layd out the tvvo sides A B C D ought to be lengthened so farre that one maye make the angles B K L C R P of 75 degrees and that the line of defense O. K. termineth in the curtaine M. Q. and to knovv the length of the faces and flanks the face shal be made double in the flanke which is done if ye place vpon the perpendicular O N the halfe of the line of Defense O K. as from O to N. and from the point K the privie right line N K being drawne cutting through the line C B at M ye shall dravv the line M L paralell to N O or perpendicular vpon C B and so the flanke L M vvilbe the halfe of the face L K. And thus vve haue finished the fortification of the abouesaid Quadrilatere irregular vvhich in my opinion is a better fortification then the precedent figure 86. because these Bulvvarks are more capable to defend the angles A D K R and the flanks of the said Bulvvarks being dravvne obliquely as they are here cannot be made into right angles in such sort that they are the better able to resist against the force vvhich maye be vsed against them and yet make a good defense as the figure 88 plainely demonstrates An other way to make the fortification of such a place regular The 19. Plate and 89. Figure FIrst of all vve vvil describe the quadrate E F. G H. after such a manner that the line E F is paralell to A. D. of the greatnesse of the poligone exteriour in the follovving table of lengths dravving the paralell E F so that its distance A D be equall to the distance of the Polygons asvvel interiour as exteriour to the intent that the side of the Quadrilatere A D may serue for the curtaine Then the angles I F E I E F being made 15 degrees because the angle interiour flanking is of 15 degrees in the square ye shal take vpon a scale 5. equall parts place them vpon the line F E and foure of the same parts vpon the line F I. from the extremity or vtmost end vvhereof and with the said distances ye shall make two arches that shall cutt through one an other at X drawing from thence a line to F cutting through the line I E at G. then E G wil be the face of the Bulwarke which will haue the like proportion to the curtaine as 4 to 5. But wee will here after in all the kinds of Polygones ordaine the curtaine to the face in proportion as 3 to 2. that is sesquilatera finding it best as we haue said before Afterwards to haue your flanks ye must make two perpendicular lines G N. and H K vpon the side A. D. in such manner that the lines G N and H K shal be the flanks and N K the curtaine which is part of the side A D. The like ye shall doe with the three other sides and so by this meanes this fortification wil be made regular and royall which will not cost much more then the former irregular fortification abouesaid the benefit whereof surpasseth the others by farre so that in such like accidents I am of the opinion that such places ought to be made regular in case that time and the situation wil permit it As for the moates ramparts and parapets they must be made as wee haue taught in the places of regular fortifications The fortification of a Pentagone irregular The 19. Plate and 90. 91 Figures LEt the Pentagone irregular be A B C D E which one would haue fortified in such sort that the Bulwarks come againe to the angles of the propounded figure To doe this ye shall first measure the outsides and the angles which I supposeye shall finde to be as they stand here vnderneath rod A B 57. B C 50. C D 46. D E 56 degrees A 72. B 135. C 111. D 97. E 125. 540. And seing the angle A is lesser then 90 degrees reason requireth that the said angle be not fortified because it would make an angle flanked lesser then 60 degrees and flanking greater then 150 degrees against our former maximes according to which ye shall make of the same angle A. an angle of the bulwarke makeing the angle of the Polygone F. so that the right lines FG and FI come to cutt through the lines lengthned BC DE in the points G and I. Vpon the angles whereof and according to the proportion of the sides shal be described the Bulwarks takeing heede that the angle of the Polygone show what forme of a Bulwarke one must built vpon to wit a Quadrate a Pentagonall or an exagonall proportioning out the parts of such a Bulwarke according to the least side of the two and then the figure wil be described according to this present forme And seing the side DE because it hath ben lengthned is longer then the proportion can beare of our regular figurs precedent It wil be necessary that betweene the two Bulwarks D E a Ravelin be made which is a loose peece that maye be defended at leastvvise from the flanks of the abouesaid tvvo Bulvvarks according to vvhich flank the angle of the Raveline shal be made a litle more open or closser as the curtaine is either longe or short The faces vvhereof shal be made of 18 or 20 rod some times a litle lesser as the place and situation of the ground requireth And to giue you to vnderstand more clearely my intention touching the fortification of places irregular vvhereof the angles are noe lesse then 90 degrees which is the angle of a Quadrate and that the sides doe not differ much from those places vvhich are regular It must be proportioned thus Suppose that one giueth me the angle C to be fortified of vvhich the magnitude is III degrees vvhich comes neere the angle of a Pentagone according to vvhich I take the shortest line of the tvvo BC C D makeing therevvith the angle B C D vvhich is C. D. contayning 46 rod we wil seeke out then in the table of the lengths of our regular fortifications the dimensions of a Pentagone and will say by the rule of proportion if a Polygone 56 88 giuâ—â— the face 24 vvhat vvill then a Polygone of 46 rod giue ye shall haue for the face 19. 41 rod. The like ye shall haue for the flanke and then the Gorge where by ye shal finde the said Bulvvarke C. as also all the other parts of this fortresse Pentagonall holding this for an infallible rule that the angles of the Polygone which you would fortifie ought to be at the least right and in case there be any angle that hath a lesse opening then the right ye must make thereof the angle of a Bulwarke or else dravve a line if you cannot lessen the place vvhich vvill forme an angle competeÌ„t to builde a Bulwarke vpon as appeareth by the 90 figure in the angle A. Which line you must so husband that if it
the midst of the line E F and for asmuch as the angle E is of 112. degrees vvhich comes neere vpon the angle of a Pentagone ye shal be vpon the foresaid angle E describe the angle of a Pentagone and seing that the line E D makes 80 rod vve vvill make the angles flanking interiour of the forme of a Pentagone to the end tha the skirts E L. and D O. be equall as we haue said before for seing the Ennemies force betvveene E D is equall reason requireth that the defense thereof be likewise made equall that by this meanes ye maye take away all occasion from an Ennemie to attempt any further place the most advantagious for him Now in regard that the distance D. C. exceedeth the measure vvhich wee haue spoken of before to wit of 114 ½ rod it vvilbe necessarry to make the Raveline K betweene the said angles D C to supply the defect of the defense the like maye be made betweene C B and the angles of the Bulwarks and B the rest shall be made according to their formes the faces flanks and Curtaines in that forme as vvee haue said aboue euen as this figure Hexagonall 95. demonstrateth The 96. Figure HErein it is requisite to note that vvhen one is bound to fortifie precisely the angles of the figure either interiourly or exteriourly ye meete many times vvith difficulties to vvit here are some angles or sides too small and others too great in so much that this irregularitie maye cause many great defects Which maye greatly be remedied vvhen ye maye haue libertie to change a litle the angles of the figure euen as wee haue done in this 96. figure in such sort that the angle E being but 112. degrees which is the angle of a Pentagone makes the angle of the bulwark S E T too much pointed as when ye would make it on the inside of the angle E. Therefore see that ye make the face E S vpoÌ„ the side ED that by this meanes ye maye haue the angle S E T broader and more open drawing the line E O so that it be equall to ED and that the angle O E D be 20 degrees so that the curtaine Q. P. comes not too farre into the figure and that the line of defense ER maye come a part of it out thereof if it be possible as here to R for the more the said line commeth out of the curtaine it is so much the better which is when the angle O E D is broad and open But this exemple if this had bene observed the Bulwarke L had bene a great distance from the curtaine C D and would haue made it much longer then it is at this present Then vpon the point O shal be made the second face of the Bulwarke W O V so made that O W and O V and ES are of an equall greatnes that the line D X be drawne in such a manner that the angle Y Z 5 be capable to receiue the Bulwark of an Exagone and for the better attayning to such a structure ye shall make first vpon the line C B the flanke noted by 4 5 and the