demy-circle on the left hand and to do as you did at right hand and at the end of the line to drive in a stake and these two stakes will represent the South-East and the North-East Angles of the Ovall then you are to turne your selfe full West and to set out with your demy-circle and the fore-said line the South-West and North-West Angles driving two stakes at the end of the line Then you are to fasten a line of 160. yards * This is the extent of the demi diametricall line of the bredth of the Ovall to the Center stake and to straine the same full South upon a strait line and at the end of the line the man with stakes is to drive in a stake then wind the same line about and straine the same full North upon a strait line and at the end of the line drive in another stake and these two last stakes represent the South and North Angles of the Ovall then remove this line from the Center stake and fasten it to the East Center circle stake strain it full East upon a strait line and at the end of the line drive in a stake then remove the same line to the West Circle Center stake and straine the same full West upon a strait line and at the end of the line drive in a stake and between these eight circularie stakes consists the superficie of the Ovall Now because the six sides of it are circularie you are to remove the fore-said line of 160 yards to the Center-stake and to fasten your iron tracing-pin to one side of the line and the other side to the stake and to straine the same full South and to trace the ground as far as the line will give you leave on both sides of the South stake and then you are to do the like on the North side and that being done you are to fasten these lines one after another to the East and West circle Center-stakes and to trace the West and the East sides of the Ovall with the point of your iron pin as you did the South and North sides joyning the tracing of your pin on all sides and this being done you are to set many Pioniers to make the tracing deeper with spades or with the flat ends of their pick-axes And when this Superficie of the Ovall is sufficiently traced you are to divide the six circularie sides into six equall parts driving a stake in everie division then you are to fasten a line of 85 yards to everie Angle-stake one after another and to straine the same upon a strait Diagonall line from the foure Angle-stakes that represent the South-west and North-west and South-East and North-East Angles but upon a strait Diametricall line from the South and North Angle-stakes and at everie end of the line you are to drive in a stake and these six stakes will represent the six vtmost points of the six Bastions then you are to fasten a line of 240 yards to everie third stake of your six sides to set out by it the faces and the line of defence of the Bastions by straining and fastning this line to everie Angle stake twice to set out the twelve faces then you are to fasten a line of 45 yards to everie second stake of the six sides or bases and to straine this line not perpendicularie-wise as you have done formerly when you did set out the Bastions with Orillons but five yards more bevell toward the next Bastion then strait and where the Line cuts the other that sets out the faces of the Bastions and the Line of defence you are to drive a stake and after this manner set out all the rest till you have gone round Now let me informe you once for all that the safest and the most frugall way to set out your Bastions after your maine Superficie is set out is to set out one halfe Bastion at a time and to have it * A generall observation to be noted presently traced before you remove your Line for these two Lines one long to set out the faces and the Line of defence and a short one to set out the Flanks will serve turne and besides it will prevent all confusion and mistakes Now when all the Bastions are traced you are to set out the dike and when all is finished the Counterscarp as you have been directed Chap. 12 and 13. The Line of defence of this Ovall is of 240 yards the distance from the Center to the point of the Bastion of 85 yards The gates and dravv bridges of this Ovall fortification are to be placed in the middest of the East and VVest courtine that represents the length of the Ovall and not South and North as other Forts are and the length of the Courtine because of her circularie Line of 170 yards the brest of the Bastion 110 yards the Gorges of 83 yards and one third part and the faces of the Bastions of 100 yards and others of 90 because of the winding of the Ovall and her Flanks of 45 yards three yards longer then ordinarie because of the circularie line of the Courtine that it may the better defend the inward Angle of the other Flanks CHAP. XVI Of the Fortifications of the Sexagon by Bastions with Orillons demonstrated in Plate 12. THe Sexagon is regularie and a most compleat Superficie the Angle of her Center is of 60 degrees the Angle flanked of 80 degrees * See in Chap. 18. vvhy these sides have been set out fiftie yards longer then any other formerly have been This Sexagon is composed of six equilacerall Triangles equall on all sides containing everie one of them 39000 yards vvhich being multiâ—lied by six containe 234000 square yards and the Angle flanking of 135 degrees her sides are of 300 yards a peece her circumference of 1800 yards her whole continent of 235000 square yards out of which the one third part being deralked for the bredth of the Rampiers the extent of the Market-place and the streets there remaineth 156000 square yards for the houses of the Inhabitants to whom wee will allow in this greater continent 200 square yards that is a peece of ground some thing more then fourteen yards square on all sides And after this allowance the fore-said number of 156000 square yards being divided by two hundred square yards it will appeare that this continent will containe 780 houses and by consequence so many Inhabitants that are according to the rules of war to billet in everie third house a Horse-man and in all the rest two Foot-Souldiers a peece And after this accompt there will be 260 Horse-men and 1040 Foot-Souldiers a verie compleat Garrison to defend a place not much above an English mile in circumference so it be stored with Ordnance Armes Ammunition victuals and all other necessaries for such a Siege I have in this Superficie as being the last of this Method of Fortification set out the broad streets that go round
the great ditch Before you set out any of your Out-guards that are not to be undertaken before the brest-work and the slope of it belonging to the Contre esearpe be fully finished only you are to leave a gate of 12 soot broad against the places where you are to erect your out-gtards and these gates are to be made up by so many strong and sufficient Turn-Pikes well ironed with iron pikes and good hasps and locks for by these you are to releive your Out-guards or make your retreat if you be driven from the Out-guards all this being finished you are to set out the Out-guards after this manner The foure Out-guards against the foure Angles of the square are foure equilater all Triangies or Holfe-moones of one hundred yards on all sides two of the sides are to have a diâ—ch of nine foot broad and six foot deep and their brest-works of six foot high with a foot-step and the brest-work at cop is to be six foot thick and in the bottome nine foot with the foot-step And the other side towards the Angle of the square is to be open that the assailants may be discovered if they should possesse themselves of these Out-guards he Points of these Triangles that are towards the Angles of the square are to be 16 foot distant from the brim of the ditch The foure smaller Triangles have their Base 13 yards longer then their two sides that are to have ditches and brestworks that are to be of the very same dimensions of their former Triangles their base is of 83. and their fortified sides of 70 yards the first defend the Angles of the square and the flanks of the Avant Guards and the last defends the faces of the Avant Guards so that this fortification is compleat strong and of great defence the coming in is to be in the middle of the South Avant Guards for the gate and the draw-bridge are flanked and covered by one of the Halfe-moons CHAP. XXIII Of the Fortifications of the Pentagon fortified by Avant Guards and Out-Guards demonstrated in Plate 17. I Have formerly shown in Plate 11 how to set out the Pentagon in the field to omit repetitions I will onely give you some directions how to set out the Avant Guards and the Out-guards of this Pentagon because this Fortification differs from the other The Angle of the Pentagon is of 75 degrees his five sides are of 240 yards apiece ten yards lesse then the former the circumference of it is 1200 yards that is almost three quarters of an English mile a very convenient form for a Royall Fort for the continent of it it differs little from the other because the circumference of it is but 50 yards lesse and therefore I will referre you to Plate 11. only I will inform you that if the circumference of it were a quarter of a mile greater then it is that it might be defended being fortified after this method by a smaller number of men then the other could be that is fortified by bastions with orillons When the Superficie of the Pentagon is fully set out and traced you are to divide his five sides into three * Note by this that the brest of the Avant Guard is 80 yards broad equall parts that will be of 80 yards apiece and you are to knock in stakes in all their divisions then you are to divide the middle division in two parts that there may be a stake knockt in to represent the middle of every side Then you are to fasten a line of 80 yards * Note that the greatest slanks of the Av nt Guards advance 80 yards into the field to the South-East Angle stake and to strain the same full East upon a strait line agreeing with the side and at the end of the line knock in a stake then remove that line and fasten the same to the North and by East Angle stake and to strain it as before and to knock in a stake then remove that line and fasten the same to the North and by West Angle stake and strain it as before and knock in a stake then remove the line and doe the like to the West and by North Angle and as much to the West and by South stake straining the line as is said before and at every fide of the line knock in a stake and these five stakes will represent the five out-most Angles or Points of the five Avant Guards Then remove that line and fasten a shorter line of * The short slank is sorcy yards 40 yards to the second stake of the South side on the left hand South West and strain the same into the field perpendiculary wise and knock in a stake at the end of the line and this line will represent the short flank of the south-South-West Avant Guard and as you have set out this short frank set out the other foure and knock stakes at every end of the line and these five stakes will represent the five short flanks Then fasten the former line of 80 yards to every one of these last stakes one after another and first of all to the south-South-West short flank and strain the same Diagonal wise fastening the same to the stakes that represent the out-most Point of the Avant Guard and before the line be removed set Pioniers to trace the same and it will set out the face * The line of defence is taken from the midale of the side or Courtine that is in this figure of 240 yards of the South-West Avant Guard and as you have set out this face set out the other foure after the same manner You are to observe that if a line of foure hundred yards could be strained from the South-East Angle of the side of the Pentagon and fastned to the outmost Point stake of the South-West Avant Guard that this Diagona line that represents and sets out the face would be more perfect for it would cut the end of the short flank and terminate it selfe at the end or point of the long flank but this cannot be done conveniently only when you set out these faces stand with your Demi-circle at every Angle stake of the side opposite to the face you set out and by the Diagonal ray of your circle you may guide the line of the faces to be set out as perfectly as if a line of 400 yards had been strained Now when you have thus set out and traced the five Avant Guards with their faces long and short flanks you are to set out all your ditches after the dimensions described in chap. 17. Casting the earth of them inward to erect the brest-works and their five foot-steps of that height breadth and thicknesse there described And when all your inward works and the great ditch is finished you are to set out the Cunette or small ditch out of the great ditch and to erect with the earth that is taken out of it the Contre escarpe brest-work distant from the
