A PRACTICAL ABSTRACT Of the Arts, of Fortification and Assailing.  
Containing Four different Methods of Fortifications, with approved rules, to set out in the Field, all manner of superficies, Intrenchments and approaches, by the demi Circle, or with lines and Stakes.  
Written for the benefit of such as delight in the Practice of these noble Arts.  
By David Papillon Gent:  

I have diligently perused this Abstract: and do approve it, well worthy of the Public view.  
Imprimatur  
Io: Booker.   
London Printed by R: Austin and are to be sold at the south side of the Exchange & in Pope's head Alley 1645  Tho: Cross f●cit  engraved title page   


PLUS GLADIUS, QVAM SCEPTRA VALENT.  
TOMAS FAIREFAX. ANAGRAMMA. FAX ERIT FAMOSA.  
THOMAS FAIRFAX.  
Generalis exercitus Anglicani Mirare tacitus, fataque vergant vide.  
IN ANAGRAMMA.  
Ferri-Fax erit haec patriae Famosa salutem Civibus ense suis exitiumore fereus.   portrait of Thomas Fairfax   

TO HIS EXCELLENCY, Sir THOMAS FAIRFAX, Generallisime of the Forces of the honourable Houses of Parliament.  
Excellentisime,  
IF the subject of this Abstract were rightly considered, it would appear to all ingenious spirits, that the dedication of it doth properly appertain to your Excellency, as the most experienced Commander in the Art of War, of all these Northern parts, as it may appear by your Martial achievements; having, like a lightning, past this Summer from the North part of this Kingd me, to the utmost point of the West of it; throwing down, like a rapid Torrent, the banks that did endeavour to stop his course: and therefore the better able to judge aright of the benefit that might redound to the State, if these Methods of Fortifications were observed in the Works of our Garrisons; and these field 
* The Arts of Defence and Assailing are two of the most essential parts of ●he Art of War.  intrenchments, and double entrenched Camps here described, were used in all our formidable sieges and pitched battles; the neglect of which hath been one of the main secondary Causes of the spinning out of this unnatural War.  
But since it hath pleased God to raise you to that eminency of place, that affords you power to rectify these defects; I have presumed to tender to your Excellency these essays, 
* The neglect of these intrenchm●nts is to be rectified.  containing some approved directions, for the future, of the Works of our Garrisons; and for the double entrenched Camps, that we are of necessity to make use of, if we intent to give (by the gracious favour of God) a speedy and a blessed period to the miseries of this poor and desolated Kingdom.  
If I were not assured that you are extraordinarily well versed in the ancient and modern Histories, I should endeavour by manifold instances, to persuade you to be the restorer (in these Northern parts) of the Military Discipline of the ancient Romans, and of the field-intrenchments, and double entrenched Camps, whereby 
* See Caesar's Commentaries in the waries of the Gauls and of Africa.  Caesar made himself the absolute Monarch of the world, as Maurice Prince of Orange was the restorer of them in the Netherlands, to his eternal fame. For certainly, it is the only means, after God's favour, to conduce these civil distractions to a speedy and a blessed accommodation: but being confident that these things are familiar to you, I will refer them to your judicious consideration; and only beseech you to be pleased, out of your gracious affability to all men, and particularly to myself, to be the 
* Maecenas was the Emperor Augustus Caesar's favourite, and the Patron of learning.  Maecenas to these Essays, and to accept of them with the like affection, as Artaxerxes the great King of Persia received two hands full of fresh water, that were presented unto him by a poor Subject of his, for want of a better gift to express his love: So shall I for ever be obliged to remain  
Your Excellencies most humble, and devoted Servant, DAVID PAPILLON. From London, Jan. 1. 1645.   

To the Reader.  
SOme will corceive this time unseasonable for the publishing of this Abstract, because of the prosperous success of our Armies this summer, and therefore (say they) it were more seasonable to write of razing to the ground our old Garrisons, then to write of directions to erect new: I answer, that I wish their conceits should prove real truths, for although I writ of two of the most essential parts of the Art of War, yet I daily pray and wish that all the Inland. Garrisons in this Kingdom were razed to the ground, that his sacred Majesty might the sooner return in love and peace to his most loyal Parliament. But when I consider, 
First Consideration.  that the virulency of the humour of a Civil War is like a canker in a woman's breast that never gives over the sucking of her blood, till by her death he slay himself; and that the two parties of all civil wars, 
Second Consideration.  may be compared to a couple of tennis-ball players, that have sometimes the best, and sometimes the worst, one after another, and that they that do rely over much upon their advantage, do commonly lose the game, I disassent in judgement with these imaginary conceits.  
For as a wise and learned Physician can partly guess by the symptoms of the disease of his patient, 
The evidences that signify our miseries are not yet come to their last period.  whether his sickness will be of a short or long continuance, even so ingenious spirits, may partly guess by these ensuing symptoms, visible to all men, that the dangerous malady of this unnatural war, is not yet near her crise.  
First, by a general antipathy that continues still in the incliclination of men. 
The symptoms of the general malady.   
Secondly, by the Heresies, Sects and Schisms that rend and make greater breaches in the Church, than ever was known since Queen Mary's days.  
Thirdly, by the great obstinacy of such as would seem more holy, than their Brethren, and yet prefer their own ends before God's glory, and the unity and concord of the Spouse of Christ.  
These dangerous symptoms, I say, are evident signs that England's mieseries are not yet nea●e to their highest period, yet God's ways are not like our ways, for he can when he pleaseth, draw light out of darkness, and deliverance from things that seem most destructive to his Church.  
As concerning these that conceive the publishing of this Abstract unseasonable at this time, and would have us because of this sumines prosperous success cast ourselves in the bed of a carnal security, I will prove by two instances that there is nothing more dangerous then to rely upon prosperous events, and upon our own● p●●ts and activity.  
1 It is recorded that Attelante running the race in the 
* See Plutarch in his discourse of the Olympian Games.  Olympian games, did so rely upon her activity, that she took up twice one after another in her race, two golden balls, that her Antagonist did cast down to retard her speed; and notwithstanding recovered her ground: but the third pall being cas●, as it seems, too near the end of the race, she l●st by the taking of it up, the Crown of honour due to the Victor: whereby it appears, that consta cie in all things carrieth the bell away.  
2 When 
* See Hannibal's Life, and Titus Livius Decades.  Hannibal did run the race against the Romans, for a Crown of no smaller value than the Empire of the whole world, he was after the three famous victories obtained against them, at the river Trebie, at the Lake of Trasymeine, and at Cannis, in greater probability to obtain the Crown he ran for, than we are at this present to obtain the Crown of the race of this unnatural war. And yet by these defects; 1 By relying overmuch upon his former success; 2 By neglecting his advantages; 3 By casting himself in a bed of carnal security in Capua, in stead to advance towards Rome with his Army, he lost not only the Crown he strove for, but also his life and Commonweal.  
These considerations and instances past, and these motives following, have therefore induced me to publish this Abstract.  

1 To procure the common safety.  
2 To rectify the deformities of our Fortifications.  
3 To enlighten the meanest capacities, that delight in the practice of these Arts.   
For the first, it is certain and known to all men, that the insufficiency of the works of our Garrisons, hath been the secondary cause, that divers of them have been lost suddenly and their Inhabitants wrought to penury. To prevent this evil for the future, I propose to our ●ounties four different method●●f Fortifications, that they ma● make choice of the most ●u●●ble to their means and abilities, assuring them that the meanest of these four Method 〈◊〉 stronger and ●●fer than their Mounts and winding Angle●; so they observe the dimensions described here for every one of them.  
For the second, the deformity of our Works is so great, and the errors in the setting out of them so gross, that they serve only as an object of derision to Foreigners that see them: And these errors proceed from a self-conceitedness inherent in some men of these days, that presume to have skill in those things, in which they have no skill at all; for the most mechanical Artificers and Shopkeepers will be meddling with the spiritual Function, and control Enginiers. And some Divines, in stead to feed their flocks, do take upon them to be Sub-Committees of the fortifications of a Garrison. And these dnorders are permitted by the over-frugalitie of some Committees, to save an Englniers pay: a destructive frugality to themselves, and to a whole County, as some have found by lamentable experience. Now to avoid these errors for the time to come, I have in this Abstract set down (without reservation) the proportions and dimensions they are to observe, and from whence they are to draw the Lines of their Flanks, and of their Line of defence to be convenient for the Cannon and Musket-shot, without which observations not Fortification can be good, or serviceable.  
For the third, the Theorical writings of Mr. Ward, Mr. Cruso, Mr. Norwood, and of the Author of the Enchyridion, have rather increased the ignorance of mean capacities, than their knowledge in the practice of these Arts: For I have conversed with some, that had all their rules upon their finger's ends, that could not set out a Superficie in the field to any purpose, and that is the reason why I writ more plainly than they; or that I should otherwise have done, if it had not been to enlighten the meanest capacities, that delight in the practice of these noble Arts. Therefore if these Essays of mine may any way be profitable to thee, I shall attain to my wished end: If not, accept how ●o●ver my good will, since I can neither offer nor give more than I have received from above. And so committing thee to the gracious protection of God, I desire to rest  
Thy servant in the Lord, David Papillon. From London the first of January, 1645.   

THE CONTENTS.  

Chap. 1. Of the true character of a complete Engineer.  
Chap. 2. Of the antiquity of the Art of Fortification.  
Chap. 3. Of the Nations that have excelled, and do excel at this present time in the Art of Fortification.  
Chap. 4. Of the true use of the Art of Fortification.  
Chap. 5. Of the best, and of the worst seats for Garrisons.  
Chap. 6. Of the Foreign Fortifications and Dimensions.  
Chap. 7. Of the superficies contained in the first Plate.  
Chap. 8. Of the superficies contained in the second Plate.  
Chap. 9 Of the superficies contained in the third Plate.  
Chap. 10. Of the five Redonts contained in the fourth Plate.  
Chap. 11. Of the two first methods of Fortification in general.  
Chap. 12. Of the fortifications of the Equilateral Triangle by Bastions with orillon's, demonstrated in Plate 9  
Chap. 13. Of the Fortifications of the Square by Bastions with orillon's, demonstrated in Plate 10.  
Chap. 14. Of the Fortifications of the Pentagon by Bastions with orillon's, demonstrated in Plate 11.  
Chap. 15. Of the Fortifications of the Oval by Bastions without orillon's, demonstrated in Plate 8.  
Chap. 16. Of the Fortifications of the Sexagon by Bastions with orillon's, demonstrated in Plate 12.  
Chap. 17. Of the third Method of Fortification, by Avantguards, and Outguards, and half Moons, in general.  
Chap. 18. Of the extent of the sides or Bases of all manner of superficies, and of the just length of the Line of Defence.  
Chap. 19 Of the Fortifications of the superficie in the form of S. Michael's Cross, fortified by eight half Moons, demonstrated in Plate 13.  
Chap. 20. Of the Fortifications of the Paralograme, fortified by Avantguards, demonstrated in Plate 14.  
Chap. 21. Of the Fortifications of the Equilateral Triangle, fortified by Avantguards, demonstrated in Plate 15.  
Chap. 22. Of the Fortifications of the Square, fortified by Avantguards and Outguards, demonstrated in Plate 16.  
Chap. 23. Of the Fortifications of the Pentagon, fortified by Avantguards and outguards, demonstrated in Plate 17.  
Chap. 24. Of the Fortifications of the demi-Sexagon, fortified by Avantguards, and outguards, demonstrated in Plate 18.  
Chap. 25. Of the fourth and last method of Fortification by small Plankers in general.  
Chap 26. Of the Fortifications of the Octogon fortified by small Flankers, demonstrated in Plate 19  
Chap. 27. Of the Fortification of the Paralograme, fortified by small Flankers, demonstrated in Plate 20.  
Chap. 28. Of the Fortifications of the Square, fortified by small Flankers, demonstrated by a Demi-Square, in Plate 21.  
Chap. 29. Of the Fortifications of the 24. Angle Poligon, fortified by small Flankers, demonstrated in Plate 22. by a demi-Poligon of 12. Angles.  
Chap. 30. Of the Fortifications of the mixed superficie, fortified by small Flankers and three Redouts, demonstrated in Plate 23.  
Chap. 31. Of the Art of Assailing in general.  
Chap. 32. Of the charge, and qualities of a prudent and experienced Governor.  
Chap. 33. Of six different ways how strong Holds may be reduced.  
Chap. 34. Of the opinion of experienced Commanders concerning sallies made by the Defendants at the beginning of a Siege.  
Chap. 35. Of the entrenched Camp, demonstrated in Plate 24.  
Chap. 36. Of the Batteries erected, and of the Mines to be sprung against a besieged Garrison, demonstrated in Plate 25.    


CHAP. I. Of the true Character of a complete Engineer.  
AS the blessed success of an Army depends (after the favour of God) upon the election of a wise and valiant General; so doth the sufficiency of the works of a Garrison depend upon the choice of a skilful Engineer. And the want of this choice hath been hitherto the essential cause, that sew or none of our Garrisons have been fortified, as they ought to be; and why divers of them have been lost in eight and forty hours. Therefore to prevent this evil for the future, I intent, in the first place, to speak of the qualities required in a good Engineer, That the Committees of our Garrisons, to whom this choice appertaineth, may be informed of them, to the end, they may hereafter be more circumspect in their election.  
1. He is to be religious; for 
b Eccles. 2 15.  the fear of the Lord is the beginning of wisdom.  
2. He is to be a soldier; for none can better judge of the sufficiency or insufficiency of Fortifications, than they that have learned from their youth to defend, and to take them.  
3. He is to be a traveller; for he that hath not seen variety of works, and the excellency of foreign Fortifications, cannot perceive the defects of ours, nor give directions to rectify them.  
4. He is to be well versed in the Arithmetic for his calculations; in the Geometry, for the setting out of all superficies; in the Architecture, for to direct all manner of artificers; and in the other parts of the Mathematics, for the taking of distances depths, and elevations, and for the inventing and the contriving of all manner of Engines and machine's of war.  
5. He is to be wise in all his proceed, punctual in all his promises, careful and diligent in his calling, and rather inclined to austerity then lenity, or otherwise he will never be respected, served or obeyed.  
6. He is to be of a solid judgement, and quick of apprehension, to judge aright of the defects and advantages of places, of raising grounds, or hollows that may endanger, or command a place committed to his trust, and what kind of method of Fortification is most convenient for it; and which method, among the rest, requires less men to man the works; or to judge of the weakest places of a Garrison, if he be desired by his General to go with him to besiege a Town, advising him where he is to begin his approaches, plant his batteries, where he is to erect his bridges, if there be a river running of one side, or in the midst of the Town, and how the line of communication is to be drawn to secure his bridges; and what redoubts or flankers are required to fortify his Camp. He is not to give account of his actions to any, but to the General, or to the lieutenant General of the Ordnance; if he be in an Army, or in a Garrison, only to the grand Committee, and to the Governor; and as for all other kind of men, inhabitants, soldiers or officers; he is not bound to expostulate the case, if they demand of him reasons for any thing he directs or commands to be done; neither ought he, if he regards his reputation, and makes conscience of his ways, to comply (when he is called to a Council of war, or before a full or whole Committee) with the humour of the greatest in authority, or be led to assent to any resolution, that is against the maxims of his Art, by the Logical and Sophistical reasons and arguments of Scholars or Churchmen; for some of them are now a days overbusy in things that go beyond their element, and endeavour to oversway Artists by rhetoric, considering not that their reasons are no reasons at all to the reasons of art. And this last quality is the essential part of a good Engineer; for all the other are but to small purpose without this.   