face Z 5 to the end that CB maye serue for a curtaine and so fitted that it maye almost be equall to the curtaine D. C. Then vpon CB ye shall make the Bulwarke I. according to the greatnesse of 4 B. answerable to the Bulwarks G. H. and seing the angles A Bare sharpe ye shall make these two Demy-Bulwarks according to our method mentioned in the 18 Plate and so ye haue finished the thing required Note AS we haue fortified this figure on the inside so ye maye doe the like on the outside in case the ground will afford it but we suppose here that it would be necessaire to make it in such a sort in regard that the lengths of the sides require more the interiour fortification then the exteriour whence appeareth that there are many vvayes to fortifie places irregular yea an infinite number yet bounded with these limits to wit that the angles of the Bulwarks ought not to be noe further assunder then 80 rod at least 60. that the angles flanked must not be lesse then 60. degrees That your line of defense ought not to exceede much aboue 60 rod for by how much the Bulwarkes haue a second flanke by so much they are the better the more spacious and larger the flanks and gorgâ—◠〈◊〉 the Bulwarks are the better for them according to our former Maxims set downe in the end of the first part according to which an expert and skillfull Ingenier will be sure as much as possibly maye be to haue all these advantages abouesaid And for the better facilitating of what is said aboue wee haue made here the figures 97 98 99 100 101 which must be cutt out vpon a pastboord drawne out vpon the same measure as the plott of the place requireth which is to be fortified and to fitt them to the places of the figure with the greater consideration that possible maye bee that he maye follow the rules abouesaid as neere as may be where vnto these figures in my opinion are of very great vse for he may turne and remoue them on what side soeuer he will and after he hath found the most convenient place then he maye joyne fasten them together with a litle waxe that afterwards he maye overcast the advantages and disadvantages which he is to expect How to fortifie an Irregular place lying vpon the side of a river The 22. Plate 102. Figure LEt the forme irregular which ye would haue be the plate of Hardervvijck noted by the numbers 1 2 3 4 5 6 7 8 whereof the extremities or vtmost ends are 1 6. touching the Dike A B and C D which ye desire to fortifie To doe this ye must first overweigh how many bulwarks the circuit of the same place will take vp husbanding them so that ye must make as few as maye be because they are parts of a fortification which will cost much and yet so that you must not place them so farre assunder but that the one bulwark must helpe to defend the other for this reason we haue made the line of defense about 60. rod which is a longer distance then is giuen when one is to defend them with the Muskett or caliver The others that must be defended with the CanoÌ„ maye be 1000 foot distant one from an other or there abouts because at the least it will carry so farr over that ofâ—entimes a Canon will carry much further then to the vtmost end of the line of defense so that they may hinder the batteries which are made to beate downe the flank of the angle from whence the line of defense is drawne also ye make it so that the distance of the said angle vnto the angle of the Bulwark be not so farre as a Canon beares but rather shorter for which reason we
S and T A namely the face upon TA and the curtaine upon T S ye haue the like distances and from the points I X the arches which cuts betweene them in a certaine place by which intersection the line T V shal be drawne cutting the line S B at V then the right line V L. being drawne passing through the center L cutting A R at G ye shall haue all the parts of this Fortresse for hauing sett downe the distance R G from R to H from the same point G is drawne a paralell to S B as E G cutting the Diagonall line L A at E the like ye shall finde for F and consequently all the other parts of the said Fortresse Pentagonall The same must ye also understand of the other figures following from the figure 60 to the figure 68. Also ye may finde the point V in setting downe upon T A 2 equall parts such as ye require and from the extremity or utmost end hauing made it a parallell to S T and upon the same 3 of those parts and drawne from the extremity the line TV the said point will consequently be knowne thereby NOte that the proportion giuen here betweene the face and the curtaine is not so much to relye fast upon it as to show that the generall rule sett downe here before in the 9 and 10 plates take place also in all other reasons which may be propounded For otherwise wee are of the opinion that the former figures would rather be accepted then these here because that the reason of the curtaine to the face is as wee haue said aboue sesquialtera as well in square Fortresse as of Pentagonall and others following Which for the facility simplicity together with the goodnesse of them ought to be preferred before the figures 60 61 62 63 64 65 66 67 and 68 of the 11 Plate aboue said Whereof the face to the curtaine is as the exemples shew of diuerse reasons in such sort that hence forward one ought to resolue that the reason of the curtaine to the face ought in all formes of Fortification to be sesquialtera and the face 24 rod each rod containing 12 foote the length whereof is sett downe in the 25 plate of our Geometrie noted with the character or the figure 1 is diuided into 12 ynches which rod is used in the Fortifications of the United Provinces to the end that the line of defence may not exceede much aboue 60 rod which is about as farre as a Musket can well beare the gorge to the flanke may be made by the rule giuen in the 11 plate according to the reason giuen but forasmuch as it is more convenient to make the angle forming the flanke GAC plate the 11 of 40 degrees which giueth the reason almost as 6 to 7 in my opinion one ought to rest thereupon and so ye shall haue a generall rule for all manner of Fortifications whither they be Quadrialtera Pentagonall Hexagonall or the others following as ye may perfectly understand by that which shal be said hereafter In the meane while note that I giue here the reason of the gorge to the flanke as 7 to 6 which ought to be understood in Fortresses without Casemates but if it were my intention to make some of them I would then alter somewhat of the said proportion The manner how to describe succinctly the designes or Plots of some regular Fortifications The 12. Plate and the 69. Figure ALthough one may by that which we haue taught sufficiently now understand the order and Method requisite to be held in all manner of Fortifications yet I haue thought it good to trace out here some from among the rest to make the louers of this Art to conceiue the better my intention and will begin with a regular Pentagone whereof the angle of the center maketh 72 degrees and the angle of the Polygone 108 degrees and seing the angle flanked according to the table before mentioned maketh 69 degrees It wil be easie to finde the angle C A D which is alwayes equall to the angle flanking interiour and shall finde the same to be 19 ½ degrees setting then your graduate Instrument upon 19 ½ degrees it makes the angle CAD and drawing first the covert line infinite AB takeing upon the scale 24 parts or rod and sett then from A to C drawing from the point C a perpendicular upon A B as is CD afterward hauing sett on DE the length of the curtaine which is here onely 34 rod because the false brayes makes the lines of defence too great then the distance AD from B to E raysing from the E the 〈◊〉 cular EF being equall to D C and FB drawne out the two faces wil be knowne for to knowe the center of the Bulwarke shal be made of 2 lines GA GB the Demy-diameter of the Polygone then your instrument being sett upon 40 degrees ye shall finde the angle HKA cutting the said demy-diameter at the same point H from which point the line HI being drawne ye shall haue the side of the Polygone interiour upon which out of the points C and F shal be drawne the perpendiculars CL FM which will forme the flanks and the gorges of the said Fortresse Pentagonall in the inside of the side of the Polygone interiour shal be drawne a parallell of 5 ½ rod for the thicknesse of the rampart as N O N R and RS and ye must draw for the parapett of the rampart a parallell of 20 feete also in the inside of the said side of the Polygone HI and on the outside thereof ye shall drawe a parallell of 20 foote for the falsebray as LX and yet more outward 20 other foote for its parapet so all the other parts wil be traced out which are within the moate for seing that there is here noe Casemates the falsebray is carried not onely about the curtaines but also about the flankes and the faces of the Bulwarks in such sort that the falsebray serueth as a Casemats to the said flankes the entrance or sallies ought in my opinion to be made in the midst of the curtaines as covertly as possibly may be the Bulwarkes are made either massiue or hollow from Earth at this present wee haue drawne them out as being hollow from earth so the superficies or plaine in the midst of the bulwarke N R S H. is of the same heigth as the rest of the enclosure of the Pentagone is the moate shal be 10 rod broad which is traced out as followeth In the point A or the angle of the Bulwarke shal be made an arch of the distance of 10 rod in the point V make an other arch of somewhat a lesser extention then the former about 10 or 12 foote then drawe upon the back thereof a covert line infinite the like must be done on the otherside of the Bulwarke and so from place to place with covert lines being drawne as abouesaid
