the Place of an equal bigness to the Line DE that is to say of five Fathoms as KI to the end that you may have the Brisure where you may place the piece of Cannon that points towards the Half Moon cannot be batter'd from the Field because it is as it were covered by the Ravelin Lastly To make the Rounding of the Flank retir'd take the Distance KE between the Points of the Compass and make Sections toward the Moat in L from whence afterwards draw the Arch from K to F. It cannot be said but that these Orillons are very good for these Roundings give less advantage to the Enemies Cannon and enlarge the room as well for placing the Cannon as for the Musketeers If you object That the Distance from that part where the Enemy may pass the Moat is too great I answer That the principal Defence of the Small Shot to hinder the Passage of the Moat consists in the Tenâ—ille where you may set a Body of Musketeers to fire continually Upon this Method Monsieur de Clermont observes That the Orillon of the Square would be too little if you allow it no more than the Third Part of the Flank as to the Polygons and therefore he requires Two Fifth Parts of the same Flank for the Orillon See the Plate P. Fig. XXII at the end of the Third Book CHAP. V. Of the Curtain IN regard that the Curtain ought to cover the greatest part of a Work it is requisite that it should be of a reasonable Length that is to say that it should never be shorter than Sixty Fathoms and never longer than an Hundred Mâ—rshâ—user allows it 72 Fathoms and Freittag as much Goldman would have the Length to be of 96 Fathoms Anthony de Ville 100. Tieu makes it 74 Fathoms in Length Himsel 84. Monsieur de Clermont allows it Three Fifth Parts of a Polygon The Count de Pagan 60 Fathoms Monsieur de Vauban forms it according to the Plurality of the Bastions As you may see Lib. 3 c. 17. As to the Figure of the Curtains there are some Engineers who will have them â—o be as is mark'd at the Letter A of which the Construction is such See the Plate P. Fig. XXII at the end of the third Book 1. Divide the Line AB into â— equal parts as AD DM NC and CB and take â— for the Demi-Gorge as BC AD. 2. Divide the same Line AB into three equal parts and take one for the Capital as BE Aâ— 3. Where these three Parts are marked as at R and G bring down from the Points R G two Perpendiculars of which seâ— each have the third part of the Capital Line for its length as RH and GI and then joyn H and I together by a Right Line 4. Make upon the Points D and C the Angle of the Curtain of 100 degrees and allow to the â—lank the length of the Demi-Gorge â—â— DP and CQ This being done joyn EQ and DP together to have the Faces The defects of the Curtain are 1. That it is too short 2. That the â—ortification takes up too much room 3. That it renders the Bastion too Acute Others there are that form an Angle without side as that which is marked with the Letter B. The Construction of which is after this manner 1. Divide the Line AB into five equal parts as AC CD DE EF and FB 2. Divide the first Line AB into three equal parts and allow one for the Capital as AI and BK then join HI and BK together to gain the Faces 3. Divide the Curtain CF into two equal parts and upâ—n the middle marked with the Letter L erect a Perpendicular which has the half of the Face GK as LM 4. Draw from CF two streight Lines to the Point M and your Curtain will be made See the Plate P. Fig. XXIV â—â—hers make the Curtain of a Câ—rcular Figure withinâ—sâ—de like that which is marked C The Construction of which is as follows See the same Plate Fig. XXV Having observed what has been said touching the three first Points of the Preceding Curtain take the Extremities of the Curtain BC and make two Arches to cross or cuâ— one another underneath and from this Point of the Intersection draw an Arch from one end of the Curtain to the other Lastly There are others that form the Curtain of a Circular Figure without side like that which is mark'd D. The Construction of which is like to that which we have already describ'd only that here you make the Intersection above the Curtain in E From which Point you afterwards draw the Arch from one end of the Curtain to the other The Breast Curtains are those which are drawn streight out-right from one Flank to another See the same â—lank Pâ— at the end of the third Book Fig. XXVI CHAP. VI. Of the Parapet IN regard that this Work is raised to cover the Cannon and the Soldiers which defend the Place it must be allowed a