CHAP. II. Of the Antiquity of the Art of Fortification.  
THe antiquity of this Art may be derived from the time of Nimrod 
c Gen. 11.4, 9 , for the Tower of Babel was an admirable structure, or Fortification, & from that time it came to a higher degree of perfection in the days of Ninus and Semiramis his Queen, that erected the incomparable Rampires, and unparallelled Towers, that did begirt the great City of Babylon, that were of such an incredible strength, height and breadth, that 
d See S Walter Rawley Histor.  Cyrus when he besieged the same, durst not attempt to assail it on the Land side, but was enforced to drain the great river of Euphrates, into small channels by the irksome and indefatigable labour of his great Army, and so entered the same the very night that King 
e Dan. 5.3.  Belshazzar was carousing with his Princes, wives and Concubines. We read also that 
f See Titus Livius in his Decade. 1.  Vejente was so strongly fortified, in the second century of years after the foundation of Rome, that the Romans could not have reduced the same in ten years' siege, if Furius Camillus their General had not invented, at the later end of the tenth year, the Art of mining, by which means he took the same, by breaking in the middle of the City with his mine, while a general assault was given by his Army, to draw all the soldiers and inhabitants of the City to man and defend their Rampires. 
g See S Walter Rawley in his history of the world.  Tyrus also was so strongly fortified in Alexander the greats days, that his Army durst never assail their works on the Land side, but were enforced after three years' siege to erect a Mole, over a bay of the sea, of an incredible structure, whereby it was reduced, because the seaside was not fortified. Syracuse also was so admirably fortified, that 
h See Plutarch in Marce lus life.  Marcellus, a rare and valiant General of the Romans with a great Army could not reduce the same in two years' siege, and had never taken it, if Archimedes, the rarest Engineer and Mathemaetician that ever was, had not preferred the completing of a Geometrical demonstration before his own life, and the preservation of his Country. 
i See Plutarch in his life.  Demetrius also king of Macedonia, with a great Army, and all his admirable Machine's of war, could never make a sufficient breach in the Rampires of Rhodes, but was enforced to raise his siege from before it, because of the impregnable Fortifications of it, but it flourished specially, and attained to the highest degree of perfection, that ever it was before: and since that time in 
* See Caesar's Comment. and joseplus history.  Caesar and Titus days, as it will appear in the next Chapter, when I shall come to speak of the siege of Alexie in France, and of Jerusalem. Therefore I do not a little wonder, that a Gentleman so well read in Histories as Mr Ward was, should disagree from the opinion of the greatest Commanders that have lived in our days, by maintaining, as he doth in his 
k ●●e from p. 50 to 60.  Animadversions of war, that we excel, in this Age, the Ancient in the Art of Fortification and assailing. But this error proceeds by the comparison he makes between the Fortifications that were erected in Christendom, some century of years after the Goths and Vandals, that had over-runne the greater part of it, and by their barbarous disposition, had destroyed all the ancient monuments, and overcast by their burning of all books of Sciences, a cloud of ignorance over all the face of Christendom: and therefore to make good his opinion, he should have taken his comparisons from the flourishing times of the Greeks and Romans, as I will show in another place.   

CHAP. III. Of the Nations that have excelled, and do excel at this present time, all other Nations in the Art of Fortification.  
IT is certain that the Chaldeans, Jews, Greeks', and Romans have anciently excelled all other Nations in the art of Fortification and assailing: And that the Italians, the French and the Hollanders, do at this day excel all others in these Arts. M. Ward in his Animadversions of war, is pleased to give the precedency to the Hollanders; yet I know no reason for it, except it be to honour that Nation, where he exercised his Militia. For if the Hollanders excel these two former Nations in their outguards, they do as much excel them in their inward works; and all Enginiers know, that the inward works are the essential parts of the Art of Fortification. And yet of late years Sr Anthony de Ville, and Honorat de Meynier, two of the last French Kings Enginiers, have gotten in my opinion the start of the Hollanders, for outworks, and avantguards also. Notwithstanding they have the most convenient soil for such works, of any Nation in Christendom, because twenty Pioneersin Holland, will do more work in one day, than threescore can do here in England, France, or Italy in two days, for the evenness of their soil, the tenderness of their ground, and their plenty of turf. But if the precedency in these Arts belong to any of these three Nations, it appertains really to the Italians, for John Baptist Zanche, Castriot Durbin, Francis Montemeillino, Lorini Florentine, and Peter Sardi a Roman, and divers other Italian Enginiers, some of which coming with the Duke of Parma into the Low-Countries, infused in the French and the Hollanders, what they know of these Arts, for they were the first that revived and adorned them, after they had been buried for divers centuries of years, in the grave of oblivion, by the inhumanity of the Goths and Vandals. I do not here place the Spaniards and Germans, to stand in competition with these three Nations, because the greater part of the best Fortifications in Germany and Spain, have been lined out and surveyed by Italian Enginiers. Now, whether our modern Fortifications do excel the Fortifications of the ancient Chaldeans, Jews, Greeks and Romans, it cannot be decided, because theirs are destroyed, and ours extant; except we refer ourselves to the testimony of the ancient Historians: which, if we do, M. Wards position, spoken of in the last Chapter, is absolutely overthrown. For although I have seen in my travels, the greater part of the rarest and strongest holds in Christendom, yet I must ingenuously confess, that I have seen none to be compared to the Towers and Rampires of Babylon, to the Fortifications of Vejente, Syracuse, Tyrus, and Rhodes, but especially, to the Citadel of Antonia, and the three Towers, and the Rampires, that Herod the great built in Jerusalem, in commemoration of his wife, brother and intimate friend. And as for the Art of assailing, that goeth hand in hand with the Art of Fortification, as two inseparable Twins or Companions; all judicious men know, that as the one increaseth in degrees of perfection, so doth the other, because if new inventions be found to fortify places, more sufficiently than one could formerly, the ingenious spirits of great Commanders have no rest, till they have found new ways of assailing to reduce them. For instance, the invention of bastions and motes of fourscore, or of a hundred foot broad, and thirty foot deep, full of water, was no sooner found out, but Gerard a French Engineer, that was in the service of the Prince of Orange, found the invention of our Galleries, whereby these large and deep motes may be passed without danger, and mines made to blow up the bastions. Whereby we may conclude, that if the ancient did excel us in the Art of Fortification, they did also go beyond us in the art of assailing. Now to prove that they did excel us in them both; we are, 1. To examine what modern Fortifications are extant, that may be compared to the ancient Fortifications before cited. 2. In which of all our modern sieges, there hath been more art and industry shown, then at the siege of Alexie, and of that of Jerusalem? But because this point may more properly be decided, when we shall have occasion to speak of the art of assailing; I will pass it over at this time, to examine another position of M. Ward, that maintains, our Ordnance to be more powerful than the great Machine's of war of the ancients; and upon this infers, that of necessity our Fortifications must be stronger than theirs were, because some of ours can hold out against the thunder of our roaring Cannons. Mistake me not, I do not speak of the Fortifications of this Kingdom, for I knew never a Garrison of ours, whose works are only of Cannon-proof, but of the best foreign Fortifications. I acknowledge that the great Machine's of war of the ancient where more cumbersome to manage then our Cannons are; but that our Cannons be more powerful than they were, it doth not appear to be so by the testimony of the ancient Historians. For the great Rams of the Romans, made great and sufficient breaches to come to an assault, in the strong Rampires and Towers of the Citadel of Antonia, and in Herod's Towers, that were built, saith Josephus, of bard freestones of an incredible thickness; against which, a battery of six of our Cannons could not have moved one of them. And in lieu of our muskets, they had balisters that were more powerful, where with they kept the defendants in such awe, that they durst not peep out thorough the portholes of their battlements. It is therefore most certain, that the ancient Greeks and Romans, have not only excelled us, in the Art of Fortification and assailing, but also in divers other Arts; as in the Art of graving, of painting, of sculpture, of architecture, and in all the parts of the Mathematics, and in the very art of war. And as for the power of their Machine's and balisters, it was also greater than that of our Cannons, and of our musket-shot; only they were, as I have said before, more cumbersome, because their great Rams required two hundred men to manage them, and their balisters four or six men: and six Cannoneers with their six mates, and four and twenty matroses, will manage six Cannons mounted upon a platform, and every one of our soldiers can manage a musket; and notwithstanding this advantage, they excelled us in the art of war.   

CHAP. FOUR Of the true use of the Art of Fortification.  
THis Art was invented at the first, to preserve a handful of men against the oppression and cruelty of a multitude; for according to the rules of it, a Garrison Town is not sufficiently fortified, except one hundred men within it, can oppose a thousand assailants without; and a thousand, ten thousand, that is, one defendant against ten assailants; but it is with this caution, that the place besieged be provided with a competent number of men, ordnance, ammunition, arms, victuals, and a Magazine furnished with all manner of fireworks, morter-pieces, engines of war, ladders, and pioners tools; for if any of these necessaries be wanting, this Garrison will not subsist against a lesser number, then is here spoken of. But the Committees and Governors of our Garrisons, are for the greater part so careless of these things, that few or none of our Garrisons are provided of victuals for a month, and of ammunitions, arms, fireworks, ladders, and pioneers-tools, so slightly, that the first assault would deprive them of all their store: nay, I have been in a Garrison so ill provided, that in their timber-yard, there was not so much good timber, as to make a drawbridge, nor a ladder, nor barrows to be had, when occasion did require to use them, but was enforced to stay while they were made. Now how such a Garrison could subsist against an active army, if it were besieged, I leave it to the judicious Reader to judge of it. But our enemies are more provident, witness the long resistance of Basin, of Lathamhouse, of Carlisle, of Skipton, and Scarborrow-Castle, and now of Chester.  
2. It was invented to preserve a small Army in the field, against a great and powerful army, or of an army against three armies. As 
l See Caesar Comment. of the war of Africa.  Caesar did preserve himself, and the small army he had with him in Africa, against the three powerful armies of King Juba, of Scipio, and of Labienus; and by his great experience in this Art, did overthrow them all, more by the spade and pickax, then by his sword. And one of the main secondary causes of the spining out of this unnatural war, hath been, that our Commanders in chief have neglected to make use of this noble Art, that Caesar himself did not disdeign to practise; for he often lined out the intrenchments of his own Camp, and would draw upon paper the models of the Forts, or Engines of war, that he would have his Enginiers to set out, and have made. And for the erecting of bridges over 
m See Caesar Commentary in the wars of Gaul  Rivers, and raising of high mounts and plat-forms to place high wooden Towers, and his Machine's of war, he excelled all his Enginiers, as may be seen in his Commentaries, by the strong and stately bridge that he erected over the Rhine, when he passed over into Germany, which bridge he fortified with four Forts, and rare intrenchments, to secure his return into France, leaving for the defence of them one of his Legions, and for the raising of incredible Towers, Mounts and Plat-forms, and for the setting out of an entrenched Camp, with a double line of Communication, I will refer the Reader, because I shall have occasion to speak of it in another place, to the siege of Alexie in France, where we may see his admirable industry and skill in this Art. But we have shamefully been enforced sundry times to raise our sieges for want of an entrenched Camp, as at Newark, Dudley Castle, Pomfret-Castle, Banbury-Castle, and Dennington-Castle, and in all these by an handful of men; whereas if we had be●● in an entrenched Camp, an Army six times as great could not have forced us to a retreat. Therefore to besiege Towns or Castles of any moment, without an entrenched Camp, except we come to a general and furious storm, the next day after our Army hath faced the same, it is properly to spin out this war wittingly; and for to receive rather an affront, then to obtain a victory, or honour and reputation.  
3. It was invented to erect strong holds upon the Frontiers of a State or Kingdom, to prevent the incursions of a foreign Enemy, that might with a great Army, come like a roaring flood, that throws down all the river banks, into the very heart of a Kingdom, without opposition, and by mere activity conquer the same; as the Duke D'Alva conquered for the King of Spain, as unjustly as suddenly, the Kingdom of 
* See the History of Spain in Ferdinand and Isabella's Reign.  Navarre, under pretext to pass thorough that Kingdom, to go against the French King, then in Languedock. And the essential cause of this great loss came by the negligence of the King of Navarre, that had not provided, as he should have done, with men, Ammunition, and victuals, his Frontier Garrison Townes.  
4. It was invented to preserve men's habitations, and the Suburbs of Corporations, and not for to burn, or pull them down, as many of our Enginiers have done in these days, to their shame and guilt of conscience. For if an Engineer, to comply with those in authority, or with the self-conceited men of a Garrison, assent to pull down Suburbs, or small Hamlets that are joined to their Corporations, except they are suddenly and certainly in danger of a Siege, it argues that he is either unskilful in his profession, or void of all Christian charity, and natural humanity; for by the experience of his Art, or alteration of his method of Fortification, he may preserve these Suburbs or Hamlets, to the great advantage of the Town; or of another Fortification, and so dispose of his works, that he may secure them, and yet the Corporation shall rather need fewer men to man their works, than it would require when these Hamlets are pulled down. This hath been the case of Leicester, for had they not rejected a good counsel, they might assuredly have been preserved by a larger Line of Communication, than there was by half a mile; for this Line might have been defended with three hundred men less than that they made, for the which they were enforced to pull down many honest men's houses, and draw a true imputation of inhumanity upon themselves; for what greater inhumanity could these poor souls expect from their cruel Enemies, then to see their houses burned, or pulled down. And by this instance you may see how dangerous it is for Committees and Governors to be led away by the chat and ridiculous reasons of ignorant and self-conceited men, that make no conscience what mischief they do to others, so they secure themselves, as they suppose; for it is often rather a supposition, than a true security or preservation, because it falls out oftentimes, that if these Hamlets or Suburbs be fortified, they serve as Bulwarks for the preservation of their Town, and so by pulling down of them, they advance their own ruin, to save some small charges; nay, they often increase them, by pulling of them down. For instance: It is supposed by the judgement of such men , that Cotton End, a small Hamlet adjoining to the South bridge of North-hampton, is to be pulled down, if they be threatened of a Siege, to make the circumference of their Works the less, and to secure their Bridge. But I will maintain that if Nature itself, and the Art of man had plotted together, to place a commodious seat to serve as a Bulwark, not only to the South bridge, but to the whole Town, they could not have found out a better than that part of Cotton End is. For being fortified as it ought to be, it will make that side impregnable; and this End might have been fortified and secured at the first, with smaller charge and a shorter Line of Circumference, then that which they have made, by which it is exposed to the Enemy's mercy, and yet their Works are by it of less validity, if they had not relied overmuch upon their own judgement.  
And although this conceit is backed with the assent of a earned Divine, yet I will judge charitably of his assent, as being in judgement so possessed, this being out of his element; yet wisdom should induce him to rely more upon the judgement of an Artist, than upon his own, and specially when it is bend upon the safest and the most charitable course. And this counsel I give them, to fortify only the said End, according to the model inserted in the 23 Plate; now they may conveniently do it, will be worthy of thanks if they embrace it; but if they do not, if ever they be besieged, it will produce an after-wish, as those of Leicester did, when it was too late; O that we had followed such an advice and counsel: And so much for the discharge of a good conscience.  
5. And lastly, it was invented to fortify some places of refuge in the time of a Civil War, that a whole County be not ruinated by a roving and plundering Army: But in this, the Committees of such Counties are to be very cautious in their election of a seat, for all the head-Towns of Counties are not convenient to erect Garrisons: And therefore I shall acquaint them in the next Chapter, of the best and of the worst seats for a Garrison: And will only for a conclusion of this point, inform them, that all seats of Garrisons, if they may be found, are to be as near the middle of the County as may be, that they may the sooner relieve all the parts of the County: And that by no means they assent to erect any more than one in one and the same County, that they may be the better able to fortify, man, and provide the same to some purpose; for plurality of Garrisons in one and the same County, whether they are foes or friends, are destructive to a County.   

