The new method of fortification, as practised by Monsieur de Vauban, Engineer General of France with an explication of all terms appertaining to that art / made English.

A NEW TREATISE OF Fortification. BOOK III. (Book 3)

CHAP. I.

Sect. 1. How to inscribe any Polygon within a Circle giv••n••

THIS Problem is commonly treated of in Geometry; Nevertheless, because it is impossible to work on a Regular For∣tification on Paper, without know∣ing before-hand how to inscribe Re∣gular Figures in a Circle given or ta∣ken at pleasure, we shall at present dis∣course something thereof.

(1.) Divide the Diameter of your Circle given, A. B. into as many equal parts, as you would give sides to your Figure: For example, into Five.

(2.) Draw the Diameter A. B. and make with this di∣stance of points A. B. 〈◊〉〈◊〉 A••••••es to intersect in C.

(3.) Draw from the Point C. through the second Part which is mark'd by the Point E. of the said Diameter, a Ri••ht Li••••, t••ll it to••ch the ••ircumfe••ence 〈◊〉〈◊〉 be••o•••• the Di••me••••r in ••.

(4.) This distance from the Intersection to the first ••••int A. of the Diameter, will be always one side of the Polygon demanded.

See the Plate B. Fig. 2.

Se••t. ••

How to make a Scale.

AS every thing is to be done by a Scale, you must know likewise the man••er how it is made, which is as fol∣lows.

• (1.) Divide a Line into 10 equal parts, and one of these to shew the 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 tha•• 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 Perpendicl••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	1••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-si••'d Table.

HAving seen the Difference between these three Man∣ners, we shall only speak of the Middle-siz'd, as be∣ing the most in use at this Day; and to begin, we will ex∣amine 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 Cir∣cle 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 tha•• have gone beyond the said Points, to

mark out the length that is to be taken for the Comple∣ment 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 Mon∣sieur 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 ano∣ther 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 Com∣pass, and with that Distance draw two Arches, which in∣tersect 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 ⅓
(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 Hol∣low 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 Parape••, before the Hollow Tower, and open the Compass to the point from which you drew the Hollow Tower, and the Base of its Ram∣part, to draw from the same point through the three Fa∣thoms put before the Hollow Tower a crooked Line joyn∣ing the Parapet of the lower Brisure, and the prolongation of the upper Brisure together; and there, where I touch the said Prolongation, from thence I draw a small Line to the next Brisure.

(3.) Take a Foot and a half, and draw with that di∣stance a Parallel round about the Parapet, toward the Base of the Rampart, which will represent to you the first Ban∣quet; round about which you must draw another Parallel of two Foot to mark out the second.

(4.) To draw the Breadth of the Moat, take from 16•• to 20 Fathoms, and draw with that distance a Parallel to the Faces, till they intersect one another before the Curtin. To draw this Parallel round about the point of the Ba∣stion, you must put the Compass of the Overture from 16 to 20 Fathoms upon the said point of the Bastion, and draw a little Rounding from thence to the Parallels of the Faces.

(5.) To mark out the Covert Way, take from four to five Fathoms, and carry a Parallel to the Moat; but set i•• from a point before the Rounding.

(6.) Where the Covert Way makes a Saliant Angle, for example, in G. put there 10 Fathoms to each side, as G. J. and G.H. and afterwards with 15 Fathoms you shall make points where the 10 Fathoms terminate, and draw from the said Points, in the point of the Intersection, streight Lines; and this is that which is called the place of Arms.

(7.) Take 36 Fathoms, or as much as the Ground will permit, and bring a Parallel round about the Covert Way, and the place of Arms to mark out the Glacis or Parapet of the Covert Way. And thus your Square will be per∣fectly finished.

CHAP. IV. Of the Structure of the Half-Moon before the Curtin of the Square.

FRom the Angle of the Moat, or Counterscarp, raise a Perpendicular as long as the Demi-curtin, with its Bri∣sure for the Capital P. Q. Observe that in Polygons the Capital ought to be 45 Fathoms in length.