reaâ—onable heighth and breadth Cellarius allows it six Feet in heighth with a Foot of sloping within sideâ— to the end the Soldiers may be able to stand the better when the Parapet is reared after that manner The heighth without side from the Cordâ—n ought not to be above four Feet because the â—loping which is made by those different Heights inward and outward gives the Soldier an easier view of the Covert-ways and the Moats that are before him As for the Thickness of the Parapet Monsieur Clermont allows it for the Basis the third part of the Basis of the Rampart The Count de Pagan makes it three Fathoms broad Of which opinion are several others as Goldman Frâ—ittag and Monsieur Vauban himself So that we may boldly say That the Thickness of the Parapet is good when it is not less than 18 Feet nor broader than 24. For being weaker the Parapet cannot long resist the force of the great Shot which would soon level it with the Earthâ— and being thicker it would hinder the Soldiers from the sight of the Moat and the Covert way If you would line the Parapet it must be allowed a little â—loaping that the Soldiers may have the better footing The best Lining of Parapets is with Turf As for the Earth or Mould which you are to make use of in erecting a Parapet it is very requisite to mix it with Withy Twigs or Brambles and to sow it with any Weeds that take a deep root to bind the Earth together so that the Cannon may not easily crumble it down Hay of Burgundy is also very good for this purpose in regard that there is no Plant that puts forth more or deeper Roots CHAP. VII Of the Banquets AT the foot of the Parapet upon the Plat-form are usually made two little Steps or small Banks of which the first is about two Feet broad Goldman makes it four Feet Frâ—ittag 3. the Count of Pagan 2. Monsieur Clermont the same and one Foot and
point G which touches the given Line only in K. 2. With the distance GK draw another Arch upon the given Line MN 3. The Line drawn by GN shall be parallel to the given Line HI III. To raise Perpendicular on a given Line from a given point 1. Take a distance from the given point what you please to the right as AB 2. Take the same distance to the lest as AC 3. Take BC and draw two Arches which intersect each other at D. 4. Joyn D and A together and you will have your Perpendicular IV. To raise a Perpendicular at the end of a given Line AB 1. Draw a Circle to the point B from the center C which may be taken at pleasure 2. From the point D where the Circle cuts the given Line draw a right Line through the Center C till it touches the Circle on the other side as at E. 3. Joyn E and B together and you will have your Perpendicular V. From a given point G to let fall a Perpendicular upon a given Line 1. Draw an Arch from the point G which may cut the given Line in two places as CD 2. From CD draw two Arches under the Line which shalâ— intersect each other at E. 3. Joyn E and G together and you will have your Perpendicular GF VI. To divide a given Line into two equal parts 1. From the points AB draw two Arches which shall intersect above the given Line at C and below it at D. 2. Joyn C and D together and you shall have your Line cut into two equal parts VII To divide a Line AB into several equal parts 1. Draw CD a Line at pleasure and mark as many parts as the given Line AB ought to have six for Example upon this Line as CE. 2. Take CE and draw two Arches which may intersect in F. 3. Draw all these six parts in F. 4. Take the given Line AB and lay it upon the Lines FE and FC as GH 5. Joyn GH together you will have your given Line AB divided into six equal parts VIII To describe an Angle equal to an Angle given 1. Let the given Angle be BAC 2. Draw the Arch ADE 3. Draw a Line IL and upon this Line an Arch with the distance AD as FG. 4. Set the distance DE upon the Arch FG as FH 5. Draw a right Line from the point I to the point H which will make an Angle equal to the given Angle IX To divide an Angle into two equal parts 1. Let the given Angle be BAC draw the Arch ADE 2. From the points DE draw two Arches which shall intersect each other at F. 3. The Line drawn from F to A will cut the Angle into two equal parts X. To draw a Circle through three given points ABC or to find the Center of a given Circle or to finish a Circle when there is but one part given 1. With the points AB make two Arches which shall intersect at D above and at E below the given points 2. Draw a right Line from the point D to G. 3. Do the same