workers constructing fortifications HR e f THE STRENGTHENING of STRONG-HOLDS: INVENTED On several Occasions, and practised during the late WARS, as well in the United Provinces, as in France, Germany, Italy, Dalmatia, Albania, and the Neighbouring Countries. By HENRY RUSE, Engineer, and Captain of a Foot-Company belonging to the City of AMSTERDAM. Translated out of the Low-Dutch-Copy, by His Majesty's Command. In the Savoy, Printed by the Assigns of John Bill and Christopher Barker, Printers to the Kings most Excellent Majesty. 1668. To the Honourable, etc. Dr FRANCIS BANNING KOCK, Knight of the Order of S. Michael, Lord of Purmerlandt, and Ilpendam, etc. CORNELIUS BICKER, Lord of SWIETEN, etc. JOHN HUYDEKOOPER, Knight, Lord of Maerseveen, etc. Dr NICHOLAS TULP: RULING BURGAMASTERS Of the City of AMSTERDAM. AS ALSO To the Honourable LORDS, CORNELIUS DE GRAFF, LORD of Zuydt-Polsbroeck, etc. NICHOLAS CORVER, Treasurers and old Burgamasters of the said City. AND ANTHONY OETGENS VAN WAVEREN Knight, Lord of Waveren, etc. Dr GERARD SCHAEP, Lord of Koerte-hoef, etc. Dr CORNELIUS WITSEN, JOHN VAN DE POLL, Old Burgamasters. MY LORDS, IF this little Treatise which I humbly present to your Lordships, may be favourably accepted as a pledge of my grateful Acknowledgements, and may beget in your Lordships a firm belief that my real intentions are to employ my best endeavours in the discharge of that Trust your Lordships have reposed in me, I have obtained the utmost of my desires; beseeching your Lordships to consider more the matter therein contained (which the greatest and wisest of men in all ages have esteemed as one of the most noble Sciences, and the most necessary for the settlement and preservation of a flourishing Commonwealth) than the rough and unpolished stile of the Writer, remembering that Soldiers and persons of my profession (as your Lordship's very well know) ought much rather to ponder their Actions, then to study the needless ornament of Words; as likewise to rest assured, that the continuation of your Lordship's affection towards me, will not only encourage me to a steadfast and unwearied perseverance in my zeal for your Service, but likewise to proceed to some other undertake of the like nature, for the good and benefit of your City, and of the whole Commonwealth. And so I remain, My Honourable, etc. Your Lordship's most devoted Servant, H. RUSE. THE AUTHOR TO THE READER. IN the year of our Lord 1639. (being the Fifteenth of my age) having a great inclination to the Wars, and my Genius leading me principally to the studies of Fortification, Artillery, Fireworks, Mines, and the like; I was first of all entertained in the service of the States, where I continued about four years; during which time I observed with great diligence the Manners and Customs used in these Countries, as well in the business of Encamping and Retrenching, as in Erecting their Fortifications. But hearing very much of the French and other Nations, for their marvellous Address and Dexterity in all Warlike Affairs, I was extremely desirous to be better acquainted with their ways, as promising myself to see wonders done by them: Wherefore I went with a Regiment of Walloons from Mastricht to France, in quality of a Lieutenant; which Regiment was joined to the Army of the Duke d' Enguin (who was then General of the French) and so they kept together till the Battle of Frybourg in Brisgow, 1644. where the said Regiment was wholly routed, and I with many other miserable Wretches shared together in our Misfortune; however with that Army we reduced the Palatinat by the Rhyne, Frankendal only excepted. Being since returned into France, I had the advantage of seeing there many places well Fortified, as also in Burgundy, Lorraine, and Germany, and did examine very curiously their Principles of War, together with the various Methods of Fortifying, attacking, defending, and embattailing their Armies, which often happened between the French and German, against the Imperialists and Bavarians, to which we were not altogether strangers. Thus having seen whatever I thought necessary in those Countries, I assisted at the Battle of Nortlingen, in and near the Village of Alderheym 1645. where the Duke d' Enguin was General of the French, V C. Tureyn of the Waymarians, and Merci of the Bavarians, which last was slain in the Fight. After this, having assisted in the Battle of Herbrausen near Mariedal, I resolved to seek my fortune in some other Country, to see what was there to be done, the French and Germane Customs and Warlike practices being sufficiently known to me already. Consequently in the year 1646. hearing that the Turks had invaded Candia, and declared War against the Venetians, I had great inclinations to follow that War, (besides the curiosity I had to see those Countries) as being against the most inveterate and irreconcilable enemy of Christendom. Whereupon I left the Germane Camp (for I was then come from the French to the Waymarians) where I had served for the space of three years, in divers employments, and endured many hard and tedious Marches, hazarded myself often in bloody Battles and famous Rencounters, with the loss of most of my Comrades and fellow-soldiers, who were either slain in fight, or otherwise lost their lives in the Service. From thence I first steered my course to Helvetia, and being arrived at Zurich, I met with the Venetian Ambassador, and other Germane Officers, with whom I made an agreement to levy Germane Soldiers, and to lead them over the Alps into Italy (Bergamo in Lombardy being the place appointed for our Rendezvouz) where having been a while, and observed the most eminent Fortifications on the Continent, we got Letters to go to Venice, from whence some of us were sent for Candia, others for Corfu, and I with some Germane Forces for Dalmatia, which was already invaded and taken by the Turks of Bosna, Macedonia, and the Grecians, who made great preparations to assault the Strong-Holds in those parts. Here, by the entreaty of Foscolo the Venetian Ambassador, I took upon me the employment of Engineer, and had many strange Adventures, too numerous to be here recited. About five years after, Lunardo Foscolo, than General in Dalmatia, was chosen Generalissimo in Candia, who desired me to accompany him thither. But when we came to Venice, his journey was retarded, and I employed my time in curing some Distempers I had gotten in the Wars, in the Paduan Baths; and afterwards returned to Venice, where I found the General, having got leave from the Senate, resolved to continue that summer at Venice. Whereupon being desirous to visit my friends and relations in my native Country, I took my leave, and went for Germany, and by the way had an opportunity of seeing some Fortifications of the Duke of Bavaria, and some others, which before I might not, because I served their enemies. Being in the Low-countrieses, I had an opportunity of offering my service to my Lords the Burgamasters of Amsterdam, in whose service I am at present employed, and hope, as occasion shall offer, I shall be able so to improve my talon, as to bring to light that which may be for the advantage of this great City, and the whole Country. In the mean time I shall begin with this small Treatise, the Subject whereof is the doctrine of Fortifications; not that I intent to discourse of the first Rudiments, but only to manifest unto those who understand this Science, the weakness of Modern Fortifications, and how the defects may be supplied, and the Works made incomparably stronger, as well the Royal Fortresses, as the Outworks, and all this with as small cost as ordinarily other Works are erected. Which expedients are no Chimaeras or idle Fancies, but such as have been sufficiently disputed of and throughly examined. For I have made it my business to observe very strictly the proper function of each distinct part of a Fortification, and that not in a Closet, but abroad, and in the Field, together with the manifold ways of improving them; and have discoursed and debated the same with the most excellent Engineers of this our age. I do not mean with such who attack Cities by a fireside or in a chimney-corner, but with such who have been trained up among the Canons and Muskets: nor do I mean with our ordinary Mathematicians, who think that Wars, and all affairs of this world ought to be regulated unchangeably after their rules. Neither do I hereby in any wise despise or undervalue Mathematical Learning; for on the contrary, I lay that for my foundation and groundwork, having for my own particular studied it with great affection and delight. But because I have found by experience, that the Principles of War are not always limited to Mathematical Rules, therefore I do not begin this Treatise with Demonstrations, but declare my opinion to the lovers of this kind of learning as plainly and as briefly as I can; not thinking it necessary to show how to erect a Fortification, but only to point at some general Amendments, which will, I doubt not, be very grateful to all ingenious Students. And in case there be any thing found which they cannot approve of, they will highly oblige me whenever they please to declare the same, and to propound expedients for the reforming of whatever is amiss. But for as much as I do not doubt but that this little Treatise will find acceptance, I shall God willing communicate unto the world my particular reflections and observations, for Attacking, Defending, Artillery, Mines, Countermines, with all other things relating thereto, as likewise for the ordering and forming of Battles; all which have been found to be practicable, and of great use in the late Wars. THE STRENGTHENING OF STRONG-HOLDS: INVENTED On several Occasions, and practised in the late Wars, as well in Holland, as in France, Germany, Italy, Dalmatia, Albania, And the Neighbouring Countries; BY HENRY RUSE. AFter I had throughly considered the best Methods of Fortification practised in the Countries before mentioned, I found that none of them had made better use of Situations (as to the Artificial part) than the United Provinces. Forasmuch as they have not only very well designed and contrived their Fortresses, but have also placed them so advantageously, that by the overflowing of Waters (which they can by the opening of Sluices let in or out as they please) they have rendered the greatest part of the Works impregnable. I do not say but that in other Countries are also found very sufficient Fortresses, and well contrived; but there hath been a necessity in these Provinces (where they have had to deal with so potent an Enemy) to use greater caution and circumspection then elsewhere, and to make choice of the best Fortifications, and yet with no great charge, being made of Earth only, which of all Materials I hold to be the best for this purpose; whereas in other countries', especially in Italy, they are of opinion, that the outsides of their Works ought to be altogether of Stone, and afterwards cut or pared, which cannot be done without excessive charge. And yet notwithstanding all their endeavours, they have not been able so to contrive their Strong-Holds, but that the best of them, if accessible, are taken in a short time, being hardly tenable for three Months, to the astonishment of the World, as examples do abundantly testify. This hath been the cause why many Military Architects have tried all ways and means to supply those Defects, of which I have seen many Conceits, but in my judgement altogether impracticable; which has encouraged me to improve my own Observations in all Occurrences, and earnestly to mind each part of the Fortification, of what use it might be, and whether it were able to perform that, for which it was ordained and intended. And having discovered very many Errors, especially in the Modern Flanques and Outworks, I did debate my Observations very particulary with many Engineers of the greatest Practice and Renown; but never met with any whose judgement I so well approved, as that of a certain noble Italian, who having had several Employments, as well in Germany and the Low-countrieses, as likewise in the French Wars, had carefully improved all opportunities and advantages of gaining Knowledge and Experience. With this Gentleman I therefore made a particular Acquaintance and Friendship, and we did mutually communicate and compare together our Observations, till such time as we had found out, and agreed upon such a Method, as seemed to us to be of all other the safest, and yet practicable with the least expense; according to which Method, almost all considerable Fortifications might without difficulty be redressed. The truth is, this Method is something near that which shall hereafter be discoursed of: For having looked yet more narrowly into this matter, and examined it with greater diligence and curiosity, I did only (as I found cause) altar something of that our first design. I do not here undertake to make Accessible places impregnable, since all that is made by man, may by man be again destroyed; for the Attacques being carried on upon a sure foot, and the Approaches being managed with skill and judgement, if in the mean time no relief come, even the strongest places must at length yield up to the Besiegers. My intention is only so to contrive Works, that they may resist much longer then ordinarily they do, that so the Besiegers may be wasted and consumed, either by ill weather or some other accidents. (For by lengthening of time, opportunity is given to the Besieged to get relief; or in the mean while to Attaque some other places in the Enemy's custody, and so to make him quit his design;) which will be a sufficient recompense for the pains and charge, which I conceive to be but little more than ordinary, in case the Work be managed by an experienced Artist, as will sufficiently appear by what hereafter follows. In the mean time I shall propound some general Rules or Principles of Fortifications, approved and owned by many skilful Captains and Engineers. The Maxims or general Rules which are observed in the Modern Fortifications. 