knock in a stake at his feet and this stake will represent the North East Angle of the Poligon then turne your face to the north-North-West and with the ray of your demy-circle on the left hand the man with the line following the same and when he is just against you and the ray of the demy-circle being at the end of the line the man with the stakes is to knocke in another stake at his feet and this stake will represent the North West Angle of the Pentagon And after this manner set out the South-East and South-West Angles of the Pentagon and having knockt in stakes these five utmost stakes will represent the five Angles of the Pentagon and by these observations the gate and the draw-bridge of this Fort will be full South and in the midst of the South Courtine to be defended by the flankes of two Bastions when this is done you are to take the line of 250. yards having a loop in the midst which line you are to strain from stake to stake to prove whether your stakes are at an equall distance driving at everie middle of all the sides a stake as you will be directed by the loop fastened to the middle of the line now if any of your stakes be amisse you may easily amend them by the demy-circle and the line and when they are right you are to fasten lines from stake to stake as neare the ground as may be and set many Pioniers to trace the superficie of this Pentagon before you set out the Bastions And this is also the way how you ought to set out the equilaterall Triangle * Hovv to set out an equilaterall Triangle by the demi-circle spoken of in Chap. 12. by the Demy-circle spoken of in the 12. Chapter by driving a stake full North to represent the North Angle of the Triangle and by turning your face South after you have set the sight of the demy-circle upon 60. degrees as being the Angle of the Center of the equilaterall Triangle turning the ray of your demy-circle on the right hand and then on the left hand and driving at the end of the line of 250. yards two stakes for by this meanes the gate and the draw-bridge of the Triangle Fort will be full South and just in the midst of the South Courtine and defended by the flanks of two Bastions The Superficie of this Pentagon being traced you are to divide the five sides of it into six equall parts driving in everie division a stake then you are to fasten to the former line of 240. yards another line of 83. yards and a third that is the just distance from the Center of the Bastion to the utmost point of it and when you have done so you are to fasten the same to the Center stake and to straine it diagonall-wise 83. yards and one third part beyond the five Angle-stakes making the line as you straine it to touch the said stake and at the end of the line to drive in five stakes that will represent the five utmost points of the five Bastions And for the setting out of the rest I referre you to avoid repetition to the two last Chapters where you had large directions to set out the flanks and faces of the Bastions with their Orillons Dikes and Conterscarpes and will onely acquaint you with the demensions of this Pentagon since I did omit the same in the square yet I will give a hint of them in this place the flankes of the square were but forty yards and the flankes of the Pentagon are forty one yards and two third parts their Courtines are alike of 166. yards and two third parts the distance from the Center to the point of the Bastion in the square was 86. yards and in this Pentagon of 83. yards the gorge of the Square and of the Pentagon alike of 83. yards and one third part And the line of defence in the square 230. yards and in the Pentagon three yards lesse The faces of the Bastions in the square of 105. yards and in this Pentagon 100. yards and the brest in the square of 95. yards and in the Pentagon 100. yards CHAP. XV. Of the Fortifications of the Ovall by Bastions without Orillons demonstrated in Plate 8. THe Ovall is as irregularie as the Triangle and one of the most difficult superficies to set out in the field because of the circulary form and the variety of the Angles foure of them being of sixty five degrees and two of thirty seven degrees and a halfe the Angle flanking of 130. degrees and the Angle flanked of 72. degrees and a halfe her circumference is of 1500. yards and her continent from out to out of 118800. yards out of which the one third part being defalked for the bredth of the Rampiers the market-place and the streets there remains for the houses of the Inhabitants 79200. square yards that is to be divided by 150. square yards for a piece of ground of 12. yards and halfe square of all sides that is allowed to everie one of the Inhabitants that are found to be by this calculation 528. that are to billit 176. horse-men and 704. foot-souldiers A sufficient Garrison to oppose an Army of eight thousand men for three months so it be provided with Cannons Ammunition Armes Victualls and all other necessaries for a Siege It is also a convenient superficie to fortifie a well-compacted market-towne that may be reduced to this forme of three fourth parts of a mile Circumference Now to set out the Superficie in the field Note once for all that you are to have a Sea-compasse vvhen you go about to set out any kind of Superficies in the field to place your angle South North East and VVest rightly you are to make choice of your Center and to drive in a stake and to fasten a line of 80 yards to that stake and to straine the same full East upon a strait line and to drive in a stake then you are to wind the line about and to straine it full West and to drive in a stake and these two last stakes divide the length of the Ovall into three equall parts of 160. yards a piece and represent the two Centers of the two circles out of which the Ovall is formed then you are to fasten a line to the Center stake of 220. yards that is the extent of the demy-diagonall line of the South-East and North-East Angles and of the South-West and North-West Angles that are of 57. degrees and a halfe upon theray of which Angle you are to set the sight of your demy-circle and standing at the Center stake to turne your face full East winding the ray of the circle on the right hand the man with the fore-said line straining the same till he come just against you and the ray of the circle then is the man that carrieth the stakes to drive a stake at his feet then you are to winde the ray of your
hath a way of some eight foot broad is presently formed that runneth between the battlements of the wall and the Rampier that is called the way of the rounds and in French Le chemin des rondes and this way goeth from one Bastion to another round about the Garrison a very commodious and necessary meanes for the Rounds to go safe in the night and to discover by looking out of the Port holes of the battlements if any appeares neare to their Counterscarp or Corridor that are on the other side of their dike and the Rampier besides the Brest-work upon it is commonly six foot higher then the battlements of the walls and the Brest-worke six foot more so that the splinters of the wall during a battery cannot offend the souldiers that defend the Brest-workes of the Rampier Fourthly the Rampiers are commonly thirty foot high besides the height of the Brest-worke that is six foot high within side for it hath a foot-step of eighteen inches high and two foot broad and the whole height of the Rampier with his Brest-worke is within side thirty six foot and without thirty three foot high because the top of the Brest-work is carried three foot slope because it is alwayes twenty foot broad at top to be of Cannon-proof and the Rampier besides the thicknesse of the Brest-worke and the slope of the two sides defalked is alwayes forty foot broad on both sides on which they plant Elmes or Sicamore Trees that in few yeares make very pleasant and shadie walkes that serve in time of siege for a way for horse men foot and carriages to come to defend and relieve the Rampier Fiftly the distance from the Center of one Bastion to another is commonly from two hundred fifty yards to three hundred yards Sixtly the faces of their Bastions are ordinarily from one hundred yards to one hundred twenty yards besides the turning of their Orillons that is about twenty yards Seventhly the whole gorge of their Bastions are from one hundred yards to an hundred and twenty yards from out to out 8 The brest of their Bastions are from 120. yards to 130. yards 9 And from the center of the Bastion to the point or the utmost Angle of the Bastion from 80 yards to 100 yards 10 The flanks of the Bastions from 42 yards to 50 yards that is divided into three equall parts if they make Orillons one part is allowed for the flank and the other two for the turning and the framing of the Orillons 11 Their curtaines are alwayes betweene 160 yards to 200 yards 12 The Line of Defence to be good for the defence of the musket shot is to be from 220 yards to 250 yards at the most 13 The slope of their Brest-works without side is one foot for every yard if the earth be good Novv let the Reader judge vvhether these costly Fortifications be for our turn and within side a foot in two yards but if it be a sandy ground or a running clay it requires a foot and halfe without side and a foot within for a yard high 14 The foundation of these walls begin from the bottome of the dike and are carried up to the upper water-table of the wall to the Cordeau and from the bottome of the dike on the field-side levell with the ground and all of free stone The middest of the Bastions are filled up with earth to the Cordeau and made slope to the firme ground of the towne and their Rampiers and Brest-works are raised fifteen yards above the Cordeau CHAP. VII Of the superficies contained in the first Plare SInce the Principles of Geometry are the very ground-work of the Art of Fortification I judge it convenient to begin this Abstract by the demonstrations of such superficies as are most commonly used in the practice of this Art Of Superficie A Superficie is properly any kinde of forme demonstrated upon paper or upon the ground inclosed with three lines at the least except it be the circulary forme that hath but one circulary line that begins at one point and ends at the same The point is a small touch of the pen Of the Point that cannot be divided because it hath no parts but is the beginning and end of all lines and the center of all Formes See Figure 1. A line is the continuance of a point that is incapable of division Of Lines but in the length of it it is distinguished by divers termes As by the strait line in Figure 2. by the circulary line in Figure 3. by the perpendiculary line in Figure 7. by the parallel line in Figure 8. by the diagonall line in Figure 11. and by the diametricall line in Figure 12. There are divers other distinctions of lines but they are not usefull in this Art All Angles derive from the conjunction of two lines in one point Of Angles whether they be strait circulary diagonall or mixt with any one of these As Figure 4. is called a plaine Angle because two strait levell lines from one and the same distance meet at one point and a strait perpendicular and a levell line falling in the midst of a strait line produceth an Obtus and a strait Angle as in Figure 7. And two circulary lines meeting at one point maketh a circulary Angle as in Figure 5. And a strait and a circulary line meeting at one point produceth a mixt Angle as in Figure 6. There are also divers other sorts of Angles some of which we shall have occasion to speak of in another place The eighth Figure demonstrates how to make a perpendicularie line cut a strait line given Of the eighth Figure and how you may cut that perpendiculary line in three parts by three demicircles to make up the line given three parallell lines without altering the compasse to any other distance but the first First let a strait line be given then take the just distance of that line with your compasse and set one of the points of it upon the right hand end of the line and with the other point make a small demicircle above then remove the point of your compasse upon the left hand side of the line given and with the other point make another small circle cutting the first and where these two small circles cut one another set your rule and draw a strait line to the line given and it will cut the same with a strait perpendicularie line Now to avoid all errour that might proceed from the mis-placing of your Rule upon the line given make but two other small demicircles below the line as you did above and where these cut one another put one end of your Rule and the other upon the upper cutting of the two small demicircles and draw a strait line and of necessity the perpendicularie line will be strait and without errour Now to cut that perpendicular Line in two equall parts more to make up the Line given three parallel
Lines set your compasse upon the just distance of the length of the perpendicularie Line then set one of the points of the Compasse upon the lower end of the perpendicularie Line and make a demy circle upwards then remove your Compasse upon the upper end of the perpendicularie Line and make a demy-circle downwards then remove the point of your Compasse upon the Center-point where the perpendicularie Line did cut at the first the Line given and make the third demy-circle upwards and this demy-circle will cut the other two in foure places and where they cut set your rule and draw two strait Lines and these will make up the Line given three perfect parallel Lines as it is clearly demonstrated in figure 8. The ninth figure sheweth how to draw as many parallel Lines as you please upon two lines Of the ninth Figure that are the upper and the lower lines in this figure First let two equall lines be given one below another above according to the length you desire to have your parallel lines then divide these two lines with your Compasse in as many parts as you desire to have parallel lines and at everie division make a point and from everie point make a demy-circle above the upper and the lower given lines then set your Rule upon them one after another and draw as many lines as there is demy-circles and these will all be perfect parallel lines Now if you will double these parallel lines it is but to divide with your Compasse the just bredth of them in two parts and at everie division to make a point and to set your Compasse againe upon its first distance and to cut your first demy-circle with it and to draw as many lines and you shall have as many more perfect parallel lines as you had before as it is clearly demonstrated in Figure 9. Of the tenth Figure The tenth Figure sheweth how to make a square and a triangle upon a line given Suppose the Base of the square is the line given now to make a perfect square and foure Scalene triangles of this line you are to set your Compasse upon the just distance of the line and to set one point of it on the right hand end of it and to make a demy-circle and to remove your compasse upon the left end and to make another demy-circle and where they cut one another set your rule and draw a perpendicularie line then turne your rule and draw a strait top line and joyne the base line with this top line by two strait lines and you will have a perfect square and foure perfect square scalene triangles as it is demonstrated in Figure 10. The eleventh Figure sheweth how to make a paralograme out of two circles Of the eleventh Figure First set your compasse upon the demy bredth of the paralograme that you intend to make and then make a circle on the right hand then remove your Compasse-point upon the extreame of the first circle on the left hand upon a strait line and with the other point mark the Center-point of the other circle then turne your compasse round and you will have two circles whose extreams will touch one another then set your rule upon the foure extreames of these two circles and draw foure strait lines and where these lines cut one another there is the foure Angles of the Paralograme as it is demonstrated in Figure 11. The twelfth Figure sheweth how to make a perfect square by the