B D and F E. till that X Z be equall to the lengthened sides B X. and F Z. Vpon which and in the very midst of them ye shall make three Bulwarks and vpon the angles X and Z the two Bulwarks X and Z which are the Bulwarks of an Hexagone because the angels X and Z make each of them 120 degrees which are indeed the angles of an Hexagone as appeareth by the said table in which are taken all the demensions belonging to an Hexagone aswell the gorges flanks as the faces and from them ye maye drawe out your Bulwarkes X and Z abouesaid which wil be more royall then the two Bulwarks D and E yea or of the others likewise so that this fortification will not cost much more then the former makeing the place more spacious the circuit almost alike and the Bulwarks much better and in my opinion this forme of fortification ought to be preferred farre aboue the other considering what advantages one maye gett thereby But if one were tyed to the forme B D E F whereof the two sides B D. and F E are longer then 90 rod which is a distance too farre for the Bulwarks D E. to help to defend the angles F and B one should be driuen to make the two Bulwarks S. T. lesser then the former whereof the faces would make but 16 rod which notwithstanding wil be capable to defend the abouesaid Angles F and B. Note that if the place requires that ye must lengthen the line O P. as farr as the riue side I K. lyeth then ye maye drawe from the furthest end of the Bulwarks O and P. right lines to I and K and then ye maye make two Bulwarks vpon the said lines one vpon the right curtaine by which ye shall make your fortification the stronger because the angles of the Bulwarks O P. wil be so much the larger and the defense of the other Bulwarks vpon the said lines the better How to fortifie a place situated by the sea-side and to make therevnto a commodious Haven The 23 24. Plates and the 103. 104. Figures PLaces lying by the sea-side haue oftentimes neede of a good hauen aswell to harbour such shipping as maye daylie come into them as also to keepe them safe from an Ennemy and from the violence of stormes and tempests And for asmuch as these places must resist the injuries of winde weather and the raging billowes of the sea as is said they ought to be soundly fortified and kept and because Earth alone will not be sufficient to withstand the beating of the sea vpon them in regard of the fragility thereof which would be washed away such places ought to be made with free-stone or at least wise with good brick with driving in on the outside of the wall next the sea-side many stronge piles by clasping them together in this manner following FIrst some 300. foote or thereabouts from the wall A B. marked figure 104 ye must driue in a rowe of piles a foote thick in diameter and some 8. or 10. foote longe as the 24 Plate and the 104 105 Figures demonstrate These must be pointed with yron and sharpned well that they maye enter the better into the ground and must be driven in with an Engine called in Dutch a Hye hauing a block plated with yron of some 1000 or 1200 pound weight which falls downe vpon the heads of these piles and is drawne vp with a pullie with some 40. men euen as one should ring at a Bell foure or fiue of them guiding the Hye that the logg maye fall downe perpendicular just vpon the head of the pile that they driue in and shall driue it in so deepe till the head thereof be but three or foure foote aboue the ground After ye haue driuen in the first row some sixe or seuen foote distance from it ye must driue in the second rovv whereof the vpper ends must be aboue the ground more then the first row by a foote and a halfe or at the most two foote so that your second row ought to be foure foote and a half or at the most sixe foote Then about sixe foote neerer the towne ye must driue in a third row of piles the heads being a foote or two foote aboue the second row as the site and the necessity of the place shall require continuing so till you come to the very wall of the towne against which you shall laye bedds made of Bundles of brush as the figures 106. and 107. showes wherevpon ye shall lay heauie stones 3 or 4 cubicall foote thick to make them lye firme and fast betweene the rowes which are also driven in with stakes or sparrs as the figure 105 106 demonstrate All these rowes must be so ordered by a masons line that they may lye euen from the one side to the other and to keepe them closse together ye must haue long sparrs sawne in two through which you must boore holes and driue yron or wooden pinnes through the said rowes and clinch them well and as is said remember that the piles of the second row are longer then the first and the third rovv longer then the second and so consequently the rest must bee Then euery ninth foote ye must laye crosse sparrs of the same weight as the first or thereabouts which ye joyne to euery row by driving great yron bolts through the piles and the other sparrs vvhich lye crosse the other rowes makeing through them quadrangular chambers vvhich you lay bundles of brush into in makeing them lye fast together by diving in of stakes and in laying first a bedd of brush and then a row of flint stones vpon it and your brush must be hedged and wreathed together to make it lye the faster and firmer that it maye not be loosened and driven away with the violence of the vvater as ye maye see in the 24. Plate and the 106. 107. Figures This being done then ye shall laye the Basis of the wall first by driving in piles into the Earth and foundation if it be moorish as the 108. figure sheweth But if your foundation be good and firme then ye shall make as it were but a Gridiron of wood vpon it as the figure 109 noteth these sparrs vvherewith you make it must be some 8 10 or 12 foote longe according to the ponderosity of the wall and as your foundation shall require and some 10 or 12 ynches thick Vpon this you shall beginn to lay your wall about 10 or 12 foote thick allowing to euery foote of tâ—lude two foote of height laying within it spurrs of wood from 16 to 20 foote and foure or fiue foote longe making them lye levell with the wall as the art of Masonrie teacheth and some sixe foote distant one from an other then by this meanes ye shall binde the vaults one to an other and the two vaults shal be comprehended by the third to make them last the longer and
better vnderstand our intention we haue added herevnto the Figure 158 which raised worke is represented in perspectiue in which ye may see the parapet of the false bray the port-holes of the Casemate and other things which we haue thought necessarie to make knowne The 38 Plate 160 Figure A Fortresse being thus provided with good false-brayes aswell vnder the Bulwarkes as along the curtaines broad according to our former plots I could wish that a Casemate weere made in that forme which wee shall now describe and that the curtaines were drawne in as the farre as the bredth of the falsebray with the parapet containes to wit that the false brayes vnder the Bulwarks might end on the outside of the foundamentall lines a b and the like and contrariewise that in the curtaines the said falsebrayes maye end within the said fundamentall line c d so that the space i f g maye be accommodated as the Figure 160 representeth to plant therein two peeces of ordinance which will worke noe small effect by this meanes the Casemates wil be better preserued then otherwise because ye neede not feare the flying of brick-batts about your eares seing that the flanck e will serue as a stay and a covert therevnto so that in stead of one shoulder ye shall haue two to wit b p and c e. The descent into the false-bray which goes round about the Bulwarke ought to be made at m and to come out at y and seing one makes sometimes some privie sallies betweene A and p one might also make the entrance into the Casemate in this place makeing a vault from m to y to wit in the vnderpart of the Casemate The entrance into the false bray from the curtaine ought to be made at w from one the other part The letters q r s t v represents the place where I would maks Catts if one resolues to make them but seing I am not resolved about this point I will rather speake nothing thereof at this present Figure 2. 160. 38. Plate IF the Bulwarke be not massie but hollow ye maye make your entrance into the Casemate as here towards o. r. p. l. z. and the entrance into it should be at the point l. all the space l. z. p. r. o. being open Of Brasse ordinance The 39. 