2. From the point Q. draw a streight Line toward the Orillon of the Bastion, terminating on the side of the Moat in S and D.

3. Take five Fathoms, and put them from S and D. upon the Counterscarp, toward the inside of the Half-Moon, as E. F.

4. Put the Rule perpendicularly upon the Curtin of the Body of the place, and erect from the points E. F. two small streight•• Lines, till they cut the Faces of the Half-Moon, as in VH, and the Lines EV, FH, will make you the Flanks of the Half-Moon.

5. Draw the Base of the Rampart AB, of 8 Fathoms, parallel to the Faces, and the Flanks of the Half-Moon to∣ward the inside, as also the Parapet AC, of 3 Fathoms, the first Banquet of one Foot and a half, the second of 2 Feet.

6. Take 12 Fathoms for the wideness of the Moat, which ought to be drawn parallel to the Faces, but not to the Flanks: You must give it also its Rounding before the Ca∣pital Point.

7. The Covert Way, Place of Arms and Glacis are made, as in Chap. 3. L. 3. Sect. 5, 6, 7. See the Plate C.

CHAP. V. Of the Structure of the Ravelin before the Curtin.

THis Work is done as the Half-Moon•• when you allow it no Flanks.

Sect. 2. To make a Ravelin with Lunettes.

HAving rais'd the Ravelin as it ought to be done,

• 1. Take two parts of the Flank of the Body of the place, and put them at the Angle of the two Moats; that is, from the Moat of the Body of the place and that of the Ravelin, upon the Counterscarp, to mark out the Demi∣gorges of the Lunettes, as AB, and AC.
• 2. Take the Flank of the Body of the place entire, and draw from the point BC, two Arches to cut one another in D, and then joyn BD, and CD, together by a streight Line, to have the Faces of the Lunettes.
• 3. You draw the Moat of these Lunettes from the half of that of the Body of the place, allowing it also a Rounding.
• 4. The Base of the Rampart, the Parapets, and the Ban∣quets, is made as for the Ravelin. See the Plate D. Fig. V.

Sect. 3. To make a Ravelin with Counter-guards.

HAving made the Ravelin alone with its Moat in the same manner as has been set down;

• 1. Prolong the Faces of the Ravelin above its Moat, and from the Intersection of that Line and of the Moat put upon the Prolongation 30 Fathoms, as AB.
• 2. Put 15 Fathoms upon the Counterscarp of the Moat of the Body of the Place, placing the Compass in the Angle of the two Moats, as CD.
• 3. Joyn DE together by a Right Line, which side, and the other AB, must be fortified with a Rampart, Parapet, Banquets, Moat, Covert Way and Glacis, like the Ra∣velin it self, the Distances of which are also here to be ob∣served.
• ...

• 4. Having fixed this Work on the other side of the Ravelin, place a small Reduit at the Head between the two Counter-gards, which are thus to be raised: First, where the Moats of the Counter-gards intersect one ano∣ther, erect from the same Angle a Perpendicular of 20 fa∣thoms, as EF; then divide the Faces of the Counter-gards into two equal parts, as BG and AG, and from the Capital Point of your Reduit draw a streight Line to∣ward the middle of the Faces, marked by the point G, terminating on the side of the Moat of the Counter-gards in H, and the Line FH will be the Face, which is only to be fortified with a Rampart, Parapet, Moat, Covert-way, and Glacis, if need require. See the Plate C, Fig. VI.

Sect. 4. To make a Ravelin, to be placed at the Entrances into Places.

1. HAving the place for a Ravelin, you must erect a Perpendicular of 12 fathoms from the Angle of the Counterscarp, as AB.