out-side of a circle Of the tvvelfth Figure Make choyse of your Center and set your compasse upon the verie Diameter that you intend to have your square then make a circle and draw foure strait lines upon the extreames of it and it will produce a perfect square as is demonstrated in Figure 12. CHAP. VIII Of the Superficies contained in the second Plate AMong all other Superficies there is none so usefull for the Art of Fortification as the Triangles and yet Mr. Ward in his Animadversions of War makes mention but of three sorts yet there are six principall sorts of Triangles from which all other mixt Triangles are derived and these six sorts may be all set out by the Circle as it is demonstrated in this Plate The equilaterall Triangle deserves the precedencie 1 Of the equilaterall Triangle and the best vvay to set out the same because it is the only Triangle that can be fortified by Bastions for all her sides are equall the best way to set it out is to set your Compasse upon the just distance of the Base of it and to make two points with your Compasse and to draw two Demy-circles one from the right point and the other from the left hand point and where these Circles cut one another make the third point and draw three strait lines to these three points and it will produce a perfect equilaterall Triangle equall of all sides Some set it out by the Circle Hovv to set out the equilaterall Triangle by a Circle dividing the Diameter of it in foure equall parts and draw a strait line upon the first quarter point as the Base of it and two lines more from the two ends of the Base to the top of the Diametricall Line of the Circle but this way is not so perfect as the other See Figure 13. The Isocele Triangle is also verie usefull in the Art of Fortification 2 Of the setting out of the Isocele Triangle for all the regularie Poligons of many Angles after the Sexagon are composed of Isocele Triangles but the Sexagon is composed of six equilaterall Triangles that have all their sides equall But the Isocele Triangle hath alwayes two sides equall and longer than her Base it is set out after this manner out of the Circle After your Circle is made draw a strait perpendicularie Line Diametricall wise upon the Center of it to the two extreames of the Circle then divide that last Line into eight equall parts and draw a strait line with your rule upon the first point of the eighth part division from one extreame of the Circle to another and that Line represents the Base then draw two strait lines from the two ends of that Base to the top-point of the Diametricall Line of the Circle and these three Lines will produce a perfect Isocele Triangle See Figur 14. The Recteligne Triangle is also usefull in the Art of Fortification to set out Halfe Moones 3 Of the rectiligne Triangle and hovv it is to be set out by the Circle her Base contrarie to the Isocele Triangle is longer then her two sides it is set out after this manner After your Circle is made draw a strait Line from the two side extreamities of the Circle and cut with that Line the center-Center-point of the Circle and this Line represents the Base then draw two other Lines from the two ends of the Base to the upper point of the Circle and two other Lines from
the two ends of the Base to the lower point of the Circle and it will produce two perfect Recteligne Triangles that makes also a perfect square Rhomb The Scalene Triangle hath all her sides unequall it is very usefull for measuring of land 4 Of the scalene Triangle and hovv it may be set out by the Circle for two of them make an Equilaterall Triangle and foure of them a perfect long Rhomb It is to be set out after this manner After your circle is made divide the side diametricall line of the circle into eight equall parts then cut with a strait line the first eighth point of that division on the left hand point and then divide the diametricall line of the circle that is drawne perpendiculary-wise into foure equall parts and cut with another strait line the first equall point of that division towards the Base or the lower side of the circle then from the two sides of these two lines draw a strait diagonall line and these three lines will produce a perfect scalene Triangle See Figure 21. The acute Angle 5 Of the Oxigon Triangle and hovv it may be set out by the Circle or Oxigon Triangle is onely usefull for measuring of land all her sides are also unequall and all her Angles acute you are to set it out after this manner After the Circle is made draw a Diametricall line perpendiculary-wise that may cut the point of the Center from the top of the Circle to the bottome then from the lower end of this line on the left hand make a point at the fourth part of the Circumference of the Circle and another point on the right hand at the third part of the Circumference of the Circle then draw a line from the left hand point to the right point and two other lines from the right hand and the left hand point to the top point of the Diametricall line and these three lines will produce a perfect Oxigon Triangle see Figure 22. The Obtus Triangle is usefull in Fortification 6 Of the Obtus Triangle and hovv it may be set out by the Circle and for measuring of Land two of her sides are equall and containe but the two third parts of her base her base being longer then her sides by a third part it is to be set out after this manner After the circle is made divide the Diametricall line of it into three equall parts and cut the first point of this division by a strait line and this line represents the base then draw two lines from the two ends of this base to the top of the Diametricall lines and these three lines will produce a perfect Obtus Triangle see Figure 23. Now I come to the 24. Superficie that containeth an Ovall Of the setting out of the Ovall and in that Ovall two long Rhombs a Paralograme two equilaterall Triangles and foure Scalene Triangles But because I have already spoken of all these the Ovall and the two long Rhombs excepted I will begin with the Ovall the most difficult of all other superficies to be rightly set out upon paper or in the field To set it out upon paper you are to set your compasse upon the scale of the third part of the length you intend to have the Ovall and this third part is to be divided againe into two equall parts and your compasse set upon that sixth part then make choice of your Center and cut the point of the Center with two strait lines one of them perpendiculary-wise and the other diametricall-wise then set one of the points of your compasse upon the Center point and with the other make a point upon the diametricall line on the right hand and another point upon the same line on the left hand then set the compasse againe upon the third part of the length of the Ovall and set one of the points of it upon the right hand point that represents the End of the third part of the line of the length of the Ovall and with the other point of the compasse make a circle then remove the point of the compasse and set it upon the left hand point of the aforesaid line and make another circle and the two extreams of these two circles represent the length of the Ovall Then remove your compasse and set one point of it upon the lower cutting of these two circles and set it at that distance that having a point upon this lower cutting of these two circles it may conjoyne with a true circularie line the two upper extreames of the two circles that being done remove your compasse without any alteration of the distance and set one of the points of it upon the upper cutting of the two circles and with the other point of it make a true circulary line to joyne the two lower extreames of the two circles and this being traced with a pen will produce a perfect Ovall one third part longer then it is broad some make it halfe as long againe as it is broad but the sides are too flat and the Ovall is by it more deformed and not so seemly and compleat as this is demonstrated in Figure 16. Now to make the most perfect Rhomb that can be made Of the setting out of the Rhomb you are but to draw foure lines dioganall wise from the upper and lower points of the perpendicularie diametricall line that cuts the two broad sides of the Ovall to the two points of the diametricall line of the length of the Ovall and it will produce a perfect Rhomb as in figure 18. And to make the two equilaterall Triangles and the foure scalene Triangles out of the smaller Rhomb Of the setting out of the 6. Triangles you are but to draw four lines diagonall-wise from the two Ends of the first line that did represent the eighth part of the Ovall to the two upper and lower cuttings of the two circles and these lines with the two diametricall lines of the length and breadth of the Ovall already drawne will produce these six fore-said Triangles And to set out the Paralograme Of the setting out of the Paralograme you are to divide the breadth of the Ovall into four equall parts and the length of it into nine equall parts and at every division to make a point and to draw foure strait lines upon the first points of these two divisions and they will produce this Paralograme that is a ninth part longer then twice his breadth CHAP. IX Of the Superficies contained in the 3. Plate THe first Circle of this Plate contains an Equilaterall Triangle Of the setting out of the equilateral triangle out of a square a Square and a Pentagon And because all the Equilateral Triangles that are set out by a Square have their two sides longer then their square by anâ— part I have drawne two demy-circles to shew where the upper Angle of the Triangle should come to be perfect and equall of all her
sides and that is where the two circles cut one another As for the square it is more easie to set it out from without the circle Of the setting out of the square by the inward side of the circle then from within the circle because it is more difficult to reduce the sides of it to that scantling proposed if in case you set it out by the inward side of the circle then it is if you set out by the out-side of the circle for the diametre of the circle is of the just length of the sides but to take out a square out of the inward side of the circle the demy-diametricall line of the circle is to be one third part longer then when you make it by the out-side of the circle But if you are not tyed to a scantling then you may make as perfect a square our of the inward side as well as from the out-side of a circle by dividing the two crosse diametricall lines of the circle into 6. equal parts and by drawing 4. straight lines cutting the foure first points of this division in the foure sides of the circle drawing the lines to the inward extremes of the circle and these lines wil produce a perfect square Concerning the setting out of the Pentagon you are to divide the circumference of the circle into five equall parts and at every division to make a point then you are to draw five straight lines from point to point and these five lines represent the five sides or bases of the Pentagon then you are to draw five other lines from the center point to the end of these five bases diagonal wise and these five lines compleat the five sides of the five triangles of the Pentagon and this being done this superficie is perfected The other three Circles contained in this place are to set out in every one of them a Poligon with different Angles viz. The first a Sexagon the second a Septagon and the third an Octogon having all of them the Basis of their Triangles of an equall length by the encreasing the circumference of the circle of the length of one of the Bases And because this is a point of great concernment to an Enginier that may by the same know at an instant how many Bastions the place will require if he doth but know the true circumference of it I will expresse my selfe more clearly Suppose then that the six Bases of the six equilaterall Triangles of a Sexagon contain 250. yards a piece that is in all 1500. yards circumference And that you would set out a Septagon with seven Bases that should contain every one of them 250. yards a piece you are then to adde to the demy-diametricall line of the Sexagon a sixt part more of the extent that it had before and by this meanes the circumference of the circle will be able to afford you seven Bases of 250. yards a piece that is in all 1750. yards The reason of it is that the circumference of a circle containes three diametricall lines so that you are of necessity to adde to the former demy-diametre line of the Sexagon a sixt part more then it had before because a demy-diametre is but the sixt part of the circumference of a circle And by this rule you may make all the Bases of any Foligon from six Angles to twenty foure Angles nay to eight and forty Angles if you please of two hundred and fifty yards a piece adding alwayes to the demy-diametre as foloweth To make a Septagon you are to adde the â…™ part to make an Octogon you are to adde a seventh part to make a ninth Angle Poligon you are to adde the eighth part and so as you goe on the ninth the tenth the eleventh or twelfth part And as I have said you are to observe that course till you come to set out a Poligon of eight and forty Angles That I conceive would be sufficient to fortifie the City of London on both sides the water with as large a Line of Communication as it hath at this present having at every two hundred and fifty yards distance an Angle to forme a strong complete and defensible Bastion A farre more beseeming a Fortification for so famous a City then such sleight winding Angles and ill flanked Redouts wherewith it is now fortified CHAP. X. Of the five Redouts contained in Plate 4. BEfore I come to speake of the Superficies of these five Redoubts it will not be amisse to inform the Reader of their extent continent and dimensions And first of their extent Of the extent of Redouts All square or circullary redouts are to bee of one hundred yards from out to out in their diametricall line otherwise their inward continent will be too small But a Triangle redout is to have her three sides of two hundred yards a piece because two equilaterall Triangles containe no more then a square Secondly their continent is to be so large Of the continent of redouts as it may lodge a competent number of Souldiers for their defence that is two hundred men at least and every two men cannot have a smaller piece of ground allowed them for their lodging then a piece of eight yards square that makes in all sixty four square yards Now a redout of one hundred yards diametre reduced in the forme of a square will contain but 10000. square yards out of which you are to defalke a third part for the Rampiers the place and the streets and then there will remaine but 6667. yards for the lodgings and this being divided by sixty four yards it will containe but two hundred and eight Soldiers lodgings if two of them be lodged together in a chamber of 24. foot square And by this you may judge whether the greater part of the Redouts about the City of London are of a proportionable extent seeing most of them have not fifty yards of diametre Thirdly for their dimensions Of the bredth and depth of their ditches Their ditches are to be tenne yards broad and five yards deep and the slope of the sides of these ditches are to be but one foot slope in three that the bottome of the ditch may remain to be twenty foot broad when it is fifteen foot deep for the reasons that will be shewn when I come to speak of the contre escarpe and the Rampiars their Breast-works are to be proportionable to this ditch Of the height and thicknesse of their Rampiers The height of it within side is to be twelve foot high and nine foot without the slope of it within side is to be but one foot in six and one foot in three without side there are to be five footsteps of two foot broad a piece Of their slope within and without and of eighteene inches high a piece that the breastwork may not be above foure foot and an halfe high that is of a convenient height for tall and middle siz'd Soldiers to