40. Plates and 161. 162. 163. 164. Figures WE were minded to haue treated of diverse other dependances belonging to fortificatioÌ„ as of bridges gates ports foundations c. how townes publick places ought to be fortified but the Printer not willing to stay any longer for the finishing of this booke it is not possible for me to effect my intention so that my project also touching the casting of brasse ordinaÌ„ce is for this reasoÌ„ also frustrated having bene minded to haue described the proportion aswell of their carriages as of their charges and other dependances about them To which end I had ordayned these 4 brasse peeces which are vsually cast in the vnited provinces according to the scale herevnto annexed whereof the least carries a bullett of 6 pound weight with the Figure noted 161 the second is the Figure 162 carries a bullet of 12 pound weight the third 163 carries a bullett of 24 pound and the fourth marked with the Figure 164. carries a bullet of 48 pound of the two last the first is a halfe Canon and the last a vvhole canon or peeces for batterie the two others are field-peeces bearing a bullet of 6 and 12 pound In the meane while he that desires to know the proportions of them maye make vse of this scale till we vvrite more at large thereof ALBERT GIRARD BEfore vve come to describe the tvvo tables vvhereof vve haue made mention before supputed of a nevv vvee vvil explaine some termes vvhich vve haue introduced because they vvere namelesse before To that end vve vvil take one of the Figures of the eleventh Plate excepting the last vvhich is the 68 and the line N C being dravvne vvhich vve vvill terme the gullet to distinguish it from N A or A C the gorges vvhich comes to cutt through the Capitall being dravvne further vvithin the Figure in a point vvhere the letter Z is made then E Z shal be called the extention that is the lengthned capitall for the Bulvvarks extends so farre outvvard Then the angle G A C the forme-flanck Also in the 60 or 61 Figure E L shal be called the Raid majour and L A the Raid minour finally in the sixth Plate the line D F or K L is called the surface as being placed before the face for surface is a vvord not much vsed and as superficies signifies all one thing ye must not thinke that the second table is calculated amisse because the progression of the second flanks doe encrease euen to that of the Heptagone and then diminisheth for if one should continevv the table from the one end to the other it vvould follovv that the angles of a Polygone should be equidistant 130 degrees vvhich vvell nigh containes the second flanke majour 8. 412 so haue the second flanks equal vve vnderstand equidistants the one so much more then 130 as the othâ—â— lesse Likevvise the defense flancking diminisheth even to a Pentagone then augmenteth The least that vve can obserue is vvhere the angle of the Polygone is 113 degrees to vvit of 53 366 the Equidistant are equal One maye say the like of the first table vvhich decreaseth to 48 rod and aftervvard encreaseth The fortification of a right line holding not vvith the one or the other table is placed betvveene them both Those that vvill make vse of them proportionally for the building of irregular Figures commits noe small errours though Marolois vvas of this opinion and so much the more because the angles of the Polygone are about the right angles for the other Polygones differ alvvaies lesse one froÌ„ an other the further they fall from the quadrate so that vve to this end if vve vvere vvilling to make vse of them the tables vvhereof the angles of the Polygones are progressiue of 3 or 4 degrees of space vvould be of a better choise should here take place if time vvould permit vs. Let there be here some small exemple thereof and suppose that one vvould fortifie an angle of 99 degrees vvhereof the tvvo sides are each of them 36 rod and 3 primes take a Pentagone or a quadrate to imitate and let vs take a quadrate by vvhich meanes he shall finde the lines as they are herevnto annexed vvhich done let vs take the 7 Figure of the second Plate to speake more intelligibly thereof let vs demaund of him hovv much the angle C B Evvilbe BF Capitall 13 15 BE The face 16 00 ED The flank 5 16 DF The gorge 6 15 BA Defen Flanc 33. 94 Angles required FBE 32 deg 15. min. BFD 130. 30 EDF 90. Angles of a quadrate 30 degrees 135. 90. He vvill say that to the halfe of 99 he hath added 15 and the summe is for the said angle C B E and that the angle B F D is adjunct of the halfe of 99 to vvit 130 30 aftervvard he cannot denie but the number of lines vvhich he hath found maye receiue the angles of the square-Bulvvarks halued as there annexed for the lines are dravvne proportionally from thence as then the consequence vvilbe absurd seing that the quadrangle having the foure lines knovvn D the right vvhich are 5 common termes of both sorts of a quadrangle abouesaid The vnknovvne angles shall receiue each of them a certaine number of degrees as appeareth by our Trigonometrie and not tvvo sorts of numbers for each angle so that if F comes to be 135 degrees as it is it can neuer make 130 and 30 and so of the rest Novv of one should take the angles as he requireth it and the tvvo sides F D D E the other lines vvilbe othervvise then he hath calculated them for in stead of 16 00 the face one shall haue 51 04 and in stead of its flanking 35 94 ye shall finde onely 32 44 and so of the rest vvhich is an errour of 3â— rod vpon 32 here then are small lines great faults vvhat would those be then in great and solid fortifications To conclude vve vvill propound one question asvvell to exercise those vvhich are addicted therevnto as for to end this discourse A square fortresse regular hath the face 24 rod the curtaine 36 vvith an angle forming the flancke of 40 degrees vvithout a second flanck hovv many then vvill the other angles and lines be The manner to resolue this and the solution ye shall see hereafter vvhen vvee haue made some treatie vpon that subject vvith hope shortly to bring to light the restauration of Geometrie touching the parts thereof vvhich haue bene lost hitherto vvhereof the Authours are Euclid Aristeus the elder Eratosthenes and Apolonius Pergeus vvith some other parts of the mathematiques all according to our vveake povver by the helpe and grace of God FINIS 1. De oude polder 2. Cassemat 3. Het nieuwe west ravelyn 4. De west poort 5. Nieu porcespic 6. Helmont 7. De oude Sluis 8. Santhil 9. Halve maen so hooch al 's de wal 10. Sluyseerst gemaeckt omt'water inde graft te setten 11. Trencement 12. Bolwerck 13. Contrescherp 14. Halve maen 15. Een sluyseerst gemaeckt 16. Sorte nae de polder halve maen 17. Eee sorte 18. Nieu polder 19. Sorte 20. Nieu helmont 21. Sorte 22. Nieu west poort 23. Vlammenburch 24. Peeckels bolwerck 25. Nieu Polder 26. Spaens bolwerck 27. Koestal oft Suyt oost bolwerck 28. Suyt bolwerck oft Treurenburch 29. De vrygaerden 30. Polder halve maen 31. Baterie 32. Catte 33. Hier leggen de schepen 34. Nieu Santhil daer de oude kerck plachte staâ—â—â— 35. Nieurve haven 36. Noortwest bolwerck 37. De oost poort en het ravelyn 38. Oost ravelyn 39. Spaens halve maen 40. Slimmers halve maen 41. Elcks verdriet 42. Suyt oost ravelyn 43. Suyt ravelyn
triangle ACG the angle A thereof wil be 36 52 11 because of the reason giuen and G 60 degrees then the sayd triangle ACG will make knowne CG 21 4933 also the face 23 5067 for DG is 45 the halfe of GC is CB 10 7466 which multiplyed by 4 3 ye shall haue BA 14 3289 DP 75 979 BH 35 2637. The 38. Figure Let the curtaine be 36 rod the line of defence flanking 45 the angle BAC 36 45 the flanked right How many will the other parts of this Fortresse Dodecagonall come to THe triangle DAG afterward ACG wil be knowne and also CBG DCF DKH whereby DC wil be found 23 974 GR 22 ½ the halfe of DG 10 5127 DH 61 0593. DP 77 52516 AB 14 733. The 39. Figure In this Dodecagone the angle BAC makes 37 degrees the flanked right the face 24 rod the fichant 62 how many makes then the other lines THe line DC 24 shal be the double of CF 12 the angle BAC being giuen the triangle DAC wil be knowne therefore DA AC and the triangles DAE ACB DGR DHK wil be knowne and consequently the lines required as AB 14 6179. BC 11 01525 BH 36 7851 DP 78 3547. DA 23 82709 He failed herein to calculate them a new together but the reason of this was that wee agree not seing that in the construction in stead of 37 for the angle BAC as he sett downe he tooke 38. All questions comming after this are defectiue euen to the discourse which endeth the order of the same questions but seing I know whither it tends I will explane them in adding thereunto the things that were wanting passing ouer the figures 40 41 and so we will beginn with the 42 as followeth The 42. Figure In a square Fortresse with foure Bulwarks let the angle flanked be 60 degrees the angle forming the flanke FID 40 degrees the face 24 rod hauing the reason to the curtaine as 4 to 5 the other lines are required Seeke the triangles DAL AID IFD DFP ye shall finde also PH for FH wil be 30 IO 48 45532 AK 