1. There aught to be no point of the whole Fortification undiscovered or unflanqued, and that from several places of Defence. 2. The Lines defending aught to be longer than the Lines defended, or at least as long. 3. A Regular Fortification is very much stronger than an Irregular. 4. The more Bastions a Regular place hath, the greater is its Strength and Defence. 5. A Fortress ought to command all places whatsoever round about. 6. Those parts of a Fortress which are nearest to the Centre, aught to command those that are more remote. 7. Those parts of a Fortification which are at greatest distance from the Centre, ought always to be Commanded by those e that are nearest the Centre. 8. The Line of Defence Fichante, ought not to be much longer than 60 Rods, that being the distance ordinarily allowed for the Port of a Musket. 9 The larger the Flanques and Gorges are, the better and stronger they are, provided the other parts are not prejudiced thereby. 10. Of second Flanques, and Courtine-Flanques, the larger is the better, in case it cause no disproportion in the other parts of the Fortification. 11. As for the Linea Stringens, (or Line of Defence Secant, which is continued from the Face to the Courtine) the shorter it is, the better, if the Flanques be not too much lessened by it. 12. That opening of the Angle of a Bastion is the best, which gives a right length to the Flanque, second Flanque, and Gorge. 13. The Angle of a Bastion ought not to be less than 60 degrees, nor greater than a Right Angle, or 90 degrees. 14. The Angle of the Poligone ought not to be less than 90 degrees. 15. The Angle of the Face and Flanque ought to be at least 150 degrees. 16. The Angle of the Courtine and Flanque ought to be evermore 90 degrees, or a Right Angle. 17. The outward Angle of Defence (or Angle Flanquant) cannot well be too Acute. 18. The inward Angle of Defence ought not to be less than 25 degrees. 19 The proportion between the Courtine and the Face ought to be as 3 to 2, or as 36 to 24. 20. The Faces should never be longer than the Courtine, nor shorter than one half of the Courtine. These are the Maxims and Rules for the structure of most of the Modern Fortifications, which I hold to be exceeding good and necessary, all but the 16th, which says, That the Angle of the Flanque and Courtine must always be a Right Angle. As for the reason of that Position, we shall see more hereafter. For I do assert the contrary, and say, That it ought always to exceed 90 degrees: which Angle is the only thing that makes the difference in the form of my Ground-Lines from those now in use; besides that, I take greater Parts, and other Profiles. The truth is, the Flanques are the most considerable parts of a Fortification, and those wherein lies its chiefest Strength, and therefore the Structure of those is of so much the greater consequence. But now the reasons of those who would have the Flanque evermore perpendicular to the Courtine, are these that follow, viz. Because all Shots coming from thence fly parallel to the Courtine; and that by night all parts of the Courtine may be better defended; and that when it is very dark, the Soldiers holding their Muskets in a right Angle to their Breasts, must needs hinder the Enemy from approaching the Courtine, as may be seen in Fig. 1. These reasons being well scanned and examined, appear so weak, that they are scarce worth the answering; nevertheless I shall briefly refute them. The first reason is, because the Shots fly all parallel with the Courtine: whereupon I say, whether the Flanque be perpendicular to the Courtine or no, the Shots may for all that fly parallel with the Courtine; for the Soldiers know not how to make a Right Angle in setting their Muskets. I do also affirm, That only one Musqueteer can with one Shot clear the whole Courtine at once, and all the rest must incline to it; for if they do fly parallel, than those who give the Assaults must have Wings likewise, that so they may be shot in the Air, in case those within are to defend the upper part of the Wall, or else the Shots must fly only the height of four or five foot above the Horizon (as out of the Fausse-bray) that so they may keep parallel to the Horizon; whereas contrariwise, the Flanques in these Fortifications are eighteen or twenty foot high, and all Shots go downwards, and therefore hit the Horizon in one place only. The principal duty of a Musqueteer is, that by nighttime he turn himself with his Musket towards the place where he heareth a noise, or seethe fire, or something else; to which neither the Perpendicularity nor the Obliquity of Flanques can give any advantage, or become the least hindrance. And these parallel-shots are only Imaginary, found out upon the Ground-Lines, which in the Profile come far otherwise, as Fig. 1. Num. 1. showeth. The Musquetteer A standing upon the Flanque, which is Perpendicular to the Courtine, cleareth the upper part of it: in case the Musquetteer B do the same, and Shooteth parallel with A; but then his Bullet flieth so far from the Wall, as he himself standeth off from his fellow; and so likewise all the rest that stand along in the same Line. Whence it followeth, That those who assault, must be upon the Wing, or in the Air, or else are not to be hit by these parallel-shots: but let the others without the Point A, as C, D, etc. not Shoot parallel with A, than their Shots cannot hit either the Courtine or Moat, or Bridge, but in one place only; which in an Obliqne Flanque of an equal height, will be the same. Now as for my flanques, I order them after another Method, and therefore they are of far greater Advantage than the former, or any other that were ever yet in use, which any Artist may easily conceive, when he vieweth only the Figure, although no Explanation or Animadversion were made upon it, in case he will but declare his judgement without partiality, according to right reason, and the practice of War. The Flanques or Defending-Lines are the chiefest part of the Fortification, and aught therefore to be considered in the first place. They have been altered several times already, but never with any advantage comparable to what is obtained by these; which advantage is distributed and has an influence upon all the parts of the Fortification. The Flanques with Casematts are odious in the United Provinces, because their orillon's could not stand, unless they were Walled up with Stone, which is too chargeable; as likewise by their Cutting and Retiring of the Flanques mounted with Canon, the entrance of the Bulworks came to be too little, which in my Work is otherwise. Those who view my Bulworks, and do not understand the Profiles. may also imagine, that they are made with Casematts; but it is very far from that, and there is something else in it, which hereafter shall be sufficiently declared and explained: only let no man flatter himself with an opinion, that forasmuch as so many brave Captains and Engineers have employed the best of their understandings and endeavours to arrive at the utmost perfection of this Art of Fortification, it cannot be, but that they have attained unto it: Whereas in the late Wars it hath been observed, and is daily seen, that the best Fortresses, made after the manner aforesaid, can scarce resist so much as two Months; and it is altogether needless to produce Examples of that which so many Histories do attest. Besides all this, we are to know, that the bravest Captains and Engineers of this Age knew very well the imperfection of the Modern Flanques, and therefore they have made it their business to think of it, and the truth is, many have conferred with me about it; but I did not find the Inventions propounded by them, practicable in all places: and in this Country it hath not been minded, because the Spanish did seldom or never Attack any place of consequence with an industrious force; but being Besieged in any of their own places, did easily Surrender it, without troubling themselves much with the knowledge of Engineership. But I shall leave this Subject, and come to my purpose, which is not to teach the Grounds or first Rudiments of Fortification, but only to Instruct the Ingenious Lovers of that Art, how to reform those errors which in these late furious and industrious Wars have been rightly discovered in the Modern Fortifications. I style them furious and industrious, because no History gives a relation of any War that was carried on with greater fury, or of any Cities that were taken with greater industry. In the sequel of this Discourse, I shall manifest the Errors of Modern Fortification, and in order thereunto, I shall begin first from the Ground-Lines, and propound a part of a Regular Fortress of Eleven Bulworks, according to the practice of Friday and other Modern Mathematicians, whose Method I esteem to be much better than those of former Ages. But before I proceed, the Enemies of Strong-Holds aught in the first place to be known, which are Sappes, Spades, Pikes, Canon, Mines, and Muskets, managed by Soldiers, and Commanded by skilful Captains and Engineers: And forasmuch as the very same things are to be made use of for Defence, it is necessary that the Fortresses, to the end they may be convenient for use, should be prepared for it long before. Now this cannot be practised in small Works, where after the springing of one Mine, all is lost. It is also necessary, that the Works should outwardly be defended, as well with Canon as with Muskets, by a greater number of men, and from more places of Defence, then can be done by the Enemy conveniently in his Attacques; And herein consisteth the virtue of a Fortification: For if the Enemy do find place to make a Battery of six or eight Pieces, to break the Flanques; we ought to have a commodious place to plant Twenty eight or Thirty pieces in Contra-Battery, which will soon ruin the Enemy's Battery, being greater in number, and standing already in advantageous places; whereas the Enemy must first raise his Battery under the danger of those Canon-shots. All which being premised and well considered, let us now inquire whether our Modern Fortresses have this conveniency; and if not, where the difference lies. For example, see Fig. 2. Num. 2. which is part of a Work of eleven Bastions, and Fortified after the best Modern Method and Practice, (being Fryday's second Way) and according to the measure of these following Lines. A B Polygone exterior 78.13 Long. F G Polygone interior 64.93 Long. F E Demy-Gorge 14.19 Long. A G Capital-Line 24.40 Long. A C Face 24.00 Long. C D Flanque 11.91 Long. D E Courtine 36.00 Long. A E Line of Defence Fichante 61.68 Long. A H Line of Defence Secant 48.85 Long. schematics of fortification Num. TWO Maete van. 110 Rÿnlanse Roden voor beÿde dese Figuren The Modern Engineers refer themselves much to the strength of their Outworks, whereof some nevertheless are very Murthering-Holes, more troublesome than useful; as I shall prove in due time: but for the present shall only show, how the faults of Modern Fortifications may be Rectified according to my Method. It is notorious to every one, who understands Fortifications, according to the Maxims , that the longer the Defending Lines are, the better they are; and that according to Axiom 9 the longer Flanques and Gorges, are much the stronger; always provided, they may be made without prejudice to other parts, or that they be weakened thereby: As also, that the great Bulworks are better than the little ones, because Retrenchments and Countermines may be made within them; and because more Pieces of Canon and Musqueteers may be placed there, for the defence of the next Bulwark; and because it is fit for all other Warlike actions. It is also notorious, that the longest Polygones and Regular Fortresses contain most room, and therefore aught to be preferred before the shorter, in case the Lines of Defence in the Fortification do not exceed the reach of a Musket, that is, 60 or 70 Rods; for after this manner more space is included with fewer Bulworks, and therefore with less charges. The other Maxims are also very strictly observed in my Fortifications. Now to obtain all these Advantages, I describe in Fig. 2. Num. 2. the Ground-Lines of part of an Eleven-angled Work, according to Friday, as also part of an Eleven-angled Work, according to my own practice, both of them Fortified after our second Methods of Fortifying. Which is the most commodious, and the fittest for Cities of an ordinary extent: but to Fortify very great Towns, it will be better to make use of the third Method. I shall therefore show first the difference of Lines in our two Methods, and afterwards the manner of applying the whole Work unto practice. See Num. 2. Fig. 2. The Length of Lines in an Eleven-angled work Fortified after Fryday's second Method. The Length of Lines, according to my second Method, in a Figure of Eleven Angles. A B Exterior Polygone 78.13 A B 90.00 F G Interior Polygone 64.38 F G 74.03 — The little Semi-diameter 114.26 — 131.36 F E The Gorge 14.19 F E 24.00 A G The Capital-Line 24.40 A G 28.32 A C The Face 24.00 A C 27.69 C D The Flanque or Shoulder 11.91 C D 16.00 D E The Courtine 36.00 D E 27.00 A E Line of Defence Fichante 61.68 A E 64.50 A H Line of Defence Secant 48.85 A H 54.00 E H Second Flanque 14.19 E H 12.00 Here the difference of Lines is clearly seen; and that my Figure of eleven Angles containeth in the Circuit of its exterior Polygones, 130.57 ② more than that of Fryday's; for his eleven Polygones are 859.43 ② in length, and my eleven 990 ⓪, and my Line of Defence is no more than 2.72 ② longer than his, which is little or no difference; my Flanques, Gorges, and consequently whole Bulworks are much larger, and more convenient. My Bulworks-Angle, (or Angle Flanqued) is equal to his; as also the Angle of the