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
former and one and a half of the latter for a distance whereby from FG to draw two arches which shall intersect each other in O. 4. From O draw a circle thro' FG and divide into twelve parts equal to FG which when joyned by right lines will give a Base of the Pyramid that was required BOOK II. AS all Rivers have their particular Branches and every general Science its Divisions and its Parts so Geometry generally taken is the Mother of several other Arts and Sciences whereof we shall treat in this Second Part. These are Measuring of Heights of Distances of Plains of Solids of Concaves and the turning of one Body into another CHAP. I. Of Measuring of Heights MEasuring of Heights is a Science which shews how they are to be measuredâ— But because there are several Instruments for that purpose as a Quadrant a Pantometre an Astrolabe a Iacob's Staff c. We shall at present only make use of the Astrolabe because it is the surest and the most convenient and we shall know how it is to be used by the following Problems PROBLEMS I. To take the Vertical Height of any thing when you can come to the bottom Let the height of a Tower AB be to be measured 1. Draw a right Line as you please from the point A aâ— AC 2. Measure the Line AC with your Scale or your Chainâ— of 26 Feet for instance 3. Set the Staff upon which the Astrolabe is Horizontally fastned upon C so that by the fixed Sights one may see the Line CA from one end to the other as fas as the Tower and that by the two other movable sights the point B which marks the height of the Tower may also be seen 4. When the Instrument is thus fixed compute whether the Angle CDE be 40 degrees 5. Then draw upon Paper a right Line of the length of AC as FG But this must be done by a small Scale made upon the Paper or by a Scale of Wood or Laâ—ten Afterwards erect a Perpendicular upon G. 6. Take the Reporter the French word is Rapporteur and set it directly upon FG so that the middle of it may answer to the point F then compute an Angle of 40 Degrees equal to CDE as FHI 7. From F draw a right Line throâ— I â—ill it touches the Perpendicular G in K. 8. With a small Scale measure the height of KG and add the height of the Staff to which the Astrolabe is fastned and the Sum will give you the height of the Tower AB II. To measure a Vertical Height where you cannot come at the bottom Let AB be the height to be measured the foot inaccessible because of a River which hinders all approaches 1. Draw a right Line upon the Ground on this side of the River as CD let it be 22 Foot long Take notice when you can raise a right-angled Triangle upon this Line opposite to the heightâ— which you would measure it is much more convenient otherwise the Operation is the same 2. Set the Instrument upon C so that by the immovable â—ights you may see the point D directly and by the two movable ones you may see the point A beyond the River When this is done compute the Angle CEF which may be of 90 Degrees 3. Set the Instrument upon D so that the fixed sights may make one Line with DC by the two others you will see the point A this Angle ought to have 28 Degrees 4. Draw upon Paper a Line equal to that drawn in the Field CD as GH of 2â— Feet 5. With the Reporter take an Angle at H equal to the Angle CEF viz. of 90 Degrees as IHK and lengthen the side HK Afterwards upon the Point G take another Angle of 28 Degrees equal to the Field-Angle DOP as GLM and then lengthen the side GM till it cuts the other HK in N and this Point N will mark the foot of the height A. 6. Having the distance from the Instrument to the foot of the Tower it will be an easie thing to work the rest by the foregoing Problem III. To measure a Perpendicular Height where you can come at the bottom with the shadow of a Staff 1. Fasten a Staff a foot long perpendicularly into the ground as AB and measure the shade by the Staff 3 Foot for Instance 2. With the shade of the Staff viz. 3 feet measure the shade of the House DE whose height you would know and as many feet as the shade of the House exceeds the shade of the Staff so many foot high will the House be For Instance if the shade of the House be 24 times longer than that of the Sâ—aff then we ought to say that the House is 24 Foot high Or thus 1. Erect a Stick divided into 10 equal Parts Feet or Inches perpendicularly in the ground and at the same time measure the shade caused by this Staff 20 Foot for Instance 2. Measure also the shadow of the House whose height you would know for Instance 38 Feet 3. By the Rule of Three say If the shadow of 20 Foot gives a height of 10 Foot what will the shadow of 38 Foot give Answ. 19 Foot IV. To measure the Inclination of a Mountain Let the Inclination of the Mountain AB be to be measured 1. Draw from the Point A which stands for the foot of the Mountain a right Line 36 Foot long as AC 2. Set the Instrument upon the Point A and look thro' the two fixed sights towards the Point C and thro' the two movable ones towards the Point B the top of the Mountain this Angle for Instance may be 110 Degrees 3. Then set the instrument upon C and look thro' the two fixed sights upon the foot A and thro' the two other fixed ones upon the top B then compute this Angle which may be for Instance 40 Degrees 4. Afterwards draw a Line upon Paper 36 Foot long because it ought to be equal to the Line AC as DE. 5. Then by the Reporter set upon D an Angle equal to that of the Figure at A viz. 110 Degrees as DFG 6. Upon the Point E set another Angle of 40 Degrees equal to that at C as EHâ— 7. Lengthen the sides DF and EI and where these lengthened Lines intersect one another as at K draw from that Point to D a right Line which will represent the Inclination which was required provided the height of the Staff upon which the Astrolabe was fastned be added V. To measure the vertical height of a Mountain This Problem must be wrought as the foregoing one provided that you let fall a Perpendicular from the Point K which marks the top of the Mountain which must touch the Line CD lengthned to L the Line KL will represent the vertical height of the Mountain VI. To measure the height of a Tower built upon a Rock Let the height BD be to be measured 1. Seek the inclining height of the Mountain by Prob. 4.
