

In these tables following,* I haue begun with the nūber of 10000 armed pikes; besides the shot and short weapons, correspondent to these proportions, where∣of I haue before sufficiently spoken in many places: for the diuision of which number of armed pikes,* with all numbers downe ward, I haue reduced into cer∣taine tables the proportions of diuerse battels, beginning with the square of men from the said number of 10000 pikes downward, and the same not decreasing, by 50 or 100 but by roote, as first beginning with the square roote of 10000, which is 100. The which multiplied into it selfe, maketh the said 10000: and so from the roote 100 vnto 099, and then 098, next 097, and so from roote to roote orderly, vnto the last square roote, which is 1.

In which tables I haue directed the order of marching of an army, as the pas∣sage or way will permit:* whether you shall march 3, 5, 7, 9, 11, 13, 15, or 17 in a ranke, and how many rankes they shall be. To do the which, worke thus. Deuide the whole nūber of men by so many in rank,* as you will haue them to march in; as by 3, 5, 7, &c. The number here I haue supposed to be 10000 men, the which 10000 to haue them to march at 3 men per ranke, I do deuide 3, and it produceth 3333 rankes, and 1 man remaining, as in the margine appeareth. And if you wold haue them to march by 5, 7, 9,* or any other number, per ranke, worke as you haue done with the number 3.

Then how to deuide the battell into Maniples or parts,* and so to march them vpon the way as strongly as the passage will permit; and how the Maniples com∣ming vp shoulder to sholder, each weapō ioyneth with his like, making again the former square battell of men,* with the remaines that make not vp a iust Maniple or part: and also how to march those sayd remaines that they may come vp shoulder to shoulder, with the rest of the Maniples, to make vp a iust square. To do the which,* worke thus: deuide the roote of your grand number of men by so many as you would haue them to march in a Maniple, and the product will be the number of Maniples, with the remaines (if any such there bee) as for ex∣ample, the square roote of 10000, is 100, the which 100 men, I do deuide by 3 and it produceth 33 Maniples, and one ranke remaining, the which 1 ranke is 100 men, the which 100 men, marching vp by 1 in a ranke, comming vp shoulder to shoulder with the grand square, maketh iust the same proportion of the grand square; as in the Tables plainly may appeare: So may you worke by 5, 7, 9, 11, Page  184 or any other number, to bring them into Maniples with their remaines. But here you shall note,* that a Maniple, doth signifie so many men in ranke quite through your grand square or battell, as you are disposed, or be constrained to deuide the sayd grand square into, whereby to passe through any straight or passage, & then comming vp shoulder to shoulder, do make your former square of men againe.

Finally in the first table of the said square of men, in proportion of equalitie, there is set down readily how many shot will girdle or impale the battell of pikes,* in what forme soeuer you dispose the same, whether it be by 3, 5, 7, or 9 shot in a ranke, which is as many as you shall neede to girdle withall, in mine opinion: and if you are to encounter or be charged with horse, I suppose 3 to be sufficient. To do the which,* worke you thus: First multiplie your quadrate roote, or square of men, by so many as you meane or bee disposed to girdle the same withall, the product whereof will amount to the girdling shot for the one side or quarter; then againe multiplie the said product by 4, for the 4 squares of the battell, and the product thereof serueth for the girdling of the sayd 4 square sides. Now there will want to fill the 4 angles or corners, the which you must consider whe∣ther you doe impale by 3, 5, 7 or 9: then to multiplie euery angle by so many per ranke,* as you doe impale by: as for example: the square roote of 10000 is 100; the sayd 100 I do multiplie by 3, (for so many doe I set to impale by) and it maketh 300 for the one square side of the battell; the which 300 I doe againe multiplie by 4, for all the 4 square sides of the battell, and it amounteth vnto 1200 shot: then for the foure corners or angles (considering that I do impale by 3) first I multiplie the sayd three by it selfe, and it maketh 9 for one angle: and then quadruple the sayd 9, it maketh 36, the which 36 being added vnto the aforesayd 1200, and it a∣mounteth in all vnto 1236 shot for the full impalement of your squadron of 100 square roote of men. And so may you do with any other number, as in the tables will appeare more at large.

Likewise on the left side of euery leafe of the sayd tables, hauing first turned the same ouer, you shall haue opposite or against the number or battell, which standeth euermore on the right side of the sayd leafe, the same battell deuided in∣to 3,* 5, or 7 battallions; the number of which battallions in each of them contei∣ned, you shall finde by drawing your finger euermore on the first Columne of euery leafe on the right side, & where you finde the number of the said battalliōs, there shall you see in that distinctiō betwixt two long rules, how euery battallion shall bee set, which two long rules are the second Columne of the tables: As for example: the grand battell of 10000 pikes, placed on the right side of the leafe in the first Table, as in folio 16 may be seene, the sayd grand battell you shall finde deuided into 3, 5 or 7 battallions, by turning ouer the leafe looking vpon the left side therof, in the same folio 190. Now to know the square root of euery of these battallions, draw your finger continually down the first Columne of euery right side of the leafe, vntill you come to finde the due number of the sayd battallions, which is, first 348, &c. the which nūber being found in the first Columne in folio 191, euen there in the second Columne you shall see the square roote thereof to be 59, and so must you do by the rest of the battallions.

*In the first Columne of the left side of euery leafe, is placed the grand square or battell of men: in the second Collumne is set the same battell deuided into 3. battallions: in the third Columne is the number of euery of their seuerall battal∣lions, Page  185 and in the fourth Columne is the remaines of the sayd battallions, which is, how much they are lesse then the grand square of men: and also in the said fourth Columne, if they do abound the number of the grand square, it shall be there set downe, alwayes marked with this word (ouer) adioyning vnto it, which word when you do finde, then suppose that the battallions are more then the grand bat∣tell, by so many as that number containeth. The like order is to be obserued in the diuision of them into fiue battallions, or into seuen battallions.

As for the reducing or inducing of all battels and battallions out of,* or into the grand square of men, I haue before in folio 77, 78, 79, and so forth, at large de∣clared; as of the battell in Diamant proportiō, of the Triangle, of the Sheeres bat∣tell and Saw battell, & of the Crosse battell, & battell cōpounded of many battal∣liōs, vnto the which I referre me: onely hereafter will I set down the figure & Ta∣bles of all, or the most of these, & the order to be obserued in the same: as I will at the beginning of euery Table declare: but first I will shew you the declaration of euery Columne of the Tables, as here is described.

    A declaration of the vse of the Columnes, and numbers expressed in the Tables following.
  • 1 The number of 1 in the first columne, containeth therein the number of the armed pikes of the grand battell of men.
  • 2 The number of 2 ouer the second columne, containeth in that part, the due number of the square roote of the battell.
  • 3 The number of 3 in the third columne, hath in it, the order of marching, as the ground will permit, be it by 3, 5, 7, 9, 11, 13, 15, or 17, in ranke.
  • 4 The number of 4 containeth in that columne, the number of rankes, either by 3, 5, 7, 9, 11, 13, 15, or 17 men in a ranke.
  • 5 The number of 5 hath in that columne, the remainders of that which maketh not vp a iust number of rankes.
  • 6 The number of 6 sheweth in that columne, the number of the Maniples or parts of each battell: whether they march by 3, 5, 7, 9, 11, 13, 15, or 17, in a ranke, the which mar∣ching vp shoulder to shoulder, do make the square battell of men, with the ensignes in the middle Maniple or part.
  • 7 The number of 7 in the seuenth columne, signifieth the surplussage of armed pikes, that maketh not a iust Maniple.
  • 8 The number of 8 in the eight columne, denoteth the whole ouerplus of the armed pikes that make not vp a full Maniple.
  • 9 The number of 9 in that columne, sheweth how many shall march in a ranke of the ouer plus, that made not vp a iust Maniple or part, which so marching vp shoulder to shoul∣der with the rest of the Maniples or parts, maketh vp the iust square of men.
  • 10 The number of 10 in that columne, sheweth how to girdle or impale your battell with shot, whether it be by 3, 5, 7, or 9. which is sufficient to girdle any battell.
  • 11 The number of 11 carrieth in that columne, what number of shot euery kinde of im∣battelling or girdling will occupie in each seuerall battell, whether the same be by 3, 5, 7, or 9 in ranke of shot.
    A declaration of the Tables of the Battallions.
  • 1 The nūber of 1 in the first columne, signifieth the whole nūber of the grand battell.
  • 2 The number of 2 hath in that collumne the diuision, be it by 3, 5, or 7.
  • 3 The nūber of 3 hath in that columne, the nūber contained in euery seuerall battalliō.
  • 4 The number of 4 hath in that columne the remaines or ouerplus.

Page  198

[illustration]
The figure of the square battell of men.

In this figure of a square battell of men, there is contained 10000 armed Pikes, Page  187 at 100 rankes, and 100 men by ranke: girdled round about with seuen rankes of shot. The rest of the shot and short weapon, are bestowed in 165 small troupes, containing 50 in euerie troupe, trouping round about the battell, so shadowing the same, and readie for skirmish, on what part soeuer the enemie should offer fight: the rest of the shot and short weapon with some pikes, are for the guard of the Artillerie and Munition.

[illustration]
The figure of the grand square of 10000 Pikes, deuided into 3 battallions.

Page  188

[illustration]
The figure of the grand square reduced into 5 Battallions.

[illustration]
The figure of the 7 Battallions reduced out of the grand square of men.