76 6464 IF 9 22766 FD 7 74298 IA 19 73479 the fichant AH 54 98265. The 43 Figure Is a Pentagone the angle flanked 69 degrees the angle forming the flanke â—0 degrees the curtaine to the face as 5 to 4 the face 24 rod wee desire to know the other lengths Ye must doe as before and then there wil be no difference in the operation Touching the number of the names of the figures in this 9 plate ye shall finde them marked about the angle flanking exteriour the reason of the face to the curtaine is marked on the point of the Bastions the length aswell of the face as of the curtaine next themselues and must be proposed as the two former hauing alwayes the angle forming the flanke of 40 degrees the opening of the flanked angles is according to the manner of the first table to wit 15 degrees more then the demy-angle of the Polygone sauing that in the figures 2 43 2 44 afterward an other time the 45 46 he taketh for the angles flanked the â…” of the angle of the Polygone according to the second table in the beginning placed before Of these things ye shall finde 2 tables in the end of this booke setting downe the faces to the curtaines as 2 to 3 the faces 24 rod which make the former-flankes 40 degrees and the flanked according to the two manners abouesaid where ye must knowe that the lines of defence fichant are about 60 61 rod. The said tables are both calculated 〈◊〉 because of the errours escaped in the other editions Moreouer after the Dodecagone ye shall haue ouer and aboue following a Fortification upon a right line which is called upon a right curtaine Now let us marke what the Authour saith Note 1. NOw not to take so much paines in remembering the diverse proportions of the face to the curtaine whereof the Fortresse quadrangular Pentagonall Fortresse is as 4 to 5 and the Exagonall as 3 to 4 it will not be amisse seing that the line of defence will beare it to make also the said Fortresses of the same proportion as the subsequent to wit in reason sesquialtere as appeareth by the 3 figures of the 9 plate quoted by the numbers 2 42. 2 43. 2 44. where the lines of defence doe not much exceede 60 rod which is as farre as a musket can well carry therefore one ought not to exceede this number because that alwayes from the flanke reciprocally the entrance into the moate must be defended which is often done and most commodiously by the Muskettiers because that Canon cannot so suddenly by reason of the weight be brought thither many good occasions are neglected for which cause they are preferred before Canon and in regard a Musket will but carrie some 700 feete point-blanke Bulwarkes ought to be made noe further one from another for otherwise the line of defence would be too long which should cause imperfection Note 2. IF in stead of takeing the face 24 rod for the line of the Polygone exteriour take 80 rod and the rest according to the former proportion the parts wil be brought very neere together as appeareth by the precedeÌ„t Examples according to the figures of the 10 plate marked with the numbers 51. 52. 53. 54. 55. 56. 57. 58 59 whereof we haue made no calculation because they are easely done by the former supputations Note 3. THat in all our designes and calculations we are resolued to use but one measure onely which is in the 25 plate of our Geometrie upon the rule of the instrument marked number 1 which is a foote deuided into 12 equall parts whereof 12 foote makes a Rheneland rodd in the territoire of Leyden Designes plat formes of diverse Fortifications WE might according to the former supputations giue diuerse constructions of the platformes of Fortifications but considering the great diversity of rules which often causes confusion and that time will not permit us wee will giue but one simple and generall rule for them which is this following The 9 Plate and the 42 43 44 45 46 47 48 49 50 Figures FIrst if the face be giuen suppose it to be 24 rod then ye must doe as followeth Ye shall draw a right line infinite AC from the point A the angle CAB shal be made according to the forme of the Polygone upon which A B shal be sett downe the 24 rod abouesayd as from A to D and by D is drawne the line which formeth the angle of the Center of the Bulwarke 40 degrees then must ye sett downe upon A C and A B the reason of the curtaine to the face that by the same ye may draw the line infinite A E makeing from the point D a parallell with A C cutting the said AE at G by which point is drawne the line that formeth the other face G K in such sort that the
because we intend to speake of them hereafter In the meane while it wil be good to note that the said Cats Ravelins and other workes may be applyed to this present Fortification but in this place is omitted for the avoyding of prolixity because we are minded to treate of them briefly in an other place The description of the designe or the plate forme of a Fortresse Hexagonall The 13. Plate and 71. Figure LEt there be giuen a Fortresse Hexagonall to be fortified whereof the face AC maketh 24 rod and the angle flanked 80 degrees according to which the angle flanking interiour will make 20 degrees and the exteriour 140 degrees and let the curtaine be 30 rod which giueth the reason of the face to the curtaine as 3 to 4. To doe this ye shall draw the covert line infinite A B by the helpe of an instrument graduate the other angle CAD of 20 degrees of 20 because that the angle flanking interiour which is alwayes equall to it maketh here 20 degrees by meanes of the line indefinite AC upon which ye make the length of the face 24 rod as from A to C from which point C the perpendicular CD being drawne upon the line A B shal be placed from D the length of the curtaine which is here 32 rod as from D to E finally the distance AD from E to B and the perpendicular EF the distance of CD as from E to F drawing the line FB ye haue the other face so that all the parts of the reason giuen are described and for to finde the curtaine ye must make first the angles GAB GBA of 60 degr seing the whole angle of the Polygone maketh 120 degr by the lines AG GB which cutting through on an other at G is the center of the Polygone and seing the gorge when as ye would make casemates in them or in a bulwarke where Cats or mounts are raised they had neede of a larger extent then otherwise we suppose that it were requisite to make Casemates in them to that end we make the angle HKA which otherwise might be but 40 degrees onely of 35 according to which the gorge in the flanke wil be almost as 4 to 3 or somewhat more by reason of the line H K cutting the line Diagonall AG at H from which point H the line HN being drawne parallell to AB ye shall haue the Polygone interiour upon which the lines CL and FM being drawne in length the lines DC to L and EF to M in so doing all the essentiall parts of the said Fortresse wil be described Now to continew the same draught or platforme in every place ye shall make from the center G a privie circle from the distance GB and shal be sett upon the privie circumference the distance AB which being the 6 part of the said figure Hexagonall the said circumference will contayne justly still fiue parts which finally will come to end at A. In the like manner is the privie circle made out of the same center G and from the distance G N upon the circumference thereof shal be set the line of the Polygone interiour HN afterward ye must onely coppie out the rest Moreouer the parapet wilbet 20 foote which shal be made in the inside of ACL MFB and as the way of the rounds or the falsebray is on the outside of the body of the Fortresse we will make parallells towards the moate of 20 foote broad then 20 foote more for the parapet thereof on the outside of the parapet before ye come to the moate is made an edge or a toe of 6 or 8 foote to keepe the said parapet from falling into the moate which is made of 140 or 150 foote or thereabouts as necessitie and the bottome requires for it must be fitted according to this consideration because the ground lying lowe it will not beare much digging before ye come to water and therefore in this place one is forced to make the moate to gett earth enough for the rampart but when the ground lies high then ye may digg very deepe before ye come to the water so by this meanes ye may haue asmuch earth as possibly ye can well use seing without it cannot be but hurtfull it wil be better not to make the moate so broad that ye may receiue noe hindrance or hurt by the store of Earth that it affordeth which may be cast upon the outside For to beleeue that the ramparts being raised higher then the dimension giuen in the former figure to wit of 14 or at least 15 foote that they were better as some haue mainteyned yet experience hath showne many times the contrarie for an ennemie hauing once approched to the brinke of the moate the bredth of the parapet hinders one from makeing any defence upon it which notwithstanding is most necessarie because the neerer an ennemie comes with his approches towards us we ought the more to defend our selues and this being committed by our default it is too manifest that one ought to