superficies of the redout if it be a Triangle Triangle-wise if it be a square after a square manner if it be of a fift sixt seventh or eighth angle form the ranges are to be after that manner that a place be left in the midst of the redout just after that forme of some 30. or 40. yards on all sides as you shal see it demonstrated in greater Forts having three or four or five or six streets according to their angles to goe from the place to the Rampiers because all things in a Redout are to be as orderly carryed as in a Royall Fort for all the difference that is to be betweene them is in their extent the Redouts extent being smaller then of a Royall Fort or Citadell Now concerning the superficies of these five redouts demonstrated in plate foure the first being the figure 24. is a perfect square set out by the out-side of the circle the sides of the square are of one hundred yards a piece It is fortified by foure halfe moones whose bases are of fifty yards a piece to agree with the foure angles of the square whose sides flank the halfe moone and the sides of the halfe moones flanke them so that a man cannot appeare at any point or side of it but he may bee in danger of his life by the Musquet shot The second redout demonstrated in figure 25. is also a perfect square set out by the out-side of a circle Of the second Redout of the same extent of the first and fortified by foure great halfe moons that reduce the forme of it to a perfect corner cap the utmost angles of the foure halfe moones extend themselves twenty yards beyond the four angles of the square for the better flanking of the sides and points of the said halfe moones that flank one another very well There is a small redout erected a Grays-Inne-lane end much like after this manner but her extent is too small and her flanke invisible and therefore no better then a plaine little square redout The third redout is a demy-Paralogramme Of the third Redout half as long again as it is broad it is set out by the foure extrems of two circles and fortified by foure halfe moones whose bases are of 75. yards a piece the better to flanke the Angles of the Paralogramme that flanke the half moones this redout for her extent requires three hundred men for her defence for it containeth 150. yards in length and one hundred yards in breath It is of a very convenient form to be placed before the comming in of a gate of a great garrison Towne to command divers rodes so the rode that traverse the same be winding like the letter S. comming in of one side of the exterior half moon and going out on the other side of the interior halfe moone The fourth redout is a perfect circle divided in six equall half moones after the forme of a Sexagon Of the fourth Redout it is very well slinked of all sides because the utmost Angles of her half moons extend themselves twenty sive yards into the field more then her circulary circumference whereby it is of a greater continent then the other redout the demy paralogramme excepted The fift redout is a perfect square Of the fift Redout sâ—t out by the out-side of a circle and fortifyed by foure Avant-gards at the foure angles of it whose utmost angles extend themselves thirty yards into the field the breast of the Avant guards are twenty five yards broad just the quarter part of the base of the square the face of the Avant guard is of the same extent and the flank of twelve yards and half If the 4. sides of this redout that are in this figure but one hundred yards a piece were of two hundred yards a piece it would make a strong and well flanked Fort so the utmost angles of the Avant guards extended themselves 60. yards into the field and the brest to be of fifty yards the flanks twenty five yards and the face of the Avant guards of fifty yards The Royall Fort neare Islington is much after this manner only the face of his Avant guards are square and doe not extend themselves farre enough into the field and therefore not so regular nor so defensible as this CHAP. XI Of the two first Methods of Fortification in generall THe small difference there is between these two first Methods of Fortification by Bastions without and with Orillons hath induced me to joyne them into one for they agree in all their essentiall parts but in two things viz. in the Line of their Flanks and in the having or not having Orillons First concerning the Line of their Flanks Mr. Ward Mr. Cruso Mr. Norwood and the Author of the Enchiridion do make no difference at all between the Line of their Flanks Of the difference that is to be observed in the dravving of the line of the Flanks vvhen you are to forme bastions vvith or vvithout Orillons for in all their Modells and Superficies they draw the Flanks of the Bastions with and without Orillons all after one manner that is upon a strait perpendicularie Line But on the other side they would have the side or the Base to be divided into eight parts when they frame Bastions with Orillons and only into six parts when they frame Bastions without Orillons in both which points I maintaine they are mistaken First for the Line of their Flanks if it be drawne as they propose strait and perpendicularie wise the Flanks by this meanes are too much exposed to the Enemies great batteries and to the volleyes of their Musketiers shot as soone as they have gained the Defendents Counterscarp and therefore to prevent this evill I say it is better and safer to draw the Line of the Flanks of the Bastions that are to be without Orillons one eighth part more slope than strait As for instance suppose the Line of the Flank to be fortie two yards then are you I say to straine that Line five yards and one quarter more slope towards the other Flank of the other Bastion then a strait perpendicularie Line will afford for these five yards make the shoulder of the Orillon to jet more into the dike then otherwise it would do being drawne strait and by this meanes this jetting out is a great safegard to the Flanks for all that thick and massie peece of earth of the shoulder with this jetty must of necessitie be battered to dust before the Flanks can receive any hurt whereas if the Line be drawne strait the Flanks lye open to the Enemies batteries if the Bastions have no Orillons or this jetting shoulder to defend them This is clearly demonstrated in Plate 7 where the Pentagon fortified by Bastions is described better then it can be in the Triangle Square or Ovall formes So that I conclude that the Line of the Flank is to be drawne strait when you intend to forme
allow them to be of 150. square yards that is a piece of ground of twelve yards and halfe square of all sides by which scantling the 41666. yards being divided there will appeare to be in this continent 277. dwelling houses and as many Inhabitants that may billet foure hundred Foot and two Troopes of Horse and this number is sufficient to maintaine this Fort against an Army of five thousand men three months so it be provided with sixteen piece of Ordnance Balls Ammunition Armes Victualls and all other necessaries fit for a Siege Object Some will wonder why so small a Fort should have sixteen pieces of Ordnance when many of our Garrisons that are of two or three miles Circumference have not so many Ans I answer the more is the pity they are no better provided But if this Method of Fortification were not better stored to what end should Forrainers be at the charges to erect upper and lower flanks and because I have not as yet spoken of these upper and sower flanks I will upon this occasion describe how they are made and for what use they are erected In the Ancient Fortifications by Bastions Of the upper and lovver Flanks of a Bastion there was formerly low Casamates to scour the dikes even with the water for they were built so low that a Cannon being mounted in them and pointed shot upon a levell Line even with the water of the dike and these Casamates were all vaulted with arches of free-stone having two Port-holer and two Demy-Cannons in every one of them their vault being some sixteen foot square and they had a slanting descent from the gorge of the Bastion with a door to come down to them but because they had no other light then the Port-holes nor no other evacuation for the smoke then the doore when the Cannoniers fired their Pieces they were so incumbred with the smoke in the vault that they could not suddenly charge their pieces againe but were inforced to sâ—ay till the evacuation of the smoke were past Whereupon the moderne Enginiers to prevent these defects have invented the upper and lower slanks where they alwaies place two pieces of Ordnance in everie one of them so that according to the Forrain Method every Bastion is to have ten pieces of Ordnance at the least two Demy-Cannons in everie flanke and two long Culverins to defend the faces and the point that is in all ten pieces of Ordnance these Flanks are made after this manner The wall of the flanks is brought up from the bottome of the dike with free-stone of two yards thick to the levell of the water of the dike and within and without laid with Tarris that the water of the dike may not pierce the same and upon this wall and the firme ground after another foundation of stone hath been laid twenty four foot from the brim of the first wall some five foot deep a Brest-work is brought up of earth and turfe of twenty foure foot thicke in the bottome and of twenty foot broad at top and six foot high having three Port-holes and beyond this Brest-worke the ground is digged lower the whole length of the flank that is ordinarily from thirteen yards to sixteen yards in length and in breadth eight yards and in depth five foot and this being laid with tracin and planked is the Platforme of the lower flanke open over-hâ—â—d in which they place two Demy-Cannons and these scouâ—â—â—â—d free the dikes from the assay lants galleries and from the scaling of the Rampiers Now to erect the upper flank they go eight and forty foot wider into the gâ—rge of the Bastion and upon the in ward foundation of the lower flanke wall and the earth of the Bastion they erect another Brest-work of the same height bredth and thicknesse of the former with three Port-holes in it and then they planke another platforme and place two Demy-Cannons more upon the same and these are the manner of their upper and lower flanks that have a slope coming downe from the upper to the lower some ten foot broad which being covered by the Orillons make the Bastions very strong and when these double flanks are taken out on both sides the gorge is not above fiftie yards broad that is narrow enough for the last re-intrenchment Now these flanks being all open over head the smoke of the Ordnance is suddenly evacuated the use of the upper Flank is to scoure the face and the points of the Bastions in the time of a storme and to beat all along the Courtine And so much will suffice once for all concerning the erection and use of these lower and upper Flanks Now I come to shew how you are to set out this Square in the field If men could as soon and as easily set out a Superficie in the field as they may upon paper it were soone done but this last requires a greater labour and care You are then in the first place to make choyse of your Center and there to knock in a stake then you are to stand close to that stake and turne your face full South and then take your Demi-circle and set the sight of it upon the ray of 90 degrees that is the Angle of the Center of the Square then you are to have two men by you one with lines and the other with stakes and he with lines is to have a line of one hundred and * You are to observe that this line of 180 yards is the just demi-diagonall line and distance that is betvveen the Cent r-stake and the Angles of the Square fourescore yards the one end of which line he is to fasten to the Center-stake and when you have taken your Demi-circle and set the sight of it as afore-said you are to take with it having your face turned to the South the right hand ray of the Angle of 90 degrees and when you have it let the man straine the line fastened to the Center-stake along the said ray to the end of the line and when he is just against you and the ray of your Demi-circle let the other man knock in a stake at his feet then turne your selfe and set your Demi-circle to take the left hand ray of the angle of 90 degrees and when you have it let the man with the end of the line come to it and when hee is just against you and the ray of your Demi-circle let the other man with stakes knock in a stake at his feet at the end of the line and these two stakes represent the South-East and the south-South-West Angles of your Square then turne your selfe fall North standing close to the Center-stake and set out after the same manner the North-East and North-West Angles of your Square and let the man with stakes knock in two stakes as hee did in the South side and these foure utmost stakes will represent the foure Angles of the Square Now to avoyd errour you are to fasten the