Page  189

The Tables of Battels in proportion of equalitie as, is 1, to 1.
1 2 3 4 5 6 7 8 9 10 11
10000 100 3 3333 1 33 1 100 1 3 1236
5 2000 0 20 0 0 0 5 2100
7 1428 4 14 2 200 2 7 2996
9 1111 1 11 1 100 1 9 3924
100 11 909 1 9 1 100 1    
13 768 1 7 9 900 9    
15 666 10 6 10 1000 10    
17 588 1 5 15 1500 5    
9801 99 3 3267 0 33 0 0 0 3 1224
5 1960 4 19 4 396 4 5 200
7 1400 1 14 1 99 1 7 2968
9 1089 0 19 0 0 0 9 3888
99 11 891 0 9 0 0 0    
13 752 12 7 8 792 8    
15 653 6 6 9 891 9    
17 576 9 5 14 1384 14    
9604 98 3 3201 1 32 2 196 2 3 1212
5 1920 4 19 3 294 3 5 2060
7 1372 0 14 0 0 0 7 2940
9 1063 1 10 8 784 8 9 3852
98 11 873 1 8 10 986 10    
13 738 10 7 7 866 7    
15 640 4 6 8 784 8    
17 564 0 5 13 1274 13    
9409 97 3 3136 1 32 1 97 1 3 1200
5 1881 4 19 2 194 2 5 2040
7 1344 1 13 6 582 6 7 2912
9 1045 4 10 7 679 7 9 3816
97 11 855 4 8 9 873 9    
13 723 10 7 6 502 6    
15 627 4 6 7 699 7    
17 553 8 5 12 1164 12    
9216 96 3 3072 0 32 0 0 0 3 1180
5 1843 1 19 1 96 1 5 2020
7 1316 4 13 5 480 5 7 2884
9 1024 0 10 6 576 6 9 2780
96 11 837 9 8 8 768 8    
13 708 12 7 5 580 5    
15 614 6 6 6 576 6    
17 542 2 5 11 1057 11    
9025 95 3 3008 1 31 2 190 2 3 1176
5 1801 0 19 0 0 0 5 2000
7 1289 2 13 4 30 4 7 2756
9 1002 7 10 5 475 5 9 3744
95 11 824 5 8 7 665 7    
13 694 3 7 4 380 4    
15 601 10 6 5 475 5    
17 530 15 5 10 950 10    
Number of pikes to be imbattailled. The quadrate roote. To march in ranke. Rankes how many. Remainder of men. Maniples of pikes. Rankes of remainder. The whole ouerplus of pikes, after the Manip. How many pikes in ranke to march vp. Number of shot to im∣pale. The whole number of shot that do impale.

Page  190

The Table of Battallions of the grand square of men.
1 2 3 4 2 3 4 2 3 4
10000 3 3481 3249 3299 21 5 2340 2025 1936 1936 1764 35 7 1444 1444 1444 1444 1444 1369 1369 0
9801 3 3600 3600 2601 0 5 2500 2500 1600 1600 1600 1 7 2025 2025 1296 1296 1296 961 900 2
9604 3 3249 3136 3136 83 5 2025 2025 1849 1849 1849 7 7 1369 1369 1369 1369 1369 1369 1369 17
9409 3 3136 3136 3136 1 5 1936 1936 1849 1849 1849   7 1369 1369 1369 1369 1296 1296 1296 45
9216 3 3249 3249 2704 14 5 2116 2116 2116 1444 1444 10 7 1369 1369 1369 1296 1296 1296 1296 25
9025 3 3025 3025 2916   5 1764 1764 1764 1849 1849   7 1369 1369 1369 1225 1225 1225 1225  

Page  203

The Table of Battels in proportions of equalitie.
1 2 3 4 5 6 7 8 9 10 11
8836 94 3 2945 1 31 1 94 1 3 1164
5 1767 1 18 4 376 4 5 1980
7 1262 2 13 3 242 3 7 2828
9 981 7 10 4 376 4 9 3708
94 11 803 3 8 6 564 6    
13 679 9 7 3 282 3    
15 589 1 6 4 376 4    
17 519 13 5 9 846 9    
8649 93 3 2883 0 31 0 0 0 3 1151
5 1729 4 18 3 279 3 5 1960
7 1235 4 13 2 186 2 7 2800
9 961 0 10 3 279 3 9 3627
93 11 786 3 8 5 465 5 11  
13 665 4 7 2 186 2    
15 576 9 6 3 279 3    
17 508 13 5 8 744 8    
8464 92 3 2821 1 30 2 184 2 3 1140
5 1672 4 18 2 184 2 5 1940
7 1209 1 13 1 92 1 7 2772
9 940 4 10 2 184 2 9 3636
92 11 769 5 8 4 368 4    
13 651 1 7 1 92 1    
15 564 4 6 2 184 2    
17 486 2 5 7 644 7    
8281 91 3 2760 1 30 1 91 1 3 1128
5 1656 1 18 1 91 1 5 1920
7 1187 0 13 0 0 0 7 2744
9 920 1 10 1 91 1 9 3600
91 11 752 9 8 3 273 3    
13 637 0 7 0 0 0    
15 552 1 6 1 91 1    
17 487 2 5 6 546 6    
8100 90 3 2780 0 30 0 0 0 3 1116
5 1420 0 18 0 0 0 5 1900
7 1157 1 12 6 540 6 7 2716
9 900 0 10 0 0 0 9 3564
90 11 736 4 8 2 180 2    
13 623 1 6 12 1080 12    
15 540 00 6 0 000 0    
17 499 13 5 5 450 5    
7921 89 3 2640 1 29 2 178 2 3 1104
5 1584 1 17 4 356 4 5 1880
7 1131 4 12 5 445 5 7 2688
9 880 1 9 8 712 8 9 3528
89 11 720 1 8 1 89 8    
13 609 4 6 11 979 11    
15 529 13 5 14 1246 14    
17 465 16 5 4 356 4    

Page  192

The Table of Battallion to the grand square of men.
1 2 3 4 2 3 4 2 3 4
8836 3 3025 3025 2704   5 1764 1764 1764 1764 1764 62 7 1296 1296 1296 1225 1225 1225 1225 48
8649 3 2916 2916 2809 8 5 1764 1764 1764 1681 1681 5 7 1296 1296 1296 1296 1156 1156 1156 7
8464 3 2809 2809 2809 37 5 1849 1849 1849 1444 1444 29 7 1296 1296 1296 1296 1089 1089 1089 13
8281 3 3249 2500 2500 32 5 1681 1681 1681 1600 1600 38 7 1296 1296 1296 1024 1024 1024 1296  
8100 3 2704 2704 2704 12 5 1936 1936 1936 1156 1156   7 1156 1156 1156 1156 1156 1156 1156 8
7921 3 2809 2809 2304   5 1600 1600 1600 1600 1520   7 1156 1156 1156 1156 1089 1089 1089 27

Page  193

The Tables of Battels in proportion of equalitie.
1 2 3 4 5 6 7 8 9 10 11
7744 88 3 2581 1 29 1 88 1 3 1092
5 1548 4 17 3 264 3 5 1860
7 1106 2 12 4 352 4 7 2260
9 860 4 9 7 616 7 9 3492
88 11 704 0 8 0 0 0    
13 595 9 6 10 80 10    
15 516 4 5 13 1144 13    
17 455 9 5 3 264 3    
7569 87 3 2523 0 29 0 0 0 3 1080
5 1513 4 27 2 174 2 5 1840
7 1081 2 12 3 261 3 7 2632
9 841 0 9 6 522 6 9 3456
87 11 688 1 7 10 870 10    
13 582 3 6 9 783 9    
15 501 14 5 12 1044 12    
17 445 4 5 2 174 2    
7396 86 3 2465 1 28 2 172 2 3 1068
5 1479 1 17 1 86 1 5 1820
7 1056 2 12 2 172 2 7 2604
9 821 7 9 5 430 5 9 3420
86 11 672 4 7 9 774 9    
13 568 12 6 8 688 8    
15 493 1 5 11 946 11    
17 431 9 5 1 86 1    
7225 85 3 2408 1 28 1 85 1 3 1056
5 1445 0 17 0 0 0 5 1800
7 1032 1 12 1 85 1 7 2576
9 802 7 9 4 420 4 9 3384
85 11 656 9 7 8 680 8    
13 555 10 6 7 585 7    
15 481 10 5 10 850 10    
17 425 0 5 0 0 0    
7056 84 3 2352 0 28 0 0 0 3 1044
5 1411 1 16 4 336 4 5 1780
7 1008 0 12 0 0 0 7 2548
9 784 0 9 3 552 3 9 3348
84 11 641 5 7 7 595 7 11  
13 542 10 6 6 504 6    
15 470 6 5 9 756 9    
17 415 1 4 16 1244 16    
6889 83 3 2292 1 27 2 166 2 3 1032
5 1377 4 16 3 244 3 5 1760
7 984 1 11 6 498 6 7 2520
9 765 4 9 2 166 2 9 3312
83 11 626 3 7 6 504 6    
13 529 12 6 5 415 5    
15 459 4 5 8 664 8    
17 405 4 4 15 1245 15    

Page  194

The Table of Battallions of the battels of equall proportion.
1 2 3 4 2 3 4 2 3 4
7744 3 2401 2401 2916 26 5 1530 1530 1530 1530 1601 23 7 1156 1156 1089 1089 1089 1089 1089 13
7569 3 2704 2704 2116 45 5 1601 1601 1601 1369 1369 18 7 1089 1089 1089 1089 1089 1089 1024 11
7396 3 2500 2500 2401 5 5 1444 1444 1444 1530 1530 4 7 1089 1089 1089 1024 1024 1024 1024 33
7225 3 2681 2681 1936 7 5 1444 1444 1444 1444 1444 5 7 1089 1089 1089 1089 961 961 961 14
7056 3 2916 2916 1089 35 5 1444 1444 1369 1369 1369 61 7 1024 1024 1024 1024 1024 1024 900 12
6889 3 2916 2916 1024 33 5 1369 1369 1369 1369 1369 1369 44 7 1024 1024 1024 961 900 900 1024 32