Polygone, and the Angle of the Tenaille, and the Faces are as long as the Courtines. My Flanques defend the next Bulworks, Faces and Moats, at right Angles: So that all parts do mutually defend themselves with great conveniency. Here it is to be observed, That I do include very near as much space with nine of my Bulworks, as Friday doth with eleven of his, keeping very near the same Line of Defence; which easeth the Charges very considerably, besides the great Symmetry of the Work. And this is all that concerns the Ground-Lines; the virtue of this Work will be seen by that which follows. I shall proceed now to the Structure of these Fortifications, and how the proportions of Lines are to be found. I doubt not, but there be many Theorici, which understand the use of Fortifications not otherwise than upon the Paper, who will imagine, that this Work cannot be good, seeing the Flanques do not (according to the profound Error before mentioned) stand Perpendicular to the Courtines; not considering what strength the Bulworks have by this Obliquity, not only those that are next, but also those that are situated on the other side. For hereby the Bulworks gain at the entrance upon each Gorge, the length D I, being 8 ⓪ twice, which is 16 Rods gained upon both the Gorges, so that the entrance of the Bulwark cometh to be 48 Rods. This affordeth place enough to Lodge upon the Flanques the supposed Artillery and Soldiers, which I esteem necessary. It affordeth also room for the making of Retrenchments, and the Flanques come to be much longer after this manner, as is proved by the 47 of the first of Euclid. It maketh also the great Line of Defence to keep its due measure, not surpassing the length of 64 ⓪, which is the true reach of a Musket. Although my Polygones be considerably longer, yet the Lines of Defence are not sensibly longer than those of Fryday's, and others. I am also of opinion, That the Modern Flanques are more for an imaginary beauty, than to make good the Defence, which notwithstanding is the main end for which they are made, and wherein consisteth the strength of Fortresses. The Calculation of my great Fortifications, consisting in the little, mean, and great Royal. TO do this, I state first my exterior Polygones, after which I regulate the proportions of the whole Work. For the exterior Polygone of the little Royal, I take 80 ⓪, for that of mean Royal 90 ⓪, and for the exterior Polygone of the great Royal 100 ⓪; and I follow the same proportions in the Calculating of my Lines, which Friday hath, that is, making the Courtine to the Face, as 36 to 24, or as 3 to 2; but the difference is, that I take my parts greater, and redress them, after the first Position is done. This Calculation is done only by the Rule of Three, thus: Admit there is a place to be Fortified with a Regular Fortification of four, five, six, or more Angles, and that after the first, second, or third of my Methods; I take then the Lines of such a Polygone, as the Fortress should be, that I intent to make, out of Fryday's Tables. For example, I would make a Square after my first Method; I take then out of the Tables the length of the Lines; as 24 ⓪ for the Faces; 36 the Courtines; for the George's 9.23 ②; for the Capital 19.73 ②; for the Flanque 7.74 ②; and so for all the Lines: these Lines I lay before me, and say, by the Rule of Three, If the exterior Polygone of a Square of Fryday's, being 82.36 ②, giveth me the Courtine 36 ⓪, what does my exterior Polygone of 80 ⓪ after the first Method in the great Royal, give me for my Courtine? and the answer is, 34.97 ②. Item, the exterior Polygone giveth for the Face, according to Friday, 82.36 ②— 24 ⓪. What giveth the Polygone of 80 ⓪?— Answer. It giveth 23.31 ② various depictions of fortifications Num. I. detail from schematics of fortification Fig. TWO Gra … Esplanade Bedock●e wegh Graft Parapet vande Fausebraye Bedecked Wegh parapet van den grooten wall Kr … des walls side-view of fortification Fig. I. schematics of fortification Maete van. 80. Rynlandtse Roeden And so observing the same Rule for a Square, whose exterior Polygone is 80 Rods (as in the Figure of Numb. 1.) there will arise the following proportions of the Lines, viz. H G The Courtine 34.97 ② A I The Face 23.31 ② C H The Gorge 8.96 ② C A The Capital-Line 19.16 ② H I The Flanque 7.52 ② H L The second Flanque 6.77 ② C D The interior Polygone 52.88 ② H B The great Line of Defence 59.05 ② D M The little Semi-diameter 39.37 ② N. B. He who is disposed to Calculate, or who has not these Tables at hand, he may find out himself, by Calculation, the chief Angles of every Figure, and afterwards by the Tables of Sines, or Trigonometry, the length of the Lines, etc. These Lines and others that may be required, being found by the foregoing Rules, I delineated the Figure (whether it be a Fortress of five, ten, eleven or more Angles) according to Art, as here in the Figure Numb. 1. the Square, which I hold to be the first Figure capable of being Fortified. This being drawn according to the Modern Practice, I redress the Ground-Lines according to my Method, very easily thus: I lengthen the Faces at pleasure, as here A I, N C, of which I N, is the Line of Defence Secant. Upon this C A, I let fall a Perpendicular-line, touching the extremity of the Face B K, in K, and I take the Line F K, for the Flanque; and thus I do round about the whole Fortification; and this from a Square, to a Figure of twelve sides inclusive. In such Fortresses, as have more than twelve Polygones, I keep always the same Courtines. And so the form of a Square with its Ground-Lines is sufficiently seen in Numb. 1. and the Structure of it shown before. From this alteration arise these Advantages; First, That the Gorges are lengthened by F G, and H E, and therefore the Bulworks at their entrance become wider and fit for Retrenchments, and the use of necessary Artillery; as may be seen in the Profile of the Flanques. But the Gorges remaining at the length of D G, the said Artillery cannot be duly Lodged. This lengthening of the Gorges maketh also the Flanques E I, F K, longer than the former Flanques K G, and I H, were: This Obliquity of Flanques causeth also the Faces A I, and K B, together with the Moats lying before them, to be Defended at Right-angles, and that the Lines of Defence F A, and E B, become shorter. And lastly, This manner of Structure giveth sufficient room for the Cutting or Retiring of the Flanques. And concerning the Angle-flanqued, or Angle of the Bulwark, which in a Square is 60 degrees; he who desires to have it greater, let him draw a Line from the Point, where the Flanque and Courtine meet together, by the extremity of the opposite Flanque; as by 5 to Q, which is the Line D 5 Q, and so at th'other side. Thus the Faces become something shorter, and the Angle something greater, according to the 21 of the first of Euclid. But the Second Flanque is lost, which in a Square signifieth but little. And this in my opinion, is sufficient as to the alteration of the Ground-Lines, and the finding of them; and the more Bulworks in any Figure keep their just distance, the more considerable will be the advantage gained by their Alteration. Of the Fausse-bray. THe Modern Engineers draw the Fausse-bray parallel, round about the foot of the Wall, at such a distance, that between the Parapet of the Fausse-bray and the Wall is left a hidden way of between 15 and 25 Foot. This Parapet is made to defend the Moat, when the Enemy is passed the Counter-scarp, and intendeth to carry over the Gallery. I make also Fausse-brays, but after another manner than the Modern, viz. thus: I draw a Parallel-Line with the Flanques, as in Numb. 1. X W, parallel with the Flanque 6 V, at the distance of five Rods; so that the place may be capable to hold Canon; afterwards I lengthen the Faces of the Bulwark, as B V, till they cut the parallel X, W; this done, I draw a parallel with the Courtine, at the distance of 3 or 4 ⓪, as X Y; so that the Lines V, W, X, Y, 2, 3, make the Fausse-bray; and this I do round about the Fortress, only before the Flanque and Courtine, and not before the Faces. The reasons hereof are these: First, It is found by experience, that the Fausse-brays are more hurtful than advantageous before the Faces; because they are not of service, before the Enemy cometh to Lodge upon the Esplanade or Parapet of the hidden way, and then they are to oppose him, which they cannot possibly do: And this so much the less, because the Enemy may plant his Canon there for the Destroying and Dismounting of them. Which is easily done, seeing it is but a bare Parapet, which is soon thrown down; so that in this part before the Faces, which are Attacked, no body can remain for Defence, by reason of the playing of the great Guns from the Batteries, which may be made as need requireth; as here Fig. 11. Numb. 1. is intimated by the Letters A, B, and C; where from the Battery A, the Face of the Bulwark D, and its Fausse-bray is pierced Perpendicularly, and from the Battery B Obliquely; but the Battery C cutteth and cleareth the Earth away, which is shaken by the two others; so that by these Batteries and Musquet-shots, coming from the Lines and Cors de Guards, the Faces, as well of the Fausse-bray, as of the great Wall, are soon ruined and left without Defence, so that no body may be seen upon these Lines without being hit; whence it followeth, That they cannot hinder the coming over of the Gallery, but it must of necessity be done from the opposite Flanque. Item, That so soon as this part of the Fausse-bray, lying before the Face, is discovered, it is presently made useless to the Defenders; and not only so, but it does them this hurt and disadvantage, that so soon as the Gallery cometh over, the Miners are able to Undermine the Faces of the Bulwark, where they please, and at several places together. The Mines being blown up, the Enemy may set Footing upon the space where the Fausse-bray lies, not only to Assault the Breach, but he may run along the Foot of the Wall through the Fausse-bray, to fall on at more places at the same time. To this it might be replied, That the Fausse-bray aught to be Cut with Trenches, to hinder this running about. But every one who has experience in these Actions, knows very well, what slender Opposition these Trenches are able to make, especially, when the Earth, which is raised by the Mine, falls down, and sometimes buries the Defenders alive. This place is also of Advantage for the Enemy, when the Breach is Retrenched, and he will make new Attacques upon it, and by that means will lodge himself conveniently in the Fausse-bray, and further in the Breach; whereas otherwise, where there is no Fausse-bray before the Faces, he findeth very inconvenient Lodging against the slooping of the Wall, seeing no other place is found to fix upon. The Miners are forced to make their Mines about the place, where the Gallery cometh on; besides that the Faces, which are surrounded with these Fausse-brays, being Attacked by Canon and Mines, all the Ruins of them remain lying in the same, and afford an easier Ascent unto the Enemy; whereas otherwise, where they are not, the Ruins roll down into the Moat, and the Breach remaineth clear, and the Enemy findeth little Earth to Retrench himself. By all which it is easy to understand, That this part bringeth more advantage than hurt unto the Enemy. To what end is it then, to be at such Charges to our Prejudice, and to cumber the Moat before the Bulworks with this needless Parapet? Therefore to conclude, I say, That the Faces of a Bulwark being Attacked, can make little Opposition of their own; but aught to be Defended from the Flanques and parts of the Courtine; and the more even and neatly the Faces lie, the better may they be Flanqued. That part of the Flanque of the Fausse-bray D, hinders also, that the Face a G from being defended at the bottom from the opposite Flanque. Some Engineers are of opinion, That the Fausse-brays aught to run out after the shape of Ravelins in the middle, before the Courtine. I think this needless, where the Lines of Defence are of a just length, not much exceeding 60 Rods; but where they be longer, this must be practised. At Breda, it is done before some long Courtines. And this is enough as to what concerns the Ground-Lines of the Fausse-bray, in the Profiles: I shall show hereafter, how the Work is to be raised. It remaineth now, that I speak of the Ground-Lines of the Counter-scarp and hidden way, and how it may be made, that it may defend itself with great Advantage, without the great Wall; and that these Counter-scarps are as strong, yea stronger, than the Modern Fortresses themselves. N. B. In those Fortresses, where the exterior Flanquing-angle (or, as the French call it, Angle de Tenaille) comes to be less than 120 degrees, (but it is never made less than 90 degrees) the Faces may be lengthened upon the Ground-Lines, till they meet together; and in such Figures the Fausse-bray may be made upon these Lines, that is, upon the Line of Defence Secant, without running parallel with the Flanque, as may be seen in Numb. II. by the three Figures 5, 6, 7. But when it happeneth, that the Lines of Defence Secant meet one another within the Courtine, or just before it; then a Parallel-Line is to be drawn before the Courtine at the distance of three Rods, to have a Communication; as the understanding Reader will easily perceive, and is seen in the Figure of Numb. TWO, etc. Of the Counter-scarp, or hidden Way. THe Modern Engineers do strengthen the outward Brink of the Moat (or Counter-scarp in Italian,) with Ravelins and Halfmoons, leaving a hidden way with a Ditch about it, and without this hidden way they make sometimes another, without a Ditch; as may be seen at Breda: Which latter I hold to be very good, because not only great Defence may be made from thence, but they are also very convenient for Sallying out, both on Foot and on Horseback; for