thing with BC so that they may intersect in FG. 4. Draw another right Line from F to G and there where this Line intersects the first as for instance at G you will find the Center by which you may draw the Circle through the three given points XI To make a Circle two three or four times bigger than the given â—ne c. 1. Divide the given Circle into four equal parts ABCD with the Center mark'd at E. 2. Take the distance AB and put it from E upon the Perpendicular as EF and with this distance draw a Circle as big again as that given 3. To make a Circle twice as big take AF and put it from E upon the first Perpendicular as EG and the distance EG will be the Semi-diameter of the demanded Circle 4. To make a Circle thrice as big put the distance AG upon the same Perpendicular as EH and the distance EH will be the Semi-diameter of the demanded Circle Thus you may enlarge a Circle for ever XII To make an Oval 1. Draw a Line and thereupon the Circle BAC 2. From C draw another Circle through B as CBD 3. Take care that these two Circles intersect each other as in EF. 4. From the point of intersection E draw right lines through BC which shall touch the two Circles in GH 5. From the point E draw an Arch from G to the point H. 6. Keep this distance and do the same thing from the other point of intersection F as IK and so your Oval will be compleat XIII To draw a Spiral Line 1. Upon a straight Line draw the Arch ABC 2. Take BC and fixing one point of the Compass upon B draw from the point C another Arch which shall touch the same Line in D. 3. Take the first Center A and draw another Arch from D that shall touch the line in E. 4. Return to the point B and from it as a Center draw from E another Arch to F. 5. Take A as a Center and draw an Arch from F to G and so on for ever XIV To divide a Circle into 360 equal parts 1. Divide a Circle into four equal parts as ABCD whose Center is E. 2. From A thro' E draw the Arch FG so also draw from B the Arch IH and from C draw and the third KL and at last from D draw the last Arch MN 3. Having by these Arches divided the Circle into twelve equal parts afterwards divide every one of these twelve into three other equal parts and then you will have thirty six equal parts 4. Divide afterwards every one of these thirty six into ten equal parts and your Circle will be divided into three hundred and sixty equal parts XVâ— To make an Equilateral Triangle Take a given line AB and from those two points draw two Arches which shall intersect at C from C draw two right lines to A and B these will make an Equilateral Triangle XVI To make a Triangle equal to a given One 1. Let the given Triangle be ABC draw a line at pleasure and mark thereupon the length AB as DE. 2. Take the distance BC and from the point E draw an Arch. 3. Take the distance AC and from D draw another Arch which shall intersect the first at F. 4. Joyn FE and FD together you will have a Triangle equal to the given one ABC XVII To divide a Triangle into several equal parts 1. Let ABC be the Triangle to be divided into five other Triangles first divide the longest side BC into five equal parts so that the fifth part marked at D may be joyned to A. 2. Divide the longest of the two other sides into four equal parts and let one of them marked G be joyned to D. 3. Divide the remaining part DC into three equal parts and joyn that marked F by a right Line to G. 4. Divide the
up It is furnished with some Sacks of Powder to which the Sawcedge is fix'd which answers to another Post to the end it may be Fiâ—'d without danger Fraises are pieces of Wood from 7 to 8 Foot long driven in almost half way into the Earth of the Rampart without side and a little below the Parapet they present their points somewhat sloping toward the Field and are made use of to prevent Deâ—erters and Surprizes G. Gabions are Baskets equally wide at top and bottom about four Foot in Diameter they are fill'd with Earth and usually plac'd upon Batteries and Parapets that have suffer'd very much and before other places to secure them from the Enemies Shot Gallery is a cover'd walk either of Earth or Turff The sides of it are made with Planks and Pillars and they are made use of in the Moat already fill'd with Fagots and Bavins to the end the Minor may approach safe to the Bastion Glacis is the Parapet of the Covert-way which looses it self insensibly in the Field The largest are the best Gorge is the entrance of the Platform of the Bastions and other Works It never ought to have a Parapet