take heede of it and to remedie this errour by the former way namely in makeing the rampart of the heigth abouesaid Some are of the opinion by a simple cōmaund that one ought to heigthen the ramparts aboue the said 14 or 15 foote and not the Bulwarks for which they haue some reason for indeede the Bulwarkes make the greatest defence and when an ennemy is become master of the said bulwarke there were a meanes to cōmaund the said bulwarke more absolutely so that an ennemy could not hinder the use of them if he raised not his works aboue the said rampart to hinder the defences of the besieged which they might make with the said ramparts so raised by a simple commaund which in some manner might hinder the intents approches of the besiegers the more easie would the entrenchements be made and seing the more the bulwarks are raised the more one ought to use diligence about the entrenchment hence would follow this difficulty that the comming to the rampart or the bulwarke would not be so easie as otherwise neither could one make any great defence from such ramparts by reason of their too much heigth in such sort that one bulwarke ought to defend an other in such a case the second flanke would be of noe use after an ennemy is entred into the moate at which time it is then most needfull to giue the greatest resistance that may be seing that when they are gotten ouer the moate and taken in the foot of the bulwarke then the courage of the besiegers begins to encrease the besieged to faile them for it is too apparant that many times resistance failes in such and the like accidents Betweene two bulwarkes are commonly made ravelins or halfe moones which are Quadrangular figures euery face containing 12 15 or sometimes 20 rod which beginn at the brinke of the moate so that its angle interiour or the tenaille O lies just
great Mathematician consumed his time wholly in this point by maintayning that all fortifications aswell great as small ought to be made in a square-forme but seing that the Bulwarks towards the 4 angles by this meanes become lesse forcible then the others as the figures A and B demonstrate in the 23 Plate me thinks this ought to be taken into consideration Whither it were not better to make a Fortresse whereof the Bulwarks and the lines of defense be of a like force then to make them as aboue For it is impossible that one should make a fortresse stronger in one place but ye must diminish the strength thereof in an other place to wit as the common proverb is one ought to cutt his coate according to his cloath But when the situation of the place and the avenues thereof be such that one maye be assured of the resistance which maye be made better here then there reason then requireth that in such a case one must make such an avenue stronger by diminishing the strength of an other which is not so subject to be attempted as the former is For the site of a place sometimes will require this irregularity But when as it falls out in a plaine field it is reason that the strength thereof be also regular so then in such a case one cannot take any advantage in one place more then a◠other without hurting and weakning of an other which one ought maturely to consider and not yeeld easely therevnto vvithout good and pregnant reasons And seing these Countries which lye lowe and are subject to invndations overflowings the rivers are commonly bounded in vvith Banks and Dikes for the preventing of such inconveniencies and the preservation of the Inhabitants from an vtter subversion These dikes coming to touch both the one and the other part of the said tovvnes as here in the points H A. vvhich sometimes are separated from the said towne by a vvall vvhich goes from A to N. and from M to H vvhich in the Figure C is called a Doudan made in the forme of an Asses back narrow in the midst and bending downwards on both sides vvhich is made ouer a moate to stop the vvater vvhich othervvise vvould breake into the land is called by those of these countries a Beer that is a Beare in regard of the strength vvhich makes it almost inviolable Therefore the Basis or foundation of such a worke is layd first with a grate of beames of timber locked one into an other with squared beames bound fast together vpon vvhich the vvall is built these beames and piles vvhich are driuen in and layd in this groundvvorke are some 8 10 or 12 foote long according to the depth of the riuer and about 7 8 9 or 10 ynches thick lying tvvo or three foote distance one from an other vvhich also ought to be in length answerable to the depth of the vvater Sometimes these Beares are made vvholly of timber and are lyned vvith huge thick oaken plancks betvveene them closse together and are much longer then the former because the vpper ends must stand of much aboue the vvater as ye thinke the vvater can rise in winter and on both sides of these piles you shall laye tvvo great beames or bands of timber the one at the endes of the piles and the other in the midst betvveene the bottome and the vpper end of them fastned together vvith yron bolts vvhich are as thick as these piles and passing through these piles and then ye shall line them with good stronge oaken boords in joyning them as closse together as possible maye bee that they maye keepe out the water the better and last the longer Now if ye resolue to make noe such separation but to let the banck or dike stand then it wil be good to cutt and pare it as narrow as you can to keepe an Ennemy from coming vpō it with many men in front or to hinder his approches the better on that side I am of the opinion also that ye ought to make the line C B. F G. about 300 foote longe that one might giue the more fire vpon an Ennemy both at his falling on and going off but when there is noe fortification made on the other side of the riuer it were much better that the dike did not stand against the point A but that it were made neerer to the inside of the towne that one might the better offend the approches made on the outside thereof to wit towards the river as is showne in the former Figure and 22 Plate but if the other side of the riner lying opposite to the towne ought to be fortified for the reasons abouesaid then it matters not greatly seing one maye sufficiently offend the Approches on that side and because the cutting off would be chargeable if it be made in a circular forme me thinks the best course is to draw the right line O P and the two others O Y and P. K so that O Y and P. K. maye be of the length of one of the sides of an Octogone or thereabouts that the Bulwarks O P. maye be well defended from the curtaines and that the Bulwarke also on the other side maye likewise helpe to defend the curtaines then betweene O and P. according to their distance maye be made the Bulwarks Q. and R but seing the distances E F. and B D. are too longe to be defended from the Bulwarks D E. ye must make the two Bulwarks S T. whereof the faces are 16 rod the flanks 8 rod the faces of the other Bulwarks are each of them 20 rod or thereabouts which distance is capable to lodge men enough in it to defend it and if neede requires to make also therein some speciall cuttings off as wee shall declare vnto you hereafter Note that if the lines D B F E be too short to make the Bulwarks vpon them marked S T it is apparant ye maye then lengthen the sides so farre that the said Bulwarks maye with conveniency be made vpon them then ye must drawe a line paralell to D E. but if the distance D B. and E F. be so that the angles B F maye be defended well from the Bulwarks E and D. as then you neede not make the said Bulwarks S. and T seing that from the others namely E D they maye be sufficiently defended And for asmuch as I finde these fortifications to be best which come neerest to the demensions giuen before in our regular fortifications termed Royall whereof the faces flankes defences and gorges which are the principall parts of a fortification are all capable to worke well their effects one ought to haue a speciall care aboue all things to fitt the sides of places to be fortified that they maye be almost of the length of Polygones which ye shall finde in the table of our demensions described hereafter euen as wee haue done here in lengthning the sides