CHAP. V Of the best, and of the worst Seats for Garrisons.  
ANd first of the best Seats, as better deserving the preccedency; a good Seat is to be freed of all sides, from hills or raising grounds that may command, or of all hollows that may endanger the Garrison itself, or the Works of it; If the Town hath walls, 
* Mr. Ward is also of the same opinion concerning our old walls. See pag. 35. and chap. 20.  a good Engineer is not to regard them, specially if there be hollows, and raising grounds within Canonshot of them; for it it is not the lining of these walls, or the erecting of Mounts near or upon them, or the drawing of ill-lined and ill-flanked dikes within five or six yards of them that will secure the same. But a prudent Engineer is to let them stand, as a second weak defence, to obtain a parley after all is lost, and yet not to rely on them, for they are rather destructive helps then profitable defences; But to draw his Line of Communication one hundred yards or more into the field beyond them, to take in those hollows that will endanger, and hills or raising grounds that will command his Works. Or if they be too fare distant from the walls, he is of necessity to erect well flanked Forts, or Redoubts to secure them, or all his Works will not be worth a button; let his Works be never so well carried up, or lined out. And these Forts are to have Corridors, or covered waves to retreat into, for to be relieved from the main Line of Communication, out of danger of the assailants shot: for a raising ground left out of the Line of Communication of Leicester, was the secondary cause of the loss of it, and of a hundred towns more, if an abstract did permit to produce divers like instances. And as for Mounts errected near or upon old walls, they are of no other service, then to hinder the assailants approaches, for a day or two; but when their approaches are made, they are of no defence at all, for having a raising ground within Canonshot, one may dismount all the Ordnance upon them in an instant of time; and for the musket-shot, they are also of no use, because the shot of the Musket doth not fly upon a level line, but upon a descending line from a great height downwards, and so can hurt none except it be at pointblank, but upon a level line, if the bullet miss one, it will hit another, and what is said here of the musket-shot, it may be applied to the Canonshot, for if the assailants had no raising ground to dismount the Cannons placed upon these Mounts, their Canonshot cannot offend them, when their approaches are within one hundred yards of these Mounts, for it is the long distance that giveth a level line to the Canonshot, when it is mounted so high. And as for the lining of old walls and the making of dikes so near them, they are destructive ways for the defendants: For the first, the earth and walls doth never bind together, but falls and helps to fin and level the town dike upon the first storm of the Canonshot that is shot against the walls. And as for the second, the very splinters of the wall during a Cannon storm will drive the defendants from the Brest-Workes of these dikes, that are so near the Walls, to a shameful desertion of them, to save their lives, and so they will become by accident a very safe entrenchment for the assayllants, and so much be it spoken upon this subject for them, to whom it concerneth.  
1. The best seat of all seats, 
Of the best Seats.  is a Haven town freed on the land side of the foresaid impeciments, having a safe road for ships, and a deep and broad channel for the coming in, and such a one was Tyrus and Rochel, for a Garrison so seated can hardly be reduced without a Sea Navy and a Land Army, and how inconstant the winds and seas are when winter is at hand, all ingenious men know. Therefore it is to be reduced in a summer, or divers accidents may fall out, to free the same from the restraint by sea, and as for Tyrus 
* See Sir Walter Ra●●● leigh his History of the world.  after three years' siege, and an incredible charge, to make a mole over a bay of the sea, to reduce the same, the great Army of Alexander found in it but a small recompense for their labours, for the richest Inhabitants saved themselves and their treasures by sea: and as for Rochel, if the Cardinal de Richelieu, or his Enginiers for him, had not found an admirable invention to make a floating bridge with great Liters over a narrow arm of the sea, fortified on both sides the Land with two strong Forts, having in the midst two great Platforms erected, every of them upon four great Liars fast chained one to another with strong iron chains, Rochel 
* See the French History.  might (according to humane reason) have been at liberty at this day.  
2. The second is a Town seated upon a raising hill in the midst of a Champion Country, well provided with springs and cisterns of water, having an even flat top, and all the sides but one, of strait down and R●ckey ●lif●es of some thousand yard's Diameter, and such a one was Beeston-castle in Cheshire, for such a place cannot be reduced but by famine.  
3. The third is a Town seated in a Champion Country, free of the aforesaid impediments having an unfordable r●v●r running in the midst or close to one side of it, and such another is Newarke, for it cannot be reduced without an entrenched Camp (if the Works be high and strong) and two brings traversing the river, that the one Army of one side may relieve the other on the other side, as occasion requireth.  
4. The fourth is a Town seated on the side of a hill having a deep river running in the foot of it; whose buildings and works extend themselves to the very top of the hill, and her Fortifications unto the two sides of the river, and such a one is Nottingham, had it not as it hath a sandy soil, yet this defect may be remedied with art and charges.  
5. The fifth is a town seated upon a raising ground, in the midst of a marish, having but one coming to it, provided with wholesome springs, and such a one is Pessaro in Italy.  
6. The sixth is a dry town seated in a Champion Country that is of a good soil, and in a place where divers Roads meet, and upon the borders of three or four Counties, for this being regularly fortified, is of great defence, and of great advantage to the owners of it, and such a one is Cremona in Lombardia.  
The worst seats are these: 
Of the worst Seats.  First, a Town seated between two hills, within Cannon shot; Secondly, a Town seated in the midst of a Marish, upon a flat and even ground: Thirdly, a Town seated upon the side of a hill, the top of the hill commanding the same: Fourthly, a Town seated upon a hill barren of water, and a rockey ground; Fifthly, a Town seated upon a sandy soil. Sixtly, a Town seated in the midst, or on the side of a Forest.   

CHAP. VI Of the foreign Fortifications and Dimensions.  
THe greater part of the foreign Fortifications are not for our imitation, because they require a long time to erect them, and more men than we have, or are able to pay, to maintain and defend them, and more means to finish them, than we have at this present, the means of this Nation having been exhausted, by this unnatural war: Therefore I will omit to speak of their Cavaliers, Faulses, Brays, Tenailles, Horne-works and Outworks of their Ravellins, and Corridors, or covered ways, as being altogether unuseful for us, for the reasons above expressed. Yet to satisfy the curiosity of the reader, I will treat of two of their methods of Fortifications, by Bastions without, and with orillon's, and of the dimensions & proportions they observe in them, that the Reader may the better judge, whether these chargeable works are convenient for us, or no. I will also speak of another of their Methods of Fortification by Avant Guards, newly invented by Honnorat de Maynier, a rare French Engineer, that would be as chargeable as any of the other two, if we did not reduce it to shorter dimensions, and wholly omit the costly Freestone Works they adorn them withal. And I do it the rather, because this kind of method (above all others) is more capable of dimintion in her proportion, and be little or nothing at all the worse.  
But I will (in the fast place) represent unto you the proportions and dimensions of the two methods by Bastions without, and with orillon's, that have no difference at all in their proportions and dimensions, but only in the Line of the Flanks, and in the turning and framing of the orillon's.  
First, the dikes of these two Methods are ordinarily between fourscore or fivescore foot broad, and their depth about twenty five, or thirty foot deep.  
Secondly, they have another smaller dike in the midst of these great dikes, if in case they be dry, calied La Cunette, that is some four and twenty foot broad, and twelve or sixteen foot deep; this small dike is commonly full of water in all places; for the rainwater descending from the Rampires, and the sides of the great dike, fill it, although the ground be void of springs; this small dike is very useful, for it preserves the Garrison from being scaled, or surprised in the night time, for the undertakers cannot pass the same without they cast a casting-bridge over it, and that cannot be done without noise, and this noise waketh the Sentinels, and alarms the Garrison; and with the earth of this dike they commonly make their Counterscarp brest-work, adorning the same within side with turf, and one foot slope, the rest being laid or spread aslope, till it come to nothing, and even with the firm ground; that the French call Glacis.  
Thirdly, their Rampires are commonly fourscore or fivescore foot broad in the bottom, with a slope on both sides of two foot or a yard high; but on the wall side it cometh no lower than the boltill of the stone walls, that the French call Cordeau: for upon that boltill they set their battlements of their wall, that are about five or six foot high, having a Porthole at every two yards, and three foot from the Cordeau, and by reason of the great slope, that the Rampire hath, a way of some eight foot broad is presently form, that runneth between the battlements of the wall, and the Rampire, that is called the way of the rounds, and in French Le chemin des rondes, and this way goeth from one Bastion to another, round about the Garrison; a very commodious and necessary means for the Rounds to go safe in the night, and to discover by looking out of the Port holes of the battlements, if any appears near to their Counterscarp or Corridor that are on the other side of their dike, and the Rampire besides the Brest-work upon it, is commonly six foot higher than the battlements of the walls, and the Brest-worke six foot more; so that the splinters of the wall during a battery, cannot offend the soldiers, that defend the Brest-workes of the Rampire.  
Fourthly, the Rampires are commonly thirty foot high, besides the height of the Brest-worke that is six foot high within side, for it hath a foot-step of eighteen inches high, and two foot broad, and the whole height of the Rampire with his Brest-worke, is within side thirty six foot, and without thirty three foot high, because the top of the Brest-work is carried three foot slope, because it is always twenty foot broad at top to be of Cannon-proof: and the Rampire besides the thickness of the Brest-worke and the slope of the two sides defalked, is always forty foot broad on both sides, on which they plant Elms or Sicamore Trees, that in few years make very pleasant and shady walks, that serve in time of siege for a way for horse, men, foot and carriages, to come to defend and relieve the Rampire.  
Fiftly the distance from the Centre of one Bastion to another is commonly from two hundred fifty yards to three hundred yards.  
Sixtly the faces of their Bastions are ordinarily from one hundred yards to one hundred twenty yards, besides the turning of their orillon's that is about twenty yards.  
Seventhly the whole gorge of their Bastions are from one hundred yards, to an hundred and twenty yards, from out to out.  
8 The breast of their Bastions are from 120. yards, to 130. yards.  
9 And from the centre of the Bastion, to the point, or the utmost Angle of the Bastion, from 80 yards to 100 yards.  
10 The flanks of the Bastions from 42 yards to 50 yards, that is divided into three equal parts, if they make orillon's; one part is allowed for the flank, and the other two for the turning and the framing of the orillon's.  
11 Their curtains are always between 160 yards to 200 yards.  
12 The Line of Defence, to be good for the defence of the musket shot, is to be from 220 yards, to 250 yards, at the most.  
13 The slope of their Brest-works without side, is one foot for every yard, if the earth be good; 
Now let the Reader judge, whether these costly Fortifications be for our turn.  and within side a foot in two yards: but if it be a sandy ground, or a running clay, it requires a foot and half without side, and a foot within, for a yard high.  
14 The foundation of these walls begin from the bottom of the dike, and are carried up to the upper water-table of the wall to the Cordeau; and from the bottom of the dike on the field-side level with the ground, and all of free stone. The midst of the Bastions are filled up with earth to the Cordeau, and made slope to the firm ground of the town, and their Rampires and Brest-works are raised fifteen yards above the Cordeau.   

CHAP. VII. Of the superficies contained in the first Plare.  
SInce the Principles of Geometry are the very groundwork of the Art of Fortification, I judge it convenient to begin this Abstract, by the demonstrations of such superficies as are most commonly used in the practice of this Art. 
Of Superficie.   
A Superficie is properly any kind of form demonstrated upon paper, or upon the ground, enclosed with three lines at the least, except it be the circulary form, that hath but one circulary line, that gins at one point, and ends at the same.  
The point is a small touch of the pen, 
Of the Point.  that cannot be divided, because it hath no parts, but is the beginning and end of all lines, and the centre of all Forms. See Figure 1.  
A line is the continuance of a point that is incapable of division; 
Of Lines.  but in the length of it, it is distinguished by divers terms: As, by the straight line, in Figure 2. by the circulary line, in Figure 3. by the perpendiculary line, in Figure 7. by the parallel line, in Figure 8. by the diagonal line, in Figure 11. and by the diametrical line, in Figure 12. There are divers other distinctions of lines, but they are not useful in this Art.  
All Angles derive from the conjunction of two lines in one point; 
Of Angles.  whether they be straight, circulary, diagonal, or mixed with any one of these. As Figure 4. is called a plain Angle, because two straight level lines, from one and the same distance, meet at one point, and a straight perpendicular, and a level line falling in the midst of a straight line, produceth an Obtus, and a straight Angle, as in Figure 7. And two circulary lines meeting at one point, maketh a circulary Angle, as in Figure 5. And a straight and a circulary line meeting at one point, produceth a mixed Angle, as in Figure 6. There are also divers other sorts of Angles, some of which we shall have occasion to speak of in another place.  
The eighth Figure demonstrates how to make a perpendiculary line cut a straight line given, 
Of the eighth Figure.  and how you may cut that perpendiculary line in three parts, by three demicircles, to make up the line given, three parallel lines, without altering the compass to any other distance but the first.  
First, let a straight line be given, then take the just distance of that line with your compass, and set one of the points of it upon the right hand end of the line, and with the other point make a small demicircle above; then remove the point of your compass upon the left hand side of the line given, and with the other point make another small circle, cutting the first; and where these two small circles cut one another, set your rule, and draw a straight line to the line given, and it will cut the same with a straight perpendiculary line. Now to avoid all error that might proceed from the mis-placing of your Rule upon the line given, make but two other small demicircles below the line, as you did above, and where these cut one another, put one end of your Rule, and the other, upon the upper cutting of the two small demicircles, and draw a straight line, and (of necessity) the perpendiculary line will be straight, and without error.  
Now to cut that perpendicular Line in two equal parts more, to make up the Line given, three parallel Lines, set your compass upon the just distance of the length of the perpendiculary Line, than set one of the points of the Compass, upon the lower end of the perpendiculary Line, and make a demi circle upwards, then remove your Compass upon the upper end of the perpendiculary Line, and make a demy-circle downwards, then remove the point of your Compass upon the Center-point, where the perpendiculary Line did cut at the first the Line given, and make the third demy-circle upwards, and this demy-circle will cut the other two in four places, and where they cut, set your rule, and draw two straight Lines, and these will make up the Line given, three perfect parallel Lines, as it is clearly demonstrated in figure 8.  
The ninth figure showeth how to draw as many parallel Lines as you please, upon two lines, 
Of the ninth Figure.  that are the upper and the lower lines in this figure. First, let two equal lines be given, one below, & another above, according to the length you desire to have your parallel lines, then divide these two lines with your Compass, in as many parts as you desire to have parallel lines, and at every division make a point, and from every point make a demy-circle above the upper and the lower given lines, than set your Rule upon them one after another, and draw as many lines as there is demy-circles, and these will all be perfect parallel lines. Now if you will double these parallel lines, it is but to divide with your Compass the just breadth of them in two parts, and at every division to make a point, and to set your Compass again upon its first distance, and to cut your first demy-circle with it, and to draw as many lines, and you shall have as many more perfect parallel lines as you had before, as it is clearly demonstrated in Figure 9 
Of the tenth Figure.   
The tenth Figure showeth how to make a square and a triangle upon a line given: Suppose the Base of the square is the line given, now to make a perfect square, and four Scalene triangles of this line, you are to set your Compass upon the just distance of the line, and to set one point of it on the right hand end of it, and to make a demy-circle, and to remove your compass upon the left end, and to make another demy-circle, and where they cut one another, set your rule, and draw a perpendiculary line, then turn your rule, and draw a straight top line, and join the base line with this top line, by two straight lines, and you will have a perfect square, and four perfect square scalene triangles, as it is demonstrated in Figure 10.  
The eleventh Figure showeth how to make a paralograme out of two circles. 
Of the eleventh Figure.  First, set your compass upon the demi breadth of the paralograme, that you intent to make, and then make a circle on the right hand then remove your Compasse-point upon the extreme of the first circle on the left hand upon a straight line, and with the other point mark the Center-point of the other circle, then turn your compass round, and you will have two circles whose extremes will touch one another, than set your rule upon the four extremes of these two circles, and draw four straight lines; and where these lines cut one another, there is the four Angles of the Paralograme, as it is demonstrated in Figure 11.  
The twelfth Figure showeth how to make a perfect square by the outside of a circle: 
Of the twelfth Figure.  Make choice of your Centre, and set your compass upon the very Diameter that you intent to have your square, then make a circle, and draw four straight lines upon the extremes of it, and it will produce a perfect square, as is demonstrated in Figure 12.   