for fear the Enemy being Maâ—ter of it he should secure himself thereby from the shot of the Garison Granado a little hollow Globe fill'd with Powder to which there answers a little Fusee of Powder to set them on Fire they aâ—e used to Fire close and narrow Places or else to disorder the Ranks of the Soldiers Grand Demi Diameter is the Line compos'd of the Capital and the small Demi-Diameter of the Polygon Gazons are peices of fresh Earth covered with Grass about a Foot long and half a Foot thick cut in the form of a Wedge to line the Parapet and the Traverses of the Galleries H. Herisson a Beam with a great quantity of Nails having their points outward it is supported by a Pivot upon which it turns to stop up any passage instead of a Barrier Herse is a Lattice or Portcullice of great pieces of sharp-pointed Wood at the lower end sustained by a Cord fastened to a Moulinet which is cut in case of surprize to the end the Herse may fall and stop up the Passage of a Gate or other Entrance of a Fortress Horse-Shoe is a Work sometime round sometime oval bordered with a Parapet It is made to secure a Gate or to relieve an over-tedious Defence L. Line Capital is a Line drawn from the Angle of the Gorge to the Angle of the Bastion Line Cogrital is the Line drawn from the Angle of the Center to the Angle of the Bastion Line of Defence is that which is represented by the Discharge of the small Shot which uncovers the Face of one Bastion by razing it Line of Defence Fichant is the Line drawn from the common Point to the Curtin and from the Flank to the Flank'd Angle of the Bastion Line of Defence Razant is the Line drawn from the Capital Line of a Bastion to that part of the Curtin where the Defence begins to discover the Face of the same Bastion Lines of Communication are the Lines that run from one Work to another to stop the Fury of the Enemy Lines within-side are the Moats toward the Place to hinder Sallies Lines without-side are the Moats toward the Field to hinder Relief Lodgment of an Attack is a Work cast up in a dangerous Post to secure themselves against the Enemies Fireâ— This Lodgment is made of all the Materials that are capable to make Resistance To Line is nothing else but to environ a Rampart Parapet or Moat with a good Wall or good Turff M. Madrier is a thick Plank sufficient to cover the Mouth of a Petard and which is applyed with the Petard against the Places they would break This Term is also applied to several Flat Beams which are put at the bottom of a Moat to support the Wall Mantellet is one or several Planks joyn'd together and cover'd with Tin carried upon two Wheels which the Pioneers in a Siege drive before them to secure themselves against the small Shot Merlon is that part of the Paparet which is between the two Embrasures Mortier is a piece of great Cannon very short which is charged with Bombs Carcasses or Stones and is mounted upon a Carriage the Wheels of which are very low Moulinet is a cross of Wood which turns Horizontally upon a wooden Stake which stands at the side of the Barrier between the Bars of which the Footmen pass Moyenau a â—ort of small flat Bastions plac'd in the middle of an over long Curtain of which the Bastions that are at the Extremities are not well defended from the small shot by reason of their distance This Work is proper for the placing in it a Body of Musketters to Fire from all sides N. Nailing of Cannon the driving of a Nail by force into the Touch hole of a great Gun O. Orgues are thick and long pieces of Wood hung up over a Gate every one by a Cord which answers to the Moulinet that is to be cut in case of a Surprize and they are to be preferred before Herse's Orillon is a small Rounding which joyning with the hollow Tower at the end of the Face of the Bastion covers one part of the Flank P. Pallisadoes are wooden Stakes from 5 to 7 Foot high arm'd with two or three Iron points which are fix'd before Fortresses Curtins Ramparts and Glaces Some there are which are not arm'd with Iron Parapet is an Elevation of Earth upon the Rampart behind which the Soldiers stand and where the Cannon is planted for the defence of the Place Park is a certain Place made choice of in the Camp out of Cannon-shot of the place Besieged to plant the Artillery and to keep the Artificial Fires Powder and warlike Ammunition which is only guarded by Pike-men Petard is a hollow Engin made of â—etal almost in the shape of a Cap from seven to eight Inches deep and five Diameter in the Muzzle It is