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
streight Line as also FR and FE 5. Divide the Lines EF into two equal parts from the middle of which set down a Perpendicular of 20 Fathoms GH 6. Draw the Faces â—s for the body of the place their length is 38 fathoms 7. For the Complement of the Line of Defence take 21 fathoms 2 feet which joyn together after the end of the Face and of the Complement to have the Flanks Draw the Curtin also 8. To make the Orillon and the Hollow Tower go the same way as is set down in Lib. 3. Chap. 2. only that you do not divide the Flank but into two equal parts Monsieur de Clermont would have allowed to the Orillon of the Square two fifth parts of the Flank 9. The Base of the Rampart is to contain 8 fathoms that of the Parapet 3 that of the Moat 12 that of the Covert-way 5 the first and second Banquet are to have the same wideness as has been mentioned above The TABLE Â Fathoms Feetâ— The Capital QG 88 00 The Wing DE 118 00 The Perpendicular GH 20 00 The Face EL 38 00 The Flank LN 15 0â— The Complement c. HN HM 21 03 The Curtin MN 38 05 The Line of Defence EM 84 04 The Base of the Rampart 08 00 The Base of the Parapet 03 00 The first Banquet 00 01 1 â— The second Banquet 00 02 The wideness of the Moat 12 00 To make a Ravelin before these Horns 1. FRom the Angle of the Moat of the Horns erect a streight Line of 24 fathom for the Capital OP 2. From the point B draw right Lines toward the Orillon of the two Bastions of the Horns terminating at the Moat as OQ OQ 3. Draw the Base of the Rampart and the other distances as in the working of the Horn-work only that the Moat ought not to be wider than 8 fathoms nevertheless it must have its Rounding 4. The Covert-way the places of Arms and Glacis are made as in the body of the place See the Plate C c. 4. l. 3. CHAP. VII To make a Horn-work before the Bastion 1. FRom the point of the Bastion draw a streight Line of 86 fathoms AB 2. From the point B draw to each side an Arch of 60 fath 3. Take from 118 to 120 fathoms and resect those two Arches in CD the Angles where the Moat of the Ravelin throws it self into the Moat of the body of the place as EF. 4. Joyn EC CD and DF together by streight Lines 5. Divide the Line CD into two equal parts from the middle of which draw down a Perpendicular from 18 to 20 fathoms as BH 6. Draw the Faces as usually their length is to be 38 fathoms as KI the Complement is 21 fathoms 2 feet as LN lastly all the rest is done as in the Horn-work before the Curtin the parts of which have the same distanâ—â— See the Plate E Fig. VIII CHAP. VIII To make a Horn-work with Shoulders 1. PRolong the Flanks towards the Field to the length of the Curtin AB CD 2. From B and D draw a Perpendicular of from 25 to 28 Fathoms as BE DF. 3. From the Points EF raise other Perpendiculars from 118 to 120 Fathoms as EG HF. 4. Joyn GH together by a streight Line which you shall divide into two equal parts and from the middle of which you must bring down a Perpendicular of 20 Fathoms as IK 5. Draw the Faces as usually the length of which must be 35 Fathoms 6. The Complement of the Line of Defence is found by putting the Compass upon the Extremity of the two Faces and then keeping one Point of the Compass standing in its place let the other fall upon the Line of Defence Which is also to be done on the other side as LM NO 7. LM and NO are drawn together for the Flanks as also MO for the Curtin 8. To have the Orillion take two fifth parts of the Flank of this Work the rest is made as usually in like manner as the hollow Tower or Flank retired 9. The Base of the Rampart c. ought to have the same wideness as the rest of the Horn-works and to be drawn parallel as far as the Moat of the Body of the place 10. The Ravelin before this Work is made as already has been set down in Chap. 6. Lib. 3. See the Plate F Fig. IX CHAP. IX To make a Horn-work with a Crown 1. DIvide the Exterior Polygon of the Hown-work into four equal parts AB CD 2. Take three parts of these four and describe them with an Arch at the Angle of the Moat of the said Work E. 3. From the point H erect a Perpendicular as far as the Arch F. 4. Put the same three parts of the point F upon that