the Moat doth not hinder it, and the Enemy doth not know from what side he must expect the Sally: Those who thus Sally out, being driven back, may always retire hither, and presently be in a posture of Defence again behind this Parapet; whereas otherwise they are many times driven into the Ditch of the hidden way, with great loss and disorder. This hidden Way (or Esplanade) costeth little, for in places where the ground is something dry, it is cut in above half its height under the Horizon, that is, three or four Foot, that it may be the better flanqued from the first Esplanade which is behind it; as also, that the Shots may fly more Horizontally, etc. I do Fortify my Moat with another kind of Work, and I shall show first the manner how I do it, and afterwards give reasons why it is so much better than the Modern Works. And at the same time I shall discover the Defects, which the Modern Works are subject unto. See Fig. 4. Numb. 3. which is part of a Regular Seven-angled Figure after my little Royal, where the exterior Polygone is 80 ② long: Now to draw my Counter-Guards (for so I call them instead of Counter-Scarps, this name being improper) about it, and to give them such a form, as may fit them for that service I expect from them; I lengthen the Half-diameter K, O to A, or further at pleasure; then I measure upon the lengthened Half-diameter from the brink of the Moat O to I, thirty Rod or more, according as I would have the Flanques N 5 and 4 R short or long. Then I draw from ⅓ of the Face, as from K the Line K, G 5, as also on th'other side the Line L, R, M, from the Point where these two Lines meet, which should be before the middle of the Courtine; as here from G, I draw the Perpendicular G H, which is the Capital-Line of the Ravelin W, G, P, H; then I measure from N to L, as also from G to P, upon the Lines K, G, on th'other side L, G, such a distance as I need for my retired Flanques: from these Points, viz. from N and 4, I draw N 5 Perpendicular to L, M, and 4 R, Perpendicular to K 5, as is clearly seen in the Figure, and wanteth no further explanation as to the Delineation of it. I make further upon the Line 5 R an equilateral Triangle, as 5 R, R, which giveth a Ravelin, whose Angle at the Point R is 60 degrees: He who desireth the Angle to be greater, may make it so, without prejudice to th'other Work. About this Work I draw a Parallel-Line at the distance of five Rods, viz. M R G 5 2; which is the Ditch about the Counter-Guard, so that the Ravelins lying before, become little Islands. At the brink of this Ditch I make a hidden way or Esplanade, whose sloping is regulated according to the Wall of the Counter-Guard, without Ditches, with small cost, which becomes a great benefit. This I continue about the whole Fortress; and all is clearly seen in the Figure, how the Work must lie according to the scale and measures. These are all the Outworks, which I look upon as necessary for a good Defence; and I make no Hornworks, etc. unless extreme necessity do require it, when perhaps there is some height; and then I make them after another manner than the Modern, as the nature of the place does require. Of the Virtues and Defects of the Modern Outworks. THe Modern Outworks are Ravelins, Halfmoons, hidden Ways, Crownworks, Hornworks, Tongues, Kettles, etc. and are made about the Fortresses, as Fig. 5. Num. 3. showeth; where the Figures marked with G are called Halfmoons, those with B Ravelins, D is a Crownwork, such as are laid before the Courtines, before which there lieth a single Tongue; E is a Crownwork lying before a Bulwark, being strengthened with a double Tongue, and at the side of it there is represented the form of a Hornwork. This Figure is part of a Regular Seven-angled Work, according to the most Modern practice, as well the Outworks as the Royal Work. The Virtues and Defects of the Royal Work are in part manifested already. But now I shall show those of the Outworks; and first Of Ravelins. THe Ravelins, marked with B, I count very necessary, seeing they multiply very much the Defence, especially of the Outworks: But because they do in a manner stand instead of a Royal Work in Modern Fortresses, they have this Defect, that their Flanqued Angles are too small, and the Points may be easily broken, as also the Faces, as may be seen in Fig. 5. where the Ravelin B being Attacked from the Batteries A, A, is easily made useless. There may be more Batteries placed to Attack these Ravelins, as it is required, because it is seen from the whole Field I A L. These Works being Attacked, it is very difficult to secure them, and no less difficult for the Defenders to retire when it is taken; and being once taken, it becomes, as it were, a Knife to cut the Throat of the whole Fortress. Of the Modern Halfmoons. THese Halfmoons marked Fig. 5. Numb. 3. with C, I look upon as Works of little use, because they can make but poor Defence, and are Defended but weakly; since they have no other Flanque, than from the Faces of the next situated Ravelins; which Defence being broken (which is easily done, as I have showed by the Ravelins, and appeareth by the Figure) they remain to the use of the Enemy, to make in it the Battery H, whereby the opposite Flanques of the Bulworks are ruined, and the Galleries are brought over with surety; all which is clearly showed. N. B. The Faces of the Halfmoons cannot be seen from the Flanque of the great Wall, the Ravelins being in the way; ergo, they cannot be Flanqued from thence, etc. Of the Modern hidden Way, or Counter-scarp, as they call it. THese hidden Ways are very advantageous before Fortresses; for lying low by the Horizon, they make all the Shots that come from thence, to Mow and Clear the Horizon: neither can they well be broken by the Canon, but must for the most part be taken by storm, and they are commanded from the great Wall: This is a work which covereth much the defects of the Modern Fortifications. They favour also the Sallying out, when they have no Ditches; but here in these United Provinces they have almost all of them their Ditches; which fault being discovered, it hath been remedied by another hidden Way, running about the Ditch of the first, and being cut in, part of it, according to the nature of the ground, under the Horizon, and the surface of the Parapet of this hidden Way, loseth itself, sloping into the Field, without a Ditch. Of Crown-works, and Horn-works. IT is many times necessary to make these or the like Works to take in any heights or suburbs, according as the place requireth it. They are made after the manner and practice of the great Fortresses, and according to the same proportion, excepting only, that their parts are smaller, and they have but half-Bulworks on either side, which are very weak; and yet their strength may be much increased by an understanding Engineer. They ought, in my judgement, to be made so, that they need not to rely upon the Defence of the great Wall; but that they be sufficient to defend themselves, especially those that lie before the Courtines, as in Fig. 5. may be seen by the Crownwork D, whose Wings have a very weak and obliqne defence from the Faces of the Bulworks, and being Attacked by night, the Lines E E cannot be well defended from the Faces of the Bulworks. Yea, in such occasions the Defence of the great Wall is but troublesome to these or the like Works; for the Musqueteers of the great Wall, shooting by night only upon the Alarm of the Assaulters of the Outworks, do hit as well within as without, and wound as well the Defenders as the Adversaries. They ought nevertheless to lie open towards the City; and to be made so, that being taken, they may be little able to hurt it. Of single and double Tongues. THese are very slight Works, and never ought to have other Profiles, than those of ordinary Trenches; for else, if the Wall should be high, they were not able to defend their own Front. Neither are they but seldom made otherwise than Trenches, or to hinder the Approaches; as also the Kettles marked with H. Hence it may be seen, wherein the strength of the Outworks now in use doth consist, which the Modern Engineers make such boast of. Let us now examine the Outworks according to my Practice. OF OUTWORKS, ACCORDING To the latest METHOD and PRACTICE. First of the Counter-Guard. OF these Outworks it might be said, That they take in much place, which is a truth; but when we shall have showed what benefit cometh by them, I doubt not but that will outweigh any inconvenience that shall be occasioned be the great space and place which these Works take in more than other Works usually do. Neither is the difference so very great: For admit, that about the Modern Seven-angled Work Fig. 5. Numb. III. there should be made another hidden Way about that which is there already, or that it should be strengthened with two hidden ways; the Semidiameter of my Heptagone Fig. 4. is but five Rod longer than that of th'other. In recompense whereof it is to be considered, That my exterior Polygones of the Heptagone are 80 Rods; whereas those of th'other (or Modern) Heptagone are but 70 Rod long, which in the whole maketh 70 Rod difference, which is an entire Polygone. Wherefore to include the place of my Heptagone after the Modern manner, there would be required eight Bulworks; so that I do include and Fortify more place with fewer Bulworks than now is usual, which understanding men will easily conceive, by comparing the one with th'other. To show then, what good this Counter-guard doth, let us suppose, That the Fortress Fig. 4. is also Attacked by the Approaches O O. Now skilful Artists know, That it is best for the Enemy to Attack the Point D, and after he hath gained the Counter-scarp, to pass the Ditch of the Counter-guards of 5 Rods. To do this, it is needful for him to render first the Flanque of this Work D, and the Face of the Ravelin F uncapable of Defence: but if he would break the Flanque of the Counter-guard D, he findeth no other place for his Battery than by the letter C, where but five Pieces can be placed, schematics of two fortifications with a sketch of battle between Num. III. Fig 4 Schale voor dese beÿde Fortificatien van. 140 roed. Fig. 5 to Dismount the lowest Flanque; and further in the Field about G there might be planted 3 or 4, to throw down the uppermost Parapets of the Retired Flanques, so that nine Pieces of Canon may be used; whereas those of the Retired Flanques may bring 17 or 18 Pieces in Counter-battery, and from the part H, 4 or 5 Pieces, for the Defence of the Face of the Counter-guard; therefore the Defenders are able with more ease to break the Battery of the Assaulters, than they to break the Flanques of the Defenders. That which hinders, that no greater place is found for the Battery of the Assaulters, is the Ravelin F, and the Angle of the Flanque of the Counter-guard I. Let us see, whether there be not where else a place to make a Battery, to break the Retired Flanques withal, and to Dismount the Canon standing upon the same. Suppose there be a Battery by B, from thence with the Line B one might boar in between the Ravelin F, and the Angle I, but not so, as to touch the lowest and first Flanque; yet this shot (which cannot be done by more than one Piece of Canon) would come obliquely against the last Shooting-hole of the second Retired Flanque, and cannot Disinount the Canon that standeth there, because the shot hitteth the Parapet obliquely in the forepart. No more can it be done from the Battery A, against which Batteries upon the Line D E, every where Counter-batteries may be made. Put the case, That the Enemy not regarding all these difficulties, do with great loss pass the Ditch by D, and undermine the Point of the Counter-guard, (which would also be very hard to do, seeing the Walls are made so, that one cannot well put a Spade into the Ground without being discovered) and make a Breach. In this case, I can first with small labour cut off this Point by the Retrenchments 1 and 2, till the great Retrenchments by 3 and 4 be finished, which are duly defended from the Flanques 6 and 7, as also from the Bulworks-point 8; besides that they secure and defend one another. And in case the Besiegers mean to pass between the Retrenchments towards the Bulworks-point, without gaining before the two Lines marked with 3 and 4, they will find hot work. But suppose they force one of these Lines, than there is within, two or three Rods after them, another ready, and those that lie before are Undermined, which Mines are blown up, when the Enemy once thinks to lodge there; and this is a thing that may be done with great advantage. There needs not one Rod of ground be lost, but what is gained with abundance of blood, and also with great toil and labour. Being forced, we have always a free retirement into the Ravelins marked with K. and L. And in case there be but men within a Fortification made after my Method, who understand the Work, it seems impossible to gain it any other way, than by length of time, and with the loss of many men. This Work helpeth itself, nothing being in the way that hindereth; and all parts are so contrived, that they are provided against all inconveniencies. Hence the understanding Reader may easily conceive, what advantage these Outworks have before the Modern. They are Flanqued within and without with Canon and Muskets from the great Wall; there may be made in haste, and with small pains, as many Retrenchments as is desired, which are all enfiled within and without from the great Wall; and the more obstacles are cast in the way, the more the strength of these Works is discovered. This is enough as to the form and advantage of my Outworks, which each according to his judgement and place may apply: In my opinion, it would be needless to propound these things in a plainer manner, seeing all particularities may be observed by the Figures. It might be said, That these Outworks would cost more, than those that are now