charg'd with Powder beaten as small as may be and then fix'd to the Madrier Petty Demi-Diameter is the Circumference drawn from the Center through the Gorges Place of Arms is a Piece of Ground sufficient to draw up the Men to be sent from thence as occasion requires Place of Arms without is a Place allowed to the Covert Ways where they make obtuse Angles whereon to plant some Pieces of Cannon or Falcons to force those that advance in their Approaches to retire Place of Arms particular is a Place near every Bastion whence the Soldiers sent from the Grand Place to the Quarters assign'd them relieve those that are either upon the Guard or in Fight Place Irregular is a Place whose Angles and Sides are unequal Place Regular whose Angles and Sides are every where equal Plane the Representation of a Work in its Heighth and Breadth Plat-Form is the whole Piece of Fortification raised in a re-entring Angle Polygon Exterior
Feet into 10 others so one of these last 10 will make the hundredth part of your Line that is to say one Fathom of your Scale 2. To make the Scale well you must divide also one Fathom into six other equal parts to shew the Feet for a Fathom is six Geometrical Feet as have been already said And by this manner you will have a perfect Scale for to know all the Breadths Lengths and Heights 3. When you would make any thing thaâ— should be very exact you must likewise take a Foot and divide it into 12 other equal parts and so you will have the Inches for a Foot contains 12 Inches CHAP. II. How to make the Design of a Square IN France there are three sorts of Fortifications the Large the Middle-siz'd and the Small but at present they never make use but of the Middle-siz'd Nevertheless we will first shew the Difference before we speak of the Middle-siz'd The Square The Large Manner  Fathoms Feet 1. The Semi-diameter 141 00 2. The Side or Exterior Polygon 200 00 3. The Perpendicular 27 00 4. The Face 60 00 5. For the Complement of the Line of Defence take 38 00 6. The Flank 22 00 7. The Curtin 73 04 8. The Line of Defence 141 04 The Middle-siz'd  Fathoms Feet 1. The Semi-diameter 127 02 2. The Exterior Side 180 00 3. The Perpendiclâ—ar 22 00 4. The Face 55 00 5. For the Complement of the Line of Defence take 33 00 6. The Flank 18 01 7. The Curtin 64 04 8. The Line of Defence 1â—6 00 The Small  Fathoms Feet 1. The Semi-diameter 113 01 2. The Exterior Side 160 00 3. The Perpendicular 21 00 4. The Face 45 00 5. For the Complement of the Line of Defence take 33 00 6. The Flank 18 04 7. The Curtin 64 00 8. The Line of Defence 115 04 The Explanation of the Middle-siâ—'d Table HAving seen the Difference between these three Manners we shall only speak of the Middle-siz'd as being the most in use at this Day and to begin we will examine the said Middle-siz'd Table 1. Take 127 Fathoms and two Foot between the Points of the Compass and make a Circle 2. Take 180 Fathoms and divide them with the Circle into four equal parts When they are joyned the one to the other they are called Exterior Sides or Polygons as A B C D. 3. Divide one of these four Sides into two equal parts with 90 Fathoms as E F G H. 4. Draw from the Points E F G H. streight Lines toward the Center which are called Perpendiculars to which must be allowed 22 Fathoms in length as I L M N. 5. Set the Rule to the Capital Points A B C D. and draw streight Lines through the end of the Perpendiculars I L M N. at pleasure 6. Take 55 Fathoms and place them upon the Lines drawn from the Capital Points to mark out the length of the Faces as a b c d e f g h. 7. Take 35 Fathoms and put them from the Point where the Perpendicular ends viz. from the Point I L M N. upon the Lines thaâ— have gone beyond the said Points to mark out the length that is to be taken for the Complement of the Line of Defence as JO. JP. LQLR MS. MT NV. NX 8. Draw the end of the Faces and these Points OPQRSTVX which terminate the Complement of the Defence and you will have the Flanks 9. Then joyn together the Feet of the Flanks and you will have the Curtins To make the Orillon MOnsieur de Vauban does not leave his Flanks as Monsieur Pagan has done or as the Dutch and Germans do at this Day but he conceals one part the better to cover the Cannon by means of the Orillon And for that Reason we will shew you his manner of raising it which is not very difficult 1. Divide the Flank into three equal parts 2. Divide the first of the three into two other equal parts to joyn from this Middle the two Extremities of the