2. You must put at the same Angle 6 Fathoms upon the Counterscarp for Demi-gorges, as AC and AD.

3. Erect upon the points CD Perpendiculars of 4 fa∣thoms for the Flanks.

4. Joynt the Flanks and the Capital together to have the Faces.

5. Draw a Moat round about this Work of 2 fathoms and a half, parallel only to the Faces, and round before the Point. In this little Work is placed a great Corps du Guard, the better to guard the Gate and the Bridge, and present the Arms to the Officers.

6. That which is left of the place designed for the Rave∣lin ought to be joyned together, as if the Corps du Guard were not there, and fortified with Ramparts, Parapets, &c. as another Ravelin. See the Plate D, Fig. VII.

CHAP. VI. To make a Horn-work before the Curtin.

1. ERect a Perpendicular from 85 to 88 fathoms at the point of the Ravelin or Half-Moon, as QG.

2. Draw from the point G to each side an Arch of 60 fathoms.

3. Take from 114 to 118 fathoms, which is most usual, and resect these Arches in EF, at the Angle of the two Counterscarps DR.

4. Joyn ED together by a 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 ••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; Mon∣sieur 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.

	Fathoms.	Feet••
The Capital QG	88	00
The Wing DE	118	00
The Perpendicular GH	20	00
The Face EL	38	00
The Flank LN	15	0••

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/••
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 distan∣ces, 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 distan••••. 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 Fa∣thoms, 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 stand∣ing 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 Arch•• as FG and FH, and joyn FG and FH together by a Right Line.

5. From the Line FG and FH, bring down a Perpen∣dicular 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 to∣wards 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•• 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 Per∣pendicular of 100 Fathoms, and if there be no Ravelin, take the Cur••in•• of the body of the place with

the Brisur•• 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 Perpen∣diculars, each from 15 to 16 Fathoms, as IM, LN.

6. You are to draw the Faces as usually, the length of which must be 31 Fathoms, as OP, QR; the Comple∣ment, &c. of 16 Fathoms, as ST, VW: The Flanks and Curtin are made, as already has been frequently shewed.

7. Divide the Flank into two equal parts, of which re∣serve one for the Orillion, and the other for the Flank retir'd.

8. The Base of the Rampart takes up 8 Fathoms, that of the Parapet 3; the first Banquet a Foot and a half, the second 2 Feet; the wideness of the Moats 12 Fathoms; in the Covert-way and Glacis, observe the same breadth as there is round about the body of the place. See the Plate G, Fig. XI.

The Table for this Work.

	Fathoms.	Foot.
The Capital Line AB	100	00
The Exterior Sides BE, BF.	100	00
The Wings EC and FD, with their Complements to the Orillions	113	00
The Perpendicular	17	00
The Face	31	00
The Flank	13	03
The Curtin	30	00
The Complement of the Line of Defence	16	00

CHAP. XI. To make a Corwn-work before the Bastion.

1. ERect upon the Capital Line of the Bastion a Perpen∣dicular of 100 Fathoms, as AB.

2. From the point B draw to each side an Arch of 100 Fathoms.

3. Take 92 Fathoms, and resect those Arches at the Con∣course of the two Moats, viz. That of the Ravelin, and that of the body of the place, in CD, as ED, FC.

4. Joyn CB, BD, FC, and ED, together by streight Lines.

5. Divide the Lines CB and BD into two equal parts, from the middle of which you shall bring down a Perpen∣dicular of 17 Fathoms.

6. You must draw the Faces as usually, allowing to the length of them 31 Fathoms; to the Complement, &c. 16 Fathoms; to the Flank 13 Fathoms, 3 Feet; to the Curtin, 29 Fathoms 3 Feet; to the Base of the Rampart, 8 Fathoms; to the Base of the Parapet, 3 Fathoms; and to the Banquets, Coverd-way, and Glacis, as usually. See the Plate H. Fig. XII.

CHAP. XII. To make a Ravelin before the Point of a Bastion.