CHAP. VIII. Of the Superficies contained in the second Plate.  
AMong all other Superficies there is none so useful for the Art of Fortification, as the Triangles; and yet Mr. Ward in his Animadversions of War, makes mention but of three sorts, yet there are six principal sorts of Triangles, from which all other mixed Triangles are derived; and these six sorts may be all set out by the Circle, as it is demonstrated in this Plate.  
The equilateral Triangle deserves the precedency, 
1 Of the equilateral Triangle, and the best way to set out the same.  because it is the only Triangle that can be fortified by Bastions, for all her sides are equal; the best way to set it out, is to set your Compass upon the just distance of the Base of it, and to make two points with your Compass, and to draw two Demy-circles, one from the right point, and the other from the left hand point, and where these Circles cut one another, make the third point, and draw three straight lines to these three points, and it will produce a perfect equilateral Triangle equal of all sides.  
Some set it out by the Circle, 
How to set out the equilateral Triangle by a Circle.  dividing the Diameter of it in four equal parts, and draw a straight line upon the first quarter point, as the Base of it, and two lines more from the two ends of the Base to the top of the Diametrical Line of the Circle; but this way is not so perfect as the other. See Figure 13.  
The Isocele Triangle is also very useful in the Art of Fortification; 
2 Of the setting out of the Isocele Triangle.  for all the regularie Poligons of many Angles, after the Sexagon, are composed of Isocele Triangles; but the Sexagon is composed of six equilateral Triangles, that have all their sides equal: But the Isocele Triangle hath always two sides equal, and longer than her Base; it is set out after this manner out of the Circle. After your Circle is made draw a straight perpendiculary Line Diametrical wise upon the Centre of it to the two extremes of the Circle, then divide that last Line into eight equal parts, and draw a straight line with your rule, upon the first point of the eighth part division, from one extreme of the Circle to another, and that Line represents the Base, then draw two straight lines from the two ends of that Base, to the top-point of the Diametrical Line of the Circle, and these three Lines will produce a perfect Isocele Triangle. See figure 14.  
The Recteligne Triangle is also useful in the Art of Fortification to set out Half Moons, 
3 Of the rectiligne Triangle, and how it is to be set out by the Circle.  her Base contrary to the Isocele Triangle is longer than her two sides; it is set out after this manner: After your Circle is made, draw a straight Line from the two side extremities of the Circle, and cut with that Line the Center-point of the Circle, and this Line represents the Base, then draw two other Lines from the two ends of the Base, to the upper point of the Circle, and two other Lines from the two ends of the Base, to the lower point of the Circle, and it will produce two perfect Recteligne Triangles, that makes also a perfect square Rhomb.  
The Scalene Triangle hath all her sides unequal, it is very useful for measuring of land; 
4 Of the scalene Triangle, and how it may be set out by the Circle.  for two of them make an Equilateral Triangle, and four of them a perfect long Rhomb. It is to be set out after this manner. After your circle is made, divide the side diametrical line of the circle into eight equal parts, then cut with a straight line the first eighth point of that division on the left hand point, and then divide the diametrical line of the circle that is drawn perpendiculary-wise into four equal parts, and cut with another straight line the first equal point of that division towards the Base, or the lower side of the circle; then from the two sides of these two lines draw a straight diagonal line, and these three lines will produce a perfect scalene Triangle. See Figure 21.  
The acute Angle, 
5 Of the Oxigon Triangle, and how it may be set out by the Circle.  or Oxigon Triangle, is only useful, for measuring of land, all her sides are also unequal, and all her Angles acute, you are to set it out after this manner: After the Circle is made, draw a Diametrical line perpendiculary-wise, that may cut the point of the Centre from the top of the Circle to the bottom; then from the lower end of this line on the left hand, make a point at the fourth part of the Circumference of the Circle, and another point on the right hand, at the third part of the Circumference of the Circle; then draw a line from the left hand point to the right point, and two other lines from the right hand, and the left hand point, to the top point of the Diametrical line, and these three lines will produce a perfect Oxigon Triangle; see Figure 22.  
The Obtus Triangle is useful in Fortification, 
6 Of the Obtus Triangle, and how it may be set out by the Circle.  and for measuring of Land, two of her sides are equal, and contain but the two third parts of her base, her base being longer than her sides by a third part, it is to be set out after this manner: After the circle is made, divide the Diametrical line of it into three equal parts, and cut the first point of this division by a straight line, and this line represents the base, then draw two lines from the two ends of this base, to the top of the Diametrical lines, and these three lines will produce a perfect Obtus Triangle, see Figure 23.  
Now I come to the 24. Superficie that containeth an Oval, 
Of the setting out of the Oval.  and in that Oval two long Rhombs, a Paralograme, two equilateral Triangles, and four Scalene Triangles. But because I have already spoken of all these, the Oval and the two long Rhombs excepted, I will begin with the Oval, the most difficult of all other superficies to be rightly set out upon paper, or in the field.  
To set it out upon paper, you are to set your compass upon the scale of the third part of the length you intent to have the Oval, and this third part is to be divided again into two equal parts, and your compass set upon that sixth part: then make choice of your Centre, and cut the point of the Centre with two straight lines, one of them perpendiculary-wise, and the other diametricall-wise: then set one of the points of your compass upon the Centre point, and with the other make a point upon the diametrical line on the right hand, and another point upon the same line on the left hand, than set the compass again upon the third part of the length of the Oval, and set one of the points of it upon the right hand point, that represents the End of the third part of the line of the length of the Oval, and with the other point of the compass make a circle, then remove the point of the compass, and set it upon the left hand point of the aforesaid line, and make another circle and the two extremes of these two circles represent the length of the Oval. Then remove your compass and set one point of it upon the lower cutting of these two circles, and set it at that distance, that having a point upon this lower cutting of these two circles, it may conjoin with a true circulary line, the two upper extremes of the two circles, that being done, remove your compass, without any alteration of the distance, and set one of the points of it, upon the upper cutting of the two circles, and with the other point of it, make a true circulary line, to join the two lower extremes of the two circles; and this being traced with a pen, will produce a perfect Oval, one third part longer than it is broad; some make it half as long again, as it is broad, but the sides are too flat, and the Oval is by it more deformed, and not so seemly and complete as this is, demonstrated in Figure 16.  
Now to make the most perfect Rhomb that can be made, 
Of the setting out of the Rhomb.  you are but to draw four lines dioganall wise, from the upper and lower points of the perpendiculary diametrical line, that cuts the two broad sides of the Oval, to the two points of the diametrical line of the length of the Oval, and it will produce a perfect Rhomb, as in figure 18.  
And to make the two equilateral Triangles, and the four scalene Triangles out of the smaller Rhomb, 
Of the setting out of the 6. Triangles.  you are but to draw four lines diagonall-wise from the two Ends of the first line that did represent the eighth part of the Oval to the two upper and lower cuttings of the two circles, and these lines (with the two diametrical lines of the length and breadth of the Oval already drawn) will produce these six foresaid Triangles.  
And to set out the Paralograme, 
Of the setting out of the Paralograme.  you are to divide the breadth of the Oval into four equal parts, and the length of it into nine equal parts, and at every division to make a point, and to draw four straight lines upon the first points of these two divisions, and they will produce this Paralograme that is a ninth part longer than twice his breadth.   

CHAP. IX. Of the Superficies contained in the 3. Plate.  
THe first Circle of this Plate contains an Equilateral Triangle, 
Of the setting out of the equilateral triangle out of a square.  a Square, and a Pentagon. And because all the Equilateral Triangles that are set out by a Square have their two sides longer than their square by an● part; I have drawn two demy-circles to show where the upper Angle of the Triangle should come to be perfect and equal of all her sides, and that is where the two circles cut one another. As for the square, it is more easy to set it out from without the circle, 
Of the setting out of the square by the inward side of the circle.  then from within the circle, because it is more difficult to reduce the sides of it to that scantling proposed, if in case you set it out by the inward side of the circle, than it is if you set out by the outside of the circle; for the diametre of the circle is of the just length of the sides; but to take out a square out of the inward side of the circle, the demy-diametricall line of the circle is to be one third part longer than when you make it by the outside of the circle. But if you are not tied to a scantling, than you may make as perfect a square our of the inward side, as well as from the outside of a circle, by dividing the two cross diametrical lines of the circle, into 6. equal parts and by drawing 4. strait lines, cutting the four first points of this division in the four sides of the circle, drawing the lines to the inward extremes of the circle, and these lines will produce a perfect square.  
Concerning the setting out of the Pentagon, you are to divide the circumference of the circle into five equal parts, and at every division to make a point, than you are to draw five strait lines from point to point, and these five lines represent the five sides or bases of the Pentagon: than you are to draw five other lines from the centre point to the end of these five bases diagonal wise, and these five lines complete the five sides of the five triangles of the Pentagon; and this being done, this superficie is perfected.  
The other three Circles contained in this place are to set out in every one of them a Poligon with different Angles: viz. The first a Sexagon, the second a Septagon, and the third an Octogon; having all of them the Basis of their Triangles of an equal length, by the increasing the circumference of the circle of the length of one of the Bases. And because this is a point of great concernment to an Engineer, that may by the same know at an instant how many Bastions the place will require, if he doth but know the true circumference of it, I will express myself more clearly.  
Suppose then that the six Bases of the six equilateral Triangles of a Sexagon contain 250. yards a piece, that is in all 1500. yard's circumference. And that you would set out a Septagon with seven Bases that should contain every one of them 250. yards a piece, you are then to add to the demy-diametricall line of the Sexagon, a sixth part more of the extent that it had before; and by this means the circumference of the circle will be able to afford you seven Bases of 250. yards a piece, that is in all 1750. yards. The reason of it is, that the circumference of a circle contains three diametrical lines, so that you are of necessity to add to the former demy-diametre line of the Sexagon, a sixth part more than it had before, because a demy-diametre is but the sixth part of the circumference of a circle.  
And by this rule you may make all the Bases of any Foligon from six Angles to twenty four Angles, nay to eight and forty Angles if you please, of two hundred and fifty yards a piece, adding always to the demy-diametre as followeth; To make a Septagon you are to add the ⅙ part; to make an Octogon you are to add a seventh part; to make a ninth Angle Poligon you are to add the eighth part; and so as you go on, the ninth, the tenth, the eleventh, or twelfth part. And as I have said, you are to observe that course, till you come to set out a Poligon of eight and forty Angles. That I conceive would be sufficient to fortify the City of London on both sides the water, with as large a Line of Communication as it hath at this present, having at every two hundred and fifty yard's distance an Angle, to form a strong, complete, and defensible Bastion. A fare more beseeming a Fortification for so famous a City, than such sleight, winding Angles, and ill flanked Redouts, wherewith it is now fortified.   

CHAP. X. Of the five Redouts contained in Plate 4.  
BEfore I come to speak of the Superficies of these five Redoubts, it will not be amiss to inform the Reader of their extent, continent, and dimensions. And first of their extent. 
Of the extent of Redouts.  All square or circullary redouts are to be of one hundred yards from out to out in their diametrical line, otherwise their inward continent will be too small. But a Triangle redout is to have her three sides of two hundred yards a piece, because two equilateral Triangles contain no more than a square.  
Secondly, their continent is to be so large, 
Of the continent of redouts  as it may lodge a competent number of Soldiers for their defence, that is, two hundred men at least, and every two men cannot have a smaller piece of ground allowed them for their lodging then a piece of eight yards square, that makes in all sixty four square yards; Now a redout of one hundred yards diametre, reduced in the form of a square, will contain but 10000 square yards; out of which you are to defalk a third part, for the Rampires, the place, and the streets; and then there will remain but 6667. yards for the lodgings; and this being divided by sixty four yards, it will contain but two hundred and eight Soldiers lodgings, if two of them be lodged together in a chamber of 24. foot square. And by this you may judge whether the greater part of the Redouts about the City of London are of a proportionable extent, seeing most of them have not fifty yards of diametre.  
Thirdly, for their dimensions. 
Of the breadth and depth of their ditches.  Their ditches are to be ten yards broad, and five yards deep, and the slope of the sides of these ditches are to be but one foot slope in three, that the bottom of the ditch may remain to be twenty foot broad, when it is fifteen foot deep, for the reasons that will be shown when I come to speak of the contre escarpe: and the Rampiars their Breast-works are to be proportionable to this ditch. 
Of the height and thickness of their Rampires.  The height of it within side is to be twelve foot high, and nine foot without; the slope of it within side is to be but one foot in six, and one foot in three without side; there are to be five footsteps of two foot broad a piece, 
Of their slope within and without.  and of eighteen inches high a piece, that the breastwork may not be above four foot and an half high, that is of a convenient height for tall and middle sized Soldiers to discharge easily their Muskets. The top of the breast-work is to be twenty foot broad, 
Of their five footsteps.  to be of Cannon proof, and is to have a slope of three foot, and that is the reason that the outside of the Rampiar is to be but nine foot high, and within side twelve foot high, for by this slope the Musquetiers can defend the very brim of their ditch, which otherwise they could not do. 
Why the slope of their top is to be a yard.  Moreover, this great slope preserves the Works from cleaving in the midst, because all the rain water falls off from them into the ditch. And by these dirnensions your Rampire with the five footsteps will be four and thirty foot in the bottom, and twenty foot at top: a very sufficient Rampire to oppose a good battery.  
These broad and high breast-works require to be brought up with brush or bavin wood, if you desire they should be of continuance; the smallest bavin wood is the best, and it is to be bound up with bands, and of some four foot long, and some four or five inches thick; the smallest end of the bavin is to lap over the turf on both sides, and the thickest end is to be turned toward the middle of the Rampire; 
How the Rampires are to be lined with bavins.  and when you have laid four rows of them, every end lopping one over another half a foot, you are to cast in the midst of the work, a row of such bavins of six foot long, to serve as a key to bind all the rest; and this course you are to observe so soon as your turf is risen to be eighteen inches high; so that in the height of a yard, there are to be two such courses of bavins, that is in all six courses of bavins for a Rampire of nine foot high without side, and of twelve foot within side; for the last course of bavins is to be placed when your outside is eight foot high, that there may be eight inches high of earth to cover the bavin wood. And after every course of these bavins, before you place another course, half a dozen of the strongest Pioniers are to ram the earth stoutly, with rammers made of a three inched plank, of a foot square, with a strong state fastened to it. If this be but observed, you will have strong and permanent works; but those that will not go to these charges, are to expect to have the greater part of their works to be repaired every spring, and these repairs will be as tedious, and almost as chargeable as to make new ones.  
Now when these ditches are finished, and the Rampires and their five foot steps perfected, and hay-seed sown on the top of the breast-work, after it hath been raked and rammed, you are to erect your Country escarpe after this manner: Your great ditch being twenty foot broad in the bottom, if in case it be dry, or if it hath but a little water, you are to cast it out, and to make in the midst of it another ditch, that the French call La cunnette of sixteen foot broad and nine foot deep, 
Of the Cunnette or small ditch.  leaving a foot-step of two foot broad on both sides; and these footsteps preserve your great ditch from calving in, and serve in Forts for the footing of casting bridges, to sally in the night upon the assailants out of salley-ports made on purpose under the orillons of the bastions; and this manner of double ditch all in one, is fare safer than these small double ditches, having a bank of earth of some two foot broad left between them, used and erected about the London Redouts. Now all the earth that is digged out of this small ditch, 
How a contre escarpe is to be made.  is to be cast on the field side; and as it is cast out, other Pioniers are to stand upon the brim of the great ditch, for to cast the said earth twelve or fourteen foot farther off into the field; and when this is done, and the smaller ditch perfected, than you are to make the breast-work of the Country escarpe with this earth, adorning the inside of it with turf, and with a foot-step of two foot broad and eighteen inches high, and the breast-work higher than that foot-step by four foot and an half. 
Of the slope of the breast-work of the contre escarpe, that the French call Glacis.  And having leveled even and rammed the top of the breast-work some two foot broad, you are to lay all the rest of the earth so slope till it come to nothing, and level with the firm ground; and this slope is called for distinction sake, by the French Glacis. And by this means a sufficient and defensible Contie escarpe will be made round about the Works of the Redouts twelve foot distance in every place from the brim of the great ditch.  
I have been the larger in the description of these dimensions, because I intent that these very same directions, shall suffice once for all, for the two last methods spoken of in this abstract; which in all parts are to be like these, if the erectors intent to have strong and permanent works. Master Ward in his Animadversions of War, would have the ditches or a Redout to be but nine foot broad, and six foot deep, and the bre●●-work six foot high and six foot thick; but these dimensions are contrary to the Rules of Art, for these reasons: 