first part on the side of the Moat and this little Rounding makes the Orillon To make the Hollow Tower or Flank retir'd AS you have seen the Reforming of the first of the three parts placed upon the Flank now you shall see another of the two remaining parts the Form of which you must henceforward call the Hollow Tower the Constructure of which is thus 1. Draw from the Capital Points of the Bastions a small streight Line within side of the Bastion through the end of the Orillon 2. Put five Fathoms upon this Line which you have drawn as also upon that which is almost parallel to the lower part of the Curtin This is called the Brisure 3. Take the Extremities of the Brisure with the Compass and with that Distance draw two Arches which intersect one another toward the Moat in Figure 8. 4. Put the Compass upon that Intersection and joyn the said Extremities of the Brisure together by a crooked Line and thus you will have the Figure which is made at this Day in France in stead of the Flanks as also the Design of the Entire Square See under B. Fig. 3. CHAP. III. Of the Structure of the Body of the Place of the Square WE are now to see what Largeness or Breadth is to be allowed to the Ramparts Parapets Moats Covert Ways and Glacis's of Squares and after what manner they are to be drawn Observe then what follows  Fathoms Feet 1. The Base of the Rampart 11 00 2. The Base of the Parapet 03 00 3 The first Banquet 00 1 â…“ 4. The second Banquet 00 02 5. The Moat from 16 to 20 00 6. The Covert Way 04 00 7. The place of Arms 13 00 8. The Glacis 36 00 In case the Ground will give you leave to take more you may do it The Explanation of this Table 1. Take 11 Fathoms and carry them parallel to the Curtins Flanks Faces Brisures and Hollow Towers on that side toward the inside of the place to know after what manner you are to draw the Parallel to the Hollow Tower Put these 11 Fathoms before then open your Compasses to the Point from whence you drew your Hollow Tower and draw from the same Point through the said 11 Fathoms a crooked Line till it joyns the Basis of the Brisure and the Face 2. Take three Fathoms and carry them in the same manner parallel to the Design to the end the Basis of the Rampart may be opposite to it and parallel But you ought to make this Parapet or three Fathoms parallel also to the Orillon as far as the Brisure For there it is that the Parapet of the Orillon ought to end As for the Hollow Towers put as already has been said three Fathoms for that is the breadth of the Parapeâ— before the Hollow Tower and open the Compass to the point from which you drew the Hollow Tower and the Base of its Rampart to draw from the same point
them upon each Triangle The Length a-cross will always give you the true Breadth of the Base of the Rampart 2. Take 3 Fathoms and bring them round about the Place without putting them upon the Triangles Draw the Banquets as usually 3. Take 20 Fathoms for the Bâ—eadth of the Moat and â—ut them upon all the Triangles the Distance taken a-cross â—ill be the true Breadth of the Moat for every side The manner of making this Fortification is the same with that â—f the Regular See the Plate T. Fig. 38. CHAP. XIV To make a Half-Moon before these Fortifications BE sure to see whether the Length of the â—urtain exceeds 100 fathoms or no. If it be from 100 to 140 Fathoms 〈◊〉 50 â—athoms for the Capital of the Half-Moon or Raveâ—â—â— But if it be larger than 140 Fathoms erect before 〈◊〉 Ravelin another Work whether a Horn or Crown-â—ork If the Curtain be not longer than 100 Fathoms 〈◊〉 the half of the Curtain with the Brisure for the Capiâ—â—â— of the Ravelin and the rest is done as in a regular Fortification For the Base of the Rampart is 8 Fathoms That of the Parapet 3. The Breadth of the Moat 12. These Distances are to be put upon the Triangles before the exterior sides of which you intend to place the Ravelin and afterwards taken a-cross CHAP. XV. To set other exterior Works before the same Fortifications IF an exterior Polygon exceeds 120 Fathoms and that you have still room to erect a good exterior Work before it whether Horn or Crown-Work as you may see in Fig. 39. which is a Crown-Work made according to the Rules of Chap. 10. lib. 3. The parts of it ought all to be mark'd upon the Triangle AB Is the Basis of the Rampart of the Ravelin and the Horn-work CD Is the Basis of the Rampart of the Body of the Place EF Is the Breadth of the Moat belonging to the Ravelin and Horn-work GH Is the Perpendicular