line of 250 yards with a loop fastened in the middest on the South-East stake and to straine it to the South-West stake if the stake be at the just distance of the line that side is rightly set out then you may knock in a stake where the loop is to represent the middle of that side where the gate and the draw-bridge of the Fort is to be placed and so prove all the other three sides with your Line of 250 yards knocking stakes in the middest on everie side for they will stand you in stead when you come to divide the sides into six parts Now if any of these sides be amisse and agree not with your Line then you are to amend them by your Demi-circle and your Line which is easily to be done and when the foure angles and sides are right you are to fasten lines to the eight stakes as neare the ground as may be and to set Pioniers to trace the Superficie of the Square with spades and pick-axes before you set out the Bastions That being done you are to divide the foure sides of the Square into six equall parts and to knock in a stake at evene division then you are to fasten a line of 90 yards to the former demi-Diagonall Line of 180 yards that will then be of 270 yards and to straine the same * The distance from the Center of the Bastion to the point is of 90 yards in this Square 90 yards beyond the foure Angle-stakes of the Square after it is fastened to the Center-stake making the said Line to touch the Angle-stake and at the end of the said line knock in a stake and these foure stakes will represent the foure utmost points of the foure Bastions and the foure former Angle-stakes will then represent the Center of the Bastions This being done fasten a line one after another to the third stake of everie side of * This Line of 230 yards is the just extent of the Line of defence of this Square 230 yards and straine the same to the foure stakes that represent the foure utmost points of the foure Bastions and this line will set out the eight faces of the Bastions and all the Lines of defence then you are to fasten a line one after another of 41 yards and two thirds to everie second stake of the foure sides * The Line of the Flanks in this Square is of 41 yards and tvvo third parts and to straine the same upon a strait perpendicularie line till it come to cut the former line that represents the line of defence and sets out the faces of the Bastions and where it cuts the other drive in a stake and these eight stakes will represent and set out the eight Flanks and the foure Courtines And that being done you are to set Pioniers at work to trace all these things before you go about to set out the Orillons Now to avoyd mistake you were better to set out one side at a time to have it traced as you set it out for it wil save charges because it will not require so many lines This being done you are to set out the Orillons and after the Orillons the dike and when all is finished you are to erect the Brest-work of the Counterscarp with the earth taken from the small dike called La Cunette adorning the same on the inside with Turffe and a foot-step as I have formerly given large directions in Chap. 12. and Plate 9. CHAP. XIV Of the Fortifications of the Pentagon by Bastions with Orillons demonstrated in Plate 11. THe Pentagon is also irregularie yet lesse then the Square for the Angle of his Center is of 75 degrees and the Angle flanked of the same extent and his Angle flanking of 142 degrees and a halfe his bases or sides are of 250 yards a peece his circumference of 1250 yards and his whole continent from out to out of 125000 square yards it is of a convenient forme for a Citadell or of a well-compact Towne whose circumference doth not exceed three quarters of an English mile Now to direct the Reader once for all * Hovv you may knovv the continent of any Poligon vvith varietie of Angles how he may speedily calculate the continent of all sorts of Angle Poligons I have in this Figure set out a demonstration of it viz. you are first to draw a strait perpendicularie from A to B then a strait parallel line from C to D and then to joyne D and A by a strait line as it is demonstrated in this Figure and it will produce a demy long square his broad sides containing according to the scale of this Figure 200 yards and his end-side 125 yards which being multiplyed one by the other it will produce 25000 yards as the just continent of one of the Triangles of this Pentagon which being multiplyed by five because it containes five Triangles the whole continent will amount to 125000 square yards Now the one third part of it being defalked for the bredth of the Rampier the Market-place and the streets there will remaine for the Inhabitants houses 83333 yards and a third part which being divided by one hundred and fiftie square yards that wee allow for everie Inhabitants dwelling house that is a peece of twelve yards and an halfe square of all sides it will according to this scantling containe 555 houses and as many Inhabitants that are according to the rules of war to billet in everie third house a Horse-man and in all the rest two Foot-Souldiers apeece so that it will containe 185 Horse-men 740 Foot-men and 555 Inhabitants a sufficient Garrison to defend this place against an Army of ten thousand men for three months so it be provided with Ordnance Armes Ammunition victuals and all other necessaries for a Siege Now to set out this Fort in the field you are to bring along with you two men one with lines and the other with stakes and when you have made choice of your Center the man is to knock in a stake and you are to stand close to this Center-stake and having set the sight of your Demy-circle upon the ray of 75. degrees that is the Angle of the Center of the Pentagon * Note that this line of 240 yards is the extent of the demi diagonall line of the Pentagon the man that carrieth the lines is to fasten a line of 240. yards to the Center-stake and to straine the same full North upon a strait perpendiculary line and at the end of it he is to knock in a stake and this stake represents the North Angle of the Pentagon that done take your demy-circle and wind the right hand ray to the right hand the man holding in his hand the line of 240. yards straining the same according to the ray of the demy-circle and when he is at the end of the line and just against you agreeing with the ray of your demy-circle let the man with the stakes
this will suffice to have been spoken concerning the sides or bases of all manner of Superficies Concerning the Line of defence * See his Animadversions Chap. 30. and pag. 74. Mr. Ward is over-bitter against Errard de Barleduck because hee draweth his Line of defence from the verie corner of the Flank and not from the third of the base or side which he calleth the Courtine I do acknowledge that it is better to draw the Line of defence from the third part of the side or base as Mr. Ward would have it then from the corner of the Flank and especially if the sides of the Fortification be of * If a side is of 300 yards it is better to dravv the Line of defence from the middle of the Courtine then from the third part of it 300 yards a peece as Mr. Ward would have them to be nay it were better if it were drawne from the middle of the side or Courtine for it is one and the same thing To rectifie the errour of the extent of his sides of three hundred yards a peece that makes the Line of defence unserviceable for the musket-shot if the Line be drawne from the third part of the Courtine whereas it would serve turne and amend the errour of the over-long extent of the fide if it were drawne from the middle of the Courtine Yet for all this small errour of Errard I see no reason why Mr. Ward should be so bitter against him for his owne Modells are not without defects for it is a verie good horse that never stumbleth And it is well knowne to all Artists that Errard de Barleduck was an experienced Enginier and the first that adorned the Art of Fortification in the French tongue Besides the Line of defence is better in the Superficies of the equilaterall Triangle and of the Square to be taken from the corner of the Flank then from the third part of the side or Courtine because it openeth the brest of the Bastion and maketh their exteriour Angle more obtus then when it is drawne from the third part of the Courtine Moreover Mr. Ward doth wrong or mistake Errard and the other French Enginier to alledge as he doth that they relye most upon the musket-shot for the defence of the Courtines faces and points of their Bastions despising the defence of them bâ— the Ordnance shot the defence of the musket-shot being saith hee no defence at all to empede the Assailant from casting their galleries over the mote But I say that Mr. Ward doth mistake the meaning of Errard and of the rest of the French Enginiers for they erect their lower Flanks and provide them with Demi-Cannon only to prevent the casting of galleries over their mote And for their upper Flanks besides the Demi-Culverins they place upon them to defend the faces and points of their Bastions they place Musketiers to discharge their shot continually while their Demi-Culverins are charging againe and so make use of Ordnance and of Musket-shot also for the defence of them Therefore I will conclude with the Assertion of one of the greatest * See the Duke of Roan in his Perfect Captaine Chap. 8. Commanders of our dayes that the extent of the Line of defence is the best that is convenient for the Musket-shot as well as for the Cannon-shot CHAP. XIX Of the Fortifications of the Superficie in the forme of S. Michaels Crosse fortified by eight Halfe-Moones demonstrated in Plate 13. THe Circumference of this Superfice is so great that it contains 3680. yards that is two English mile and one third part of a mile and therefore fitter to fortifie some Corporation town then for a Fort so it may be reduced to this forme the Angles of the Center of it are of fifty five degrees and the exteriour Angle of the halfe-Moones are of sixty five degrees halfe of the faces of the halfe-Moones are of 250. yards and the other halfe of 210. yards a piece whereby they require to be defended by small drakes or sacres besides the musket-shot but if upon every point of the halfe Moone a platforme were erected as they are most commonly in all Redoubts or Forts after this manner viz. the Angle upon which you intend to erect a platforme is to be brought up twelve foot high from the ground to be levell with the inward side of the Brest-worke and towards the towne slope nothing and when it is so you are upon the last course of turfe to place a frize with sharp picked quarters of six foot long four inches broad and three inches thick * Seven or eight inches distance one from another jetting one yard over the dike and running a yard into the brest-worke that is to be raised so farre as the platforme goeth on both sides fix foot higher then the other Brest-work in which Brest-work the Port-holes are to be made two on every side so that these Angle-Brest-workes are to be 18. foot from the ground having a frize as is above said round about the Platforme to free it from scaling to place two Sacres two Drakes upon everie platform this Fortification being so provided will be of great defence and very offensive to the assaylants because the halfe Moones flanke one another so well that none can approach the sides or the points of them without great danger of their lives but if the diametricall line of this Superficie were reduced lesse by one halfe or the scale of it brought from 30. yards to 15. yards it would have been of a great defence without Drakes or Sacres by the musket-shot onely But I have purposely set out the same so large to show how such great sides may be set out in the field for they are farre more difficult to set out uhen shorter demensions Now to set it out in the field you are to make choice of the Center and to drive in a stake then you are to have a line ready of 330. * This Line of three hundred and thirtie yards is the just Demi-Diagonall and Diametricall extent of the Line that is to set our the eight invvard Angles of this Superficie yards having at everie fiftie yards a loop fastened to it of one colour and another loop of another colour fastened to it at everie hundred yards then you are to stand at the Center-stake and to turne your selfe full South after you have set out with your Sea-compasse as neare as you can to that distance of the line the South North East and West points because the foure sides of your crosse are of necessity to be lined so then set the sight of your demi-circle upon the ray of 55. degrees and wind the ray of your circle first on the left hand and let the man with the line fasten the one end of it to the Center-stake and follow with the other end of the line the ray of your demi-circle and when he is one hundred yards distance from you