1. PRolong the Parapet of the body of the place above the Moat, so that it may cut it in QS.

2. From the point of the Bastion erect a streight and perpendicular Line, upon which put 36 Fathoms, beginning at the Moat, as CV for the Capital.

3. Upon the prolongation of the Parapet by the points SQ, put 14 Fathoms for the length of the Flanks, as ST, QR.

4. Joyn TV, VR, together, and you will have also the Faces.

5. Round about the Faces of the Flanks you shall draw the Base of the Rampart of 8 Fathoms; that of the Parapet 13 Fathoms, and the two Banquets as usually; and the Moat of 12 Fathoms, parallel to the Faces and the Flanks, with its Rounding, before the Capital Point V, and the Flanks TR. See the Plate I. Fig XIII.

CHAP. XIII. To make a Single Tenail.

1. PRolong the Flanks of the Body of the place to 110 Fathoms, as ABCD.

2. Joyn BD together by a right Line; divide it into two equal parts, and let fall from the Middle a Per∣pendicular of 26 Fathoms, as EF. But you must observe, that this Line ought not to be longer than 20 or 22 Feet, when there is a Ravelin or a half Moon before the Curtain of the Body of the place.

3. Draw the Extremities of the Wings in the point F. as BF. and DF.

4. Draw the Base of the Rampart 8 Fathoms, that of the Parapet 3, the two Banquets as usually. The Moat 12 Fathoms, the Covert Way and Glacis as for the Body of the place.

The Ravelin before the Work.

1. DIvide the Faces of the Tenaille BF and FD. into two equal parts, and put the half of the one upon the Perpendicular erected upon the Angle of the Counter∣scarp, as GP.

2. From the point G, toward the Middle of the said Faces of the Tenaille, draw streight Lines for the Faces of the Ravelin, as GL, and GM.

3. The Distances for the Body of the place of the Rave∣lin are the same with those of the Tenaille, only that the Moat belonging to it is no wider than 8 Fathoms. See the Plate K. Fig. XV.

CAAP. XIV. To make a double Tenail.

1. PRolong the Flanks of the Body of the place to 110 Fa∣thoms, as AB and CD. and joyn BD together by a right Line.

2. Divide the Line BD into two equal parts, and let fall from the Middle of it a Perpendicular of 26 Fa∣thoms, as EF.

3. From the points BD draw streight Lines in the point F for the Faces, each of which must be divided into two equal parts, as BG. DH.

4. Erect a Perpendicular upon the Angle of the Faces of 45 Fathoms, as FJ.

5. From the point J. draw the Counter-Faces in the points GH.

6. To the Wings, to the Faces, and Counter-Faces, draw the Base of the Rampart parallel of 8 Fathoms, and all the other Distances as in the single Tenaille. See the Plate K. Fig. XVI.

CHAP. XV. To make a Bastion with Counter-Guards.

FOrmerly they were wont to put these Works before the Bastion, the better to cover them. The Structure is thus.

• 1. Draw Lines parallel to the Faces of the Bastion of 15 Fathoms, terminating upon the Counterscarp of the Rave∣lin or Half-Moon, and forming a point before the point of the Bastion, as ABC.
• 2. Draw the Base of the Rampart to these two Faces of 18 Fathoms, as ED. All the other Distances are the same with those of the Ravelin or Half-Moon. See Plate I. Fig. 14. C. XII. Lib. III.

CHAP. XVI. Of the Structure of a Pentagon.

	Fathoms.	Feet.
1. THe Semi-diameter	153	01
2. The Exterior side AB•• CDJ.	180	02
3. The Perpendicular EF.	25	00
4. The Face AF.	50	00
5. For the Complement of the Line of Defence FG. take	38	03
6. The Line of Defence GB.	131	03
7. The Flank JG.	22	02
8. The Curtain GH.	73	04

The Explication of this Table.

SEe Chap. 2. Book 3. There you shall find all that is ne∣cessary for the Structure of a Pentagon; provided you take the Distances prescribed here, for those that are men∣tioned in the same place. See the Plate F. Fig. 16.