of the Horn-work from the end of which are drawn the Faces IK Is the Breadth of the Moat belonging to the Body of the Place 23 is the Perpendicular of the Body of the Place LM Is the Face of the Horn-work NO The Complement of the Line of Defence to thâ— Bâ—dâ— of the Place PQ The Face of the Body of the Place RS The Capital of the Horn-work TV The Distance which joins tâ—e Point of the Capiâ—â—â— to the Horn-work WX Are the Wings of the Horn-work CHAP. XVI How to fortifie an Irregular Place already built TO avoid much Labour you must fortifie the parts of an Old Fortification and finish them in the same manner as they were begun unless they are gone utterly to decay and then you may make what alterations you please To the end therefore that Money may be laid out to good purpose when the Flanks are repaired they must allow an Overture of 100 deg If the Faces are tolerable let them alone as they are to avoid the vast expenceâ— in making others Whence it comes to pass that there is no ancient place which is fortifi'd after the French manner because the Engineers have been always forc'd to labour upon Dutch Fortifications As for the Rampart and Parapet they may be better fortifi'd whatever Face they have But to come to the Thing it self let us observe the following Rules Iâ— The exterior Side the Length of which is from 60 to 80 fathoms requires a Demi-Gorge from 14 to 15 fathoms and a Flank of 15 fathoms II. If the exterior Side takes up from 80 to 140 fathoms it is to be divided into 5 equal parts of which one is retained for the Demi-Gorge The Flank changes according to the variety of the Sides For example if the exterior Side is of 80 fathoms the Flank shall be of 16. If of 90 the Flank of 17. If of 100 the Flank of 18. If of 105 the Flank of 19. If of 110 the Flank of 20. If of 115 the Flank of 21. If of 120 the Flank of â—2 If of 125 the Flank of 23. If of 130 the Flank of 24. If of 135 the Flank of 25. If of 140 the Flank of 25 Fathoms 3 Feet This being well understood it will not be difficult to reduce it into Practice Suppose the Pentagon following of which the Side AB is 130 Fathoms BC 124 CD 130 DE 113 Fathoms 3 Feet EA 146 Fathoms and that you design to Fortifie it 1. Allow the fifth part of each exterior Side for the Demi-Gorges as AF BG CI CK DL DM EN EO and AP. 2. Raise upon FG HI KL MN OP Perpendiculars for the Flanks in case you cannot allow them an Overture of 100 degrees the Length of which must be proportionable to the Length of the Sides For Example The Flanks FG shall have 24 Fathoms HI 22 KL 24 MN 20 EA 25 Fathoms and 3 Feet 3. In drawing the Line of Defence you will have the Faces at the same time 4. The Base of the Rampart takes up 11 Fathomâ— That of the Parapet 3. The Breadth of the Moat 20 Fathoms The Covert way and the Glacis are made as is usual See the Plate W. Fig. 40. Observation The Flank is left after the Holland-manner that is to say without either Orillon or hollow Tower to avoid overmuch Expence III. If the exterior side be from 140 to 170 Fathoms the Flanks are allowed the following Length If it be 145 allow the Flank 25 fathoms 3 feet If 150 to the Flank 26 fathoms If 155 to the Flank 26 fathoms 3 feet If 160 to the Flank 27 fathom IV. The exterior Side surpassing the Length of 160 fathoms to 280 is look'd upon then as if it had two sides that is to say that besides the Bastions which are placed upon the Angles there should be a Plat-form in the middleâ— as you see in Fig. 41 where the Side AB is 200 fathoms and the Construction of it thus 1. Divide the Side AB into two equal parts as AC CB. 2. Divide either the Distance AC or the other CB into five equal parts to give one of them to the Demigorge as AD EB CF CG 3. Raise upon DG FE the Flanks of an Overture of 100 deg the Length of which shall be the Demi-gorge 4. From the Point C draw the Capital which takes up the Length of the entire Gorge as CH. 5. Join the Extremities of the Flanks and the Point H together by a streight Line to gain the Faces See the Plate W Fig 41. Observation These sorts of Bastions are perfectly well defended for the Flanks of the neighbouring Bastions play backwards upon their Faces besides that almost all the Curtain serves them instead of a second Flank and very much augments their Defence V. The Exterior Side surpassing 280 Fathoms two flat Bastions are placed there holding this for a Maxim that the greatest Side ought to be 140 fathoms CHAP. XVII How to Fortifie an Acute Angle IF you find by chance an Acute