wil be the better able to resist the waues of the sea when the winde makes them beate against the vvall filling the vaults vvhich are betvveene the spurrs vvith good Earth stamped and beaten in wel that there be noe holes or hollovvnesse betvveene them In doeing so ye make your hauen as the greatnesse of the place vvill beare it and according to the number of ships vvhich you meane to harbour in it The mouth or entrance into the hauen being some 20 24 or 30 foote broade according to the greatnesse or smallnesse of the ships that are to come into it Ye maye make the hauen either of a round forme ovall square or a paralellogramma vvith a right angle as the site of the place and the accommodation of the Inhabitants shall require On the outside of the mouth ye shall driue in the breath of 100 or 150. foote rovves of piles from one end to the other as abouesaid which maye serue for the comming in and going out to make the entrance of the ships the more easie as appeareth by the 104 figure in vvhich the paralell lines AB CE EF FG GH HR are rovves of piles filled and stuffed vvith bundles of brush and stones vpon them as vvee haue noted in the 106. figure where ye must obserue that the vvall of the figure 106 vvhich ye see on the outside is the same as the figure 110 is vvhich ye see on the inside The rest of the tovvne asvvell that part of it vvhich lies next the sea as the other side maye be fortified in that forme as the plate of Ostend demonstrates vvhich is the next follovving makeing your fortification soe that the faces of the Bulvvarks maye be about 100 foote or more to hinder the better the approches vvhich an Ennemie maye make on that side seing those places wil be the weakest in regard of the banks and shelues of sand noted Z which are commonly in such places Therefore one is constrained to raise the ramparts higher in such places then the order of fortifying vvel requireth that one maye lye the safer vnder couvert from an ennemies batterie If the vtmost ends A and B be of a rock ye must cutt them off as much as possible maye be both in the height and in the bredth as the commodiousnesse and the site of the place vvill afford if it be sandie it vvilbe safer to deepen the moate euen vp to ones neck in case the countrie circumjacent vvil permit it as ye maye see here in the 25. Plate of Ostend the Figure 112 in vvhich towne hath bin practized found out as many inventions to make it invincible as in any tovvne of our age and noe lesse inventions tryed on the ennemies part to gaine it vvhich they did at last after three yeares three months and odd daies siege vsing all manner of industrie in makeing their the approches galleries mines and other inventions which the art of man could invent them Neither was there lesse art vsed on the defensiue part to make them get it by ynches meale as appeared by the generall and particular cuttings off counter mines counter-batteries and other vvorkes vvhich vvere made in such sort that this place vvas as it vvere a schoole and a studdie of euells to bring men to thier ends vvhere nothing vvas either omitted or forgotten but many strange engines invented aswell to stop the mouths of the channels and hauens as for the approches towards the tovvne as this 25. Plate demonstrateth where ye shall see the approches made with gabions or great Bassketts filled with Earth woolsacks to stop the water breaches and at other times sand-baggs for the reason why they made vse rather of these things then to advance their workes and by approches sapps whereof we intend to treate hereafter was because the countrie lay low and was sometimes overflowne with water in regard of the ebbing and flowing of the sea entring in and going out betweene the mouths A B. Of some loose Peeces in regular fortresses The 23. Plate 111. Figure MAny men are of the opinion that in places of great importance to forslow and hinder an ennemy the more one ought on the outside of a place regular to make diverse works separated from the bodie of it by that meanes to giue the Assaillant the more worke that he cannot come to advance his dessigne And though I dare not approue much of them in regard of the great expence which they will cost and the number of men necessary to keepe and defend them yet I will giue here some instruction to those that are desirous to make such works Let AB then be the side of a Decagone vpon which ye shall make by the helpe of our former table the Bulwarks Q T Y Z S R then ye shall drawe the paralell lines G I H and HP for the faces of the Bulwarks of the distance of some 10 or 12 rod for the bredth of the moate and for to finde the angle L M N ye shall draw the angle of the shoulder passing through the angle of the Bulwarke R. the line RM the like ye shall doe vvith the line Q M then ye shall make the faces LM MN of 24 rod from whence ye shall dravv the flanks LK NO equall to the flanks TY or SZ and finally the lines IK OP ansvvering to the points Q and R. for the better keeping of them ye shall make the Ravelins VWX vvhereof the angle W comes noe further from the center of the fortresse then the angle M dravving from the angle of the flanke O a line vnto the point W and the face V W of the length M N. Ye maye make likewise the flanks 3 4 V 6 but then the defenses of the Bulvvarks vvilbe of noe vse because they blinde the faces LM MN on the outside of these loose vvorks ye maye make a good moate vvith a couvert vvay and a parapet as the figure 111 demonstrateth These vvorks vvill cost much and ye must haue a great many men to guard them so that one ought to be vvell advised ere he vndertakes the makeing of them and to see if the meanes of the Lord of the place his forces and time will permitt it more ouer he ought to consider that the entrances in and commings out of the said loose peeces are dangerous and difficult and therefore hardly to be relieued How to make a fortresse where two great riuers are not aboue 15 or 18 rod assunder one from an other or thereabouts The 26. Plate 113. Figure THat you maye the better vnderstand my intention and meaning I haue thought good to make vse of the Plate of S. Andrews Fort made by the Admirant of Arragon that yeare as he withdrew his army from the siege of Bommel which is a Fort situated in Bommelsvvard betweene these two great rivers called the Mase and the VVhale haueing noe great distance betweene A C then
of 200 or 250 foote or thereabouts called the Alarm place to drawe in armes at the end whereof the line of entrenchment for the Campe runneth to wit haueing a ditch some 6 7 or 8 foote broade 5 or 6 foote deepe and the parapet of the same bredth and height to wit the basis of 8 foote and 4 or 5 foote high but when it is 6 foote high then ye must make a foote banke which must be a foote high and 2 or 3 foote broad that ye maye the better discouver the fields about ye Behinde the Regiment are the sutlars Hutts or tents leaving a street betweene them and the souldiers Hutts of 20 foote and the bredth of their hutts are likewise 20 foote Betweene the sutlars and the other Regiments there is a streete or a separation made betweene regiment and regiment about 40 50 yea 100 foote as the ground will afford it and the greatnesse of the said Regiments And the better to accommodate euery Regiment the Quartermaster Generall ought to know the greatnesse and the number of the companies of them And so as is said ye haue the depth of a regiment which is 300 foote in which are contained the Captaines and the sutlars lodgings with their streets and the distances betweene them and the souldiers The Colonell is lodged in the midst of his regiment leaving a streete of 80 foote as the Figures 114 115 demonstrate to lodge therein his traine and the officers of his Regiment as the Quartermaster the Marshall Chirurgian others In the midst of the quarter the Generall of the Armie is lodged some 600 foote or more from the entrenchment according to the greatnesse of the Campe and the accommodation of the place having a front of some 700 foote more or lesse as his traine is either great or small being 300 foote deepe as all the other quarters are having in the midst where they sett his pavillions an overture of 400 foote broad for to discouver by sight the place where they drawe vp in armes Behinde him the master of the ordinance is quartered having his quarter 300 foote deepe and 700 foote in front more or lesse according as his traine is great For in case that the carrages and victualls must be lodged within the compasse of the Campe it is very necessarie the said place be larger that it maye containe them all and as then ye maye separate the traine of victuals from the traine of the ordinance Upon the right hand are lodged sometimes the other Officers belonging to the armie leaving betweene them and the rest a streete of some 40 50 or 60 foote that they maye freely passe through it with the ammunition of warre to the place where they are to be vsed and then round about it are the foote lodged according to the former order being as is said 300 foote deepe with the Captaines tents and the sutlars hutts and the bredth of the front according to the greatnesse of the regiment euery companie of 100 men takeing vp 32 foote with the streets which are betweene the hutts and before them is the place of Armes 200 or 250 foote to draw vp by companies into their divisions and battallions to wit euery companie directly before his Captaines lodging their to draw vp in parado to receiue the commaunds of the Generall of the Army In the front of the hutts the Lieutenants and Ensignes are lodged and the Sergants Gentlemen of the armes in the reere next the 〈◊〉 they maye presently prevent any disorders which might fall out And for the more easie vnderstanding of what is said aboue in the 27 Plate 114 Figure wee haue here represented the quarter of an English Regiment consisting of 20 Companies as they were quartered as I remember before Gulick whereof the Plate K L M N O P is the Colonels