1. The top of the rig of the lodgings of the Soldiers is to be covered by the height of the Rampire, which cannot be done if they be so low.  
2. When a ditch and rampire require a ladder of 30. rounds to scale the same, it is more dangerous and difficult to scale and to storm then when it requires but a ladder of 12. rounds.  
3. When the ditches are so shallow and so narrow, they are presently leveled with bavins, and one soldier helping another with a Pike, may easily get up on the Rampire, and the other with his Pike drive the defendants from the defence of the Rampires. In a word, it were better to erect no redouts at all, then to erect any so sleight, and to expose men's lives to danger after that manner, for such a redout will be gained at an instant by a Storm. Moreover, there is to be a good Well, and two Cisterns made of Freestone, plastered with Tarris, to receive all the rain water that falls upon the tiles of the soldiers lodgings, that are to be built by long ranges, and not to exceed in height 12. foot when the rig tiles are up, to be free from the enemy's battery; and every room of 24. foot broad, may be divided in two of 12. foot broad, and 24. foot long; in the one may be the two soldier's beds, their apparel and Arms; and in the other, their drink, victuals, fuel, and all other necessaries. And these ranges are to be lined out according to the form of the superficies of the redout; if it be a Triangle, Trianglewise; if it be a square, after a square manner; if it be of a fift, sixth, seventh, or eighth angle form, the ranges are to be after that manner, that a place be left in the midst of the redout just after that form of some 30. or 40. yards on all sides, as you shall see it demonstrated in greater Forts, having three, or four, or five, or six streets, according to their angles, to go from the place to the Rampires, because all things in a Redout are to be as orderly carried as in a Royal Fort, for all the difference that is to be between them, is in their extent, the Redouts extent being smaller than of a Royal Fort, or Citadel.    
Now concerning the superficies of these five redouts demonstrated in plate four; the first being the figure 24. is a perfect square set out by the outside of the circle; the sides of the square are of one hundred yards a piece. It is fortified by four half moons, whose bases are of fifty yards a piece to agree with the four angles of the square, whose sides flank the half moon, and the sides of the half moons flank them, so that a man cannot appear at any point or side of it, but he may be in danger of his life by the Musket shot.  
The second redout demonstrated in figure 25. is also a perfect square, set out by the outside of a circle, 
Of the second Redout.  of the same extent of the first, and fortified by four great half moons that reduce the form of it to a perfect corner cap; the utmost angles of the four half moons extend themselves twenty yards beyond the four angles of the square, for the better flanking of the sides and points of the said half moons that flank one another very well. There is a small redout erected a: Grays-Inne-lane end much like after this manner; but her extent is too small, and her flank invisible; and therefore no better than a plain little square redout.  
The third redout is a demy-Paralogramme, 
Of the third Redout.  half as long again as it is broad; it is set out by the four extremes of two circles, and fortified by four half moons, whose bases are of 75. yards a piece, the better to flank the Angles of the Paralogramme that flank the half moons; this redout for her extent requires three hundred men for her defence, for it containeth 150. yards in length and one hundred yards in breath; It is of a very convenient form to be placed before the coming in of a gate of a great garrison Town to command divers roads, so the road that traverse the same be winding like the letter S. coming in of one side of the exterior half moon, and going out on the other side of the interior half moon.  
The fourth redout is a perfect circle divided in six equal half moons after the form of a Sexagon; 
Of the fourth Redout.  it is very well slinked of all sides; because the utmost Angles of her half moons extend themselves twenty sieve yards into the field, more than her circulary circumference, whereby it is of a greater continent than the other redout; the demi paralogramme excepted.  
The fift redout is a perfect square, 
Of the fift Redout.  s●t out by the outside of a circle, and fortified by four Avant-gards, at the four angles of it; whose utmost angles extend themselves thirty yards into the field; the breast of the Avant guards are twenty five yards broad; just the quarter part of the base of the square, the face of the Avant guard is of the same extent, and the flank of twelve yards and half. If the 4. sides of this redout that are in this figure but one hundred yards a piece were of two hundred yards a piece, it would make a strong and well flanked Fort, so the utmost angles of the Avant guards extended themselves 60. yards into the field; and the breast to be of fifty yards, the flanks twenty five yards, and the face of the Avant guards of fifty yards. The Royal Fort near Islington is much after this manner, only the face of his Avant guards are square, and do not extend themselves fare enough into the field, and therefore not so regular, nor so defensible as this.   

CHAP. XI. Of the two first Methods of Fortification in general.  
THe small difference there is between these two first Methods of Fortification, by Bastions without, and with orillon's, hath induced me to join them into one; for they agree in all their essential parts, but in two things, viz. in the Line of their Flanks, and in the having or not having orillon's. First, concerning the Line of their Flanks, Mr. Ward, Mr. Cruso, Mr. Norwood, and the Author of the Enchiridion, do make no difference at all between the Line of their Flanks; 
Of the difference that is to be observed in the drawing of the line of the Flanks, when you are to form bastions with, or without orillon's.  for in all their Models and Superficies, they draw the Flanks of the Bastions with, and without orillon's, all after one manner, that is, upon a straight perpendiculary Line: But on the other side, they would have the side, or the Base, to be divided into eight parts, when they frame Bastions with orillon's, and only into six parts when they frame Bastions without orillon's, in both which points I maintain they are mistaken: First, for the Line of their Flanks, if it be drawn as they propose, straight and perpendiculary wise, the Flanks by this means are too much exposed to the Enemies great batteries, and to the volleys of their Musketeers shot, as soon as they have gained the Defendants Counterscarp; and therefore to prevent this evil, I say it is better and safer to draw the Line of the Flanks of the Bastions that are to be without orillon's, one eighth part more slope than straight: As for instance, suppose the Line of the Flank to be forty two yards, then are you (I say) to strain that Line five yards and one quarter more slope towards the other Flank of the other Bastion, than a straight perpendiculary Line will afford; for these five yards make the shoulder of the Orillon, to jet more into the dike then otherwise it would do, being drawn straight; and by this means this jetting out is a great safeguard to the Flanks; for all that thick and massy piece of earth, of the shoulder with this jetty, must of necessity be battered to dust, before the Flanks can receive any hurt; whereas if the Line be drawn straight, the Flanks lie open to the Enemy's batteries, if the Bastions have no orillon's, or this jetting shoulder to defend them. This is clearly demonstrated in Plate 7, where the Pentagon fortified by Bastions is described better than it can be in the Triangle, Square, or Oval forms, So that I conclude, that the Line of the Flank is to be drawn straight, when you intent to form your Bastions with orillon's; and more slope by five yards and a quarter then straight, when you intent to set out, or form Bastions without orillon's.  
As concerning their dividing of the Base, 
Of the error of dividing the base into eight parts, when they intent to set out Bastions with orillon's.  or side of any Poligon, when they intent to frame Bastions with orillon's, into eight parts; and only into six parts, when the Bastions are to be without orillon's: I say it is superfluous, except they will imitate altogether the best Italian method; that is, first to divide the Base into ten equal parts, and to allow four parts for the two Flanks, and the other six parts for the Courtine, which they divide again into eight parts, to take their Line of defence from the seventh first part of it. But if they intent to follow the Low-country method, they are not to divide their Base, but only into six parts, because the forming of the orillon's doth not take or shorten the Courtine at all, as it will be clearly proved in the next Chapter.   

CHAP. XII. Of the Fortifications of the Equilateral Triangle by Bastions with orillon's, demonstrated in Plate 9  
THe Equilateral Triangle is fit to be fortified by Avantguards then by Bastions, because her Angles be so acute, that they produce these defects in some essential parts of her Fortifications, her Flanks are shorter, the face of the Bastions longer, and their Breast narrower than they should be, and these defects cannot be avoided, except the Line of defence be defective, that all Enginiers are to shun, as the most essential part of all; and therefore I have had special regard to make that perfect, rather than to amend the other imperperfections. The Angle of her Centre is of sixty degrees, her Angle flanked of forty five degrees, and her Angle flanking of 160 degrees; her three sides are of 250 yards a piece, her circumference of 750 yards, and her continent from out to out, of 26230 yards; and therefore fit for a large Redout then for a Royal Fort, for when we have defalked the third part of her continent for the breadth of the Rampires, the Marketplace and the streets, there will remain but 17500 square yards for the houses of the Inhabitants, to every one of which cannot be allowed in this small continent, above one hundred square yards, that is a piece of ground of ten yards square on all sides, and according to this scantling there will be 175 Inhabitants, that are according to the rules of war, to billet two hundred and forty Foot, and a Troop of threescore Horse, that is, for every third house an Horseman, and for all the other houses two Footmen appece, or otherwise 350 Foot, and no Horsemen; for the continent is too small for to billet Horse. But 350 Foot, with the Inhabitants, commanded by a valiant Commander in chief, may defend the place three months, against an Army of four thousand men, so it be provided with all necessaries for a Siege.  
To set out the same in the field, 
How an equilateral Triangle may be set out in the field without a Demi-circle, or any Geometrical instruments but a Square.  have a line of two hundred and fifty yards, having a loop fastened in the midst of it; and when you have made choice of the Seat, turn yourself to wards the South, and strain your line from the Southeast to the South-West, and where the loop is, and at the two ends of the Line, knock in three stakes; then take a line of 210 yards, and fasten the same upon the middle stake, and strain the same full North, and with a great wooden Square try (by setting one of the sides of it to the first line, and the other side of the Square to the second line) whether the last line be a perfect straight perpendiculary line, and when it is so, knock in a stake at the end of the line, 
The Centre of the equilateral Triangle is in the third part of her perpendiculary line, and not in the midst, as the Centre of circulary Superficies is.  And these three out stakes will represent the three Angles of the Triangle, then take a six foot rule, and measure from the South stake along the perpendiculary line, seventy yards Northwards, and at seventy yard's end knock in another stake, and it will represent the Centre of the Triangle; for the Centre of the Equilateral Triangle is in the third part of the perpendiculary line of it, and not in the midst, as it is in all square or circulary Superficies: then remove your line of 250 yards from one Anglestake to another, and then if you find them all of an equal distance, fasten small lines about them, and have the Superficie of the Triangle traced by many Pioniers, with pick-axes and spades; but if any of the Angle-stakes are not equal, you are to amend the error by the line.  
You may also set out the equilateral Triangle by the Demy-circle, as I will give you directions in the next Chapter saving one, when I shall come to set out the Pentagon. In the mean time observe this for a general rule, that the 
* Note once for all, that the gate or drawbridge of a Fort is always to be South, if the seat will permit, and in the midst of a Courtine, to be defended by the Flanks of two bastions.  gate o● drawbride of a Redout, Fort, or Citadel, is always to be full South, if the seat will permit; but howsoever it must be seated in the midst of a Courtine, that it may be secured by the Flanks of two Bastions.  
The Superficie of the Triangle being traced, you are to divide the three sides into six equal parts, and at every division to knock in a stake: than you are to fasten a line to the Center-stake, and to strain it Diagonall-wise towards the Southeast and South-West Angle-stakes, and straight perpendiculary-wise towards the North stake, making the line thus strained touch every one of these stakes; and you are to strain this line of 95 
* The distance from the Centre of the bastion to the point, is in this Triangle of 95 yards.  yards beyond these three Angles stakes, for it is the distance that is to be between the Centre of the Bastion of the Triangle, and the uttermost point of her Bastions, and at this distance knock in three stakes, and they will represent the three exterior Angles of the three Bastions. Then fasten a 
* This Line is to be of 240 yards long, the just extent of the Line of defence.  line to the third stake of every one of the sides, and strain it till it be fastened one after another to these three Angle-stakes, and it will set out all the faces of the three Bastions, and all the six lines of defence; then fasten a short 
* This Line is to be forty yards long, the just extent of the length of the Flank of this Triangle.  line to all the second stakes of your sides, one time after another, and strain the same straight perpendiculary-wise, till they cut the other lines that represent the faces and the lines of defence, and where they cut one another, knock in six stakes, and they will set out the six Flanks of the three Bastions and the three Courtines; then have all these things traced by divers Pioniers, after you have fastened lines as near the ground as you can to them all.  
And that being done, you are to set out the six orillon's of the three Bastions after this manner; divide the Line of the Flank into three equal parts, and allow one part for the Flank, and in that part knock in a stake, and the other two parts for the turning of the Orillon; than you are to advance the shoulders of every one of the Bastions beyond the stake that did represent the end of the Flank and of the shoulder, seven yards; 
How a perfect Orillon is to be set out in the field.  than you are to knock in a stake, and to fasten a line of seven yards to the stake that represents the first division of the Flank, and to strain this Line parallel-wise with the former, and at the end of the Line to knock in a stake; than you are to divide the just distance of the breadth that is between these two last stakes, that will fall out to be thirteen yards and a third part, and in that division you are to knock in a stake, and to that stake you are to fasten a line of thirteen yards & a third part, & at the end of it being strained upon a straight line, you are to knock in a stake; than you are to fasten your iron tracing pin to the other end of the line, and to draw with the point of it a circulary Line from one stake to another, touching as you pass by the very last stake that you knocked in, representing the extreme, or the midst of the circulary line of the Orillon; and by this means you will form the Orillon perfectly, and very round; and as you have set out this Orillon, set out all the other orillon's after this very minner: for this one direction will suffice once for all, for the setting out truly of a perfect Orillon.  
By the setting out of this Orillon, the truth of the former position made in the last Chapter, viz. that the Base or side of any Poligon is not to be divided into eight parts, but only into six parts, whether you intent to erect Bastions with, or without orillon's, because the Courtine is not shortened at all by the forming of the orillon's; for the dike runneth between the Rampire of the Courtine, and the inward side of the Orillon, as it is clearly demonstrated in this Triangle fortified by Bastions with orillon's, the Courtine having the same extent as the other Triangle hath, that is fortified by Bastions without orillon's, except you please to imitate (as I have said) the best Italian method, that is perfectly set out in a demi Sexagon, in the last Plate of this Abstract, where you shall find the Base to be divided first into ten parts, four of which are allowed for the two demi gorges, and the other six parts for the Gourtine, which Courtine is again divided into eight equal parts, that the Line of defence may be taken from the first division of the eight equal parts. And this they do to increase the breadth of the breast and of the gorge of their Bastions, that they may be more capable of a second, or a third reintrenchment, when the Flanks, or the points of their Bastions are beaten down; but these Bastions erected out of a Base divided into six equal parts, are reputed here to have their breast and their gorge already too spacious, and therefore it were superfluous to make them larger.  
To conclude: The irregularity of the Triangle causeth the dimensions of her Bastions to be these: The Flanks are forty yards with the thickness of the orillon's, the Courtines 166 yards, and two third parts, the Line of defence 240 yards, the breast from out to out 90 yards, the whole gorge 80 yards, the face of the Bastion of 120 yards, the orillon's 26 yards thick, and twenty yards long, jetting over the dike, that is a great preservation to the Flanks; and the distance from the Centre of the Bastion to the point, is of 95 yards, the orillon's being set out: Then you are to set out all the dikes round about the Fort and Works, observing the dimensions described in the Chapter, where is spoken of foreign Fortifications, casting the earth of the dikes inward, to raise your Rampires; and when all your inward works are finished, and the broad dike perfected, than you are to set out the small dike called La Cunnete, in the midst of the great dike, that you may make with the earth of it, the Counterscarp round about the Fort, according to the directions before described.  
But if in case your great dike be full of water, and that it is impossible to dig the small dike, to get earth to make your Counterscarp brest-work, you are to line the 
* How to erect the brest-work of the Counterscarp, when the great dike is full of water.  great dike round about the Fort, at four yard's distance from the brim of the dike, and to dig that twelve foot distance a foot deep, and with that earth you are to erect the brest-work of your Counterscarp; that is (as I have formerly said) to be six foot high, having one foot-step of two foot broad, and eighteen inches high, being adorned on the inside with good Turf, and the outside made slope to nothing, and level with the ground, sowne with hay-seed; and the twelve foot space that hath been digged a foot deep, is to be leveled with an ascent to the foot-step of the brest-work, falling towards the brim of the dike, that the rainwater may fall into the dike, and keep that space and your works dry.   