Page  195

The Table of Battels in proportion of equalitie.
1 2 3 4 5 6 7 8 9 10 11
6724 82 3 2241 1 27 1 82 1 3 1020
5 1344 4 16 2 164 2 5 1740
7 960 4 11 5 410 5 7 2492
9 747 1 9 1 82 1 9 3276
82 11 611 3 7 5 410 5    
13 517 3 6 4 328 4    
15 448 4 5 7 574 7    
17 395 9 4 14 1148 14    
6561 81 3 2187 0 27 0 0 0 3 1008
5 1312 1 16 1 81 1 5 1728
7 937 2 11 4 324 4 7 2464
9 729 0 9 0 0 0 9 3240
81 11 596 5 7 4 324 4    
13 504 9 6 3 243 3    
15 437 6 5 6 486 6    
17 385 16 4 13 1053 13    
6400 80 3 2133 1 26 2 160 2 3 996
5 1280 0 16 0 0 0 5 1700
  914 2 11 3 240 3 7 2436
9 711 1 8 8 640 8 9 3204
80 11 581 9 7 3 240 3    
13 492 4 6 2 160 2    
15 428 4 5 5 400 5    
17 376 8 4 12 960 12    
6241 79 3 2080 1 26 1 79 1 3 984
5 1248 1 15 4 316 4 5 1680
7 891 4 11 2 158 2 7 2408
9 693 4 8 7 553 7 9 316
79 11 567 4 7 2 158 2    
13 480 1 6 1 79 1    
15 416 1 5 4 316 4    
17 367 2 4 11 869 11    
6084 78 3 2028 0 26 0 0 0 3 972
5 1216 4 15 3 234 3 5 1660
7 869 1 11 1 78 1 7 2380
9 676 0 8 6 468 6 9 3132
78 11 553 1 7 1 78 1    
13 468 0 6 0 0 0    
15 405 9 5 3 234 3    
17 322 10 4 10 780 10    
5929 77 3 1976 1 25 2 154 2 3 960
5 1185 4 15 2 154 2 5 1640
7 847 0 11 0 0 0 7 2332
9 658 7 8 5 385 5 9 3096
77 11 539 0 7 0 0 0    
13 456 1 5 12 924 12    
15 395 4 5 2 154 2    
17 348 13 4 9 693 9    

Page  196

The Table of Battallions of the battels of equall proportion.
1 2 3 4 2 3 4 2 3 4
6724 3 2209 2209 2304 24 5 1369 1369 1369 1296 1296 25 7 961 961 961 961 961 961 961 3
6561 3 2401 2401 1764 5 5 1369 1369 1369 1225 1225 4 7 961 961 961 961 900 900 900 17
6400 3 2116 2116 2116 12 5 1296 1296 1296 1296 1225 9 7 900 900 900 900 900 900 961 19
6241 3 2116 2116 2025   5 1296 1296 1296 1156 1156 41 7 900 900 900 900 900 900 841  
6084 3 2025 2025 2025 9 5 1025 1025 1025 1025 1156 28 7 900 900 900 900 900 784 784 20
5929 3 2304 2304 1296 25 5 1156 1156 1156 1225 1225 11 7 900 900 900 900 784 784 729 32

Page  197

The Table of Battels in proportion of equalitie.
1 2 3 4 5 6 7 8 9 10 11
5776 76 3 1295 1 25 1 76 1 3 948
5 1155 1 15 1 76 1 5 1620
7 825 1 10 6 456 6 7 2324
9 641 7 9 4 304 4 9 3060
76 11 525 1 6 10 760 10    
13 444 4 5 11 830 11    
15 384 8 5 1 76 1    
17 339 13 4 8 608 8    
5625 75 3 1875 0 25 0 0 0 3 936
5 1125 0 15 0 0 0 5 1600
7 803 4 10 5 375 5 7 2276
9 625 0 8 3 225 3 9 3024
75 11 511 4 6 9 675 9    
13 432 9 5 10 750 10    
15 375 0 5 0 0 0    
17 30 15 4 7 525 7    
5476 74 3 1825 1 24 2 148 2 3 924
5 1095 1 14 4 296 4 5 1580
7 753 5 10 4 296 4 7 2248
9 608 4 8 2 148 2 9 2988
74 11 497 9 6 8 592 8    
13 421 3 5 9 666 9    
15 365 1 4 14 1036 14    
17 322 2 4 6 456 6    
5329 73 3 1776 1 24 1 73 1 3 912
5 1065 4 14 3 219 3 5 1560
7 761 2 10 3 219 3 7 2240
9 592 1 8 1 73 1 9 2952
73 11 484 8 6 7 511 7    
13 409 12 5 8 584 8    
15 355 4 4 13 949 13    
17 313 8 4 5 365      
5184 72 3 1728 0 24 0 0 0 3 900
5 1036 4 14 2 144 2 5 1540
7 740 4 10 2 144 2 7 2192
9 567 0 8 0 0 0 9 2910
72 11 471 3 6 6 432 6    
13 398 10 5 7 504 7    
15 345 9 4 12 864 12    
17 304 16 4 4 288 4    
5041 71 3 1680 1 22 2 142 2 3 888
5 1008 1 14 1 71 1 5 1520
7 720 1 10 1 71 1 7 2184
9 560 1 7 8 568 8 9 2888
71 11 458 3 6 5 355 5    
13 387 10 5 6 426 6    
15 336 1 4 11 781 11    
17 296 9 4 3 213 3    

Page  198

The Table of Battallions of the battels of equall proportion.
1 2 3 4 2 3 4 2 3 4
5776 3 2304 2304 1156 12 5 1156 1156 1155 1156 1156 4 7 841 841 841 841 841 784 784 3
5625 3 2304 2304 1024 ouer 7 5 1089 1089 1089 1156 1156 46 7 784 784 784 784 784 841 841 23
5476 3 1764 1764 1936 12 5 1089 1089 1089 1089 1089 33 7 784 784 784 784 784 784 784 12
5329 3 1764 1764 1764 33 5 1089 1089 1089 1024 1024   7 784 784 784 784 729 729 729 2
5184 3 1936 1600 1600 48 5 1024 1024 1024 1024 1089 1 7 784 729 729 729 729 729 729 26
5041 3 1681 1681 1681 2 5 1024 1024 1024 961 961 47 7 729 729 729 729 729 729 676 9

Page  199

The Table of Battels of proportion of equalitie.
1 2 3 4 5 6 7 8 9 10 11
4900 70 3 1633 1 23 1 70 1 3 876
5 980 0 14 0 0 0 5 1500
7 700 0 10 0 0 0 7 2136
9 544 4 7 7 490 7 9 2844
70 11 445 5 6 4 280 4    
13 376 12 5 5 350 5    
15 326 10 4 10 700 10    
17 288 4 4 2 140 2    
4761 69 3 1587 0 23 0 0 0 3 864
5 952 1 13 4 276 4 5 1480
7 680 1 9 6 414 6 7 2118
9 551 2 7 6 414 6 9 2808
69 11 432 9 6 3 207 3    
13 366 3 5 4 276 4    
15 316 6 4 9 621 9    
17 280 1 4 1 69 1    
464 68 3 2541 1 22 2 136 2 3 52
5 924 4 13 3 204 3 5 1480
7 632 0 9 5 340 5 7 2090
9 513 7 7 5 340 5 9 2772
68 11 420 4 6 2 136 2    
13 355 9 5 3 204 3    
15 308 4 4 8 544 8    
17 272 0 4 0 0 0    
4489 67 3 1496 1 22 1 67 1 3 840
5 897 4 13 2 134 2 5 1440
7 641 2 9 4 268 4 7 2062
9 498 7 7 4 268 4 9 2736
67 11 408 1 6 1 67 1    
13 345 4 5 2 134 2    
15 299 4 4 7 469 7    
17 264 1 3 16 1072 16    
4356 66 3 1452 0 22 0 0 0 3 820
5 871 1 13 1 66 1 5 1420
7 622 2 9 3 198 3 7 2034
9 472 8 7 3 198 3 9 2700
66 11 396 0 6 0 0 0    
13 355 1 5 1 66 1    
15 290 6 4 6 396 6    
17 256 4 3 15 990 15    
4225 65 3 1408 1 21 2 130 2 3 816
5 845 0 13 0 0 0 5 1400
7 603 4 9 2 130 2 7 2006
9 469 4 7 2 130 2 9 2664
65 11 384 1 5 10 650 10    
13 325 0 5 0 0 0    
15 281 10 4 5 325 5    
17 248 9 3 14 910 14    

Page  200

The Table of Battallions of the battels of euen square.
1 2 3 4 2 3 4 2 3 4
4900 3 1600 1600 1681 19 5 1024 1024 1024 900 900 28 7 729 729 729 729 676 625 7
4761 3 1520 1520 1520 20 5 961 961 961 961 900 28 7 676 676 676 676 676 676 676 29
4624 3 1521 1521 1521 34 5 961 961 900 900 900 2 7 676 676 676 676 676 625 625  
4489 3 1444 1444 1600 1 5 900 900 900 900 841 48 7 676 676 625 625 625 625 625 12
4356 3 1444 1444 1444 24 5 961 961 961 739 739 5 7 625 625 625 625 625 625 625 19
4252 3 1369 1369 1369 43 5 841 841 841 841 841 20 7 625 625 625 625 625 676 676 3