Of the Structure of a Tenaille in the Moat.

TO justifie what has been said above of the Line of De∣fence, observe this Work, the Structure of which is thus.

• 1. Put the Rule upon the advanced Flank of the Body of the place, and draw a Parallel to that Flank of from 5 to 6 Fathoms, which touches the Line of Defence before the Orillon in EB.
• 2. Divide the rest of the Line of Defence from BE. to the nearest Angle C, into two equal parts, as BF. EG.
• 3. Take the Distance FG, between the points of the Compass, leaving one upon the point F: Carry the other from the point G upon the Complement of the Line of De∣fence, mnrk••d F. Then fix one point of the Compass up∣on the point G. and carry the other from F. upon the other opposite Complement, mark'd H. Then joyn HF and JG together, to form the Flanks: Do the same for the Curtain HJ.
• 4. Draw the Base of the Rampart of 8 Fathoms to the Faces, and to the Flanks of the Tenaille; and to the Curtain from 4 to 5 Fathoms. Then the Base of the Para∣pet of 2 Fathoms 3 Feet round about. You shall make the 2 Banquets as usually. See the Plate M, Fig. 16.

CHAP. XVII. Of the Structure of a Hexagon, and other Polygons.

1. THe Semi-diameter takes up

Fath. 180

2. The Exterior Polygon

180

3. The Perpendicular

27

4. The Face

50

5. For the Complement of the Line of Defence

38

6. The Line of Defence

136

7. The Flank

25

8. The Curtain

71

The other Distances are equal to those of the Pentagon.

Sect. 2. The Heptagon.

	Fathoms.	Feet.
1. THe Semi-diameter takes up	207	03
2. The Exterior Side	180	00
3. The Perpendicular	27	00
4. The Face	50	00
5. For the Complement, &c.	38	00
6. The Line of Defence	135	03
7. The Flank	24	00
8. The Curtain	72	03

Sect. 3. The Octogon.

	Fathoms.	Feet.
1. THe Semi-Diameter	238	01
2. The Exterior Polygon	180	00
3. The Perpendicular	28	00
4. The Face	50	00
5. For the Complement, &c.	28	00
6. The Line of Defence	137	03
7. The Flank	25	04
8. The Curtain	71	04

Sect. 4•• The Enneagon.

	Fathoms.	Feet.
1. THe Semi-diameter	263	01
2. The Exterior Polygon	180	00
3. The Perpendicular	32	00
4. The Face	50	00
5. For the Complement, &c.	38	00
6. The Line of Defence	138	00
7. The Flank	29	00
8. The Curtain	70	03

Sect. 5. The Decagon.

	Fathoms.	Feet.
1. THe Semi-diameter	291	03
2. The Exterior Polygon	180	00
3. The Perpendicular	36	00
4. The Face	52	00

5. For the Complement, &c.	38	00
6. The Line of Defence	135	00
7. The Flank	32	00
8. The Curtain	70	00

Sect 6. The Hendecagon.

	Fathoms.	Feet.
1. THe Semi-diameter	319	00
2. The Exterior Polygon	180	00
3. The Perpendicular	37	00
4. The Face	152	00
5. For the Complement, &c.	38	00
6. The Line of Defence	135	00
7. The Flank	32	02
8. The Curtain	70	00

Sect. 7. The Dodecagon.

	Fathoms.	Feet.
1. THe Semi-diameter	347	04
2. The Exterior Polygon	180	00
3. The Perpendicular	42	00
4. The Face	52	00
5. For the Complement, &c.	38	00
6. The Line of Defence	137	00
7. The Flank	37	00
8. The Curtain	69	00

CHAP. XVIII. To make the Profil.

HAving now treated of the Breadths and Lengths of the parts of a Place, it is requisite to say something of the Heighth of the said parts; or rather after what manner to make the Profil of a Place. To which purpose two things are to be observed.