and just against you and the ray of your demi-circle let the other man that carrieth the stakes drive in a stake at his feet and twift the line once or twice about the stake observing alwaies to make the line to come to be strained againe on that very side * In sides that are above one hundred yards that require above tvvo stakes you are carefully to observe to vvind the Line upon the stakes all of a side to prevent breaks that he first twisted the same to avoid breakes because the thicknesse of a stake of two inches thick will cause a great break in the extent of three hundred yards that being done let him follow still the ray of your demi-circle and when he is another hundred yards distant from the last stake and two hundred yards from you but just against you and the ray of your demi-circle let the man with stakes drive in a second stake at his feet and winde the line about the stake â—he did before then let him go forward and straine still the line till he be a hundred yards more from the second stake and when he is just against you and the ray of your demi-circle let the man with stakes drive the third stake at his feet and having twisted the line about that stake as he did before let the man with the line go forward 30. yards and when he is just against you and the ray of the demi-circle let the man with stakes drive in the fourth stake at his feet and betweene these foure stakes there will be 330. yards and the last stake will represent the South-East inward Angle of the Crosse then you are to wind the ray of your demi-circle on the right hand and to set out after the verie same manner the South-West inward Angle and having driven in foure stakes as before you are to set out the other six Angles after the verie same manner as you have done these two and when the eight Angles are set out thus and stakes driven in them all then remove the line of three hundred thirtie yards and fasten another line to the Center-stake of 250. * The extent of the Demi-Diametricall and Diagonall Line from the Center to the vtmost point of the Hasse Moone is 500 yards yards and straine it South-East diagonall wise this line being the just moytie of the demi-diogonall and diametricall line from the Center-stake to the utmost points of the eight halfe Moones and at the end of it drive in a stake and this stake represents the Center of the South-East halfe Moon then remove the line from the Center-stake and fasten the same to the last stake and straine it againe diagnail-wife and that stake will reprsent the utmost point of the South-East halfe Moone then set out after the verie same manner the other seven Centers and utmost points of the halfe Moones Now because-the sides or faces of your halfe Moones are not equall eight of them being 250. yards a piece and the other eight but 210 yards a piece you are to set out the eight longest first by fastening a line of 250 yards one after another to the foure stakes that represents the foure ends of the two diametricall lines of the prickt Square demonstrated in this Plate and to straine this line eight times one after another to the utmost Angle stakes that represent the utmost points of the halfe Moones and as you straine it fasten the same to the stakes as neare as you can to the ground that the Pioneers may trace that side or face of the halfe Moone before you remove the line to another side and one side being set out and traced set out and trace all the other seven sides after this verie manner Then you are to remove this line of 250. yards and to fasten another line of 210. yards to the foure diagonall inward Angles Center stake that are just oposite to the Angles of the prickt Square demonstrated in this Plate to set out the eight shorter sides or faces of the halfe Moones after the very same manner as you did set out the longer sides or faces and these being also set out and traced the superficie of this Fortification will be perfected then you are to set out the dikes according to the demensions described in Chapter 17. and when the inward Works are finished then you are to erect the Counterscarp with the earth that is taken out of the small dike called La Cunnette CHAP. XX. Of the Fortifications of the Faralograme fortified by Avant-guards demonstrated in Plate 14. THe broad side of this Paralograme is of 900 yards and the end side of it of 450 yards and all the circumference of it 2700 yards that is an English mile and three fifth parts of a mile for her continent I will not stand upon because it is not of a convenient forme to erect a new garrison but onely fit to fortifie some market towne if need should require of which form there are many in this Kingdome most of them being as long againe as they are broad Yet let the Reader observe that incase he be required to fortifie a towne that may be reduced to this forme that hath her broad side of 700 yards and her end side of 350 yards that he may boldly undertake to fortifie the same after this manner so he divide his end into five parts and his broad side into ten parts and doth reduce the rest of the demensions of the faces brests flanks courtines and line of defence after the proportions of his sides for then the dimensions of such a fortifiation will be more complete then this and altogether defensible by the musket shot But I have set out this so on purpose to shew what may be done when men are tied by the extent of a place and inforced to omit to erect foure Avant-guards lesse then they should to avoid charges The Angle of the Center of her broad side is of 135 degrees and of her end side of 45 degrees This is the most frugall way that can be invented to fortifie a long town of so large an extent as this is for it is almost a mile and three quarters in the circumference her end side individed into five parts two of which are allowed for the brest of the two end Avant-guards that contain 90 yards apeece and the courtine 270 yards her broad side is divided into ten equall parts two of which are allowed for the brest of the Avant-guards that are of 90 yards a peece uniforme with the end of the Avant-guards the foure Angle Courtines are longer then the middle Courtine by 120 yards because of the addition of the long Flank to everie one of them that extend themselves into the field 120 yards more then the vtmost angles of the Paralog rame the end and the middle Courtines are defensible by the Musket-shot because they are between two Flanks and also because the Line of defence of the faces of
yards to every one of the stakes that represent the beginning of the long flank and to strain the same into the field upon a Diagonal line taken from the midst of the Courtine or side opposite to it and at the end of the line knock in a stake and six of these stakes will represent all the utmost parts of the long flank and set out the sides of them that are to be traced as you set them out then fasten a line of fifty yards to every inward stake that represents the inward parts of the brest and the beginning of the short flank and straine the same into the field parallel with the line of the long flank and at the end of a line knock in a stake and these six stakes will bound and set out all the short flanks that are to be also traced as you remove the line from one stake to another Then you are to fasten a line of one hundred and threescore yards to every one of the middle stakes of the side and to strain and fasten the â—â—me one after another to the utmost stakes that represent the Angles or Points of the Avant Guards and they will set out all the faces of the Avant Guards and the lines of defence for they will out the line of the short flanks and end at the point of the long flanks and these faces are also to be traced before you remove this line from one stake to another and these being all traced you are to set out all the ditches according to the dimensions described in the 17 chap. of this abstract And when all the ditches and inward works are finished you are to set out the small ditch called La cunette out of the great ditch and with the earth of it to erect the brest-work of the Contre escarpe as it is described in chap. 17. Here followeth the Itchnographie of this method of Fortification but specially of the fortifications of this equilaterall Triangle The letter A. represents the Market place that containes in extent one hundred yards on every side B. Represents the brest of the Avant guards that are in this figure out 65 yards bread C. Represents the Courtines that are in this figure but 130. yards D. Represents the ditches that are 10 yards broad and 5 yards deep besides the small ditch called La cunette that is 16 foot broad and nine foot deep L. F. Represents the long flanks that are 100 yards long S. F. Represents the short flanks that are 50 yards long F. Represents the faces of the Avant guards that are in extent 100 yards G. Represents the broad street that goes round about the Rampiars and from the Rampiars to the Market place that are to be 30 foot broad H. Represents the places for the lodgings and the small streets that are to be 15 foot broad I. Represents the middle of the South Courtine where the gate and the draw-bridge is to be placed K. Represents the brest-works with his five foot-steps that is 34 foot in the bottome with the five foot-steps and twenty foot at top 12 foot high within side and 9 foot without side with a slope at top from twelve to nine that is a yard the five foot-steps are two foot broad and eighteen inches high apiece CHAP. XXII Of the Fortifications of the square fortified by Avant Guards and Out-Guards demonstrated in Plate 16. THe foure sides of this square containes 400 yards apiece and by consequence the circumference of it is of 1600 yards that is almost an English mile the Angle of his Center is of 90 degrees I will omit his continent for it is fitter to fortifie a compact Market town that may be reduced to this form then for a Fort it is to be set out after the manner as hath been described in Plate 10. And therefore I will only here insert some directions how you are to set out the Avant Guards and Out-Guards by which it is fortified The square being set out and traced you are to knock four stakes in the midst of the foure sides of it then you are to fasten a line one after another to these foure stakes of 125 yards and to strain the same upon a strait perpendicular line from the Center stake 125 yards into the field and at every end of the line to knock in a stake and these foure stakes will represent the middle of the faces of the foure Avant Guards then you are to fasten a line of 41 yards â…” to the very same stakes whereon the line of 100 yards was fastned to that is to be removed and put by and this line of 41 yards and â…” is to be strained first on the right hand and then on the left hand upon the traced sides of the squares and at every end of the line you are to knock a stake and having done so to all the four sides one after another these eight stakes will represent the breadth of the brest of the foure Avant-Guards that is of 83 yards â…“ for the Avant Guards are to be one third part longer then they are broad then you are to fasten to every one of these last stakes the former line of one hundred yards one after another and to straine the same paralel wise to the stakes that represent the middle of the face of the Avant Guards and at the end of every line you are to knock a stake and to trace that flanke of the Avant Guards before you remove the line to the other flanks stake and having done so round and knockt in eight stakes all the flanks will be set out and traced then you are to remove the line of 100 yards and lay it by and to fasten the former line of 41 yards 1 5. to the utmost middle stakes that represent the middle of the faces of the Avant Guards and to straine and fasten the same first to the right hand stake and then to the left hand stake that represents the utmost Angles of the Avant Guards but before you wind the line from the right hand to the left hand stake have that moity of the face of the Avant Guard traced then wind the line on the left hand and trace the other moity of the face and as you have set out and traced that face of the Avant Guard doe all the rest after this manner which being done your foure Avant Guards will be perfectly fet out and traced Then you are to set out all your ditches after the same dimensions described in chap. 17. and to cast all the earth inward to erect your brest-works and their foot-steps of that height and breadth mentioned in the said Chapter And when all the ditches brest-works and foot-steps are finished then you are to set out the small ditch called La cunette out of the great ditch end with the earth that is taken from it you are to erect the brest-work with the foot-step of it of your Contre escarpe foure yards beyond the brim of
orim of the great ditch foure yards observing the rules and dimensions described in chap. 17. and also five places of twelve foot apiece to be left open in the brest-work of the Contre escarpe to set five Turn-Pikes right against these five Halfe-moones here demonstrated which Halfe-moones you are to set out after your Contre escarpe brest-work is finished placing the open side of them within 16 foot distance of the slope of your Contre escarpe that there may be a cleare passage for horse and foot to come to the Halfe-moones without spoyling of the slope of the Contre escarpe that the French call glasis The five Out-guards of this figure are five Halfe-moones that have one side longer than the other by twenty yards * And this must of necessity be observed that the Ling side of the Halt-moones may cover the slanks of the Avant Guards the long side is of 80 yards and the short side of 60 yards their ditch is to be nine foot broad and fix foot deep their brest-work is to be 9 foot broad in the botteme with the foot-step and six foot thick at top having a foot slope and their height six foot from the ground and foure foot and a halfe from the footstep The gate and draw-bridge of this Fort is to be in the middle of the South side that it may be defended with the South-West flank and covered with the South Halfe-moon marked with the letter A. CHAP. XXIV Of the Fortification of the Demi-Sexagon fortified by Avant Guards and Out-guards demonstrated in Plate 18. THis Sexagon is of a large extent for her sides are of 800 yards apiece and by consequence her cucumference is of 4800 yards that is almost two English miles and a halfe and therefore fitter to fortifie a good Corporation then for a Citadell or Fort the Angle of her Center is of 60 degrees And the same directions that were given you for to set out the Sexagon demonstrated in Plate 12. fortified by bastions with orillons will suffice with the observations contained in chap. 19. viz. to knock in stakes at every hundred yards when sides or Diametricall or Diagonall lines exceed 250 yards The Superficie of this Sexagon being then set out and fully traced as it hath been showne in the foresaid Plate you are to divide every one of the Bases into three equall parts that will be of 266 yards and â…” apiece and to knock in a stake at every division then you are to fasten a line to the two inward stakes one after another of 60 * 60 Yards is the just moity of the brest of the Avant Guards yards and to strain the same first on the right hand and upon the side traced and the end of the line you are to knock in a stake then you are to winde the said line about on the left hand and to strain the same upon a strait line upon the sidetraced and at the end of the line you are to knock in a stake then you are to remove the line and to fasten the same to the other in ward stake of that side and to doe as you did before and to knock in two stakes at the end of the line and these foure stakes represent the breadth * That is of 120 Yards broad of the two brests of these two Avant Guards and the middle stake represents the Center of the Avant Guards Then you are to set out the brest of the other ten Avant Guards of the other five sides after the very same