Page  201

The Table of Battels in proportion of equalitie.
1 2 3 4 5 6 7 8 9 10 11
4096 64 3 1365 1 21 1 64 1 3 804
5 819 1 12 4 256 4 5 1380
7 585 1 9 1 64 1 7 1976
9 455 1 7 1 64 1 9 2628
64 11 372 4 5 9 576 9    
13 315 1 4 12 768 12    
15 273 1 4 4 256 4    
17 240 16 3 13 832 13    
3969 63 3 1323 0 21 0 0 0 3 792
5 0791 4 12 3 189 3 5 1360
7 567 0 9 0 0 0 7 1946
9 441 2 7 0 0 0 9 2592
63 11 360 9 5 8 504 8    
13 305 4 4 11 693 11    
15 264 9 4 3 189 3    
17 223 8 3 12 756 12    
3844 62 3 1281 1 20 2 124 2 3 780
5 768 4 12 2 124 2 5 1340
7 549 1 8 6 372 6 7 1918
9 427 1 6 8 496 8 9 2556
62 11 349 5 5 7 434 7    
13 295 9 4 10 620 10    
15 256 4 4 2 124 2    
17 226 2 3 11 682 11    
3721 61 3 1240 1 20 1 61 1 3 768
5 744 1 12 1 61 1 5 1320
7 531 4 8 5 305 5 7 1904
9 413 4 6 7 427 7 9 2520
61 11 338 3 5 6 366 6    
13 286 3 4 9 549 9    
15 248 1 4 1 61 1    
17 218 3 3 10 610 10    
3600 60 3 1200 0 20 0 0 0 3 756
5 720 0 12 0 0 0 5 1300
7 514 2 8 4 240 4 7 1862
60 9 400 0 6 6 360 6    
11 327 3 5 5 300 5    
3481 59 3 1160 1 19 2 118 2 3 744
5 696 1 11 4 236 4 5 1280
7 497 2 8 3 177 3 7 1834
59 9 386 7 6 4 296 4    
11 316 5 5 4 236 5    
3369 58 3 1121 1 19 1 58 1 3 732
5 672 4 11 3 174 3 5 1260
7 480 4 8 2 116 2 7 1806
58 9 373 7 6 4 232 4    
11 305 9 5 3 174 3    
3249 57 3 083 0 19 0 0 0 3 720
5 649 4 11 2 114 2 5 1240
7 401 1 8 1 57 1 7 1778
57 9 378 3 6 3 171 3    
11 295 4 5 2 114 2    

Page  202

The Tables of Battallions to the battels of euen squares.
1 2 3 4 2 3 4 2 3 4
4096 3 1369 1369 1369 11 5 784 841 841 841 784 5 7 576 576 576 576 576 576 625 15
3969 3 1225 1369 1369 6 5 784 784 784 784 841 8 7 576 576 576 576 576 529 529 31
3844 3 1296 1296 1225 27 5 784 784 784 739 739 14 7 576 576 576 529 529 529 529  
3721 3 1225 1225 1225 46 5 739 739 739 739 739 26 7 529 529 529 529 529 529 529 18
3600 3 1225 1225 1156 6 5 739 739 739 676 676 31 7 529 529 529 529 529 484 484 13
3481 3 1156 1156 1156 13 5 676 676 676 676 739 35      
3364 3 1089 1089 1156 9 5 676 676 625 625 625 35      
3249 3 1089 1089 1089 1 5 676 676 625 625 625 11      

Page  203

The Table of Battels in proportion of equalitie.
1 2 3 4 5 6 7 8 9 10 11
3136 56 3 1045 1 18 2 112 2 3 708
5 627 1 11 1 56 1 5 1240
56 7 448 0 8 0 0 0 7 1750
9 344 4 6 2 112 2    
11 285 1 5 1 56 1    
3925 55 3 1008 1 18 1 55 1 3 696
5 605 0 11 0 0 0 5 1220
55 7 432 1 7 6 330 6 7 1722
9 336 1 6 1 55 1    
11 275 0 5 0 0 0    
2916 54 3 972 0 18 0 0 0 3 684
5 583 1 10 4 216 4 5 1200
54 7 416 4 7 5 270 5 7 1694
9 334 0 6 0 0 0    
11 265 1 4 10 540 10    
2809 53 3 936 1 17 2 106 2 3 672
5 561 4 10 3 159 3 5 1180
53 7 401 2 7 4 212 4 7 1666
9 312 1 5 8 424 8    
11 255 4 4 9 477 9    
2704 52 3 901 1 17 1 52 1 3 660
5 540 4 10 2 104 2 5 1160
52 7 386 2 7 3 156 3 7 1638
9 300 4 5 7 364 7 9 2164
11 245 9 4 8 416 8    
2601 51 3 867 0 17 0 0 0 3 648
5 520 1 10 1 51 1 5 1140
51 7 371 4 7 2 102 2 7 1610
9 289 0 5 6 306 6    
11 236 5 4 7 357 7    
2500 50 3 833 1 16 2 100 2 3 636
5 500 0 10 0 0 0 5 1120
50 7 359 1 7 1 50 1 7 1582
9 277 7 5 5 250 5    
11 227 3 4 6 300 6    
2401 49 3 800 1 16 1 49 1 3 624
5 480 1 9 4 196 4 5 1100
49 7 343 0 7 0 0 0 7 2554
9 266 7 5 4 196 4    
11 218 3 4 5 245 5    
2304 48 3 786 0 16 0 0 0 3 612
5 460 4 9 3 144 3 5 1080
48 7 329 1 6 6 288 6 7 1526
2209 47 3 736 1 15 2 94 2 3 600
5 441 4 9 2 94 2 5 1060
47 7 315 4 6 5 235 5 7 1498
2116 46 3 705 1 15 1 46 1 3 588
46 5 425 1 9 1 46 1 5 1040
7 302 2 6 4 184 4 7 1470

Page  204

The Tables of Battallions of the battels of euen squares of men.
1 2 3 4 2 3 4
3136 3 1024 1024 1089   5 625 625 625 625 625 625  
3025 3 1024 1024 961   5 625 625 625 576 576  
2916 3 1024 961 900 14 5 576 576 576 576 576  
2809 3 961 961 900 13 5 576 576 576 529 529  
2704 3 900 900 900 4 5 529 529 529 529 576  
2601 3 900 841 841 19 5 529 529 529 529 484  
2500 3 841 841 784 34 5 529 529 529 441 441 31
2401 3 841 784 784 8 5 484 484 484 484 441 24
2304 3 784 784 739 3 5    
2209 3 739 739 739 8      
2116 3 739 739 625 13      

Page  205

The Table of Battels in proportion of equalities.
1 2 3 4 5 6 7 8 9 10 11
2025 45 3 675 0 15 0 0 0 3 576
5 405 0 9 0 0 0 5 1000
45 7 289 2 6 3 135 3    
1936 44 3 646 1 1 2 88 2 3 564
5 387 1 8 4 176 4 5 980
44 7 276 4 6 2 88 2    
1849 43 3 516 1 14 1 43 1 3 555
5 369 4 8 3 129 3 5 980
43 7 264 1 6 1 43 1    
1764 42 3 588 0 14 0 0 0 3 540
5 352 4 8 2 84 2 5 940
42 7 252 0 6 0 0 0    
1681 41 3 560 1 13 2 82 2 3 528
5 356 1 8 1 41 1 5 940
41 7 240 1 5 6 246 6    
1600 40 3 53 1 13 1 40 1 3 510
5 320 0 0 0 0 5 900
40 7 228 4 5 5 200 5 0 4
1521 39 3 316 0 13 0 006 0 3 504
5 306 0 7 4 156 4 5 880
39 7 218 4 5 4 156 4 7  
1444 38 3 481 1 12 2 76 2 3 492
5 288 4 7 3 114 3 5 860
38 7 206 2 5 3 114 3    
1369 37 3 456 1 12 1 37 1 3 480
5 273 4 7 2 74 2 5 840
37 7 194 3 5 2 74 2    
1296 36 3 432 0 12 0 0 0 3 468
5 259 1 7 1 36 1 5 820
56 7 185 1 5 1 36 1    
1225 35 3 408 1 1 2 70 2 3 456
5 245 0 7 0 0 0 5 800
35 7 175 0 5 0 0 0 0  
1156 34 3 385 1 11 1 34 1 3 444
5 231 1 6 4 136 4 5 780
34 7 163 5 4 6 204 6    
1089 33 3 363 0 11 0 0 0 3 432
5 217 4 6 3 99 3 5 760
33 7 155 4 4 5 165 5    
1024 32 3 341 1 10 2 64 2 3 420
5 204 4 6 2 64 2 5 740
32 7 146 2 4 4 128 4 7  
961 31 3 320 1 10 1 31 1 3 408
  192 1 6 1 31 1 5 720
31 7 137 2 4 3 93 3    
900 30 300 0 10 0 0 0 3 396
  180 0 6 0 0 0 5 700
30 7 128 4 4 2 60 2    

Page  206

The Tables of Battallions to the battels of euen squares of men.
1 2 3 4
2025 3 676 676 676 3
1936 3 625 625 676 10
1849 3 625 625 676 23
1764 3 576 576 576 38
1681 3 576 576 529  
1600 3 529 529 529 13
1521 3 529 529 441 23
1444 3 484 484 484 81
1369 3 441 441 484 65
1296 3 441 441 400 14
1225 3 441 400 361 23
1156 3 400 400 324 32
1089 3 361 361 361 6
1024 3 361 324 324 16
961 3 324 324 289 24
900 3 324 289 289 2