in use: the contrary of which is true; for the Parapet of the Modern hidden Way having a Base of 60 or 70 Foot, costeth as much as my Counter-guards-wall, whose Profile I do make so, that it is just Canon-proof. I shall not add here the charges of the Modern Crownworks, Hornworks, etc. but I put my two Ravelins against the Modern Halfmoon and Ravelin; the Counter-guard against the Counter-scarp now in use, my outward hidden Way without Ditches (which is made with small charges) against the Modern second hidden Way, being also without Ditches. And although this Work should cost much more, yet the charge is sufficiently balanced by the benefit that is had thereby: For the Fortresses made after this manner, have quite another Defence, and are, besides their Out and In-works, provided against all Occurrences, with 2, 3, a 4, double Flanques, made as well for Canon, as for Muskets. If any body thinketh, that I propound new and strange things, as doubtless those will do, who are possessed with the Modern practice of Fortifying, and never did search after more convenient means, or examine the strength of every part of it distinctly; or what may be the cause, why Strong-Holds are lost so soon, neither understand the force of the Maxims of War now in use: To those I reply, That if they will consider these new things judiciously, they will find, that the practices of War now in use, aught to be preferred before those old things; and that the Work is very proper and capable of making a good Defence; and that these things were not practised conjecturally in a Closet, but in occasions of Besieging, or being Besieged; and that in several countries and grounds, and in such places where indeed flew swift Bullets, not Sugar-plums, or roasted Capons. Many things may be projected upon Paper; but we ought to look, whether they be practicable in the open Fields. The Latin proverb, Facile est inventis addere, might be applied here, I do confess, but it hath not been done as yet by others. I have been about this a long time; but always observing more and more, whether any thing might hinder it, which perhaps I had not considered of; and possibly there may be some such thing, but whatever it be, it may with ease be rectified by time and practice. All things devised by men, do not immediately come to perfection. Let them who please to use this way, first consider the Work well; and if there be any thing that they do not like, let them practise the Latin proverb abovesaid. There are yet many Particularities in this Work, which I do not describe here, but keep them for my use, and propound only the Generals. It is true, That the Art of Fortifying is highly improved in these United Provinces, by reason of the continual exercise in it: But here have been but few alterations or diversities of Attacques, seeing they are almost all of them made after the same manner; as also the Defences of the Spaniards, who were furnished most commonly with ignorant Engineers, and their places ill Fortified; so that being Besieged, and much pressed, they wanted many things that were most necessary. Here in these parts they have been a while at a stand, without practising any thing at all, which might serve to rectify their Errors; although understanding men saw well enough, that there was something wanting, and that the Work did want another Form; and this proceeds chief from the impression which many had, and still have, that the Fortifications were at perfection, contrary to experience and matter of Fact in the late Wars. In this opinion they were confirmed by the curious searches, experiences and amendments, made by His Excellency Prince Maurice, and His Highness Friderick Henrick, Princes of Orange, of glorious Memory: These indeed did in those days reform many things exceeding well; but the manner of Attacking being much altered since, the Fortifications ought also to be strengthened against them. The Practitioners have only joined to the first Inventions, those things which serve to establish Fortifications upon sure Rules, according to the Mathematics, to which we ought not to be tied too close; however it is necessary to take their assistance in this Science. The question is not, Whether the Fortifications do lie exactly according to the Rules of Mathematics; but whether the Lines be well Flanqued, and all things ordered for most conveniency. I confine myself indeed to these Rules and Calculations, for so much as the first Ground-Lines do require; but upon these I make my Observations afterwards: so that my Work receives no small benefit from thence, by reason of the firm and well-contrived Flanques, and the giving of little advantage and place to the Enemy to erect his Batteries against them. Many places (though well Fortified) are also lost in a short time, for want of skilful Officers and Governors. For although a man had the best Sword he could wish for, and yet did not know how to use it for his advantage, the worst would be as good for him as the best. Let the best Fortress be defended by a Governor, who knows it not, that Fortress shall be gained sooner than a mean place Commanded by an experienced Officer. This hath been sufficiently made good in these late Wars, which also Histories do testify abundantly. For, Retrenchments, Cuts, Counter-approaches, Countermines, besides the ordering of Sallies at due times; as also the managing of Fireworks, contrived by an expert person and skilful Architect, are all very advantageous for Places, and detain the Enemy long. And yet they cannot well be known, before there is Attack made; and then they may easily be so ordered, as to be made more advantageous for the Enemy, then for the Place itself: Hereof there are examples enough, and these Works cannot have a good success, unless they be directed by a skilful Architect, who has not only a perfect knowledge in Fortification, but understands also the power of Artillery and Fireworks, as also the manner of managing them, and how Mines ought to be made upon all occasions. And this I think sufficient for the designing of Ground-lines, and have described only three Figures more of three Regular Hexagones' Fortified; see Num. FOUR one of them, after the great Royal, whose exterior Polygone is 100 ⓪; another after the mean Royal, whose exterior Polygone is 90 ⓪; and a third after the little Royal, the exterior Polygone being 80 ⓪. NOTE. No body is confined to these lengths of Polygones, but they may be taken shorter or longer; only care must be had, that the Lines of Defence be not too long. The lengths of the Lines of these three Demy-Hexagones are of several Quantities; viz. the first, whose outward Polygone is 80.35 ②, and is equal to the Modern Polygones of an Hexagone, according to Friday: the second is of 90 ⓪: the exterior Polygones of the third are of 100 Rods, and the proportion of the Courtines to the Faces (which is to be understood in the first design, which afterwards is altered) Sesquialter, or as 3 to 2. Lengths of the Lines according to the first Calculation. Lengths of the Lines after the first manner, where the outward Polygone C D is always 80.35 Rod in length, in a Regular Hexagone. Lengths of Lines after the second manner, where the out ward Polygone is always 90 Rods long, in a Regular Hexagone. The outward Polygone being 100 Rod, in a Hexagone. Lengths of the Lines, after my alteration, in an Hexagone, as followeth: The I. manner The II. manner The III. manner The Courtine F I 36.00 40.44 44.82 29 30 33 Face C M 24.00 26.88 29.86 the same. Gorge G F 11.36 12.72 14.43 14 17 19 Capital G C 21.26 24.20 26.89 the same. Fanque F M 9.54 10.68 11.87 11 12 13.5 Second Flanque F N 12.98 14.53 16.16 8.5 10 10 Line of Defence Fichante C I 61.11 68.44 76.05 58 63.5 69 Interior Polygone G L 58.73 65.89 73.09 the same. Distance of Polygones F E 18.72 20.96 23.29 the same. three fortifications rendered from above and in profile Num. 4. Profil voor die Flanc 35 ●…oet h●ogh die vierde flanc Linea Horizontalis CD. die B ytenste Poligone 80.35 ● nae die I Maniere CD. 90 nae endue TWO manier CD 100 nae die III manie● Maete van 100 Roedon voor dese dry Figuren end is e●n maete voort profil der flancquen de roede voor een voet genoomen Maete van 25 Roede vort Profyl der Linie AB Thus I finish my Discourse, as concerning the Ground-lines of my Fortification, as well of the Inworks as of the Outworks. Now I come to the Profiles, and shall first treat of those that must be made in wet places, where the Ditches are full of water: And first of all, Of the Walls of the great Strong-Holds. THe Walls ought not to be too high, nor too low: For when they are very high, the Moat can hardly be defended from them; and the nearer the Enemy getteth under them, the more he is sheltered. They have also this fault, that they are very chargeable; for they ought also to have a thickness proportionable to their height; and the thicker the Walls be, the better they may be Undermined, and the Mines that are made in them, do better Execution than in lesser Walls; for the more the Powder is enclosed, and the more it findeth resistance, the greater force it hath, which is evident. Some are of opinion, That the Walls ought to be of such a height, as to cover the Houses from those Canon-shots that come from without: which is ridiculous: For although Walls were made so high, that no houses might be seen; yet by all this we cannot hinder the shots from flying through the Houses; neither are the Mortar-pieces hindered by it, which do the most hurt to houses; besides that, I being Besieged, could rather wish, that the Enemy would busy himself with shooting through the houses, than against the Wall, in case it were a Frontier-town, where more Soldiers lodge, than Citizens; for this shooting through the houses is only to frighten the Inhabitants or Citizens, to compel them the sooner to composition. But Soldiers count this their pastime: they had rather that the tiles and laths should fly from the houses, than that the earth should be torn as rags from the Parapet. To show that the high Walls cannot hinder this nevertheless, See Fig. 6. Numb. V Let there be a Battery by A, from whence out of the Canon A is made the shot A B F, so that it goeth just over the Parapet of the Wall; this shot offendeth the roof of the houses more or less according as the Wall is low or high; as is seen by the shot A C. Suppose the Wall to be as high again as B C, and that the shot be A C G, this goeth indeed far over the houses; but let the Canon D be elevated some degrees, and it will make the shot D E H, against which the height of the Wall availeth nothing, although it were five times higher; for the Bullet cometh down with a Circular-line. It might be said, That the Canon would carry the Bullet over and beyond the City: which is true, in case the Piece standeth near by it; but it can be placed further off, at a convenient distance, which is easily found by a good Cannoneer: which I intent to show clearly in my Treatise of Artillery, which, God permitting, I shall communicate to the Lovers of this Art. Such Pieces may be placed here and there in the Fields, or even in the Quarters, where they please, without making any Beds for them, and so be used; for they ought to stand without the true Line or ordinary Canon-shot. Besides that the houses may be troubled after this manner by the Canon; the same may be done more conveniently by Fire-Mortars, out of which Granades, several images of fortifications Num. V. Fig. 8. portion of fortification rendered in profile Profil van de geretireerde Flancken Flank vande Conter gùarde Face Fla … Raù●llÿn sinned vast aen de contra guard Laeste geretireerde Flanc t●…eede Flanc Horizont Eerste ver laegerde Flanc van den Grooten wall Fousebraies Flanck Maete van. go. voeten voor die Flank Fig. 7 angles of defensive cannon fire Fig. 6 angles of attackers 'cannon fire Fig. 9 portion of fortification rendered in profile Fig 10 schematics of portion of fortification wall Fig. 11. portion of fortification rendered in profile Fig. 12. portion of fortification rendered in profile and Fire-balls are cast; as may be seen by the F I. In case the Walls be too low, the Enemy can heighten the outward Batteries, from whence he may enfile the Wall of the Fortress. It is true indeed, That the Canon or Musquet-shots, the nearer they are shot the Horizon, the more they sweep and clear the same, and the greater Execution they do over the Fields against the Assaulters: For a shot coming from aloft, can hit the Horizon but in one place; whereas contrariwise a shot being made about the height of a man parallel with the Horizon, doth sweep the same off continually; as is seen in the Fig. 7. Numb. V where the shot made by the Musqueteer 4, standing at the top of the high Wall, hitteth and sinketh into the Horizon but in one place, as in 1: but the Musqueteer standing in the Fausse-bray A, shooteth the Line 3 2 6, parallel with his height; whence it is manifest, that in such manner it has a greater effect. To help these deficiencies, I betake myself to mediocrity, that is, to a mean height, and make the Wall in my great Fortification with Parapet, and all from 18 to 24 foot high, and the upper breadth of it, not reckoning the Parapet, as much as a Demy-Canon, having discharged an ordinary load, will run back. I take it from 20 to 30 foot broad, the Base is regulated according to the sloping of the Wall: but I do not make my Walls alike every where, but make the Profiles lighter or stronger according as the part is; for I make the Profiles of the Faces of Bulworks much lighter, than those of the Courtines or Flanques, and that with great reason, as I shall show in its due place. Of the Faces of Bulworks. THe Faces are the weakest parts of the Fortification, seeing they lie nearest to the Enemy, and cannot defend themselves; but their Defence must come from the next situated Flanques, which are made for that purpose. The Faces are