• 1. That you erect the Profil of the Exterior Works af∣ter the same manner as that of the Body of the principal Place; provided that you apply thereto the Heighths, of

• which I shall speak as much as is necessary to be known, whereof the Breadths have been above exhibited.
• 2. That 10 Fathoms of the Scale of which I make use in delineating the Body of the Place, make but one, when I would make the Profil of the same Place. So that 100 Fathoms which I have applyed to the Body of the Place, for this purpose, afford only a Length of 10 Fathoms.

The Profil of the Body of the Place.

FOr Examples sake, let us make the Profil of a Penta∣gon; and then observe that which follows.

• 1. Draw a long streight Line, and there mark 11 Fa∣thoms for the Base of the Rampart, beginning at the Left Hand, as AB.
• 2. Put 1 Fathom 4 Feet immediately behind the Point A, upon the same Line as AC. This Triangle marks out the Interior Talus. And to mark out the Exterior Talus, put 1 Fathom immediately before B, as BD. But in the Field you must allow larger Talus to the Rampart, accor∣ding to the Nature of the Ground.
• 3. Erect upon CD two Perpendiculars, each of which contain 3•• Fathoms in height, as CE, DF, and then joyn AE, EF, and FB, by a right Line, and that will afford the heighth of the Rampart with its Talus.
• 4. Put 4 Fathoms of the Point E toward the Right Hand, to mark out the Platform of the Rampart, as EG.
• 5. Erect upon G a small Perpendicular of a Foot and a half for the heighth of the first Banquet, as GJ. Then draw from the point J a Parallel to the heighth of the Rampart a Foot and a half broad, as JH; that is, the breadth of the Banquet. Then set another Perpendicular upon the point H, of the same heighth as HJ; and from the point J draw also another Parallel of two Feet broad, as LM, and then you will have both the Banquets.
• 6. Put 4 Feet immediately behind the point G, as GN, and then upon that point erect a Perpendicular of 8 Feet, as NO; which done, joyn the point M, and the point O together to get the Interior heighth of the Parapet with its Talus.
• ...

• 7. Prolong the Exterior Talus BF two Feet farther, as HP, and joyn OP together to have the breadth of the Parapet with its Exterior Talus.
• 8. Put four Feet upon the first Line behind the point B, as BQ; from which point let fall the Perpendicular QR, of 3 Fathoms, and joyn BR together for the Scarp. Which done, put 20 Fathoms behind the point B, for the breadth of the Moat, as BS, then put two points before the point S, as ST; from whence let fall another Perpendicular of 3 Fathoms, as TV; then joyn VS to∣gether to have the Counterscarp of the same RV, and so the Moat will be entirely represented.
• 10. After this take 36 Fathoms, so far as the Ground will permit, and put them behind the point W, upon the same first Line, as WA, and then joyn them together by a streight Line, to represent the Glacis. After this man∣ner you shall have the Body of the Pl••ce according to its Lengths, Breadths, and•• Heighths. See the Plate N. Fig. 17.

The Profil of Exterior Works.

THis Profil is made as the preceeding in respect of the 7 first points, saving only that the Base of the Ram∣part be no broader than 8 Fathoms, nor the Rampart higher than 14 Feet. As to the 8 point of the Description of the preceeding Profil, the only difference consists in this, that the Moat is not larger here than 12 Fathoms, nor deeper than 2 and a half. All the rest is done as in the preceeding. See the Plate N. Fig. 18.

CHAP. XIX. How to trace out the Draught of a Fortress in the Field.

AFter you have seen the manner of Fortifying upon Paper, it is requisite for an Engeneer, or any one that would discourse of Fortresses, to understand of

what breadth, height, and depth, their Parts ought to be; whence the one or the other part derives its defence, whe∣ther it be necessary to fortify one part more than another; where to attack a Place, and after what manner to fru∣••trate the Enemies design. We shall therefore now shew how to trace out a Fortress in the Field: To which pur∣pose it is necessary to know which are the Angles of Exterior Polygons; being these that follow.