Page  207

The Table of Battels in proportion of equalitie.
1 2 3 4 5 6 7 8 9 10 11
841 29 3 280 1 9 2 58 2 3 384
29 5 168 1 5 4 116 4 5 680
7 120 1 4 1 29 1    
784 28 3 261 1 9 1 28 1 3 372
5 156 4 5 3 84 3 5 660
28 7 112 0 4 0 0 0 0  
729 27 3 243 0 9 0 0 0 3 360
27 5 145 4 5 2 54 2 5 640
676 26 3 225 1 8 2 52 2 3 348
26 5 135 1 5 1 26 1 5 620
625 25 3 208 1 8 1 25 1 3 336
25 5 125 0 5 0 0 0 5 600
576 24 3 192 0 8 0 0 0 3 324
24 5 115 1 4 4 96 4 5 580
529 23 3 176 1 7 2 46 2 3 312
23 5 105 4 4 3 69 4 5  
484 22 3 161 1 7 1 22 1 3 300
22 5 96 3 4 2 44 2    
441 21 3 147 0 7 0 0 0 3 288
21 5 88 1 4 1 21 1    
400 20 3 133 1 6 2 40 2 3 276
20 5 80 0 4 0 0 0    
361 19 3 120 1 6 1 19 1 3 264
19 5 72 1 3 4 76 4 0  
324 18 3 108 0 6 0 0 0 3 252
18 5 64 4 3 3 54 3    
289 17 3 96 1 5 2 34 2 3 240
17 5 57 4 3 2 34 2    
256 16 3 85 1 5 1 16 1 3 228
16 5 51 1 3 1 16 1    
225 15 3 75 0 5 0 0 0 3 216
15 5 45 0 3 0 0 0    
196 14 3 65 1 4 2 28 2 3 204
14 5 39 1 2 4 56 4    
169 13 3 56 1 4 1 13 1 3 192
13 5 33 4 2 3 39 3    
144 12 3 48 0 4 0 0 0 3 180
12 5 28 4 2 2 24 2    
141 11 3 40 1 3 2 22 2 3 168
11 5 24 1 2 1 11 1    
100 10 3 33 1 3 1 10 1 3 156
10 5 20 0 2 0 0 0 0  
81 9 3 27 0 3 0 0 0 3 144
9 5 16 1 1 4 36 4    
64 8 3 21 1 2 2 16 2    
8 5 12 4 1 3 24 3    
49 7 3 16 1 2 1 7 1    
7 5 9 4 1 2 14 2    

Page  208

The Table of Battallions, reduced out of the grand square of men.
The end of the Table of Battallions reduced out of the battels of g. and squares of men: vpon the right side of euery leafe.
1 2 3 4
841 3 289 289 256 7
784 3 256 256 256 16
729 3 256 256 225 8
676 3 225 225 225 1
625 3 225 196 196 8
576 3 196 196 196 15
529 3 196 169 169 5
484 3 169 144 144 17
441 3 144 144 144 9
400 3 144 144 121 9
361 3 121 121 121 2
324 3 121 100 100 3
289 3 100 100 81 8
256 3 81 81 81 13
225 3 81 81 64 1
196 3 64 64 64 4
169 3 64 64 49 8
144 3 49 49 49 3
121 3 49 36 36 6
100 3 36 36 25 3

Page  209

The Table of Battels in proportion of equalitie.
Here endeth the Tables of Battels in proportion of equalitie, or the Battels of due square of men: that is, how many rankes, so many men by ranke; or how ma∣ny rankes, so many files.
1 2 3 4 5 6 7 8 9 10 11
36 6 3 12 0 2 0 0 0    
6 5 7 1 1 1 6 1    
25 5 3 8 1 1          
5 5 5 0 0          
16 4 3 5 1 0          
4 5 3 1 1 1 4 1    
9 3 3 3 0            
3 5 1 4 36 4        
4 2 3 1 1            
2 5 0 0            
2 1 0                
1 0                
The whole number of armed pikes. The quadrate, or square roote. Per ranke to march by: Rankes how many. Remaines of rankes. Maniples, or partes. Remaines of pikes by ranke. The whole ouer plus of remaines. How many to march in rankes of remaine. The rankes to impale by. The number of shot that impale.

Page  210
Hereafter ensueth the Tables and figures of two fold Battels; called broad squares or hearst Battels: with the Battallions of that kinde.

IN these Tables ensuing, I haue set downe the order and setting of sundry Battels in proportiō of inequalitie, as 2, vnto 1, that is, twise so many men in front as in flanke, the which sort of Battels do come to cōtaine neare a iust square or quadrate of ground, which the bat∣tels of proportiō of equalitie (that is so many mē in flank as in front) doe not: for they containe in ground, twise and more the quantitie of ground, in flanke or length that they doe in front or breadth; the reason and order thereof I haue in my 3. booke, in fol. 45, 46 &c. & 50 at large declared, & so cōtinuing, shew∣ing therein, rules Arithmeticall to set all such sortes of Battels, & their impale∣ment with armed pikes; and diuisions into Maniples: here onely contenting my selfe with setting forth the figures and Tables of the sayd Battels in proportion of inequalitie; and how they are to be ordered into ranks for marching, & into Mani∣ples, and girdling with shot, as before in the Tables of squares of mē, or Battels in proportion of equalitie, is at large set downe and declared. And also on the left side of euery leafe is set downe the said Battels or broad squares, deuided into sun∣dry battallions of that kinde, as into 3 or 5 battallions: the number of which bat∣tallions in each of them contained, you shall finde euermore in the first Columne of euery leafe on the right side; & where you find the number of your battallions, there shall you see, betwixt two long rules in that distinction (placed in the 2 Co∣lumne) how euery battallion shall be set in front & flanke, which is the iust square roote of euery battallion. Finally, I haue here before you set downe first, the figure of the sayd broad square of men, or Battell in proportion of inequalitie, as 2 vnto 1, which commeth to containe, neare the iust quadrat of ground, girdled round about with 7 rankes of shot; and the rest of the shot, and short weapon due to this number and proportion of pikes, are deuided into sundry troupes of 50, in euery troupe, trouping round about the maine Battell; as I haue done before in the fi∣gure of the iust square of men. I haue here also desseigned in figure the said broad square or hearst Battell, deuided into sundry battallions of that kinde, as first into 3 battallions, then into 5 battallions, as in page 212 may appeare: each battal∣lion is girdled with 3 rankes of shot; the rest of the shot and short weapon belon∣ging vnto the sayd numbers, may bee placed in sundry small troupes, as is in the broad square, trouping round about the same: or as the Sergeant Maior shall o∣therwise thinke good: or as the ground will permit, or occasions offered to fight.

[illustration]

Page  211

[illustration]
The figure of a Broad square Battell, trouped round about with shot.

Page  212

[illustration]
The figure of 3 Battallions, reduced out of the Broade square.

[illustration]
The figure of fiue Battallions, reduced out of the Broade square.

Page  195

The Table of Broad square, or twyfold Battels.
1 2 3 4 5 6 7 8 9 10 11
10082 71 3 3360 2 47 1 71 1 3 1314
5 2016 3 28 2 142 2 5 2230
142 7 1440 3 20 2 142 2 7 3178
9 1120 3 15 7 497 7 9 4158
11 916 7 12 10 710 10    
9800 70 3 3266 2 46 2 140 2 3 1296
5 1980 0 28 0 0 0 5 2200
140 7 1400 0 20 0 0 0 7 3136
9 1088 8 15 5 350 5 9 4104
11 890 10 12 8 560 12    
9522 69 3 3174 0 46 0 0 0 3 1278
5 1904 2 27 3 207 3 5 2170
138 7 1360 2 19 5 345 5 7 3094
9 1058 0 15 3 207 3 9 4050
11 865 7 12 6 414 6 11 5038
9248 68 3 3082 2 45 1 68 1 3 120
5 1849 3 27 1 68 1 5 2140
136 7 1321 1 19 3 204 3 7 3052
9 1027 0 15 1 68 1 9 3996
11 840 8 12 4 272 4    
8978 67 3 2992 2 44 2 134 2 3 1242
5 1795 3 26 4 268 4 5 2110
134 7 1282 4 19 1 67 1 7 3010
9 977 5 14 8 546 8 9 3942
11 816 2 12 2 134 2    
8712 66 3 2904 0 44 0 0 0 3 1224
5 1742 2 26 2 132 2 5 2080
132 7 1230 2 1 6 396 6 7 2968
9 968 0 14 6 396 6 9 3088
11 792 0 12 0 0 0    
8450 65 3 2815 2 43 1 65 1 3 1206
5 1690 0 26 0 0 0 5 2050
130 7 1207 1 18 4 260 4 7 2926
9 938 8 14 4 260 4 9 3834
11 768 2 11 9 585 9    
8192 64 3 2730 2 42 2 128 2 3 1188
5 1638 2 25 3 192 3 5 2020
128 7 1170 2 18 2 128 2 7 2884
9 910 2 14 2 128 2 9 3780
11 744 8 11 7 449 7    
7938 63 3 2646 0 42 0 0 0 3 1170
5 1580 3 25 1 63 1 5 1990
126 7 1134 0 18 0 0 0 7 2842
9 882 0 14 0 0 0 9 2726
11 721 7 11 5 315 5    
7688 62 3 2562 2 41 1 62 1 3 1152
5 1537 3 24 4 248 4 5 1960
124 7 1098 2 17 5 310 5 7 2800
9 854 2 13 7 434 7 9 3670
11 698 10 11 3 186 3    

Page  214

The Tables of Battallions reduced out of the Broad squares.
1 2 3 4 2 3 4
10082 3 3362 3362 3362 3 5 1922 1922 1922 1922 2312 83
9800 3 3200 3200 3362 38 5 2048 2048 2048 1800 1800 56
9522 3 3200 3200 3042 78 5 1922 1922 1922 1922 1800 34
9248 3 3042 3042 3200 36 5 1800 1800 1800 1922 1922 4
8978 3 3042 3042 2888 6 5 1922 1922 1922 1922 1250 40
8712 3 2888 2888 2888 48 5 1800 1800 1800 1800 1458 54
8450 3 2888 2738 2738 86 5 1682 1682 1682 1682 1682 40
8192 3 2738 2738 2738 ouer 22 5 1682 1682 1682 1568 1568 10
7938 3 2738 2592 2592 16 5 1568 1568 1568 1568 1568 16
7688 3 2592 2592 2450 64 5 1568 1568 1568 1568 1352 69