Archâ— as FG and FH and joyn FG and FH together by a Right Line 5. From the Line FG and FH bring down a Perpendicular of 16 Fathoms as IK LM then draw the Faces as usually of which let the length be 29 Fathoms 6. For the Complement of the Line of Defence take 15 Fathoms and then draw the Flanks and the Curtin as above 7. Prolong the Faces of the Horns to 27 Fathoms as AN DO and joyn GN and HO together by a Right Line 8. Put 24 Fathoms upon the Wing of the Horn on the side of the Place at the points AD as AP and DQ 9. From the Points N and O draw streight Lines towards the Points PQ which terminate on the side of the Moat of the Hornwork in RS. 10. To make the Orillion divide the Flank into two equal parts of which the one serves for the said Orillion and the other for the Flank retired You are to observe that the Flanks which joyn their Faces to the Moat of the Hownwork are left without an Orillion â— and a retired Flank as NR OS 11. The Base of the Rampart c. and all the other distances are formed as in the Horn-work See the Plate F Fig. X. CHAP. X. To make a Crown-work before the Curtin 1. FRom the Capital Point of your Ravelin erect a Perpendicular of 100 Fathoms and if there be no Ravelin take the Curâ—inâ— of the body of the place with the Brisurâ— to draw two Arches which cut one the other before the Curtin From which Point of the Intersection you must do as I have already said concerning the Capital Point of the Ravelin as AB 2. Take the same 100 Fathoms and make an Arch from the point B to each side 3. Take 113 Fathoms and resect those two Arches as the beginning of the Orillon CD and EF. 4. Joyn EB and BF together by right Lines and draw streight Lines from the points EF towards the Orillion of the place terminating upon the side of the Moat GH 5. Divide the Line EB and the other BF into two equal parts from the middle of which bring down Perpendiculars each from 15 to 16 Fathoms as IM LN 6. You are to
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
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
but little expos'd so neither do they not survey very far and it is impossible to make good Embrasures upon a Parapet ordered after that manner For to play the Cannon above the Parapet is to make it impossible to preserve it in a good condition besides that a Flank disposed after that manner can never defend the Passage of the Moat nor flank the Breach nor in the last place uncover the covert Ways As for Monsieur le Chevalier de Ville who makes the Flank perpendiculaâ— to â—he Curtain he has more Reason for what he does than Erbard though his Flaâ—ks are less than those which Monsieur Vauban makes use of and that they do not batter the Moat sufficiently nor the Counterscarps which is the most essential part of the Defence Besides it is but too well found by Experience that when the Counterscarp is gained the rest holds out but a short time the Reason of which if it be demanded is because the disposing of the Places is so disadvantageous that one Day sees them reduced to Dâ—st and the Embrasureâ— made upon these Parapets perpendicular to the Curtain are too acute especially if it be required that they should clear the covert Ways I know it may be said that it is easie to mâ—ke an Orillon or Ear and a retired Flank in a circular fashion But the Orillon will be too feeble unless you allow it the half of the Flank and the remainder will not suffice for its Defence not having room enough for several Pieces to be placed upon it besides that there must be a mixture of great and small Shot which will cause an inevitable Trouble Monsieur Pagan a Person experienced to perfection in the Art of War and one who has jusâ—ly acquired the Reputation of being one of the most skilful Engineers of our Time was the first that alter'd the disposing of Flanks perpendicular to the Curtain by allowing them much more overture for he makes them perpendicularly upon the Line of Defence and he gives very good Reasons for it in his Book of Fortifications where he says That his being present at above twenty Sieges convinc'd him that Flanks perpendicular to the Curtains were of little duraâ—ce And he wonders that the Reputation given to the Hollâ—nders