lodging Q R S T his Kitchin Stable H I the Captaines lodgings 24 foote broad and 30 or 32 foote deepe G the crutches or the forks against which the Pikes and Muskets stand CA the souldiers Hutts whereof euery file containeth 25 and 8 foote in depth and bredth the goings out are betweene the two files but the foure vtmost hutts of euery companie haue their goings out towards the streets CH AE which is the Sutlars streete E F are the Sutlars Hutts which are made either large or straight as euery ones occasion shall require leaving a litle space betvveene them for their more freedome and for the danger of fyring The scale which is herevnto annexed will shew you the true measures The 28 Plate and 115. Figure THe 28 Plate is the draught of a Colonels lodging in a larger forme that one may the better vnderstant the order which is here to be obserued 9 is his tent his gallerie to goe into his tent 5 6 is his sleeping tent where it maye be so ordered which would not be amisse that there be a gallery from 5 to 6 to goe in and out prively from one tent to an other 7 is a hutt for the Colonels servants 11 his Kitchin 10 12 are also Hutts 13 in his Stable 14 and 15 are the officers Hutts of the Regiment and all other officers which are not ranged vnder any Companie are lodged in this streete behinde the Colonell 2 3 are the Captaines tents 16 17 the places where they draw vp in armes 4 4 4 4. are the souldiers Hutts the side KL from the colonels lodging is a right line with the Captaines lodgings not to hinder the sight of the front of the Hutts But as for mee I thinke it were more convenient that the front of the Captaines lodgings were made in a right line euen with the front of the Colonell to wit that 2 3 and M N maye be in a right line whereby the alarme place should be of an equall bredth The 29. Plate 121. Figure IF necessitie requires to quarter the Horse vvith the foote within the circuit of one line which is vsually done when one feares an Ennemie to fall on vpon many sides and that there is noe other accommodation for the horse without the campe otherwise it were much better to lodge the Horse out of the foote quarter for the avoyding of many inconveniences which the foote might receiue by them and which the Horsemen might receiue from the foote leaving betweene the Sutlars Hutts of the foote and them a streete of 40 50 yea sometimes of 100 foote according as the place will afford it having their front towards the place of armes euery regiment quartred together being commonly 8 troupes in a regiment allowing to euery hutt 10 foote in length betweene them and their Horse there is a space or a streete giuen them of 5 or 6 foote broad to lay in their fourrage then betweene the same 5 foote the great streetes which are ordinarily 20 foote is made a space of 10 foote for their horse allowing to euery
if the cutting off be in the tenaille of the angles t. l. Figure 156 b 159 of an easie accesse being raised as litle as possibly may be whereof the one maye serue for an entrance the other for a comming out choosing the one or the other for the most commodious according to the situation of the place And seing the cuttings off as we haue said before are esteemed the best which haue two angles flanking ye must at the first make the cutting off h k l m n i Figure 159 to be raised euen with the height of the rampart or according to the height of the Bulwarks if they be a litle lower then the curtaine if that the batteries doe not commaund them For in such a case you must raise it much higher that from thence with the more vivacity and courage ye maye repulse the Assaillants But seing this cutting off is of a better defense and is much more labour then the cutting off a b c ye must consider well it time will giue you leaue to doe it if not ye maye make vse of the cutting off a b c for oftentimes necessity hath noe lawe And seing experience hath taught vs too much what difficulties one shall meete with all in such cutting off the onely way is in my minde to hinder as much as possibly maye be the Ennemies descent into the moate which besides other inventions that are in vse maye be done by the meanes of the cuttings off at the lines a b c d Figure 159 which are made here right opposite to the angles of the Bulwarkes from one part to an other besett with small muskett baskets filled with Earth as we haue said before Of Casemates The 37 Plate 157 158 Figures FOr asmuch as we haue seene the difficulties which Casemates haue caused to the besieged and the small benefit they haue receiued by them which not withstanding haue bene made with all the industrie that possibly might be thereby to hinder an Ennemie from putting ouer a moate and makeing his batteries vpon the brinke of the moate to beate downe the flanks and to dismount the peeces of ordinance planted in the said Casemates to wit that besides the expence the gorges are made by this meanes lesser the Orillon or pillow being noe more then the 2 3 of the flanck and is of litle resistance and on the other side giues but litle advantage being soone stopt as we haue seene in time past I was minded not to haue spoken of them at all though I esteeme them good if they were made in such a sort that there mouths might not be stopped vp and the peeces within them dismounted which hath not bene done hitherto to my remembrance Forâ—fâ—hese Casemates be made of brick batts when the Besiegers shall play vpon them with there ordinance the bricks flying into the port-holes will doe more hurt to the Canoniers and other men then the Ennemies bullets themselues and by this meanes the portholes wil be easely filled and stopped vp as wee haue seene in diverse places If your Casemate be made of Earth ye must giue it a great Talude that is much slooping which maketh the gorge so narrow namely in those Fortresses which are vnder an Hexagone that oftentimes there wil be hardly any entrance into the bulwark which we call the gullet the Orillon and the flanke very litle and consequently wil be of litle resistance wherein they finde so many difficulties that many great Captaines haue resolued wholly to leaue them vnmade If one could not preserue them otherwise then they haue done to this present I should approue of them But seing I cannot resolue of a thing which I dare not wholly approue off because experience and many men slaine in the warres haue not found it good this is my opinion also In the Figures 157 158 of the Plate 37 a b is the vtmost end of the shoulder the double of p a Figure 157 the mouth or port-hole of the Casemate and as b p maketh 150 foote so p a will make 50 foote p t equall to p a wil be likewise 50 foote t v is 36 foote from a ye shall draw a line to u that ye maye the better discouver the exteriour brinke of the moate and the said t u shall containe three portholes for three peeces of Canon which shal be vauted ouer from d e to t u with steps as the Figure 158 demonstrats marked betweene t v and e d in such sort that the first Vault on the side of e d is closse by the superficies of the water enlarging or raising the said Vaults more and more vntill that the last vault towards t v be raised aboue the superficies l f g k which is the plateforme of the Casemate some 3 foote or thereabouts and seing that t e d v are about 20 foote ye shall advance as farre as possibly ye can the parapet t f and g v as much as the canon and the place will permit you to giue the better soliditie firmenesse to the parapet of the Casemates Then vpon the topp of the basis f g e d the said parapet shal be so raised that the inside f g shal be lined with a wall that it maye prevent the falling downe of such a heigth so that the ennemie maye not discover the vpper part of your vault h i k l and firmely joyned asvvel to the wall as to the Orillon and on the outside with hard Earth as strong as possibly maye going downe sloopingly that it maye not be subject to tumble downe into the moate and this will hinder the Ennemie greatly from entring into the moate and putting his gallerie ouer For by this meanes they must be driuen first to beate downe the shoulder and make it to fall into the moate at the space p a e d which for this reason must be made as deepe as possibly ye can to the end that the portholes 3 4 5 be not easely stopt the place l k f g is about 20 foote vncovered and the vault i h l k also 20 foote broade The line h i is about some 54 foote the Colomne is made in the midst of l k to make the vaults crosswise because the distance betweene l k is too great to make there a single vault which maye serue to make vpon it the parapet of the superiour place to gayne more place for the gorge and to lodge the Canoniers and there amunition dry The entrance into the Casemate must be in that place where m n is vnder the rampart and must be vaulted from m to i from n to o being some 10 or 12 foote broad or thereabouts that ye maye the better draw in your ordinance all what ye haue neede of into the Casemate and make it as high as necessity requires The orillon a v y b is al together massie that it maye giue the greater resistance And because ye maye the