Page  215

The Table of Broad square of men, or twofold Battels.
1 2 3 4 5 6 7 8 9 10 11
7442 61 3 2480 2 40 2 122 2 3 1134
5 1488 2 24 2 122 2 5 1930
122 7 1063 1 17 3 183 3 7 2758
9 826 8 13 5 305 5 9 3616
11 676 6 11 1 61 1    
7200 60 3 2400 0 40 0 0 0 3 1116
5 1440 0 24 0 0 0 5 1900
120 7 1028 4 17 1 60 1 7 2716
9 800 0 13 3 180 3 9 3562
11 654 6 10 10 600 10    
6962 59 3 2320 2 39 1 59 1 3 1098
5 1392 2 2 3 177 3 5 1870
118 7 994 4 16 6 354 6 7 2674
9 773 5 13 1 59 1 9 3508
11 632 10 10 8 472 8    
6728 58 3 2242 2 38 2 116 2 3 1080
5 1345 3 23 1 58 1 5 1840
116 7 961 1 16 4 232 4 7 2632
9 742 5 12 8 464 8 9 3454
11 611 7 10 6 348 6    
6498 57 3 2166 0 38 0 0 0 3 1062
5 1299 3 22 4 228 4 5 1810
114 7 928 2 16 2 114 2 7 2590
9 722 0 12 6 342 6 9 3400
11 590 8 10 4 228 4    
6272 56 3 2090 2 37 1 56 1 3 1044
5 1254 2 22 2 112 2 5 1780
112 7 896 0 16 0 0 0 7 2548
9 696 8 12 4 224 4 9 3346
11 570 2 10 2 112 2    
6050 55 3 2016 2 36 2 110 2 3 1026
5 1210 0 22 0 0 0 5 1750
110 7 864 2 15 5 275 5 7 2506
9 672 2 12 2 110 2 9 3292
11 550 0 10 0 0 0    
5832 54 3 1944 0 36 0 0 0 3 1008
5 1166 2 21 3 162 3 5 1720
108 7 833 1 15 3 162 3 7 2464
9 648 0 12 0 0 0 9 3238
11 530 2 9 9 486 9 11  
5618 53 3 1872 2 35 1 53 1 3 990
5 1123 3 21 1 53 1 5 1690
106 7 802 4 15 1 53 1 7 2422
9 624 2 11 7 371 7 9 3184
11 510 8 9 7 371 7    
5408 52 3 1802 2 34 2 104 2 3 972
5 1081 3 20 4 208 4 5 1660
104 7 727 4 14 6 312 6 7 2380
9 600 8 11 5 260 5 9 3130
11 491 7 9 5 260 5    

Page  216

The Table of Battallions reduced out of Broad squares or hearsts.
1 2 3 4 2 3 4
7442 3 2738 2592 2048 64 5 1458 1458 1458 1458 1568  
7200 3 2450 2450 2312 12 5 1458 1458 1458 1458 1352 16
6962 3 2312 2312 2312 26 5 1352 1352 1352 1458 1458 10
6728 3 2312 2312 2178 60 5 1352 1352 1352 1352 1250 70
6498 3 2450 2450 1568 30 5 1352 1352 1250 1250 1250 49
6272 3 2178 2048 2048 2 5 1250 1250 1250 1250 1250 22
6050 3 2048 2048 1920 42 5 1250 1250 1250 1152 1152 4
5832 3 2048 2048 1682 54 5 1152 1152 1152 1152 1152 72
5618 3 2048 2048 1458 64 5 1152 1152 1152 1058 1058 46
5408 3 1800 1800 1800 8 5 1058 1058 1058 1058 1152 27

Page  217

The Table of Broad squares, or twyfold Battels.
1 2 3 4 5 6 7 8 9 10 11
5202 51 3 1734 0 34 0 0 0 3 954
5 1040 2 20 2 102 2 5 1630
102 7 743 1 14 4 204 4 7 2338
9 578 0 11 3 153 3 9 3076
11 472 10 9 3 153 3    
5000 50 3 1666 2 33 1 50 1 3 936
5 1000 0 20 0 0 0 5 1600
100 7 714 2 14 2 100 2 7 2296
9 555 5 11 1 50 1 9 3022
11 490 10 9 1 50 1    
4812 49 3 1604 0 32 2 98 2 3 918
5 962 2 19 3 147 3 5 1570
98 7 687 3 14 0 0 0 7 2254
9 534 6 10 8 292 8 9 2964
11 437 5 8 10 390 10    
4508 48 3 1502 2 32 0 0 0 3 900
5 901 3 19 1 48 1 5 1540
96 7 644 0 13 5 240 5 7 2212
9 500 8 10 6 288 6 9 2914
11 409 9 8 8 384 8    
4418 47 3 1472 2 31 1 47 1 3 882
5 888 3 18 4 188 4 5 1510
94 7 631 1 13 3 141 3 7 2170
9 490 8 10 4 188 4 9 2860
11 401 7 8 6 288 6    
4232 46 3 1410 2 30 2 92 2 3 864
5 846 2 18 2 92 2 5 1480
92 7 604 4 13 1 46 1 7 2128
9 470 2 10 2 92 2 9 2806
11 384 8 8 4 184 4    
4050 45 3 1350 0 30 0 0 0 3 846
5 810 0 18 0 0 0 5 1450
90 7 578 4 12 6 150 6 7 2086
9 450 0 10 0 0 0 9 2752
11 368 2 8 2 90 2    
3872 44 3 1290 2 29 1 44 1 3 828
5 774 2 17 3 152 3 5 1420
88 7 553 1 12 4 176 4 7 2044
9 430 2 9 7 298 7 9 2698
11 352 0 8 0 0 0    
3698 43 3 1232 2 28 2 86 2 3 810
5 739 3 17 1 43 1 5 1390
86 7 528 2 12 2 86 2 7 2002
9 410 8 9 5 215 5 9 2644
11 336 2 7 9 387 9    
3528 42 3 1176 0 28 0 0 0 3 792
5 705 3 16 4 168 4 5 1360
84 7 504 0 12 0 0 0 7 1960
9 393 0 9 3 126 3 9 2590
11 320 8 7 7 294 7    

Page  218

The Table of Battallions reduced out of Broad squares.
1 2 3 4 2 3 4
5202 3 1682 1682 1800 38 5 1058 1058 1058 1058 968 2
5000 3 1800 1800 1352 24 5 1058 968 968 968 968 70
4812 3 1568 1568 1682 6 5 968 968 968 968 882 58
4508 3 1568 1568 1352 20 5 882 882 882 882 968 12
4418 3 1458 1458 1458 18 5 882 882 882 882 882 8
4232 3 1458 1458 1250 66 5 800 800 800 882 882 68
4050 3 1250 1250 1568 18 5 800 800 800 800 800 50
3872 3 1250 1250 1352 20 5 800 800 800 722 722 28
3698 3 1352 1352 968 26 5 722 722 722 720 800 10
3528 3 1250 1250 968 60 5 722 722 722 722 648 8
Page  219The Table of Broad squares, or Hearst Battels.
1 2 3 4 5 6 7 8 9 10 11
3362 41 3 1120 2 27 1 41 1 3 774
5 672 2 16 2 82 2 5 1330
82 7 480 2 11 5 205 5 7 1918
9 372 5 9 1 41 1 9 2536
11 305 7 7 5 205 5    
3200 40 3 1066 2 26 2 80 2 3 756
5 640 0 16 0 0 0 5 1300
80 7 457 1 11 3 120 3 7 1876
9 355 5 8 8 320 8 9 2482
11 290 10 7 3 120 3    
3042 39 3 1014 0 26 0 0 0 3 738
5 608 2 15 3 117 3 5 1270
78 7 434 4 11 1 39 1 7 1830
9 338 0 8 6 234 6 9 2428
11 276 6 7 1 39 1    
2888 38 3 962 2 25 1 38 1 3 720
5 577 3 15 1 38 1 5 1240
76 7 412 4 10 6 468 6 7 1792
9 320 8 8 4 312 4 9 2374
11 262 6 6 10 380 10    
2738 37 3 912 2 24 2 74 2 3 702
5 547 3 14 4 148 4 5 1212
74 7 390 8 10 4 148 4 7 1750
304 2 8 2 74 2 9 2320
11 248 10 6 8 296 8    
2592 36 3 864 0 24 0 0 0 3 684
5 518 2 14 2 72 2 5 1180
72 7 372 2 10 2 72 2 7 1708
9 288 0 8 0 0 0 9 2266
11 235 7 6 6 216 6    
2450 35 3 810 2 23 1 35 1 3 666
5 490 0 14 0 0 0 5 1150
70 7 350 0 10 0 0 0 7 1666
9 272 2 7 7 245 7 9 2212
11 222 8 6 4 140 4    
2312 34 3 770 2 22 2 68 2 3 642
5 462 2 13 3 102 3 5 1120
68 7 330 2 9 5 170 5 7 1624
9 256 8 7 5 170 5 9 2158
11 210 2 6 2 68 2    
2178 33 3 726 0 22 0 0 0 3 624
5 437 3 1 1 33 1 5 1090
66 7 311 1 9 3 99 3 7 1572
9 248 0 7 3 99 3 9 2104
11 198 0 6 0 0 0    
2048 32 3 682 2 21 1 3 3 606
5 409 3 12 4 128 4 5 1060
64 7 292 4 9 1 32 1 7 1530
9 227 5 7 1 32 1 9 2050
11 186 2 6 9 288 9    

Page  220

The Table of Battallions reduced out of the Broad squares.
1 2 3 4 2 3 4
3362 3 1058 1058 1250 4 5 722 648 648 648 648 48
3200 3 1058 1058 1058 26 5 648 648 648 648 578 30
3042 3 1058 968 968 42 5 648 648 578 578 578 12
2888 3 968 968 968 16 5 578 578 578 578 578 2
2738 3 968 882 882 6 5 578 578 512 512 512 16
2592 3 968 800 800 24 5 512 512 512 512 512 32
2450 3 800 800 800 50 5 512 512 512 450 450 14
2312 3 800 800 722 ouer 10 5 450 450 450 400 592  
2178 3 722 722 722 12 5 450 450 450 392 392 44
2048 3 722 648 648 30 5 392 392 392 392 450 30