for their Perfection in the Art of Fortification should be so great â—ince the Places fortified according to their Method make so little Resistance and for that there is not one which is well defended from the Canon Neverthelessâ— we may presume to say that Monsieur Pagan'◠〈…〉 altogether without defects for the Enemy 〈…〉 nk so dispos'd before he comes upon the covert 〈…〉 â—efore to make the best of all the Advantages wh 〈…〉 one and the other produces in his defence Monsieur Vauban allows an Overture to this Angle from 98 deg to 106 as may be seen Book IV. C. â— Sect. 3. For by this means the Embrasures made in the Paâ—rapet in this Flank perfectly uncover the Moat and the covert Way And though Monsieur Vauban should not have made this Flank in a crooked Line by means of the Orillon and the retired Flank however it ought to be preferr'd before others because the Ravelin covers the Overture which is allowed it above the Perpendiculars to the Curtain and consequently it is not too much exposed bâ—â—ides that it considerably enlarges and diminishes the Faces which are the weakest Parts of a Fortification CHAP. II. Of the Flank HERE we must repeat what we have already said That though the largest Flanks are the best nevertheless it is a Thing disputed among the Engineers Morsheuser made thâ— Flank to a Square of 16 Fathoms to a V of 18 to a VI of 20 to a VII of 22 to an VII as far as a Dodecagon of 24. Freittag made it to a Square of 12 to a V of 14 to a VI of 16 to a VII of 18 to an VIII of 20 to IX of 22 to X of 24 which Length he retains also in Polygons of 11 and 12 Bastions Goldman made it a Square of 12 to V of 16 to VI of 1â— to a VII of 20 to an VIII of 22 to a IX â—ll he came to Polygons of 12 Bastions of 24 Fathoms In general the Hâ—llandeâ—s make their Flanks to a Square of 16 Fathoms 2 Feet to a V of 18 Fathom 2 Feet to a VI of 19 Fathom 2 Feet to VII 19 Fathoms 5 Feet to an VIII 2â— Fathoms 1 Feetâ— to a IX of 22 Fathoms 1 Foot and a half to a X 23 Fathoms 2 Foot to XI of 24 Fathoms 2 Feet Monsieur the Count of Pagan allows the Flank in a Square 19 Fathoms 1 Footâ— to a V 24 c. as you may see L. 3. C. 16 17. CHAP. III. Of the Faces AS the Face is the most dangerous Part of a Fortress and for that it is exâ—reamly expos'd to the view of the Enemy 't is requisite that it should be as short as may be for that by how much it is the more advanced towards the Field by so much it is the more liable to be atâ—ack'd Whence it câ—mes to pass thaâ— the Enemy of â—â—â—e generally makes choice of that Part to begin his Breaches As to the length of the Faces the Engineers differ as much one among another as they do about the Flanks Adrian Mâ—tins would have the Face to carry two third parts of the Curtain Monsieur the Count of Pagan allows it in a Square 55 Fathoms and permits the same Length for the Polygons Freittag would have the Face to be always 48 fathoms according to the practice of all the Hollanders As for the Length of the Faces after Vauban's Methodâ— see Chap. 16. of the Third Book CHAP. IV. Of the Orillon and Flank retir'd together with the Brisure or Place where the Great Guns are to be planted AS for what concerns the erecting of the Orillon and Flank retir'd according to Monsieur de Vauban's Method there needs no more than to read what he has written thereupon in the Second Chapter of his Third Book But here is a new Method which though it be not better however it is as good 1. After the Out-Lines of the Fortress are drawn divide the Flank of one of the Bastions into three equal parts and the Face of the opposite Bastion into two as A â— B C. 2. Draw from the Point B which makes the middle of the Face a Line through the third part of the Flank which is the nearest to the Angle of the Shoulder D prolonged in the Body of the Bastion of 5 fathoms as DE. 3. Divide this same Third part of the Flank into two equal parts as FG and GDâ— from which Point G erect a Perpendicular of about two fathoms as GH Lastly Set the Compass upon the Point H and so draw the Rounding of the Orillon joyning FD together 4 Draw from the re-entring Angle of the Moat P a streight Line through the Angle of the Curtain L prolonged in the Body of