always first Attacked by the Enemy, unless the Courtines be too long. When the Enemy is passed the Moat, he Undermineth this part, to make a Breach fit for an Assault. To prevent this, as far as it is possible, there is no better remedy, than to hinder the coming over of the Gallery by well ordered Flanques: But being weakened by time, and the Enemy bringing, as it were with leaden shoes, his Work as far as to the Wall of the Faces; than it is time to know the way of making Countermines in wet places: for where the Moats are dry, there is made another kind of Attacque. To make these Countermines very hastily ready, as it ought to be done, the Wall of the Faces must be no thicker than only to be Canon-proof, and that there be only place for some Canon, to be used there, when occasion requires. For in case it be very thick, the Miners can the more securely accomplish their work, and the Mines do greater execution than otherwise. The Canon which is placed upon the Faces, is commonly set upon the point of the Bulwark, where the Lines meet; and where this is done, there is after this manner place enough at the top of the Wall near the Point of the Bulwark, though the Wall be very thin. I make it in my great Fortifications from 16 to 24 foot broad, to be reckoned from the Parapet, whose top or surface I extend to the breadth of from 12, to 18 foot. Of the Flanques. I Make the Wall of this part of several heights, see Num. II. I divide first the Flanque 5, 4 into two equally, as in 8; then I draw from ⅓ of the opposite Face the right Line A 6, 8, 7, by the Point 8, so long, till it touch the Perpendicular upon A, 9 as 9, 7. This done, the Lines of the retired Flanque are made. The Profile of the Flanque I defigne thus, following the Fig. 8. Numb. V Let here the Line K, H, G, D, A be taken for Horizontal, beginning from A, which is the inner brink of the Moat; I mark from A to B, 5 or 6 foot for the berme; from B to B, 24 foot, or so thick as I desire to have the Base of the Parapet of the Fausse-bray; from B I dig under the Horizon 2, 3 or 4 foot, according as the water standeth high or low in the Ditches. At this depth I make an even place from B to D, 30 or 35 foot broad, fit for the Canon or Musqueteers. Before this place I ordain the Parapet of the Fausse-bray, 7 or 9 foot high, as from B to L: in case one would lodge Musqueteers there, Benches are made behind, and besides a convenient form is given to the Parapet; then the Flanque of the Fausse-bray is made, which I make as low, as the place will permit, yea so deep, that the Canon-shots are even with the Horizontal Line, and lower when the Moats be dry. After this I measure from D to E 27 foot, from E, I draw a Perpendicular E, 8 foot high from the Horizon. At this height I make the first Flanque of the great Wall, with its Parapet of 8 foot high, the breadth, as need requireth; as is seen clearly in the Figure: this place or Bedding for the Canon is 10 foot higher than the lowermost. After the same manner I proceed with the last, second and third Flanques: But observe always, that one place with its Parapet may come so much lower than th'other, as that the shots coming from the one or other, be not interrupted; and the smoke and blow of the upper Canon do not much trouble those, that are in the lower Flanques. But for these inconveniencies, I shall prescribe sufficient remedies hereafter. There are many more Considerations, required by the places and situations, which I leave to the understanding Architect. The Figure 8 showeth the particularities something near. Against these raised fourfold Flanques, one might object and say, That the Canon standing upon the two hindermost places, being Discharged, would let fall its stops, and Fire into the two foremost, and kindle the Powder, which is used for the Artillery standing below, and so make dumb the Cannoneers that are ordered to be below. Concerning the stops, I have seen many a time, and observed, that they fly 20 or 30 Rod from the mouth of the Pieces, especially being wrapped close together, and sometimes much further; so I did not see where they fell. Here it is to be observed, That those Pieces that stand upon the last and highest Flanque, are distant but 13 Rod from the first or Fausse-brays Parapet, from whence it appears, that such stops can do no harm: Put the case it were so, yet this obstacle cannot hinder the advantage, which I reap by these places; for in time of Attacques, I make in the Courtines little houses supported with Wood, like Mines, wherein the Powder being in Casks, and other things necessary for the great Guns are put. Those Pieces that are Charged and Primed, I cover with a small Leaden Plate, till they are to be Discharged. It is also to be remembered, That all the Pieces of these Flanques must not be discharged at once; but first from the uppermost or lowermost, and then from the others; and those in the lower Flanques may be advertised to retire themselves into the said little Houses, or in the entry of the raised Flanque, in case this precious Music do too much offend their ears. Of the Moats. THere are two kinds of Moats, viz. Wet and Dry. Of the Dry I shall speak afterwards, because they require another kind of Prosile; but now only of the Wet Moats. What they serve, and are made for, every one knoweth: Concerning their fashion and making, I give them a convenient wideness, yet according to the nature of places, broader or narrower: where there is good Ground, I make them ordinary as broad, as the length of the Flanque, which falleth Perpendicular upon the Courtine, or 10 Rods; and as deep, as I have need of earth for the Wall. He who desires to calculate, may cast up their depth according to the Profiles; I esteem the deepest for the best, as well in dry as wet places. To design then the Ground-lines of the Moats, I draw Parallel-lines with the Faces, at such a distance, as their breadth should be; and where the Parallel-lines intersect one another (which in Regular places is before the midst of the Courtines, and Bulwork-points) there are the extremities of the Ground-lines; as is seen in the Figures Numb. III. and 4. Just before the Bulworks-point I make the circular Ark, 1, 2, 3, at the distance of the breadth of the Moat; see the Figure, Num. II. by Y. And this is sufficient as concerning the wet Moats. The Construction of the Profile of the Walls for Ravelins, Counter-guards, Hidden Ways, and what dependeth on it. TThe Walls of the Ravelins joining to the Counter-guards, I make something higher and stronger; and those of the Counter-guards, lower and weaker. Likewise those of the Ravelin before the Counter-guard, still something several portions of fortification in profile Num VI Fig 8 Maete uppr dese vier profylen van. 110 voeten Profile van die linie KW in die plaete Num. 4 nae die 111. manner Groote wall van de Coúrtine groote graced Binnenste Rauelli●● wall Profil van die linie AB. indy plate Num: 4 nae die 111 manner esplanaede Buytenste ravellyns wall Profil met e'en drooge graced Groote wall Horizont Linie Foúsebreÿ Wech der ronden Binnenste Raúellins profil Horizont E'en ander profil met drooge graften Horizont linie Cúnette Profil van die Contra gúarde Perspectif weaker and lower, and I order the Profiles as follows: The great Wall with its Parapet being 20 foot high, I make the joining Ravelin with its Parapet 13 foot high; the top of the Wall, to be measured from the Parapet 20 foot broad; the Surface of the Parapet 12 or 15 foot, and the rest proportionally; the Wall of the Counter-guard with its Parapet is made 11 foot high; the top of it 16 or 18 foot broad, to be reckoned from the Parapet; the top of the Parapet from 10 to 15 foot; the rest accordingly. The Wall of the uttermost Ravelin with the Parapet I make 9½ foot high; the upper breadth of the Parapet also from 10 to 15 foot; the top of the Wall from 12 to 16 foot; the Ditches from 50 to 60 foot wide, and the deeper the better; the Hidden Way from 15 to 25 foot; its Parapet 6 foot high; the sloping (or Esplanade) is regulated after the Wall of the Counter-guard. To have a clearer declaration of this, see the Profiles Fig. 8. which are both made after the Scale adjoined; and the uppermost showeth the Profile of the Wall of the Courtines, with the Moat before it; besides the whole Capital-line with the Profile of the innermost Ravelin, or Counter-Guards-Ravelin and its Ditches, which continueth by the letter A, A; the remaining space is the Capital of the outmost Ravelin with its Profile and Ditches, as also its Hidden Way and Esplanade, which in the Print Numb. FOUR by the III. manner is showed. The lowermost Profile showeth the thickness of the Wall upon the Faces, the wideness of the Moat, the distance of the Counter-guards Wall, with the Profile of it; and the wideness of the same Ditch, which continueth by the letters B, B, on which the Hidden Way and Esplanade is also described. This is enough as touching the Profiles of the wet Moats, for such as are skilled in this Art. Where dry Moats are, I make quite other Profiles, for they are to be designed according to the nature of places. In the Print Numb. VI there are described Profiles for two several dry Moats. In the Moat of the first by the letter A is the Cunette, or false Moat, strengthened with a thin Parapet and Palisadoes, which serveth for Enterprises, and is also very good in Sieges; whose use I shall describe in the second part of Defences and Attacques. The Ditches of the Counter-guards and Ravelins, may also be sunk to the half, or above one third part, to be measured from the Wall, and strengthened with Palisadoes against Invasions, as may be observed by the letters C and D: the inward sloping of the great dry Moat must be raised of a Brickwall; as is seen by E E. These Brick-walls must be made thick and high, according to the nature of places, and the Princes or Lords purse. At the top of these Walls, there is planted a Thorn-hedge, which is either bound, as by F and D; or else planted wild, and left to grow close through one another, as by C and G. These are also very good, for they make the Earth stand sirm with their roots. The Profile A continueth with the letters H, H, where the cutting in of the two hidden Ways without Ditches are described. In the Architecture or Building of dry Profiles, there is required great experience in the practice of War; for they must be made with great skill; and being so made, I prefer them before those that are filled with water, of which I shall give reason in my Discourse of the business of Defence. The Profile of the Retired Flanques is seen Numb. V Fig. 8. according to its Scale. In the same Print is also seen a Bulwark with part of the Courtines on both sides; as it appeareth from within Fig. 12. Numb. V Fig. 11. is a Bulwark, looking against the Flanques, which Ground of two Bulworks is designed, Fig. 10. Fig. 9 is a perspective of the Counter-guard, with its two Ravelins, viz. that which joins to it, and the other, which after the manner of an Island lieth before it. In the Print Numb. VII. is seen the Perspective of this whole Work. First the Ground-lines of two Bulworks of an Hendecagone according to the middle Royal, whose outward Polygone is 90 Rods, wherein the disposition of the whole Work is perfectly seen, with that of the Counter-guard, besides their Ravelins and Counter-scarp. In the second is seen, how the whole Work lieth in Profile; yet this forelying Counter-guard hath another disposition, and is without Flanques of its own; but it is Flanqued from the joining Ravelin, and from that, which lieth in the Island. This manner of Counter-guards is also very good, and doth not take in much space. In the Figures all this is clearly seen, and therefore it requires no further explanation for the understanding thereof. I have yet many other speculations and particularities, concerning these manners of Fortifying; which I shall keep to myself, till I find a fit opportunity to put them in practice. If God give overhead schematics of fortification Num. VIII Mate van 90 Ry●lantse Roeden me health, till I bring to light the other parts (viz. of Attacques and Defence, of Undermining, Counter-mining, Fireworks and Artillery, when it may be done most conveniently) than the advantages of this manner of Fortifying will be better conceived and understood; for the quality of every part of a Fortification shall there be declared one by one separately and distinctly. Of Irregular Fortresses. I Shall say only this, That it would be too long to show here particularly the manner of working, which I esteem as needless, seeing that Irregular Fortresses are made up out of parts of Regular ones: The calculation thereof may be done after the Modern practice, and the parts afterwards reform according to my way; as hath been showed in the Regular. There are many Engineers, who think it an Art to Fortify any places altogether Irregular, although they might well enough alter them. I do not glory in this; but am very well content, when I meet with such an unfit Figure, to reform it after the Regular, as near as the place will permit. A Regular place, besides that it hath its Defence more equal, is also the fit, and taketh in with the same Lines more space, which I prove thus: Let there be a Rightangled Square, each of whose sides is 12 Rod, and the four together 48 Rod, whose content is 144 square Rod: Let there be another Irregular Square or Rhomboides, having also four straight Lines each of 12 Rod, that is, the four of 48 Rod; let this Rhomboides be made of two Equilateral Triangles, than the shortest Diameter is 12 Rod, and the longest 20 Rod, and 8 foot, whose content is therefore 124 square Rods, and 8 square Feet; From whence it appeareth, That the Rhomboides containeth 19 Rod, and 2 square Feet less than the Quadrat; and the more the Rhomboide recedeth from Regularity, the less is the content of it, etc. But this is true of Irregular