Page  221

The Table of Broad squares, or Hearst Battels.
1 2 3 4 5 6 7 8 9 10 11
1922 31 3 640 2 20 2 62 2 3 588
5 384 2 12 2 62 2 5 1030
7 274 4 8 6 186 6 7 1488
62 9 214 4 6 8 248 8 9 1996
11 174 8 5 7 217 7    
1800 30 3 600 0 20 0 0 0 3 570
5 360 0 12 0 0 0 5 1000
7 257 1 8 4 120 4 7 1446
60 9 200 0 6 6 180 6 9 1942
11 163 7 5 5 150 5    
1682 29 3 527 1 19 1 29 1 3 552
  5 316 2 11 3 87 3 5 970
58 7 226 0 8 2 58 2 7 1404
1568 2 3 522 2 18 2 56 2 3 534
  5 313 5 11 1 28 1 5 490
56 7 244 0 8 0 0 0 7 1362
1458 27 3 486 0 18 0 0 0 3 516
  5 291 3 10 4 108 4 5 910
54 7 208 2 7 5 135 5 7 1320
1352 26 3 450 2 17 1 26 1 3 498
  5 270 2 10 2 52 2 5 880
52 7 193 1 7 3 78 3 7 1278
1250 25 3 416 2 16 2 50 2 3 480
  5 250 0 10 0 0 0 5 850
50 7 178 4 7 1 25 1 7 1236
1152 24 3 384 0 16 0 0 0 3 462
  5 230 2 9 3 72 3 5 820
48 7 168 4 6 6 144 6 7 1194
1058 23 3 352 2 15 1 23 1 3 444
  5 211 3 9 1 23 1 5 790
46 7 151 1 6 4 92 4 7 1152
968 22 3 322 2 14 2 44 2 3 426
  5 193 3 8 4 88 4 5 760
44 7 138 2 6 2 44 2    
882 21 3 294 0 14 0 0 0 3 408
  5 176 2 8 2 42 2 5 730
42 7 126 0 6 0 0 0    
800 20 3 266 2 13 1 20 1 3 390
  5 160 0 8 0 0 0 5 700
40 7 114 2 5 100 5    
722 19 3 240 2 12 2 38 2 3 372
  5 144 2 7 3 57 3 5 670
38 7 103 1 5 3 57 3    
648 18 3 212 2 12 0 0 0 3 354
  5 192 3 7 1 18 1 5 640
36 7 92 4 5 1 18 1    
578 17 3 192 2 11 1 17 1 3 336
  5 115 3 6 4 68 4 5 620
34 7 82 4 4 6 102 6    

Page  222

The Table of Battallions reduced out of the Broad squares.
1 2 3 4 2 3 4
1922 3 648 648 578 48 5 392 392 392 392 338 16
1800 3 578 578 648 4 5 392 392 338 338 338 2
1682 3 578 578 512 14      
1568 3 512 512 512 32      
1458 3 512 450 450 46      
1352 3 450 450 450 2      
1250 3 450 450 338 12      
1152 3 392 392 338 30      
1058 3 392 338 338 10      
968 3 338 338 288 4      
882 3 338 338 200 6      
800 3 288 288 200 24      
722 3 242 242 242 4      
648 3 200 200 242 6      
587 3 200 162 200 10      
512 3 144 200 162 6      
450 3 162 162 98 18      
392 3 162 162 72 4      

Page  223

The Table of Broad squares, or two fold Battels.
1 2 3 4 5 6 7 8 9 10 11
512 16 3 170 2 10 2 32 2 3 318
  5 102 2 6 2 32 2    
22 7 73 1 4 4 64 4    
450 15 3 150 0 10 0 0 0 3 300
  5 90 0 6 0 0 0    
30 7 64 2 4 2 30 2    
392 14 3 130 2 9 1 14 1 3 280
  5 78 2 5 3 42 5 5 520
28 7 56 0 4 0 0 0    
338 13 3 112 2 8 2 26 2 3 264
  5 67 3 5 1 13 1 0 490
26 7 48 2 3 5 65 5    
288 12 3 9 2 8 0 0 0 3 246
  5 57 3 4 4 48 4    
24 7 41 1 3 3 36 3    
242 11 3 80 2 7 1 11 1 3 228
  5 48 2 4 2 22 2    
22 7 34 4 3 1 11 1    
200 10 3 66 2 6 2 20 2 3 210
  5 40 0 4 0 0 0    
20 7 28 4 2 6 60 6    
162 9 3 54 0 6 0 0 0 3 192
  5 32 2 3 3 27 3    
18 7 23 1 2 4 36 4    
128 8 3 48 0 5 1 8 1 3 174
  5 28 4 3 1 8 1    
16 7 20 4 2 2 16 2    
98 7 3 36 0 4 2 14 2 3 156
  5 21 3 2 4 28 4    
14 7 15 3 2 0 0 0    
72 6 3 24 0 4 0 0 0    
  5 14 2 2 2 12 2    
12 7 10 2 1 5 30 5    
50 5 3 16 2 3 1 5 1    
  5 10 0 2 0 0 0    
10 7 7 1 1 3 15 3    
32 4 3 10 2 2 2 8 2    
  5 6 2 1 3 12 3    
8 7 4 4 1 1 4 1    
18 3 3 6 0 2 0 0 6    
  5 3 1 1 3 1      
6 7 2 4 0 0 0      
8 2 3 2 2 1 2 4 2    
  5 1 3 0 0 0      
4 7 1 0 0 0 0      
The number of pikes to be im∣battailed. The nūber of mē in flanke & front. How many mē to march in ranke. The number of rāks, how many. The remaines of men out of rank. The Maniples or parts. The remaines of ma∣niples or parts. The whole num∣ber of remaines of Maniples. The marching of re∣maines of Maniples. The nūber to im∣pale or girdle by. The whole nūber contained in the girdling shot.

Page  224

Hereafter shall follow the figures and tables of sundry euen Battallions, to sundry vses, &c.

HEre next will I set down the Tables and figures of sundry euen Bat∣tallions, as by 3, 5, or 7. euen battalliōs: the which are very strong of themselues; yet neuerthelesse may you chuse whether you will fight in the same order of battallions, or, by marching them vp shoulder to shoulder, bring thē into a two, or threefold battell, at your owne discretion, or as occasion shall best serue. The number of which seue∣rall battallions you shall finde (as I sayd before) placed in the Tables of squares of men, or battels in proportiōs of equalitie, on the right side of euery leafe, by draw∣ing your finger downe the first columne of the same, and then considering what number of pikes you haue whereof to deuide your battallions, you shall finde in the 4 columne of your euen battallions, the same number set downe, or a number vnder the same, which (I thinke good) you rather chuse then the iust number, be∣cause you may then cast out some remaines to imploy otherwise; for better it is to leaue then to lacke. As for example; here in these Tables of euen battallions, first there is set downe 3 euen battallions containing in each 49 pikes, which be∣ing summed together doe make 174 as appeareth in page. 225. Now turne vnto the first table of battels in proportion of equalitie, or euen squares of men, & loo∣king in the first columne of the right side thereof, there shal you find in page 207 the said number of 49, whose square roote is 7: for 7 multiplied in it self is 49: & 7 men & 7 rāks is the square of euery of the said 3 Battalliōs. And in this sort shal you find the order & setting of all the other Battallions, and of all the other num∣bers: as in these figures next ensuing of 3 Battallions, cōtaining in each 3364 mē, whose square roote is 58, so is each Battallion of 58 rankes, & 58 men per ranke: and the whole summe of all these 3 Battallions do amount 10092 pikes, as appea∣reth in these Tables following in page. 225.

[illustration]
The figure of three Battallions.

Page  225

The Table of three euen Battallions.
1 2 3 4 5
7/7 49 3 49 49 49 174
8/8 64 3 64 64 64 192
9/9 81 3 81 81 81 143
10/10 100 3 100 100 100 300
11/11 121 3 121 121 121 363
12/12 144 3 144 144 144 432
13/13 169 3 169 169 169 507
14/14 196 3 196 196 196 588
15/15 225 3 225 225 225 675
16/16 256 3 256 256 256 768
17/17 289 3 289 289 289 867
18/18 324 3 324 324 324 972
19/19 361 3 361 361 361 1083
20/20 400 3 400 400 400 1200
21/21 441 3 441 441 441 1323
22/22 484 3 484 484 484 1442
23/23 529 3 529 529 529 1587
24/24 576 3 576 576 576 1728
25/25 625 3 625 625 625 1875
1 2 3 4 5
26/26 676 3 676 676 676 2028
27/27 739 3 739 739 739 2217
28/28 784 3 784 784 784 2352
29/29 841 3 841 841 841 2523
30/30 900 3 900 900 900 2700
31/31 961 3 961 961 961 2823
32/32 1024 3 1024 1024 1024 3072
33/33 1089 3 1089 1089 1089 3267
34/34 1156 3 1156 1156 1156 3468
35/35 1225 3 1225 1225 1225 3676
36/36 1296 3 1296 1296 1296 3888
37/37 1369 3 1369 1369 1369 4107
38/38 1444 3 1444 1444 1444 4332
39/39 1521 3 1521 1521 1521 4563
40/40 1600 3 1600 1600 1600 4800
41/41 1681 3 1681 1681 1681 5043
42/42 1764 3 1764 1764 1764 5292
43/43 1849 3 1849 1849 1849 5547
44/44 1936 3 1936 1936 1936 5808

[illustration]

Page  226

The Table of three euen Battallions.
1 2 3 4 5
45/45 2025 3 2025 2025 2025 6075
46/46 2116 3 2116 2116 2116 6348
47/47 2209 3 2209 2209 2209 6627
48/48 2304 3 2304 2304 2304 6912
49/49 2401 3 2401 2401 2401 7203
50/50 2500 3 2500 2500 2500 7500
51/51 2601 3 2601 2601 2601 7803
1 2 3 4 5
52/52 2704 3 2704 2704 2704 8112
53/53 2809 3 2809 2809 2809 8427
54/54 2916 3 2916 2916 2916 8748
55/55 3025 3 3025 3025 3025 9075
56/56 3136 3 3136 3136 3136 9408
57/57 3249 3 3249 3249 3249 9747
58/58 3364 3 3364 3364 3364 10092

Here after do ensue the figures and Tables of 5 euen Battallions; beginning at the roote of 100, which is 10, and so continuing.