manner as you did these last And that being done you are to fasten a line of 120 yards to every one of the exteriour stakes that represent the breadth of the brests of the Avant Gnards and to strain the same into the field upon a strait Diagonall line derived from the Center stake of the Sexagon that you are to guide by the sight of your Demi-circle standing at the Center stake while the man that carrieth your lines straineth the foresaid line into the field and at the end of it the man that carrieth your stakes is to knock in a stake and this stake represents the utmost Point of the long flank of your first Avant Guard And as you have set out this long * Note and observe This course is to be taken lecause the Demi Diagonal line of this Sexagon from the Center stake to the utmost Point of the long flank is of 680 yards that is too long a line to be conveniently strained flank set out the other eleven that remaine And that being done you are to fasten a line of 60 yards to the inward stake of that Avant Guard that represents the breadth of the brest of it and to strain the same into the field parallel-wise to that of the long flank and at the end of it you are to knock in a stake and this stake represents the utmost point of the short flank of that Avant Guard But observe * These long flanks are of 120 yards apiece to trace the long and short flanks before you remove the line to another flake to avoid mistake And as you have set out this short * These short flanks are of 60 yards apiece flank set out the eleven that remain That being done knock fix stakes in the middle of the six sides of this S xigon then you are to fasten a line to every one of them one ofter another of 240 yards and to strain and fasten the same first on the right hand stake that represents the utmost Point of the long flanks and this line will cut the end of the line of the short flank and set out the face of that Avant Guard and withall doth represent the line of defence * The line of defence is taken from the midst of the Courtine and the extent of it in this figure is oâ— 240 yards And the extent or all the Courtines are oâ— 186 yards â…“ aprece but before you remove this line you are to trace the face of this Avant Guard that extends it selce from the stake of the short flank to the stake that represents the utmost Point of the long flank Then you are to wind the very same line about and to fasten it to the left hand inward stake that represents the utmost Point of that long flank and to doe as you did before to the other on the right hand and then the two Avant Guards of that fide of the Sexagon will be perfected and as you have done this side doe the other five sides after the very same manner When the twelve Aven Guards are thus set out and traced you are to set out all the ditches of it after the very same dimensions set downe in chap. 17. Casting all the earth inward to crect the brest-works and their five foot-steps of that height breadth and thicknesse described in the aforesaid chapter And when they are all finished you are then to set out the small ditch
brest-works broad and eighteen inches high The slope * the slope of brest-work walls of the in-side wall is to be but a foot in six foot because the foot-steps serve instead of buttresses to that inward side but the step of the out-side wall is to be a foot in three and a water table is to be left of eight inches broad if the earth be good between the brim of the ditch and the turfe of the out-side wall if the ground be sandy or a tunning clay it is to bee eighteen inches broad notwithstanding the chat of ignorant men The bottome or foundation of the brest-work is to be thirty five foot in the bottome with the five foot-steps and twenty foot broad at top that it may be of Cannon proofe and it is to have a slope towards the ditch of three foot and for that purpose Of the water table of the brest-works Of the slope of the top of the brest works and of their thicknesse the out-side wall is but nine foot and the inward twelve foot that the slope may be from twelve to nine And observe once for all that all the Angles of this method where you erect Platformes are to have another brest-work fix foot higher then the rest in which you make your Port-holes and that this brest-work is to have a * Of the frize of the Platform frise when it is twelve foot from the ground made of wooden pikes sharpe at one and of six foot long and foure inches broad and three inches thick that are to be placed eight inches distant one from another jetting three foot over the ditch and running a yard into the brast-works These high brest-works are at every foure course of turfe to be laid with brush or bavin wood well rammed with the carth if the crectors intend they should be of continuance Having so clearly expressed the dimensions of this method of Fortification I shall not need hereafter to speak any thing at all of them because I have observed in these five Superficies following these proportions related in their Sides Courtines Flanks Brests Faces Gorges and Lines of defence and so I come to the method it selfe CHAP. XXVI Of the Fortifications of the Octogon fortified by small Flankers demonstrated in Plate 19. THe eight sides of this Octogon containes two hundred and fifty yards apiece and by consequence the circumference of it is of two thousand yards that is an English mile and the â…• part of a mile The Angle of her Center is of 45 degrees it is to be set out in the field as the Sexagon by the Demi-cirle and Lines as it is described in Plate twelve and Chapter 15. I will therefore only give you some directions how to set out the small flankers because it is a new method of Fortification that wee have not as yet given you any directions for When the Superficie of this Octogon hath been set out and fully traced after the manner you were directed to set out the Sexagon you are to divide all the sides of it in two equall parts and to knock in a stake * From these middle stakes is the line of defence drawn that is in this figure of 150. yards and the Courtine 200 yards in every one of their divisions then you are to fasten a line of twenty five yards to every one of the eight Angle stakes one after another and to strain that line first on the right hand and then at the left hand upon a strait line upon the sides traced on the left and right hand of that stake and at the end of the line you are to knock a stake and these two stakes will represent the two Demi-Gorges * The whole Gorge of the flankers is to be 50 yards of that flanker then remove your line to another Angle stake and doe as you did before till you have set out all the demi-gorges after that manner Then set by that line and fasten another line of fiftie * The Line of fiftie yards represent the distance from the center to the point of the flanker yards to every angle-stake of the sides and straine the same into the field upon a strait diagonall line standing at the center-stake with your demi-circle to guide the same because the demi-diagonall line from the center-stake to the utmost point of the flank is of 380 yards in this Figure and therefore too long to be strained conveniently and at the end of this line of fiftie yards drive in a stake and this stake will represent the utmost angle or point of the said flanker and as you have done this set out the other seven angles of the flankers after this verie manner then you are to fasten a Line of 28 * 28 yards is the extent of the slope flank yards to everie one of the sixteene stakes one after another that represent the Demi-Gorges of the Flankers and to straine it three yards more slope then upon a strait perpendicularie Line towards the other Flanker of that side of the Octogon and at the end of th Line you are to drive in a stake The reason why you straine this Line three yards more slope then strait is to preserve the Flankes from the Enemies batterie that are otherwise too much exposed to be ruinated by it when the Line of the Flank is drawne upon a strait perpendicularie Line you are also to observe that the strait perpendicularie Line of the Flank is but five and twentie yards and that these three yards are added to it that the Flanks may be three yards more slope then strait because a slope line in five and twentie yards extent comes to be three yards longer then a strait And as you have set out this Flank set out the other sixteen after this manner and drive in stakes in them all that being done you are to fasten a Line of 150 yards to the middle stake of every side and straine it first on the right hand and then on the left and as you straine it make it touch the Flank-stake and fasten it to the stakes that represent the vtmost point of your Flankers and this Line doth represent the Line of defence and the * The face of the flanker is to be 25 yards besides the three yards added to thicken the Angle of the shoulder face of that Flanker and before you remove the Line have the face traced by the Pioniers and this face extends it selfe from the Flank-stake to the stake that represents the vtmost angle of the Flanker And as you have set out this face-stake set out all the fifteene other and they being set out and traced your eight Flankers will be perfected Then you are to set out all your dikes after the dimensions described in Chap. 25. And these directions for the setting out of the Flankers of all the other ensuing Superficies shall suffice once for all to avoyd repetitions This Octogon thus set out and
the proportions of her Flankers thus observed it will produce a strong and a verie regularie Fortification fit to fortifie a faire Market-Towne of a mile and a quarter circumference that may be reduced to this forme CHAP. XXVII Of the Fortifications of the Paralograme fortified by small Flankers demonstrated in Plate 20. THis Paralograme fortified by 18. Flankers hath his broad sides of 1500. yards and his end sides of 750. yards for a long Paralograme is to be as long againe as broad and a Demi-Paralograme one third part longer then it is broad his Circumference is of 4500 yards that is of two English miles and one third part of a mile a large Circumference for so small a Continent for it containes from out to out but 1125000. square yards whereas if there had been 750. yards added to his bredth to reduce it to a Square it had contained 2250000. square yards that is just as much againe so much availeth in the Art of Fortification to make choice of compact Townes for a Garrison when a place of three miles and two fifth parts of a mile Circumference can be fortified for one quarter part more of charges then a Towne that is smaller by halfe and all because of her ill forme yet because there are many Townes in this Kingdome of this forme I have inserted two different kind of Fortifieations for them in this Abstract for his Angles if you take the Angle of the Center of the end side from the Center of one of the two Cirdes of which it is composed you shall find it of 90 degrees but if you take it from the Center of the Paralograme it self you will find it is but of 45. degrees and the Angle of his broad sides is of 135. degrees a very open and obtus Angle This Superficie is easie to be set out upon paper as you may see by this Figure but because it is more difficult to set out in the field when the broad sides of it are of so large an extent I will here add some observations to my former direction given in Plate 14. The best and the most speedy way to set out so large a Paralograme in the field is to make choice of your Center and to drive in a stake and to fasten a line to it of 375. * This line of 375 yards is the fourth part of the diametricall line of the long side of the Paralograme yards and to straine it full East and at the end of it to drive in a stake then you are to wind that line about and to straine it full West upon a strait line and at the end of the line drive in a stake these two last stakes will represent the two Centers of the two circles from which this Paralagrame is composed Then you are to set the sight of your demi-circle upon the ray of 90. degrees and to stand at the East circle stake turning your face full East winding your demi-circle on the right hand to set out the South-East Angle the man that carieth your lines following the ray of your demi-circle till he be five hundred and thirtie * The ray of this line of 530 yards is the diagonall line from the center of that circle to the angle of the Paralograme yards and just against you and upon the ray then your man that carrieth the stakes is to drive in a stake at his feet and with a line of 100. yards that they are to straine between them let them cast with it if there be just 530. yards from that stake to the Center stake you stand at if there be just so much then is that Angle perfectly set out but if the distance begreater or lesse they are to remove the stake and amend it you guiding them by the sight of your demi-circle then you are to wind your demi-circle on the left hand to set out as you did this the North-East Angle and that being set out and a stake driven in you are to remove your selfe from that East circle Center stake to go to the West circle stake and to set out with your demi-circle the South-West and North-West Angles after the very same manner as you did the former and two stakes being driven in them the foure Angles of the Paralograme will be perfected Then you are to stand with your demi-circle at the middle Center stake of the whole Paralograme and after you have set the sight of it upon the ray of 135. degrees you are to turne your selfe full South and to try whether your South-East and North-East Angle stakes are just of 135. degrees which being so that broad side is perfected then returne your selfe full North and try whether the North-East and the North-West Angle stakes are just upon 135. degrees which if they be then is the Paralograme perfect in all his foure Angles then you are to stand at every Angle stake one after another and to fasten a line to them of 250. * This Line of 250 yards is the distance that is to be betvveen the center of one flanker to the other center yards and the man with the lines is to straine the same from one Angle stake to another drive in at everie end of the line a stake till he hath gone round guiding his stakes with the sight of your demi-circle that all the stakes may be upon a perfect strait line then you are to fasten lines as neare the ground as may be to these stakes and to set many Pioniers to trace out the whole Superficie of this Paralograme and that being done you are to set out all the 18 Flankers one after another as you were directed in the last Chapter CHAP. XXVIII Of the Fortifications of the Square fortified by small Flankers demonstrated by a Demi-Square in Plate 21. THis Square fortified by twentie foure small Flanks if of 6000 yards circumference that is three English miles and two fifth parts of a mile It is verie convenient to fortifie a great Corporation Towne that may be redeced to that forme his continent is great because of the soliditie of his body for it contains 2250000 square yards The Angle of his Center is of 90 degrees and it is to be set out in the field after the verie same manner of the end-sides of the Paralograme described in the last Chapter and his Flankers are to be set out according to the directions given in Chapt. 26. and therefore to avoyd repetitions I will omit to speake of these things and will only set forth what number of Ordnance Foot-Souldiers and Horse-men will be required to defend a place thus fortified against an Army of twentie thousand men the circumference of it being so great as it is 1 It requires to be provided with fortie eight Peeces of Ordnance of all sorts for there cannot be lesse then two upon everie Flanker six Demi-Cannons to dismount the Assailants Cannons if they erect their batteries twelve Demi-Culverins to hinder