Fortifications, That the Rules and Maxims of the Regular being known, the good or bad Form, as also the strength or weakness dependeth wholly on the knowledge and experience of the Engineers, etc. SOME QUESTIONS That might be moved concerning this manner of Fortifying; together with the Answers to the same: by which the use of this Work may be the better understood. I. Question. FOr what are the Flanques not drawn Perpendicular or Rightangled upon the Courtine or inward Polygone, in this Way of Fortifying; but Rightangled upon the Line of Defence Secant: For it is esteemed more graceful after this manner, and the Ground-lines may be found more easily by Calculation; it being also believed, that being thus made, they defend the Outworks the better? Answer. I Give this Obliquity to the Flanques for the Reasons following. See Numb. II. the Figure being Calculated and stated after the foregoing manner and proportion, or being measured in the Fields, the longest Defence-line would exceed a Musquet-shot; whereas now the said Line by this Obliquity is brought to its due length; whereby I reap this advantage, that with fewer Bulworks than the Modern do use, I can include a far greater space. Examples have been before alleged. And with an Octogone of my great Fortification I do include as much place, wanting only about half a Polygone, as the Modern do with an Hendecagone, or Fortress of Modern Bulworks; whereby so much charge is saved, and the Lines of Defence remain within Musquet-shot. Item, By this Delineation, the George's gain on each side in length 8 Rods in an Hendecagone, whereby the Bulworks get the desired opening at their entrance, which maketh place for the Retired Flanques, and affordeth conveniency for the making Retrenchments speedily and easily. By this Obliquity the Flanques do likewise become also longer, and therefore fit to lodge a competent number of Canon and Musqueteers upon them. This Obliquity causeth also the Gun-holes not to stand Obliquely, and that the Moats are Rightangled and defended from the Flanques. And whereas they say, that the Perpendicular Flanques defend the Outworks the better, this doth not stand to reason; but it is known, that the Obliqne ones do it better, seeing they come more flat against them, and the Outworks are better seen from the Obliqne Flanques, when they are made after this manner, etc. II. Question. FOr what are there three Flanques and the great Wall, set at the top of one another, and yet below a Fausse-bray's Flanque; whereas nevertheless the Canon being placed thus above one another, the uppermost cannot be discharged conveniently, without prejudice to those that are in the lower Batteries. Besides that, the flame coming out of the upper Canon, and falling upon the lower, might give Fire to them also sooner than would be desired? Answer. THese three or four Flanques, I make at the top of one another, not to plant them all full of Canon; but to fit the uppermost with Musqueteers and Falconets, as occasion requireth. But if need should require, that I must have a strong Counter-Battery upon the Flanques, or that much Canon must be there, to hinder the coming over of the Galleries: then put the case, that all four Flanques are filled with Canon; what should hinder me from using them at pleasure, without endamaging the lower, or giving fire to the lower Canon before the due time, if I go to work after the manner following? At one side of these Retired Flanques, I place a skilful person, either an Officer of the Artillery, or some other. This Officer, when they are upon Discharging, commandeth the men in the lower Flanques, to retire themselves at the side of the Battery into the Way, by which the Canon is let into the Flanques, till such time as the uppermost have Discharged; which Shooting beginneth from the last Retired Flanque, where the longest and heaviest Canon may most conveniently be used. When these have Discharged, they Charge presently again, and then those of the second Retired Flanque give Fire; which being done, they also Charge again with all possible expedition: For those that have Discharged (beginning from the hindermost) cannot be prejudiced by the following Canonadoes; and this continueth, till the Flanque of the Fausse-brays (being the last to give Fire) hath also done. In this time the hindermost can have almost Charged and Leveled; so that after this manner one may orderly Charge and Discharge the Canon, as if it were a Band of Musqueteers, without hindering or prejudicing another. These Canon-shots are alternatively favoured by Musquet-shots, coming from the second Flanques; (where I would Lodge no Canon, except there were great need, for the reasons before mentioned) as also from the second Flanque of the Fausse-bray, and also from the half of the great Walls Flanque and Faces, etc. Concerning what is objected, That the lower Canon might be kindled by the upper before its time; for this, no other remedy needs to be used, but to cover the Holes with a Plate of Lead, as they do in Ships. Now it may be considered, Whether it be easy or no, to bring a Gallery over a Moat, that is seconded by such a Hail of Canon and Musquet-shot. III. Question. SInce here is mention of so many Canons, there must be great number of them, to furnish one of these Fortresses with Artillery: For besides that the great Wall (or Royal Work) requireth much Canon, the Outwork ought to have part of it too, seeing it defendeth itself, as well as the great Work, with Artillery and Muskets; and according to the number of Gun-holes, there must upon the four heightened Flanques on each side of every Bulwark be at least 20 ●●eces, which is 40 Pieces for each Bulwark; which in a Fortress of seven Bulworks amounts to 208 Pieces, for the entire Fortress only. Now in the Outworks there is by the joining Halfmoons of the Counter-guard, on each side place for 12, 13, or 14 Pieces: If it be 14, it is for every Courtine 28, which for the Counter-guard of an Heptagone comes to 196 Pieces of Artillery, and so the whole Work to 476; to which Ammunition being added proportionally, all other things necessary, the charge would be extraordinary. Answer. IN this my Fortification I want no more, or at least very few more Canon, than in the Modern; which I prove thus: In a Modern Heptagone there must be at least eight Pieces for every Bulwark, when a Siege is expected; namely 3 upon every Flanque, and two upon the Bulworks Point, that is 4 Demy-Canons, two Pelicans shooting a Bullet from 3 to 8 pound, and two half or whole Dragons as occasion requireth. Whereunto are commonly joined 4 or 6 whole Canon, to be used upon Counter-Batteries; these being reckoned together make up 56. It is an old custom, to keep in Fortresses that are considerable, twice as many Pieces in the Arsenal, as are upon the Wall, to fill up the places of those that shall happen to be Dismounted or to crack, or to become useless by any other accident; as also to be used upon the Crown, and Hornworks: This number is in all 188; which the Modern Engineers appoint in their Works. These I distribute in my Fortification, when there is no Siege, after this manner: Upon every middle Flanque of the great Wall two, and upon every Bulworks-point two, which is 6 for every Bulwark, and so for the Royal Work 42: In the Counter-guard none are required, but however, in case one would Plant them there, there might be set near every joining Halfmoon, two, which maketh 4 for every Courtine, that is 28 for seven Courtines, in all 70 Pieces; and then the place is furnished round about with Artillery, as well for the Inworks as Outworks. But instead of lodging these 28 Pieces upon the Flanques of the Counter-guards, I think it more convenient to use them upon the next Ravelin, because I keep there the outward Sentries, or Cors de Guards, which do Flanque the Counter-guards from within, and hit the Enemy from behind, in case he should undertake to pass the great Moat. But in time of Siege, I distribute my Canon quite otherwise, and do as follows. At the first coming on or surrounding, I take my lightest Canon and place them upon the points of the Counter-guards, to keep off the Enemy's Quarters, as far as it is possible; yet, the Quarters being closed, and I perceiving whereabout they open their Approaches, whether they bring on 2 or 3, although they make seldom more than two, and have sometimes a third, only for diversions sake: Admit, they carry on two Approaches, by which they intent to Attack two Bulworks; to promote these Approaches, it is needful for the Besiegers to raise Batteries, under whose favour they may make their Labourers work with more surety. Against these Batteries I raise Counter-batteries (that is, when they come near, within 150 or 200 Rod,) these Counter-batteries I can raise every where, as well in the outmost Ravelin before the Counter-guard, as upon the Faces of the Counter-guards themselves, whereto I use some heavy Pieces: upon the other Bulworks or Outworks there is then little need of any Pieces, but only of Falconets, or other small Guns. Now the Besiegers being after all difficulties, come so far with their Approaches, that they are ready to pass the Ditch of the Counter-guards, than I use not where any Pieces more to defend the Outworks, but only upon the Flanques of the Counter-guards, where in Fortresses according to the great Royal, might be used 14. Yet in case two Bulworks be Attacked at once, the Ditches and Faces may also be defended by two opposite Flanques, upon which two there must then be 28 Pieces. If three Bulworks be Attacked, there must be 42. These Pieces I can always retire again from the Flanques into the joining Ravelin, and from thence into the Fausse-bray of the great Wall, and further upon the Flanques of the great Wall, which are opposite to the Faces Attacked; and upon all occasions there need be no more upon these Flanques than 14, seeing the Enemy cannot place any more against them with advantage, but 10, unless they come to stand one in another's way. Suppose one would have 18 upon every Shoulder or Flanque, this would make 54 Canons for three Flanques, which being also trebled, the whole number amounts to 162. Whence it appeareth, That in my Fortification no more Canon is required than in the Modern; and one might in time of need very well make shift with a third part, that is with 54, in a Fortress of seven Bulworks, if a skilful Governor had the management of it: But for want of such men, the best Strong-Holds are soon lost; For let a place be Fortified with as much providence as it will, in case he who Commands it, has no skill, it signifieth nothing. iv Question. WHat may this way of Fortifying cost more than the Modern, seeing they are far larger in their parts; and much more is spent for the retired Flanques, than for the simple ones, as well to make the Shooting-holes, as also the paved Batteries: The Wall of the great Work, or of the Fortress must also needs be something higher, than that of the Modern, so it may command the better over the Wall of the Counter-guard; and with these Counter-guards much Field is also taken in, which is chargeable, in places where it must be bought from the Commonalty or Owners? Answer. THis Work being well considered, it will be found, that the charges differ little from the Modern: For I with my Pentagone take in as much or more place than the Modern with an Hexagone; my Line of Defence Fichante remaining still within Musquet-shot, whereby the charges of one whole Courtine and a Bulwark in a Pentagone are saved. Concerning the charges of the retired Flanques, against them I put the two Faces of the Modern Fausse-brays, which I do not make; as also the charges that are required for the digging of the Moat before the Courtine, where in my Fortification out of that part of the Moat nothing near so much Earth is taken. N. B. It is not necessary, that these Flanques should be brought presently into this order round about the Fortress, when they are made. One may make up the first paved Flanque of the great Wall, which falleth upon the Ground-line, something higher then usually, and lay 2 or 3 Benches behind the Parapet, and putting Palisadoes at the top of the Parapet, which come to be so high as the great Wall; and being Besieged, whilst the Outworks are disputed, there is time enough to bring all things into order. Concerning the great compass of the Counter-guards, the charges bestowed that way are little, seeing in time of Peace, (as is said before,) the enclosed Land and Wall, and all may serve for civil uses as well, as if these Walls were not there at all: Besides, that these being compared with the Modern Outworks, as Halfmoons, Horn and Crown-works, etc. as are about many Strong-Holds, it will be found, that these my Counter-guards do not enclose so much place, nor do not cost so much. It might be further said, that these my Fortresses would require more men for Defence than the Modern: In order whereunto, it is to be considered, How the Garrisons ought to be ordered in time of an Attacque? I shall only answer this, That the Outworks ought first to be Defended well; and to do that well in my Fortifications, no more men are required, than in one of the Modern, having but one Bulwark more than one of mine; for by my Method, I include more place with fewer Bulworks. I shall only tender this, That the Flanques being well furnished, the Fronts are easily defended; for herein consisteth the strength of Fortresses: which may be compared with a man that hath strong and long arms; it is evident, that such a one can better defend himself, than another who hath short and stiff arms. Thus I conclude this little Work, hoping that it will be acceptable to the Lovers; and stir them up, in case it do not please them, to bring to light something better. TO please those who desire to study Engineership, I have added an Abridgement, which shows how all Calculations necessary for this Science may be made with little pains, only by Decimals, without being subject to the intricacies of Fractions; as also the most usual manners of Working with ease, by Compasses, etc. Arithmetic in Decimals. THis Calculation doth not differ from the ordinary Method, only in the understanding of the Signs of the Fractions, and how to place them rightly, which is as follows: First take a Rod, (which is the usual measure of the Country where you are,) or what measure you please, and call that an Integer; this divide into ten equal parts, and take one part for a Foot; this Foot divide again into ten parts, and one of them take for an Inch; the Inch divide again into ten parts, and call one of them a Grain; the Grain divide again into ten, one of which call a first Scruple; and that divide again into ten, and let one of those parts be called a second Scruple; and so on to the tenth Scruple; which tenth Scruple is 1/10000000000 part of a Rod, and is so small, that it cannot be comprehended otherwise, than by understanding the following Signs: A Rod, or Integer, ⓪ Foot, ① Inch, ② Grain, ③ First Scruple, ④ Second Scruple, ⑤ Third Scruple, ⑥ Fourth Scruple, ⑦ Fifth Scruple, ⑧ Sixth Scruple, ⑨ and so on to the Ninth Scruple. Addition in Decimals. OBserve here the same manner, as in the Addition of Integers; but have a care, that the Signs of the Fractions of one sort, do stand under one another; as Rods under Rods, Inches under Inches, etc. Example. THere are to be added 2 ⓪ Rods, 3 ① Feet, 4 ② Inches, 7 ③ Grains, 0 ④ Scrup′. 