[illustration]
The figure of fiue Battallions.

Page  227

The Table of fiue Battallions.
1 2 3 4 5
10/10 100 5 100 100 100 100 100 500
11/11 121 5 121 121 121 121 121 605
12/12 144 5 144 144 144 144 144 720
13/13 169 5 169 169 169 169 169 845
14/14 196 5 196 196 196 196 196 980
15/15 225 5 225 225 225 225 225 1125
16/16 256 5 256 256 256 256 256 1280
17/17 289 5 289 289 289 289 289 1445
18/18 324   324 324 324 324 324 1620
19/19 361 5 361 361 361 361 361 1805
20/20 400 5 400 400 400 400 400 2000
21/21 441 5 441 441 441 441 441 2205
1 2 3 4 5
22/22 484 5 484 484 484 484 484 2420
23/23 529 5 529 529 529 529 529 2643
24/24 576 5 576 576 576 576 576 2880
25/25 625 5 625 625 625 625 625 3125
26/26 676 5 676 676 676 676 676 3380
27/27 739 5 739 739 739 739 739 3685
28/28 784 5 784 784 784 784 784 3920
29/29 841 5 841 841 841 841 841 4205
30/30 900 5 900 900 900 900 900 4500
31/31 961 5 961 961 961 961 961 4805
32/32 1024 5 1024 1024 1024 1024 1024 5120
33/33 1089 5 1089 1089 1089 1089 1089 5445

Page  228

The Table of fiue Battallions.
1 2 3 4 5
34/34 1156 5 1156 1156 1156 1156 1156 5780
35/35 1225 5 1225 1225 1225 1225 1225 6125
36/36 1296 5 1296 1296 1296 1296 1296 6450
37/37 1369 5 1369 1369 1369 1369 1369 6845
38/38 1444 5 1444 1444 1444 1444 1444 7220
39/39 1521 5 1521 1521 1521 1521 1521 7605
1 2 3 4 5
40/40 1600 5 1600 1600 1600 1600 1600 8000
41/41 1681 5 1681 1681 1681 1681 1681 8405
42/42 1764 5 1764 1764 1764 1764 1764 8820
43/43 1849 5 1849 1849 1849 1849 1849 7245
44/44 1936 5 1936 1936 1936 1936 1936 9680
45/45 2025 5 2025 2025 2025 2025 2025 10125

Next after do follow the Tables and figures of 7 euen Battallions, beginning at the roote of 100, which is 10, and so continuing vnto 10108.

[illustration]
The figures of seuen euen Battallions.

As for the shot proportionable vnto euery seuerall Battallion, you may bestow them in small troupes round about euery of them, or otherwise as the ground & occasions shall yeeld best aduantage: the one alwayes to second an other: as also may the seuerall Battallions by good conduction do the like.

Page  229

The Table of seuen euen Battallions.
1 2 3 4
10/10 100 7 700
11/11 121 7 847
12/12 144 7 1008
13/13 169 7 1183
14/14 196 7 1373
15/15 225 7 1575
16/16 256 7 1792
17/17 289 7 1923
18/18 324 7 2268
19/19 361 7 2527
20/20 400   2800
21/21 441 7 3087
22/22 484 7 3388
23/23 529 7 3703
24/24 576 7 4032
The quadrat roote. The number of euery seue∣rall Battallion. Bt••llions how many. The whole number of the seuen Battallions.
1 2 3 4
25/25 625 7 4375
26/26 676 7 4732
27/27 739 7 5173
28/28 784 7 5488
29/29 841 7 5887
30/30 900 7 6300
31/31 961 7 6727
32/32 1024 7 7168
33/33 1089 7 7623
34/34 1156 7 8092
35/35 1225 7 8575
36/36 1296 7 9072
37/37 1369 7 9583
38/38 1444 7 10108
       
The quadrat roote. The number of each Bat¦tallion. Battallions how many. The whole number of the Battallions.

In these Tables of 7 euen Battallions, I haue not set downe the 7 Battallions se∣uerally, as I haue done in the Tables of 5 and 3 Battallions: for it were superflu∣ous; seeing that the seuerall number of euery one of them is to be seene in the 2 Columne.

Page  230

The figures and tables of sundry Battallions for Crosse battels.

I Haue here ensuing figured & layd down diuerse euen Battallions, by 4, 8, 12, or 16, to make a Crosse battell without filling the center, so as euery 4 battallions do make a Crosse battel with center vnfilled: 8 maketh 2 Crosse battels; 12 ma∣keth 3, and 16 maketh 4, without filling the center of either of them. Also there is for 5 battallions, to make a Crosse battell with the center filled, 10 to make 2, and 15 to make 3, and 20 to make 4, euen from the root of 5, which multiplied in it self maketh 25; and so vpwards vnto 1000, as by these figures & tables folowing may appeare. Where in the first columne is set downe the square root of euery se∣uerall battallion: in the 2 columne, the number contained in euery-seuerall bat∣tallion: in the 3 columne, whether they be set by 4 battallions, with the center vn∣filled; or by 5 battallions with the center filled: and in the 4 columne, the whole nūber contained in the whole Crosse battel. In the 5 columne, there is 8 to make 2 Crosse battels, with the center vnfilled; and 10 make 2 Crosse battels, with the center filled. In the 6 columne, the nūber contained in the said crosse battels. In the 7 columne is 12 to make 3, with center vnfilled; and 15 to make 3 with the center filled. In the 8 columne, the number contained in each. And in the 9 co∣lumne is set downe 16 to make 4 Crosse battels with center vnfilled; and 20 to make 4 Crosse battels with center filled. The 10 columne signifieth the number of each of them Crosse battels. Note, that in the said void spaces of the 4 angles of each of these Crosse battels, is to be placed the shot belonging to the sayd Crosse battels, as in the two other small figures may appeare.

[illustration]
The figures of Crosse battels, with center vnfilled and filled.

Page  231

The Table of Battallions for Crosse Battels.
1 2 3 4 5 6 7 8 9 10
5 25 4 100 8 200 12 300 16 400
5 5 125 10 250 15 375 20 500
6 36 4 144 8 288 12 432 16 576
6 5 180 10 360 15 540 20 720
7 49 4 196 8 392 12 588 16 784
7 5 245 10 490 15 735 20 980
8 64 4 256 8 512 12 768 16 1024
8 5 320 10 640 15 960 20 1280
9 81 4 324 8 648 12 972 16 1296
9 5 405 10 810 15 1215 20 1610
10 100 4 400 8 800 12 1200 16 1600
10 5 500 10 1000 15 1500 20 2000
11 121 4 484 8 968 12 1452 16 1936
11 5 605 10 1210 15 1715 20 2420
12 144 4 576 8 1142 12 1618 16 2304
12 5 720 10 1440 15 2160 20 2880
13 169 4 676 8 1352 12 2308 16 2704
13 5 845 10 1690 15 2535 20 3380
14 196 4 784 8 1568 12 2352 16 3136
14 5 980 10 1960 15 2940 20 3920
15 225 4 900 8 1800 12 2700 16 3600
15 5 1125 10 2250 15 3375 20 4500
16 256 4 1284 8 2048 12 3072 16 4096
16 5 1280 10 2560 15 3840 20 5120
17 289 4 1156 8 2312 12 3468 16 4624
17 5 1445 10 2890 15 4335 20 5780
18 324 4 1296 8 2592 12 3888 16 5184
18 5 1620 10 3240 15 4860 20 6480
19 361 4 1444 8 2888 12 4332 16 5776
19 5 1804 10 3610 15 5415 20 7220
20 400 4 1600 8 3200 12 4800    
20 5 2000 10 4000 15 6000    
21 441 4 1764 8 3528 12 5292    
21 5 2205 10 4410 15 6615    
22 484 4 1936 8 3872 12 5808    
22 5 2420 10 4840 15 7260    
23 529 4 2116 8 4232 12 6340    
23 5 2645 10 5290 15 7935    
24 576 4 2304 8 4608 12 6912    
24 5 2880 10 5760 15 8640    
25 625 4 2500 8 5000 12 7500    
25 5 3125 10 6250 15 9375    
26 676 4 2704 8 5408 12 8112    
26 5 3380 10 6760 15 10140    
27 739 4 2956 8 5912 12 8864    
27 5 3695 10 7390 15 10185    
28 784 4 3136 8 6272 12 9408    
28 5 3920 10 7840 15 11760    

Page  232

The Table of Battallions for Crosse Battels.
1 2 3 4 5 6 7 8 9 10
29 841 4 3364 8 6728 12 10092    
29 5 4205 10 8410 15      
30 900 4 3600 8 7200        
30 5 4500 10 9000        
31 961 4 3844 8 7688        
31 5 4805 10 9610        
32 1024 4 4096 8 8192        
32 5 5120 10 10240        
33 1089 4 4356 8 8712        
33 5 5445 10          
34 1156 4 4624 8 9248        
34 5 5780            
35 1225 4 4900 8 9800        
35 5 6125            
36 1296 4 5184 8 10368        
36 5 6480            
37 1369 4 5476            
37 5 6845            
38 1444 4 5776            
38 5 7220            
39 1521 4 6084            
39 5 7605            
40 1600 4 6400            
40 5 8000            
41 1681 4 6724            
41 5 8405            
42 1764 4 7056            
42 5 8820            
43 1849 4 7396            
43 5 9245            
44 1936 4 7744            
44 5 9680            
45 2025 4 8100            
45 5 10125            
46 2116 4 8464            
46 5              
47 2209 4 8836            
47 5              
48 2304 4 9216            
48 2401 5              
49 4 9604            
49 2500 5              
50 4 10000            
50   5