CHAP. XIII. Of the Fortifications of the Square by Bastions with orillon's, demonstrated in Plate 10.  
THe square is also irregulary, yet not so much as the Triangle, because the Angle of his Centre is of ninety degrees, his Angle flanked of sixty five degrees, and his Angle flanking of one hundred forty seven degrees: and by these helps the faces of his Bastions are not so long, their Breast broader, and their exterior Angle more Obtus, than those of the Triangle, his four sides are of two hundred fifty yards a piece, his Circumference of one thousand yards, and his continent from out to out of 62500. square yards, out of which is to be defalked the third part, for the breadth of the Rampires, the Marketplace, and the Streets, and there remaineth for the lodgings of the Inhabitants and Soldiers, 41666 yards square, and two third parts, and because this continent is greater than the former, we will accordingly increase the scantling of the Inhabitants houses, and allow them to be of 150. square yards, that is a piece of ground of twelve yards and half square of all sides; by which scantling, the 41666. yards being divided, there will appear to be in this continent 277. dwelling houses, and as many Inhabitants, that may billet four hundred Foot, and two Troops of Horse: and this number is sufficient to maintain this Fort against an Army of five thousand men three months, so it be provided with sixteen piece of Ordnance, Balls, Ammunition, Arms, Victuals, and all other necessaries, fit for a Siege.  
Object. Some will wonder why so small a Fort, should have sixteen pieces of Ordnance, when many of our Garrisons that are of two or three mile's Circumference, have not so many.  
Ans. I answer the more is the pity, they are no better provided. But if this Method of Fortification were not better stored, to what end should Foreigners be at the charges to erect upper and lower flanks: and because I have not as yet spoken of these upper and sour flanks, I will upon this occasion describe how they are made, and for what use they are erected. In the Ancient Fortifications by Bastions, 
Of the upper and lower Flanks of a Bastion.  there was formerly low Casamates to scour the dikes even with the water, for they were built so low, that a Cannon being mounted in them and pointed, shot upon a level Line, even with the water of the dike; and these Casamates were all vaulted with arches of freestone, having two Port-holer, and two Demy-Cannons, in every one of them, their vault being some sixteen foot square, and they had a slanting descent from the gorge of the Bastion with a door to come down to them, but because they had no other light then the Portholes, nor no other evacuation for the smoke, than the door, when the Cannoneers fired their Pieces, they were so encumbered with the smoke in the vault, that they could not suddenly charge their pieces again, but were enforced to s●ay till the evacuation of the smoke were passed: Whereupon the modern Enginiers to prevent these defects, have invented the upper and lower slanks, where they always place two pieces of Ordnance in every one of them, so that according to the Foreign Method, every Bastion is to have ten pieces of Ordnance, at the least, two Demy-Cannons in every flank, and two long Culverins to defend the faces and the point, that is in all ten pieces of Ordnance, these Flanks are made after this manner: The wall of the flanks is brought up from the bottom of the dike with freestone of two yards thick, to the level of the water of the dike, and within and without laid with Tarris, that the water of the dike may not pierce the same: and upon this wall and the firm ground, after another foundation of stone hath been laid, twenty four foot from the brim of the first wall, some five foot deep, a Brest-work is brought up of earth and turf, of twenty four foot thick in the bottom, and of twenty foot broad at top, and six foot high, having three Portholes, and beyond this Brest-worke the ground is digged lower the whole length of the flank, that is ordinarily from thirteen yards, to sixteen yards in length, and in breadth, eight yards, and in depth five foot, and this being laid with tracin; and planked, is the Platform of the lower flank open over-h●●d, in which they place two Demy-Cannons, and these scou●●●●d free the dikes from the assay lants galleries, and from the scaling of the Rampires. Now to erect the upper flank they go eight and forty foot wider into the g●rge of the Bastion, and upon the in ward foundation of the lower flank wall, and the earth of the Bastion they erect another Brest-work of the same height, breadth, and thickness of the former, with three Portholes in it, and then they plank another platform and place two Demy-Cannons more upon the same, and these are the manner of their upper and lower flanks, that have a slope coming down from the upper to the lower some ten foot broad, which being covered by the orillon's, make the Bastions very strong; and when these double flanks are taken out on both sides, the gorge is not above fifty yards broad, that is narrow enough for the last reintrenchment. Now these flanks being all open over head, the smoke of the Ordnance is suddenly evacuated: the use of the upper Flank is to scour the face, and the points of the Bastions in the time of a storm, and to beat all along the Courtine. And so much will suffice once for all, concerning the erection and use of these lower and upper Flanks.  
Now I come to show how you are to set out this Square in the field. If men could as soon and as easily set out a Superficie in the field, as they may upon paper, it were soon done; but this last requires a greater labour and care. You are then in the first place to make choice of your Centre, and there to knock in a stake, than you are to stand close to that stake, and turn your face full South, and then take your Demi-circle, and set the sight of it upon the ray of 90 degrees, that is the Angle of the Centre of the Square; than you are to have two men by you, one with lines and the other with stakes, and he with lines is to have a line of one hundred and 
* You are to observe, that this line of 180 yards, is the just demi-diagonall line and distance that is between the Cent r-stake and the Angles of the Square.  fourscore yards, the one end of which line he is to fasten to the Center-stake; and when you have taken your Demi-circle, and set the sight of it as aforesaid, you are to take with it, having your face turned to the South, the right hand ray of the Angle of 90 degrees, and when you have it, let the man strain the line fastened to the Center-stake along the said ray, to the end of the line, and when he is just against you and the ray of your Demi-circle, let the other man knock in a stake at his feet; then turn yourself, and set your Demi-circle to take the left hand ray of the angle of 90 degrees, and when you have it, let the man with the end of the line come to it, and when he is just against you and the ray of your Demi-circle, let the other man with stakes knock in a stake at his feet at the end of the line, and these two stakes represent the Southeast and the South-West Angles of your Square; then turn yourself fall North, standing close to the Center-stake, and set out after the same manner the North-East and North-West Angles of your Square, and let the man with stakes knock in two stakes, as he did in the South side, and these four utmost stakes will represent the four Angles of the Square. Now to avoid error, you are to fasten the line of 250 yards with a loop fastened in the midst, on the Southeast stake, and to strain it to the South-West stake, if the stake be at the just distance of the line, that side is rightly set out; than you may knock in a stake where the loop is, to represent the middle of that side, where the gate and the drawbridge of the Fort is to be placed; and so prove all the other three sides with your Line of 250 yards, knocking stakes in the midst on every side; for they will stand you in stead, when you come to divide the sides into six parts. Now if any of these sides be amiss, and agree not with your Line, than you are to amend them by your Demi-circle and your Line, which is easily to be done; and when the four angles and sides are right, you are to fasten lines to the eight stakes as near the ground as may be, and to set Pioniers to trace the Superficie of the Square with spades and pick-axes, before you set out the Bastions.  
That being done, you are to divide the four sides of the Square into six equal parts, and to knock in a stake at evene division, than you are to fasten a line of 90 yards to the former demi-Diagonall Line of 180 yards, that will then be of 270 yards, and to strain the same 
* The distance from the Centre of the Bastion to the point, is of 90 yards in this Square.  90 yards beyond the four Angle-stakes of the Square, after it is fastened to the Center-stake, making the said Line to touch the Anglestake; and at the end of the said line knock in a stake, and these four stakes will represent the four utmost points of the four Bastions, and the four former Angle-stakes, will then represent the Centre of the Bastions. This being done, fasten a line one after another to the third stake of every side, of 
* This Line of 230 yards is the just extent of the Line of defence of this Square.  230 yards, and strain the same to the four stakes that represent the four utmost points of the four Bastions, and this line will set out the eight faces of the Bastions, and all the Lines of defence; than you are to fasten a line one after another of 41 yards and two thirds to every second stake of the four sides, 
* The Line of the Flanks in this Square is of 41 yards and two third parts.  and to strain the same upon a straight perpendiculary line till it come to cut the former line, that represents the line of defence, and sets out the faces of the Bastions; and where it cuts the other drive in a stake, and these eight stakes will represent and set out the eight Flanks and the four Courtines: And that being done, you are to set Pioniers at work, to trace all these things before you go about to set out the orillon's.  
Now to avoid mistake, you were better to set out one side at a time, & to have it traced as you set it out, for it will save charges, because it will not require so many lines. This being done, you are to set out the orillon's, and after the orillon's the dike; and when all is finished, you are to erect the Brest-work of the Counterscarp with the earth taken from the small dike, called La Cunette, adorning the same on the inside with Turf and a foot-step, as I have formerly given large directions in Chap. 12. and Plate 9   

CHAP. XIV. Of the Fortifications of the Pentagon by Bastions with orillon's, demonstrated in Plate 11.  
THe Pentagon is also irregularie, yet less than the Square; for the Angle of his Centre is of 75 degrees, and the Angle flanked of the same extent, and his Angle flanking of 142 degrees and a half, his bases or sides are of 250 yards a piece, his circumference of 1250 yards, and his whole continent from out to out of 125000 square yards, it is of a convenient form for a Citadel, or of a well-compact Town, whose circumference doth not exceed three quarters of an English mile.  
Now to direct the Reader once for all, 
* How you may know the continent of any Poligon with variety of Angles.  how he may speedily calculate the continent of all sorts of Angle Poligons, I have in this Figure set out a demonstration of it, viz. you are first to draw a straight perpendiculary from A to B, than a straight parallel line from C to D, and then to join D and A by a straight line, as it is demonstrated in this Figure, and it will produce a demi long square, his broad sides containing, according to the scale of this Figure, 200 yards, and his end-side 125 yards, which being multiplied one by the other, it will produce 25000 yards, as the just continent of one of the Triangles of this Pentagon, which being multiplied by five, (because it contains five Triangles, the whole continent will amount to 125000 square yards. Now the one third part of it being defalked for the breadth of the Rampire, the Marketplace and the streets, there will remain for the Inhabitants houses 83333 yards and a third part, which being divided by one hundred and fifty square yards, that we allow for every Inhabitants dwelling house, that is a piece of twelve yards and an half square of all sides, it will according to this scantling contain 555 houses, and as many Inhabitants, that are according to the rules of war, to billet in every third house a Horseman, and in all the rest two Foot-soldiers apiece; so that it will contain 185 Horsemen 740 Footmen, and 555 Inhabitants, a sufficient Garrison to defend this place against an Army of ten thousand men for three months; so it be provided with Ordnance, Arms, Ammunition, victuals, and all other necessaries for a Siege.  
Now to set out this Fort in the field, you are to bring along with you two men, one with lines, and the other with stakes: and when you have made choice of your Centre the man is to knock in a stake, and you are to stand close to this Center-stake, and having set the sight of your Demy-circle upon the ray of 75. degrees that is the Angle of the Centre of the Pentagon, 
* Note that this line of 240 yards is the extent of the demi diagonal line of the Pentagon.  the man that carrieth the lines is to fasten a line of 240. yards to the Center-stake, and to strain the same full North upon a straight perpendiculary line, and at the end of it he is to knock in a stake and this stake represents the North Angle of the Pentagon; that done, take your demy-circle and wind the right hand ray to the right hand, the man holding in his hand the line of 240. yards, straining the same according to the ray of the demy-circle, and when he is at the end of the line and just against you agreeing with the ray of your demy-circle, let the man with the stakes knock in a stake at his feet, and this stake will represent the North East Angle of the Poligon, then turn your face to the North-West, and with the ray of your demy-circle on the left hand, the man with the line following the same, and when he is just against you and the ray of the demy-circle, being at the end of the line, the man with the stakes is to knock in another stake at his feet, and this stake will represent the North West Angle of the Pentagon. And after this manner set out the Southeast and South-West Angles of the Pentagon, and having knocked in stakes, these five utmost stakes will represent the five Angles of the Pentagon, and by these observations, the gate and the drawbridge of this Fort will be full South, and in the midst of the South Courtine, to be defended by the flanks of two Bastions; when this is done, you are to take the line of 250. yards having a loop in the midst, which line you are to strain from stake to stake to prove whether your stakes are at an equal distance, driving at every middle of all the sides a stake, as you will be directed by the loop fastened to the middle of the line: now if any of your stakes be amiss you may easily amend them, by the demy-circle, and the line, and when they are right, you are to fasten lines from stake to stake as near the ground as may be; and set many Pioniers to trace the superficie of this Pentagon, before you set out the Bastions. And this is also the way how you ought to set out the equilateral Triangle 
* How to set out an equilateral Triangle by the demi-circle spoken of in Chap. 12.  by the Demy-circle, spoken of in the 12. Chapter, by driving a stake full North to represent the North Angle of the Triangle, and by turning your face South after you have set the sight of the demy-circle upon 60. degrees, as being the Angle of the Centre of the equilateral Triangle, turning the ray of your demy-circle on the right hand, and then on the left hand, and driving at the end of the line of 250. yards two stakes, for by this means the gate and the drawbridge of the Triangle Fort will be full South, and just in the midst of the South Courtine, and defended by the flanks of two Bastions.  
The Superficie of this Pentagon being traced you are to divide the five sides of it into six equal parts, driving in every division a stake, than you are to fasten to the former line of 240. yards, another line of 83. yards, and a third, that is the just distance, from the Centre of the Bastion to the utmost point of it, and when you have done so, you are to fasten the same to the Centre stake, and to strain it diagonall-wise 83. yards and one third part beyond the five Angle-stakes, making the line as you strain it to touch the said stake, and at the end of the line to drive in five stakes, that will represent the five utmost points of the five Bastions. And for the setting out of the rest, I refer you to avoid repetition to the two last Chapters, where you had large directions to set out the flanks and faces of the Bastions, with their orillon's, Dikes, and Conterscarpes; and will only acquaint you with the dimensions of this Pentagon, since I did omit the same in the square, yet I will give a hint of them in this place: the flanks of the square were but forty yards, and the flanks of the Pentagon are forty one yards, and two third parts, their Courtines are alike of 166. yards and two third parts, the distance from the Centre to the point of the Bastion, in the square was 86. yards, and in this Pentagon of 83. yards; the gorge of the Square and of the Pentagon alike, of 83. yards and one third part.  
And the line of defence in the square 230. yards, and in the Pentagon three yards less.  
The faces of the Bastions in the square of 105. yards and in this Pentagon 100 yards, and the breast in the square of 95. yards, and in the Pentagon 100 yards.   

CHAP. XV. Of the Fortifications of the Oval by Bastions without orillon's demonstrated in Plate 8.  
THe Oval is as irregularie as the Triangle, and one of the most difficult superficies to set out in the field, because of the circulary form, and the variety of the Angles, four of them being of sixty five degrees, and two, of thirty seven degrees and a half, the Angle flanking of 130. degrees, and the Angle flanked of 72. degrees and a half; her circumference is of 1500. yards, and her continent from out to out of 118800. yards; out of which the one third part being defalked for the breadth of the Rampires, the marketplace, and the streets, there remains for the houses of the Inhabitants 79200. square yards, that is to be divided by 150. square yards, for a piece of ground of 12. yards and half square of all sides, that is allowed to every one of the Inhabitants, that are found to be by this calculation, 528. that are to billit 176. horsemen and 704. foot-soldiers: A sufficient Garrison to oppose an Army of eight thousand men for three months, so it be provided with Cannons, Ammunition, Arms, Victuals, and all other necessaries for a Siege. It is also a convenient superficie, to fortify a well-compacted market-town, that may be reduced to this form of three fourth parts of a mile Circumference.  
Now to set out the Superficie in the field, 
Note once for all, that you are to have a Sea-compasse, when you go about to set out any kind of Superficies in the field, to place your angle South, North, East, and West rightly.  you are to make choice of your Centre, and to drive in a stake, and to fasten a line of 80 yards to that stake, and to strain the same full East upon a straight line, and to drive in a stake; than you are to wind the line about, and to strain it full West, and to drive in a stake, and these two last stakes divide the length of the Oval into three equal parts, of 160. yards a piece, and represent the two Centres of the two circles, out of which the Oval is form, than you are to fasten a line to the Centre stake of 220. yards, that is the extent of the demy-diagonall line of the Southeast and North-East Angles, and of the South-West and North-West Angles, that are of 57 degrees and a half, upon theray of which Angle, you are to set the sight of your demy-circle and standing at the Centre stake to turn your face full East, winding the ray of the circle on the right hand, the man with the foresaid line straining the same till he come just against you, and the ray of the circle, then is the man that carrieth the stakes, to drive a stake at his feet, than you are to wind the ray of your demy-circle on the left hand, and to do as you did at right hand, and at the end of the line to drive in a stake, and these two stakes will represent the Southeast and the North-East Angles of the Oval, than you are to turn yourself full West, and to set out with your demy-circle, and the foresaid line the South-West and North-West Angles, driving two stakes at the end of the line. Then you are to fasten a line of 160. yards 
* This is the extent of the demi diametrical line of the breadth of the Oval.  to the Centre stake, and to strain the same full South, upon a straight line, and at the end of the line the man with stakes is to drive in a stake, then wind the same line about, and strain the same full North upon a straight line, and at the end of the line drive in another stake, and these two last stakes represent the South and North Angles of the Oval: then remove this line from the Centre stake, and fasten it to the East Centre circle stake, & strain it full East upon a straight line, and at the end of the line drive in a stake, then remove the same line to the West Circle Centre stake, and strain the same full West upon a straight line, and at the end of the line drive in a stake, and between these eight circulary stakes consists the superficie of the Oval.  
Now because the six sides of it are circulary, you are to remove the foresaid line of 160 yards to the Center-stake, and to fasten your iron tracing-pin to one side of the line, and the other side to the stake, and to strain the same full South, and to trace the ground as far as the line will give you leave, on both sides of the South stake, and then you are to do the like on the North side; and that being done, you are to fasten these lines one after another to the East and West circled Center-stakes, and to trace the West and the East sides of the Oval with the point of your iron pin, as you did the South and North sides, joining the tracing of your pin on all sides; and this being done, you are to set many Pioniers to make the tracing deeper with spades, or with the flat ends of their pick-axes.  
And when this Superficie of the Oval is sufficiently traced, you are to divide the six circulary sides into six equal parts, driving a stake in every division; than you are to fasten a line of 85 yards to every Anglestake one after another, and to strain the same upon a straight diagonal line from the four Angle-stakes that represent the South-west and Northwest, and Southeast and North-East Angles; but upon a straight Diametrical line from the South and North Angle-stakes, and at every end of the line you are to drive in a stake, and these six stakes will represent the six utmost points of the six Bastions; than you are to fasten a line of 240 yards to every third stake of your six sides, to set out by it the faces and the line of defence of the Bastions, by straining and fastening this line to every Angle stake twice to set out the twelve faces, than you are to fasten a line of 45 yards to every second stake of the six sides or bases, and to strain this line not perpendicularie-wise, as you have done formerly, when you did set out the Bastions with orillon's, but five yards more bevell, toward the next Bastion, then straight; and where the Line cuts the other that sets out the faces of the Bastions and the Line of defence, you are to drive a stake, and after this manner set out all the rest, till you have gone round.  
Now let me inform you once for all, that the safest and the most frugal way to set out your Bastions after your main Superficie is set out, is to set out one half Bastion at a time, and to have it 
* A general observation to be noted.  presently traced before you remove your Line; for these two Lines, one long to set out the faces and the Line of defence, and a short one to set out the Flanks will serve turn; and besides, it will prevent all confusion and mistakes.  
Now when all the Bastions are traced, you are to set out the dike; and when all is finished, the Counterscarp; as you have been directed Chap. 12, and 13.  
The Line of defence of this Oval is of 240 yards, the distance from the Centre to the point of the Bastion of 85 yards; 
The gates and draw, bridges of this Oval fortification are to be placed in the midst of the East and West courtine, that represents the length of the Oval, and not South and North, as other Forts are.  and the length of the Courtine, because of her circulary Line, of 170 yards; the breast of the Bastion, 110 yards; the Gorges of 83 yards and one third part; and the faces of the Bastions of 100 yards, and others of 90, because of the winding of the Oval; and her Flanks of 45 yards, three yards longer than ordinary, because of the circulary line of the Courtine, that it may the better defend the inward Angle of the other Flanks.   