2 ⑤ Scrup″. 3 ⑥ Scrup‴. to Rods 89 ⓪ 2 ① 3 ② 4 ③; I place then Rods under Rods, as 2 ⓪ under 89 ⓪, and the other Signs also under one anoother; as may be seen and where the Signs want, fill up the places with 0, and put the last Signs of the Fractions behind them in a crooked or round stroke; which showeth, how many places or kinds of Decimals there be, as is seen in the Example, and the Sum is 91. 581023 ⑥, that is, 91 Rods, 5 Foot, 8 Inches, 1 Grain, 0 First Scruple, 2 Second Scruple, etc. and the Sign of the Fractions being , therefore six Figures are to be counted from the last towards the left hand; and so many kinds of Decimals there be. Substraction in Decimals. PUt here also the Signs of one sort under one another; and where they fail, fill up the place with 0. Example. There are 56. 32 ② to be substracted from 982. 345 ③, therefore put 982. 345 ③, and 56. 32 ② underneath, so that Rods come to stand under Rods; so the remainder is 926. 025 ③, and so forth in all cases, fill the places of the Signs with 0, where they are not. Multiplication in Decimals. HEre follows also the common rule; but you must add the Signs of the Fractions together. Example. Division in Decimals. THis is also done the ordinary way; but here the Sign of the Divisor must be substracted from the Signs of the Dividend, or the Number to be divided: and in case the Number to be divided, be less than that by which it must be divided, join so many 0 to it, till it come to be equal to it. Example. THere are 5. 76 ② to be divided by 3482 ④; here the Divisor is greater than the Dividend; therefore add so many 0 to it, till it come to be as great or greater; as here 0000 Ciphers, and there will be 5. 670000 ⑥, this divide by 3482 ④, as is usual in common Divisions; and put the Signs as here is seen, & the Quotient is 165 ②; Now to know what kind of parts they be, subtract the Signs of the Fractions, as 4 from 6, and there remaineth 2, and this 2 is the Sign of the Quotient, as may be seen; and this is a general way: There remain yet 772, of which if you desire to have yet smaller parts; then put so many Ciphers behind it as you desire. NOTA. If you put one 0 behind it, or Multiply it by 10, that is all one; and by so doing it is brought to 10 lesser parts, etc. The Rule of Three in Decimals. THis is performed after the same manner, as in the Integers: and forasmuch as it consisteth of Multiplying and Dividing, observe the foregoing Rules. Example. quotient. The proof make thus: Say 7 ② giveth 116 ⓪, what then does 3 ④ give? There ariseth by Multiplication 348, to which adding 2 which remained, the whole is 350 ④; these divided by 7 ②, the Quotient 50 ②, and putting away the 0, as signifying nothing, there remaineth the sign ①, and then the Quotient is as above 5 ①, and the Work is right. To extract the Square Root in Decimals. TO sinned the Root of a Number given, even in its smaller parts, put after the Number given towards the right hand, as often two Ciphers, or 00, as you desire parts, and half the Number of the Ciphers is the Sign of the Fractions that belongs to the Root; as may be seen in the Example. Example. 20345, Out of this Number I desire to have the Square Root, to the second Scruple, or nearer; therefore I put as often two Ciphers to it, as I desire to have parts, as here 4; wherefore I join eight Ciphers to it, and work, as is usual in Integers; as may be seen here beneath. various geometric shapes Num. VIII To extract the Cube-root in Decimals, or Fractions. OPerate in the same manner, as in Integers, and look how many Fractions you desire, so often put 3 Ciphers behind it; and this wanteth no further declaration, etc. Having thus shown the Arithmetic in Decimals, I proceed to show some Draughts and Operations with the Compasses, which any one may use at pleasure. How a given Circle is to be divided into equal parts, and the Polygones of all Regular Figures, necessary for Fortification, are to be inscribed within it. LEt the given Circle be A, B, F, E, Numb. VIII. Fig. 1. through which draw the Diameter A B; and where it toucheth the Circumference, as in A and B, put one foot of the Compasses, and make the two Intersections, C and D; and from the Points, where they cut, draw a straight Line C D, falling Perpendicular upon the Diameter A, B: these two Lines A, B and C, D divide the Circle into four equally, and A, E is a side of a Square. Taking F for the Centre, and drawing at the distance F, G an Ark H, G, I, and then a right Line from H to I; where this Ark cutteth the Circumferencc, as H, I, this is a side of an Equilateral Triangle, which may be inscribed within this Circle. The half of this Line, as H, K, is a Polygone of an Heptagone, and the distance I B is the side of a Dodecagone; Take K for the Centre, and at the distance A, K describe the Ark A, L, the Line drawn from the Section L to A is a side of a Pentagone, the Line G, L is the side of a Decagone; G, N of an Hexagone; E and B are the Centres of the Arks G, M, which Line divideth the fourth part of the Circumference into two, and N, B is the side of an Octogone; divide the Ark H, F, I into three equal parts, and one third, as H, O is the side of an Enneagone; from L to P is the side of an Hendecagone; E, L is the Polygone of a Figure of 16 sides. Another way to find the Sides of every Regular Figure, that may be inscribed within a Circle. THis is done thus; Divide the Circumference into four equal parts, and then one fourth part of the Circle into so many equal parts, as the Figure should have sides; and take four of those parts, and that will be the length of the Polygone of such a Figure as you seek. Example. THe Circle Q, P, V, R, in the Plate Numb. VIII. Fig. 2. is first divided into four equal parts by the two Diameters Q, V, and P, R; ¼ part Q, P is divided into ten equal parts, four of those parts is the side of a Decagone, viz. the length K, P, which being set off ten times about the Circumference, describeth a Regular Decagone; after the same manner do with all other Figures, dividing always ¼ of the Circle into so many parts, as you desire sides; and four of these parts being taken with the Compasses, make up the side. This manner may be also proved by Arithmetic. N. B. In the making of Geometrical Figures, the Compasses ought always to be set perfectly upon the Lines, and marks made softly with the feet, to do the work with more perfection. There are many other ways, which we pass over for brevity sake. To divide a Line with the first opening of the Compasses, into as many parts as you desire. LEt the given Line be D, E, which you desire to divide into ten equal parts; therefore draw an undetermined Line B, H, and open the Compasses at pleasure, and with that opening set off as many parts upon the Line as you desire, (as here ten from B, to H;) so the tenth part reacheth to H; upon this Line B, H make an equilateral Triangle B, A, H, and from A draw the Lines AI, AK, ALL, AM, etc. Thus you have by the parts of the Line B, H, a Triangle, which is divided proportionally: then take with the Compasses the given Line D, E, and set it off from A to G, and also from A to P, and draw the Line P, G, equal to D, E, which by the intersecting Lines is divided into 10 equal parts; as also the Line F, G, if it be required, and so with all other Lines whatsoever. To let fall a Perpendicular upon a given Line. THe given Line is G, F, and upon the point G we let fall the Perpendicular G, H; therefore set one foot of the Compasses in G, and open th'other at pleasure, as here to I; from thence make the Circumference H, G, F; and where this cutteth the Line G, F, (as in F) from thence draw a Line just by the Centre, till it touch the Circumference in H, and from the Point H draw the Line H, G, which standeth rightangled or Perpendicular to G, F. There are many other ways, which I here omit for brevity sake. From a given Point in a Line, to raise a Perpendicular. THe given point is A, and the Line B, C, in Fig. 5. Set one foot of the Compasses in the point A, making with th'other the Ark B, C; upon these Points set one foot of the Compasses, opening th'other at pleasure, as to D, and make from these Points the intersection of the Arks in D, at the distance D, C, and draw a Line from the intersection by the given point A, to the Line B, C, which is Perpendicular to B, G. To make an Equilateral Triangle. UPon the Line B, H, in Fig. 6. set one foot of the Compasses in B, and with th'other take the distance B, H, and with that make an Ark about A; as also out of H: where these Arks intersect one another, there is the third Point of the Triangle; and draw from thence the Lines A B, and A H, and so the Triangle is made. To make a Triangle of three right Lines given, whatever they be, provided that two of them be longer than the third. THe Lines are AB, CD, OF; take with the Compasses the length of one of the three, which you would have to be the Base, (which is here A, B) and mark two Points, one in H, and th'other in L; from the Point L describe the length of the Line C, D with an Ark in K, and from H the length of the Line E, F, and cut the former Ark in K, and there is the third Point: from K draw the Line K, H, equal to E, F; K, L, equal to C, D; and L, H, equal to A, B, etc. Three Points being given, and not standing in a right Line, to draw a Circumference, which shall pass through all three. THe Points are O, P, Q; make the equal sections on both sides of the Centre, as from P and also from Q, which is done in V; as likewise from O, which falleth in 5, Perpendicular upon Q, P, and P, O. Where these touch one another, there is the Centre (as is seen in Fig. 7. Numb. VIII.) of the Circular Ark O, P, Q, which being drawn, etc. The same manner observe in the finding of the Centre of a Circular Ark, or a whole Circle. To divide a given Circle into 360 degrees, and to make an instrument from it which Geomemetricians call a Theodolit, or Astrolab. THis Instrument is of great use in the Mathematics; for by the same all inaccessible distances, heights and depths are measured, the use of which I shall declare in its own place in the following parts, and it is divided thus: The Circle A, B, C, D being first divided into four equal parts by the two Diameters A, B and C, D, take with your Compasses the exact length of the half Diameter; as A, E or E D, by which the Circle is divided into six equal parts, and after the manner following into 12; with this opening of the Compasses, set one foot in C, and with th'other make upon the Circumference marks on both sides in F and G, likewise from D in H and L, etc. Thus the Circumference is divided exactly into 12 equal parts. The part D, A, or a quarter of a Circle, containeth 90 degrees, as a quarter of 360 degrees; F, C being a sixth part, 60 degrees; and D H as a twelfth part, 30 degrees; then divide a twelfth part, as D, H or D L into two, as in O and P, and such a part holdeth 15 degrees; then divide one of these parts into 3, and one of them will hold 5 degrees, of which one being exactly divided into 5, one of these is a degree, of which 360 make up the whole Circumference of every Circle, whether it be great or small, and are always proportional, viz. the least Circle that can be made, to the greatest Circle of the Sun, or any other Astronomical Circle: For if you draw several Circles out of one Centre, and from the same Centre several Semidiameters to the utmost Circle, the Arks intercepted in the innermost Circles contain as many degrees, as those in the outmost, etc. Each degree containeth 60 Minutes, a Minute 60 Seconds, a Second 60 Thirds, a Third 60 Fourths, and so on; and they are written thus, 4. ° 5. 6. 7. 8. which is as much, as 4 Degrees, 5 Min. 6 Seconds, 7 Thirds, 8 Fourths. How all kind of Ovals may be drawn by the Compasses, is to be seen by the marks 1, 2, 3, 4, 5, and needeth in my opinion no further declaration, seeing the manner of working appeareth enough by the Figures. By 6 is an Oval, which can be made by a Cord and 2 or 3 Nails: This manner is of much use in Architectura civili, to make obliqne Vaults. By 7 and 8 are seen two sorts of spiral Lines, whose structure may also be perceived by the Figures. And thus I have showed the principal Draughts with Compasses, serving for Geometrical use. END. For the Bookbinder, To place the Prints of the Copper-Plates. Numb. after Fol. II. 8 I. 12 III. 22 IU. 28 V. 30 VI. 34 VII. 36 VIII. 48