The Angle of the Exterior Polygon.

Degrees.

The Angle of a Square is of

90

That of a Pentagon of

108

Of a Hexagon of

120

Of a Heptagon of

128

Of an Octogon of

135

Of an Enneagon of

140

Of a Decagon of

144

Of an Hendecagon of

147

Of a Dodecagon of

150

The Explication of this Table.

For Example: If you would trace a Polygon of five Bastions, which is called a Pentagon, of which every Ex∣terior Polygon must have the length of the Line given AB, which is 180 fathoms, then proceed thus:

• 1. Fix the Ba••oon, upon which you have your Astro∣labe, in the hole that is made by the little Peg B, so that you may see through both the Sights of the Astrolabe, from the Point B, or the place where your Instrument is fixed, the Peg A.
• 2. Count from the left hand towards the right an Angle of 108 degrees, which is the Angle of the Exterior Poly∣gons, to the Pentagon, (if you make an Hexagon, you take this Angle of 120 degrees, &c.) there fix a little Peg, which you may see through the moveable Sights, for Ex∣ample, C: That done, fix a Cord or a Chain to the Peg B,

• and draw a streight Line toward the Point C, upon which you shall then put the length of the first Line given AB, as BD.
• 3. Put the Instrument upon the Point D, so that through its Diopters or Sights you may see the Peg B. Then seek by the Rule of the Diopters for the Angle of 108 degrees, and there fix another Peg, which you may see through the Diopters, as DE. That done, draw a streight Line from the Point D to the Point E, and then put the length of the Line BD upon the Line DE, as DF.
• 4. Do this as many times as is requisite for a Penta∣gon.
• 5. Divide the Flank into three equal parts, and the first also into two others, in the middle of which fix the Peg H. Then fasten the Chain to the Point H, and draw the Rounding, as upon Paper, with the Compass: That done, draw the Brisures of 5 fathoms, and make in their Extremities two Arches to cut each other in I. Then ••ix in the place of the Point I a little Peg, and with the Chain that is fastened to it, you shall draw the Flank re∣tired.
• 6. To make the Rounding of the Moat, set the Peg upon the point of the Bastion or Ravelin, and with the Chain draw the Rounding. See the Plate O, Fig. XIX, XX

CHAP. XX. To make the Streets in a Fortress.

1. DRaw to the Curtains of the place a Parallel of 10 fathoms for the place of Arms near the Rampart.

2. Draw all the Points made of that Line before the Bastion of the place; for Example, ABCDE.

3. Take the Demi-gorge of the place, or which is bet∣ter, 30 fathoms, and put them from the Center upon those

Lines ABCDE, as abcde: Which distances joyn to∣gether likewise by streight Lines.

4. Take 3 fathoms, and put them at the Points Aa, to∣wards Bb and Cc, as Ff, Gg; which must also be done afterwards with Bb, Cc, Dd, Ee, &c.

5. Joyn Ff and Gg together by Right Lines.

6. Take 8 Fathoms of the Line Ff, and divide the rest into three equal parts. Then take one part of the three, and put it at the Points F and G, upon the Lines drawn in the Grand Place of Arms, as FG, GL. Which done, put four fathoms upon the same Lines, after the Points HL, as HM. LN. Lastly, joyn HL and MN together by right Lines.

7. Take the second part of the three first, and put them after MN upon the same Lines, as MO, NP, and joyn the Line OP together. Which done, you shall re∣place 4 fathoms after the Points OP, as QR, and then likewise joyn QR together.

8. Divide each Side, FG, fg, into two equal parts, as ST, and joyn the Lines ST together by a Right Line. Then put 3 fathoms on each side of the Points ST, as Sss, Ttt, and draw ST together; and these will form the Streets of your Fortress. See the Plate P, Fig. XXI.