CHAP. XVI. Of the Fortifications of the Sexagon, by Bastions with orillon's, demonstrated in Plate 12.  
THe Sexagon is regularie, and a most complete Superficie, the Angle of her Centre is of 60 degrees, the Angle flanked of 80 degrees, 
* See in Chap. 18. why these sides have been set out fifty yards longer than any other formerly have been. This Sexagon is composed of six equilacerall Triangles equal on all sides, containing every one of them 39000 yards, which being multiplied by six, contain 234000 square yards.  and the Angle flanking of 135 degrees; her sides are of 300 yards a piece, her circumference of 1800 yards, her whole continent of 235000 square yards; out of which the one third part being deralked for the breadth of the Rampires, the extent of the Marketplace and the streets, there remaineth 156000 square yards for the houses of the Inhabitants, to whom we will allow in this greater continent, 200 square yards, that is a piece of ground some thing more than fourteen yards square on all sides: And after this allowance, the foresaid number of 156000 square yards, being divided by two hundred square yards, it will appear that this continent will contain 780 houses, and by consequence so many Inhabitants, that are according to the rules of war, to billet in every third house a Horseman, and in all the rest two Foot-soldiers a piece: And after this account, there will be 260 Horsemen, and 1040 Foot-soldiers, a very complete Garrison to defend a place not much above an English mile in circumference, so it be stored with Ordnance, Arms, Ammunition, victuals, and all other necessaries for such a Siege.  
I have in this Superficie, as being the last of this Method of Fortification, set out the broad streets, that go round about the Rampires, and from the Rampires to the Marketplace, that are to be ten yards broad, and the Marketplace of an hundred yards in her Diametrical Line, and of the same form of the Fortification of the Sexagon; for you are to observe in all new erected Forts, 
* The Market place of a new erected Fort, Citadel, or Garrison, is to be of the same form of the out-Superficie of the works.  Citadels, or Garrisons, to reduce the Marketplace after the form of the outside works, to be the more complete, viz. if it be an equilateral Triangle, or a Square, or a Pentagon, the Marketplace is to be of the same form of a Triangle, or a Square, or a Pentagon. Moreover, you are carefully to observe to line out in every one of them, broad streets of thirty foot broad round about the Rampires, and from the Rampires to the Marketplace, and these broad streets that run from the Rampires to the Marketplace, are always in this Method of Fortification, to be upon a straight diagonal, or Diametrical Line from the Centre of the Bastion, to the Centre of the Marketplace, as these are drawn in this Figure for these reasons: 1 The streets round about the rampiers serve for all manner of carriages to be brought to the works, and for the Horsemen to ride to the relief of any of the rampiers in the time of a siege or storm. 2 The great streets that run from the 
* For what use broad streets lined round about the Rampters and the Marketplace, are erected.  Marketplace to the Bostions, serve for a Troop of Horse, of five of a breast; or for a Company of Foot, with five or six men on a breast, to come to the relief of any of the Bastions that are stormed. 3 The Marketplace is always to serve as the Randezvouz for Soldiers to gather themselves together, to be sent by the Governor where occasion requires. I have also set out the order that is to be observed in the erecting of the houses for the Inhabitants, that are to be lined out with straight double ranges, that gardens or backsides may join one against another, that houses may have the more air and light, and that all their doors may open to the streets, that are to be fifteen foot broad; for narrow lanes are dangerous in Garrison Towns. The Storehouses or Magazines of Powder, Bullet, Fireworks, Engines, Ladders, Pioniers tools; and provision of victuals, as Corn, Meal, Oatmeal, Oats, Malt, Hay, Salt, Powder Beef, Bacon, Dry fish, Butter, Cheese, Rice, White Pease, and all such necessaries, are to be in those houses seated round about the Marketplace, as the most safest seat of the Town.  
All these observations are carefully to be regarded, if in case the State should erect any new Forts, Citadels, or Garrison towns, where there never was any habitation before; for such a new erected Hold would ten times be more serviceable than any old erected Town in this Kingdom; (provided all the dimensions of this Method be observed, that shall clearly be described in the Ichnography of this Chapter) because they are for the greater part of deformed shapes, and of a vast extent, and not compacted together, nor their streets well lined, nor ranged in order, nor their houses well contrived, some of them being very high, and some very low; but these of this new 
* Of the height of the new-erected Houses in a new Fort, Citadel, or Garrison town.  erection are to be all alike, and not above two stories high, that may not exceed with with their roof thirty foot high at the most, that the ridge of the top of their houses may be lower than the top of the Rampire Brest-work by nine foot.  
Now to set out this Sexagon in the field, you are to make choice of the Centre, and to drive in a stake and to fasten to that stake a line of three hundred yards, and a foot over, which line the two men that are always to be with you to carry your instruments, lines, and stakes, are to strain full East, after you have taken with a good 
* An Engineer is never to be without a demi-circle, and a good Sea-Compasse.  sea-compasse the East and West points. But if by the long extent of the line the line swags and cannot be drawn straight, they are to strain it but one hundred yards very straight, and stiff, and to drive in the ground very deep a strong stake, and to wind the line about it, then to strain the line again another hundred yards, and to drive in another stake as before, and to 
* Observe to wind the line always of one and the very same side of the state, to avoid breaks.  observe to wind the line always of one and the same side, and to make it come to be strained again, on that very side you did first wind it upon the first stake, to avoid all breaks; than you are to strain the line again for the third time, and to drive in a stake, and this last stake will represent the East Angle of the Sexagon. Then your men are to untwist the line from the stakes and to wind it about to the West point, and to strain it and to drive in three stakes as they did before, and the last stake will represent the West Angle of the Sexagon: Then you are to stake your demi-circle, and to set the sight of it upon the ray of 60. degrees, and to stand at the Center-stake and to turn your face and demi-circle to the East stake, winding the ray of the demi-circle East and by South, then are your men to follow that ray with the line, driving at every hundred yards a stake, and when they are at the end of the line just against you, and the ray of your demi-circle of 60. degrees, let them drive in a third stake and it will represent the East and by South Angle of the Sexagon; then turn yourself and your demi-circle East and by North, and set out after this very manner the East and by North Angle, and when that is done, turn your self full West, and set out after this manner the West and by North, and West and by South Angles, and when all the six angle stakes are driven in, 
Note that a good line of three double whipcord wound together of 300 yards and a foot, having loops fastened at every fifty yards, and another coloured loop at every hundred yards, will suffice to set out all this great superficie.  than you are to remove your line from the Centre stake, and to strain the same from Anglestake, to Anglestake, to try whether your Angle-stakes, and sides be equal, and to amend them if any be amiss, by the demy-circle and your line; and when they are all equal, than you are to fasten this three hundred yard line, one after another from Anglestake to Anglestake, as near the ground as may be, and to set Pioniers to trace that fide before you remove the line, and that side being traced, you are to trace the other five sides, one after another, after the very same manner, before you undertake to set out your six Bastions, that are to be set out after this manner.  
When the Superficie of the Sexagon is traced, you are to divide your six sides into six equal parts, that will be of fifty yards a piece, and to drive in every division a stake, than you are to fasten one end of your three hundred yards line to every one of the six angles-stakes, one after another, and to strain the same into the field one hundred yards beyond the 
* Because the distance from the centre of the bastion to the utmost point, is in this Sexagon of 100 yards.  Angle-stakes, according to the former rows of stakes you did drive in, whether the lines of them were diametrical or diagonal, and these six stakes will represent the six utmost angles of the Bastions; the six former Angles of the sides of the Sexagon, being by these last six stakes become the Centre of the Bastions. Then you are to fasten one end of your long line to the third stake of every side, and to strain and fasten the same to the stakes that represent the utmost points of the Bastions, and for the first, we will suppose to be the East Angle, then fasten a line of 50. yards to the second stake of the East and by South side, and strain it perpendicularie wise till it cut the long line fastened to the third stake of the said East and by South side, on the right hand that is strained and fastened to the utmost anglestake on the left hand of the East and by South side, and where this short line cuts the long line, drive in a stake, for that stake binds the Courtine, and sets out that flank, and the long line that runs from the third stake and toucheth the East stake to the utmost point of the bastion, represents the line of defence, and the face of the bastion on that side, and to this face, and the flank, you are to set Pioniers to trace the same, before you remove your lines, and this side being traced you are to set out and trace after this very manner all the eleven other sides, before you undertake to set out the orillon's.  
For the setting out of which, 
The gates and draw-bridges of this Sexagon Fortification are to be placed South and North, that they may be defended by the Flanks of two Bastions, and in the midst of the South Courtine, because the East and the West points have two Bastions.  I refer you to the 12. Chapter of this Abstract, where directions are described to set them out, and when the orillon's are set out, you are to set out the great dike, that is to be thirty yards broad, and ten yards deep, and the Cunnette five yards deep, and ten yards broad, and the Counterscarp is to be made with the earth taken out from this small double dike, called La Cunette.  
To conclude, this second Method of Fortification, by Bastions with orillon's, is the best and the strongest that ever was invented, to fortify all manner of Angle-Polligons, that are regularie, especially if the dimensions contained in this ensuing ichnography be observed.  

The ichnography of the Sexagon demonstrated in Plate 12.  
A represents the sides or base of the Sexagon, that are of 300. yards a piece.  
B represents the Centre of the Bastion, and the distance from the Centre to the point of the Bastion, that is 100 yards.  
C represents the Courtine that is of 200. yards.  
D represents the faces of the Bastions, of 120. yards.  
E represents the exterior Angle or point of the Bastion.  
F represents the circulary compass of the Orillon.  
G represents the Line of defence, by two pricked lines that is from 240. yards to 260. yards.  
H represents the Flanks that are of 50. yards with the orillon's, but sixteen yards and half besides the orillon's.  
I represents the jetty of the orillon's over the dike that is of 20. yards.  
K represents the demi gorge that is of 50. yards.  
L represents the whole gorge of the Bastion, that is 100 yards.  
M represents the Breast of the Bastion, that is 140. yards.  
N represents the Angle flanking of 135. degrees.  
O represents the Angle flanked of 80. degrees.  
P represents the Marketplace, that is of 100 yard's diameter.  
Q represents the breadth of the dike that is of 30. yards.  
R represents the Rampires of 30. yards broad in the bottom, and 20. yards at top, because the parapet of it with the three footsteps take 30. foot of it, and the brest-worke is nine foot high within side, and six foot without side, and twenty foot thick at top, with a slope of three foot.  
S represents the broad streets, that go round about the Rampires and to the marketplace that are thirty foot broad.  
T represents the small streets that are of fifteen foot, and the rows or ranges of the houses of the Inhabitants.    

CHAP. XVII. Of the third Method of Fortification, by Avantguards and outguards, and half Moons in general.  
THe third method of Fortification would be as chargeable as the second, if we should imitate in the erecting of it, the dimensions and proportions of the Italian and French Enginiers, or adorn them as they do with freestone of all sides to the Cordeau, or water-table, that is always five yards higher than the firm or even ground, and sometimes from the bottom of the dike, that are ordinarily 30. yards broad, 10 yards deep, and their Rampires 20. yards broad, besides the Brest-workes, and three foot steps that are also 10. yards broad in the bottom, and 20. foot thick at top, their Rampire's being ordinarily brought up fifteen foot with stonework from the even-ground and fifteen foot with turf and earth, besides the brest-work of nine or ten foot high, that is in all some forty foot high, besides the depth of the dike, and this they term in the French Tongue, Tells Ramparts sont hors de danger deseallade, that is, such Rampires are out of danger of scaling; and so they are, for ladders of fifty rounds, cannot be raised in the night time without noise, although they be made never so artificially, to be dismounted or set up by screws in five or six pieces.  
But since we have neither time, nor means, nor men, to man, to erect, or to finish such great works, we will reduce this third Method of Fortification, that is capable above all others, to endure without being much the worse, alterations or diminutions in her dimensions and proportions, to these ensuing scantlings.  
The dikes are to be ten yards broad and five yards deep, not slope to nothing, as our Country ignorant Surveyors make theirs, more like hedge-dikes, then of Works and Fortifications; but only allowing a foot slope in every yard; and by this means the broad dike when it is finished, will be twenty foot broad, out of which is to be taken a small dike of sixteen foot broad, and eight or ten foot deep, called by the French La Cunnette; and the slope of this dike is not to be on every side above a yard, that it may remain ten foot broad in the bottom; and these dikes are far better, and more difficult to be filled, or to be passed over, than those that are not a foot broad in in the bottom, as I have already proved in Chap. 16.  
And because the great dike is no broader nor deeper than is abovesaid, and that the earth that is to be digged out of the small dike is to be thrown on the field side, some twelve foot beyond the brim of the great dike, for to erect when all the inward works are perfected, a Counterscarp with a Brest-work round about the Garrison, of six foot high with a step, we will absolately cut off from this foreign Method the whole Rampire, and erect only with Turf, and the earth that is taken out of the great dike, a Brest-work of twelve foot high within side, and nine foot high without side from the firm ground, leaving a water-table between the Turf and the brim of the dike, of eight inches, if the earth be good; but if it be sandy, or of a running clay, it must be left eighteen inches, or two foot broad, notwithwithstanding the chat of self-conceited and ignorant men. The slope of the Brest-work without side is not to be above a yard in three yards, if the earth be good; but if it be naught, a foot more will serve, so it be well filled and rammed at every four courses of Turf with small brush bavins, as I have formerly given'directions. And for the flope within side, it is sufficient if it be two foot in twelve, or one foot in six; for the three footsteps are as a butteresse unto it. And the reason why the outside of the Brest-work is but nine foot, and the inside twelve, is, that the Brest-work is to be with five footsteps, four and thirty foot in the bottom, and twenty foot at top, and so great a thickness is to have at least a yard slope to convey the rainwater away, and to make way for the Musketeers to clear with their shot the brim of the dike. But in this place I will confute the gross ignorance and foolish frugality of some Country Surveyors, that set the inward wall of their Brest-work upon lose earth, in stead of bringing it up as well as the outside from the firm ground, and all to save some few loads of Turf, and a little labour; but this is a destructive frugality; for by it, within a year or two, all their Brest-works cleave in the midst, and fall as much inward as outward. Now if these dimensions and proportions be observed in this third, and in the fourth Method; and the Faces, Flanks, and Angles of the Avantguards, Outguards, Half Moons, and small Flanks truly lined and set out according to Art, our works should not be an object of derision to Foreigners, as they are, and the charges would not have been greater than they have been, to erect our slight and ill-flanked Redouts, Scarecrow mounts, and ridiculous winding Angles as we have done, for it were better not to fortify at all; but if we fortify thus, we need not fear with God's favour, to lose our Garrisons as we have done, in eight and forty hours.   