of his garrison and to repaire the Workes of it in due and in convenient time not delaying from day to day but pressing the effecting of it to the utmost of his power although there be no likelihood of a siege for when an enemy is at hand it is too late to go about such imployments neither is it a sufficient excuse for a Governour to say who would have thought the enemy had a design upon this place 7 He is to be acquainted with all the principles of the Mathematiques and especially with the essentiall parts of the Art of Fortification that he may be able to controle the ignorance of selfe-conceited men that take upon them to set out ridiculous and destructive workes He is to be skilfull in the Art of fortification and assailing improper for the defence of the place where they live with whom he is by no meanes to combine as some do for private or politike respects because such deformed and ill flanked Works indenger his owne life and will one time or other blemish his honour and reputation and therfore he is to be skillfull in the Art of Fortification and assayling For if the towne be lost by these defects the blame will onely be laid upon him and not upon the contrivers of these works now because the safety of the Towne is intrusted to his care hee ought not to indure that ignorant Shop-keepers bee chosen Sub-Committees of the Workes of a Garrison for these places belong more properly to the wise and prudent Gentlemen of the County and to the most experienced Officers of the Garrison then to such men as these that will precipitate their owne ruine rather then they will be crost in their destructive waies 8 He is to dispose of all the Functions of Warre He is to dispose of all the functions of vvar and not to meddle vvith politike affaires and to command absolutely over Horse and Foot or otherwise he is but a titularie Governour and it is no wonder if divers of our Counties are plundered daily by the incursions of the Enemies Garrisons since he that should send out parties to curb and restraine these disorders hath his hands tied In all things without order nothing can be successefull for a Governour to anticipate upon the prerogative of Committees and be medling in civill and politike affaires it is to go against order or for Committees to anticipate and be medling with those things that belong properly to a Governours place as to command over a Colonell of Horse Committees are not to meddle in vvarlike affaires onely in civill and politique affaires and to send out parties at randome it is against order and against the rules of war for Committees should not be answerable for the defects errours and omissions of martiall designes nor the Governour be answerable for any dismeanour committed or dutie omitted in civill or politike affaires but everie one should be answerable for such things that belong to their places Therefore if a Countie bee daily molested by the incursions of the Enemies Garrisons the Governour should be answerable to the State for his neglect and carelesnesse in this case because the protection and preservation of the whole Countie depends upon his charge On the other side if the men of war of such a Countie be not duly paid and notwithstanding the Countie is oppressed the Committees are answerable to the State for this omission and dismeniour But by the common disorder there is in the greater part of our Counties betweene the Committees and the Governours of the head Garrisons by the anticipation they do upon one anothers charges the State knowes not whom to call to accompt for divers grosse abuses that are daily committed under which divers Counties groane and become desolate In a word there is no wisdome nor policie to suffer the Committee to manage or to dispose of the designes of war or to suffer the Governours to raise contributions for their owne Garrisons pay or to meddle in any manner of way in civill or politike affaires except it be to decide some differences that may befall between some Souldiers and some of the Inhabitants 9 He is to observe an austere militarie discipline and to suffer none of the Inhabitants to be wronged and abused by any of the Souldiers of the Garrison for if hee give them an inch this way they will take a foot and of the two hee is rather to take the part of the Inhabitants then of the Souldiers because the Souldiers are most commonly the first Aggressours He is to be austere in the Militarie Discipline and just in his judgment Yet for feare this rule should not be generall hee is to examine the case and to distribute justice impartially Hee is also to traine his Souldiers everie week and withall to command the Sargeant of everie Company to instruct them daily when their Company enters in guard and especially the youngest and rawest Souldiers how they should manage their muskets and pikes that they may be the more perfect when they traine before him in the handling of their Armes And for the Horse when they are at home once a fortnight he is to appoint their Colonel a place in the field near the walls where he is to be himselfe to see them exercise by dividing their Regiment in two equal parts He is to be carefull and present at all militarie exercises the Colonel commanding one partie and the Lievtenant-Colonell the other the one being the Assailants and the other the Defendents And in all these exercises the Governour is to take exact notice both of the Horse and Foot that are defective in their horses armes and apparell and to censure them severely for the first time and to panish them the next training day if these defects be not amended 10 He is to be active and vigilant that Centinells be placed and relieved punctually at their hours and to over-see the Courts of Guards everie night not relying altogether upon his Major for two eye-witnesses are better then one the French whose Garrisons are not ordinarily above one English mile and halfe circumference Of the number of the Courts of Guard content themselves with six Courts of Guards the greatest in the Market-place of 120. men foure more at the foure gates of 60. men a piece and one before the Governours lodging of twenty men and by this calculation there is to be in that Garrison 1140. Foot-souldiers of which 380. are so enter into guard every night that they might have two dayes respit in three Their Centinells or Centries are relieved in the night time everie houre and in the day time every two houres and they place at everie 200. yards distance a Centry Of the number of Sentinells if their Garrisons be fortified by Bastions they place besides the above-said Centries three upon everie Bastion one at the point of it and two at the two ends of the faces next to the flanks
the Avant-guards is taken from the middle of the Courtine whereby the Line of defence cometh to be from two hundred and fortie to two hundred and fiftie yards but the long Angle Flanks cannot sufficiently be defended by the Musket-shot alone without foure Drakes and foure Sacres one Sacre and one Drake mounted upon everie one of the long Flanks and with them this Fortification will be of great defence The short Flanks are of 60 yards a peece and the faces of the Avant-guards of 120 yards a peece uniforme with the long Flanks To set out this Superficie in the field you are to knock a stake in your Center and to stand close to it and to set your selfe East after you have set the light of your Demi-circle upon the ray of 45. degrees to set out the East and by South and the East and by North Angles as you have been directed for merly and then to turn your selfe West and to set out the West and by South and the West and by North Angles and these bâ—ing rightly set out and stakes knockt in them your two broad sines North and South cannot be amisse But if it be an erected Town take the just length on the broad and end-side of it with a line of 100 yards and set out your Angles with the Demi-circle accordingly and divide your end-side into five and your broad side into ten equall parts and then set out your Avant Guards thereafter CHAP. XXI Of the Fortifications of the Equilateral Triangle fortified by Avant Guards demonstrated in Plate 15. ALL the sides of this Equilateral Triangle are equall and contain 520 yards apiece so that her circumference is of 1560 yards that is an English mile wanting 64 foot the Angle other Center is of 60 degrees I omit her continent because of her large extent that is fitter to fortifie a well compacted town that may be reduced to this form then for a new Fort. Her sides are divided into eight equall parts two of which are allowed for the two brests of the Avant Guards that contain 65 yards apiece and the other six pares are divided equally for the three Courtines that containe 130 yards apiece Her long flanks are 100 yards apiece and her short flanks of 50 yards apiece and the faces of her Avant Guards are uniform to her long flanks whereby they are also of 100 yards apiece And by these dimensions it is apparent that this Superficie is a compact and compleat Fortification because all her Faces Flanks Courtines and Angles can be easily defended by the Musquet shot her line of defence is taken from the middle of the Courtine and by this meanes of 160 yards Yet let me inform the reader that if he had occasion to fortifie a town that might be reduced into this Triangle for me although her sides were from 520 yards apiece to 750 yards apiece that he may boldly fortifie the same after this manner so he divide his three sides into 8 equall parts and doth preportion his Flanks Faces Brests Courtines and line of defence after this extent for notwithstanding this addition of 230 yards to every side of the Triangle all the dimensions of his fortification will be defensible by the Musquet shot Now to set out this Superficie in the field you are to make choice of your Center and to knock in a stake and after to set the sight of your Demi-circle upon 60 degrees and to follow the same directions given you in plate 9 for the setting out of a Triangle fortified by bastions And because these sides are as long againe as they were I referre you to the directions given you in chap. 19. for the straining of a long line by knocking in at every hundred yards of it a stake But if it be an erected town that you are to fortifie after this manner goe up to the end of the town where you intend the North Angle of the Triangle shall be and turn your face South and with your Demi-circle when the sight of it is set upon the ray of 60 degrees set out the South-East Angle of the Triangle cauâ—ing the man with lines to strain a line from the North Anglestake where you stand to follow the ray of your Demi-circle the man with stak s knocking at every hundred yards a stake and by this plurality of stakes you may lengthen your line as you please twisting the same alwayes of one and the same side of the stake till he come to the just distance of your side of the Triangle whether it be five hundred and twenty yards or 720 yards and at the side of the distance knock in a stake and that last stake will represent the South-East Angle of the Triangle then set out after this manner the South-East Angle and knock in a stake at the same distance that it may represent the South-West Angle then measure with a line of 100 yards whether the distance between the South-East and South-West Angle stake is equall with the two other sides and finding it to be equall then is the Superficie of the Triangle perfected that you are presently to have traced by many Pioniers but if there be any errour you are to amend the same by your Demi-circle and your lines The Superficie of the Triangle being traced you are to divide the sides into 8 parts and at every division to knock 8 stakes knocking in also a stake in the middle of every side for it will serve to set out the faces of the Avant guards and the lines of defence allowing two parts to every Courtine and two parts to the two brests of the Avant guards and at every third stake of every side you are to fasten a line of 32 yards and ½ and to strain it first on the right hand along the side traced and at the side of the line you are to knock in a stake and then you are to wind the same line on the left hand and to straine it along the side traced and at the end of the line you are to knock in a stake and these two stakes will represent the breadth of the brest of the Avant Guards the exteriour stake toward the Angles of the Triangle representing the beginning of the long flank and the inward stake toward the middle of the side representing the beginning of the short flank and as you have set out this first brest of the Avant Guard you are to set out the other five after the same manner That being done you are to fasten a line of one hundred * If you can strain a line from the middle stake of the side of 320 yards that is the just distance from the side opposite to every long flank it would â—e the better if not this way will serve turn so you stand with your Demi-circle At the middle stake of the side â—o guide the end of the line of 100 yards to the very out most Point or Angle of the Avant Guard