CHAP. XVIII. Of the extent of the sides or bases of all manner of Superficies, and of the just length of the Line of defence.  
THe opinion of Enginiers doth  much, concerning the extent of the sides or bases of any manner of regulary Superficie, that is to be fortified by Bastious: 
* See his Animadversions, Chap. 17. and pag. 49.  Mr. Ward would have it 900 foot, or 1000 foot at the most. The Italian Enginiers from 700 foot to 800 foot, and yet their foot is smaller than ours; and Errard de Barleduck, an ancient French Engineer, would have it from 600 foot to 700 foot: But Sir Anthony de Ville, and Honorat de Meynier, two later rare French Enginiers, would have the extent of it of 750 foot, that is 250 yards, and with their opinion I concur and assent: And to that end I have drawn all the sides or bases of the two first Methods, the Sexagon excepted, of 250 yards a piece, as the most convenient to reduce all the proportions of a Fortification by Bastions, to a perfect dimension or scantling; 
Of the true extent of the side, to have the Line of defence from 200 yards, to 240 yards.  but above all, the Line of defence to her true extent, and have only drawn the sides of the Sexagon of three hundred yards a piece, to show that Mr. Ward was as much out in that extent, as Errard de Barleduck was, in maintaining it should be from six to seven hundred foot at the most; for if his opinion be followed, the Courtines and the Line of defence will be something too short, as it may appear in all his Models, and specially in his regularie Angle Poligons, that exceed seven Angles. On the other side, if Mr. Wards opinion be followed, the Courtine and the Line of defence will be some thing of the longest, as it may appear by the Sexagon demonstrated in Plate 12. And therefore I conclude, that 750 foot is the best extent for the side or the base of any Poligon fertified by Bastions.  
But as concerning the sides or bases of these two last ensuing Methods, by Avantguards and small Flankers, the bases or sides of all manner of Superficies may be (if you please) from five hundred, to two thousand yards, so you observe in your division, or in the placing of your Avantguards and small Flankers, two hundred and fifty yards between Centre and Centre of every one of them. But as for Forts that have no need to have neither Avantguards, nor small Flankers, but only in their Angles, you are then to observe carefully to make their sides of no longer extent then of 250 yards a piece.  
Now if any should so much mistake himself, as to erect two or three Bastions upon a side of 500 or 750 yards, these Bastions are no more true Bastions, but Ravelias; for it is improper for a Bastion to be placed any where, but upon an Angle. Suppose than you would fortify a Town that containeth some three mile's circumference, that can be reduced in a circulary form: if you will fortify the same by 24 Bastions, you must reduce this circulary form into four and twenty sides, and as many Angles; but if you fortify the same by Avantguards, or small Flankers, you need not to divide this circulary form, but into eight sides, and place in every side two Avantguards, and one half Moon beyond the dike, to defend the Angle; but if you fortify the same by small Flankers, than every one of these eight Angles is to have a Flanker, and every side two Flankers more, as it is demonstrated in Plate 18, and 23. And this will suffice to have been spoken, concerning the sides, or bases of all manner of Superficies.  
Concerning the Line of defence, 
* See his Animadversions, Chap. 30. and pag. 74.  Mr. Ward is over-bitter against Errard de Barleduck, because he draweth his Line of defence from the very corner of the Flank, and not from the third of the base or side which he calleth the Courtine. I do acknowledge that it is better to draw the Line of defence from the third part of the side or base, as Mr. Ward would have it, then from the corner of the Flank, and especially if the sides of the Fortification be of 
* If a side is of 300 yards, it is better to draw the Line of defence from the middle of the Courtine, then from the third part of it.  300 yards a piece, as Mr. Ward would have them to be; nay, it were better if it were drawn from the middle of the side or Courtine, (for it is one and the same thing.) To rectify the error of the extent of his sides, of three hundred yards a piece, that makes the Line of defence unserviceable for the musket-shot, if the Line be drawn from the third part of the Courtine; whereas it would serve turn, and amend the error of the overlong extent of the fide, if it were drawn from the middle of the Courtine. Yet for all this small error of Errard, I see no reason why Mr. Ward should be so bitter against him, for his own Models are not without defects; for it is a very good horse that never stumbleth. And it is well known to all Artists, that Errard de Barleduck was an experienced Engineer, and the first that adorned the Art of Fortification in the French tongue. Besides, the Line of defence is better (in the Superficies of the equilateral Triangle, and of the Square) to be taken from the corner of the Flank, then from the third part of the side or Courtine, because it openeth the breast of the Bastion, and maketh their exterior Angle more obtus, then when it is drawn from the third part of the Courtine. Moreover, Mr. Ward doth wrong or mistake Errard, and the other French Engineer, to allege as he doth, that they rely most upon the musket-shot for the defence of the Courtines, faces, and points of their Bastions, despising the defence of them b● the Ordnance shot; the defence of the musket-shot being (saith he) no defence at all, to empede the Assailant from casting their galleries over the mote. But I say that Mr. Ward doth mistake the meaning of Errard, and of the rest of the French Enginiers; for they erect their lower Flanks, and provide them with Demi-Cannon; only to prevent the casting of galleries over their mote: And for their upper Flanks, besides the Demi-Culverins they place upon them, to defend the faces and points of their Bastions, they place Musketeers to discharge their shot continually, while their Demi-Culverins are charging again, and so make use of Ordnance and of Musket-shot also, for the defence of them. Therefore I will conclude with the Assertion of one of the greatest 
* See the Duke of Rouen in his Perfect Captain, Chap. 8.  Commanders of our days, that the extent of the Line of defence is the best, that is convenient for the Musket-shot, as well as for the Canonshot.   

CHAP. XIX. Of the Fortifications of the Superficie, in the form of S. Michael's Cross, fortified by eight Halfmoons, demonstrated in Plate 13.  
THe Circumference of this Superfice is so great that it contains 3680. yards, that is two English mile, and one third part of a mile, and therefore fit to fortify some Corporation town then for a Fort, so it may be reduced to this form; the Angles of the Centre of it are of fifty five degrees, and the exterior Angle of the halfmoons are of sixty five degrees, half of the faces of the halfmoons are of 250. yards, and the other half of 210. yards a piece, whereby they require to be defended by small drakes, or sacres, besides the musket-shot, but if upon every point of the half Moon a platform were erected as they are most commonly in all Redoubts, or Forts after this manner, viz. the Angle upon which you intent to erect a platform, is to be brought up twelve foot high from the ground, to be level with the inward side of the Brest-worke, and towards the town slope nothing, and when it is so, you are upon the last course of turf, to place a freeze with sharp picked quarters, of six foot long, four inches broad, and three inches thick, 
* Seven or eight inches distance one from another.  jetting one yard over the dike and running a yard into the brest-worke, that is to be raised so fare as the platform goeth on both sides, fix foot higher than the other Brest-work, in which Brest-work the Portholes are to be made two on every side, so that these Angle-Brest-workes are to be 18. foot from the ground, having a freeze as is above said round about the Platform to free it from scaling, to place two Sacres, & two Drakes upon every platform, this Fortification being so provided, will be of great defence, and very offensive to the assailants, because the half Moons flank one another so well, that none can approach the sides or the points of them, without great danger of their lives; but if the diametrical line of this Superficie were reduced less by one half or the scale of it, brought from 30. yards to 15. yards, it would have been of a great defence, without Drakes or Sacres, by the musket-shot only. But I have purposely set out the same so large to show how such great sides may be set out in the field, for they are fare more difficult to set out, uhen shorter dimensions.  
Now to set it out in the field, you are to make choice of the Centre, and to drive in a stake; than you are to have a line ready of 330. 
* This Line of three hundred and thirty yards is the just Demi-Diagonall and Diametrical extent of the Line that is to set our the eight inward Angles of this Superficie.  yards, having at every fifty yards a loop fastened to it of one colour, and another loop of another colour fastened to it at every hundred yards, than you are to stand at the Center-stake, and to turn yourself full South, after you have set out with your Sea-compasse as near as you can to that distance, of the line, the South, North, East, and West points, because the four sides of your cross are of necessity to be lined so; then set the sight of your demi-circle upon the ray of 55. degrees, and wind the ray of your circle first on the left hand, and let the man with the line fasten the one end of it to the Center-stake, and follow with the other end of the line, the ray of your demi-circle, and when he is one hundred yards distance from you, and just against you, and the ray of your demi-circle, let the other man that carrieth the stakes, drive in a stake at his feet, and twift the line once or twice about the stake, observing always to make the line to come to be strained again on that very side, 
* In sides that are above one hundred yards, that require above two stakes, you are carefully to observe, to wind the Line upon the stakes all of a side, to prevent breaks  that he first twisted the same, to avoid breaks, because the thickness of a stake of two inches thick will cause a great break in the extent of three hundred yards, that being done, let him follow still the ray of your demi-circle, and when he is another hundred yards distant from the last stake, and two hundred yards from you, but just against you, and the ray of your demi-circle, let the man with stakes drive in a second stake at his feet, and wind the line about the stake ●he did before, then let him go forward and strain still the line till he be a hundred yards more from the second stake, and when he is just against you, and the ray of your demi-circle, let the man with stakes drive the third stake at his feet, and having twisted the line about that stake as he did before, let the man with the line go forward 30. yards, and when he is just against you and the ray of the demi-circle, let the man with stakes, drive in the fourth stake at his feet, and between these four stakes there will be 330. yards, and the last stake will represent the Southeast inward Angle of the Cross; than you are to wind the ray of your demi-circle on the right hand, and to set out after the very same manner the South-West inward Angle, and having driven in four stakes as before, you are to set out the other six Angles after the very same manner as you have done these two, and when the eight Angles are set out thus, and stakes driven in them all, then remove the line of three hundred thirty yards, and fasten another line to the Center-stake, of 250. 
* The extent of the Demi-Diametricall and diagonal Line, from the Centre to the utmost point of the Hasse Moon, is 500 yards.  yards, and strain it Southeast diagonal wise, this line being the just moiety of the demi-diogonall and diametrical line, from the Center-stake to the utmost points of the eight half Moons, and at the end of it drive in a stake, and this stake represents the Centre of the Southeast half Moon; then remove the line from the Center-stake and fasten the same to the last stake, and strain it again diagnail-wife, and that stake will reprsent the utmost point of the Southeast half Moon, than set out after the very same manner the other seven Centres, and utmost points of the half Moons. Now because-the sides or faces of your half Moons are not equal, eight of them being 250. yards a piece, and the other eight but 210 yards a piece, you are to set out the eight longest first by fastening a line of 250 yards one after another to the four stakes, that represents the four ends of the two diametrical lines of the pricked Square demonstrated in this Plate, and to strain this line eight times one after another to the utmost Angle stakes that represent the utmost points of the half Moons, and as you strain it, fasten the same to the stakes as near as you can to the ground, that the Pioners may trace that side, or face of the half Moon, before you remove the line to another side, and one side being set out and traced, set out and trace all the other seven sides after this very manner.  
Then you are to remove this line of 250. yards, and to fasten another line of 210. yards to the four diagonal inward Angel's Centre stake, that are just oposite to the Angles of the pricked Square demonstrated in this Plate, to set out the eight shorter sides or faces of the half Moons after the very same manner as you did set out the longer sides or faces, and these being also set out and traced, the superficie of this Fortification will be perfected, than you are to set out the dikes according to the dimensions described in Chapter 17. and when the inward Works are finished, than you are to erect the Counterscarp with the earth that is taken out of the small dike, called La Cunnette.   

CHAP. XX. Of the Fortifications of the Faralograme, fortified by Avantguards, demonstrated in Plate 14.  
THe broad side of this Paralograme is of 900 yards, and the end side of it of 450 yards, and all the circumference of it 2700 yards, that is, an English mile, and three fifth parts of a mile; for her continent I will not stand upon, because it is not of a convenient form to erect a new garrison, but only fit to fortify some market town, if need should require; of which form there are many in this Kingdom, most of them being as long again as they are broad: Yet let the Reader observe, that incase he be required to fortify a town that may be reduced to this form, that hath her broad side of 700 yards, and her end side of 350 yards, that he may boldly undertake to fortify the same after this manner, so he divide his end into five parts, and his broad side into ten parts, and doth reduce the rest of the dimensions of the faces, breasts, flanks, courtines, and line of defence after the proportions of his sides; for then the dimensions of such a fortifiation will be more complete than this, and altogether defensible by the musket shot. But I have set out this so on purpose, to show what may be done, when men are tied by the extent of a place, and enforced to omit to erect four Avantguards less than they should, to avoid charges. The Angle of the Centre of her broad side is of 135 degrees, and of her end side of 45 degrees. This is the most frugal way that can be invented to fortify a long town of so large an extent as this is; for it is almost a mile and three quarters in the circumference, her end side individed into five parts, two of which are allowed for the breast of the two end Avantguards, that contain 90 yards apiece, and the courtine 270 yards: her broad side is divided into ten equal parts, two of which are allowed for the breast of the Avantguards, that are of 90 yards a piece, uniform with the end of the Avantguards, the four Angle Courtines are longer than the middle Courtine by 120 yards, because of the addition of the long Flank to every one of them, that extend themselves into the field 120 yards more than the utmost angles of the Paralog rame, the end and the middle Courtines are defensible by the Musket-shot, because they are between two Flanks, and also because the Line of defence of the faces of the Avantguards is taken from the middle of the Courtine, whereby the Line of defence cometh to be from two hundred and forty to two hundred and fifty yards; but the long Angle Flanks cannot sufficiently be defended by the Musket-shot alone, without four Drakes and four Sacres, one Sacre and one Drake mounted upon every one of the long Flanks, and with them, this Fortification will be of great defence: The short Flanks are of 60 yards a piece, and the faces of the Avantguards of 120 yards a piece, uniform with the long Flanks.  
To set out this Superficie in the field, you are to knock a stake in your Centre, and to stand close to it, and to set yourself East, after you have set the light of your Demi-circle upon the ray of 45. degrees; to set out the East and by South, and the East and by North Angles, as you have been directed for merly, and then to turn yourself West, and to set out the West and by South, and the West and by North Angles; and these b●ing rightly set out, and stakes knocked in them, your two broad sins North and South cannot be amiss But if it be an erected Town, take the just length on the broad and end-side of it, with a line of 100 yards, and set out your Angles with the Demi-circle accordingly: and divide your end-side into five, and your broad side into ten equal parts, and then set out your Avant Guards thereafter.   

CHAP. XXI. Of the Fortifications of the Equilateral Triangle fortified by Avant Guards, demonstrated in Plate 15.  
ALL the sides of this Equilateral Triangle are equal, and contain 520 yards apiece, so that her circumference is of 1560 yards, that is an English mile wanting 64 foot; the Angle other Centre is of 60 degrees. I omit her continent, because of her large extent, that is fit to fortify a well compacted town, that may be reduced to this form, then for a new Fort. Her sides are divided into eight equal parts; two of which, are allowed for the two breasts of the Avant Guards, that contain 65 yards apiece; and the other six pares are divided equally for the three Courtines, that contain 130 yards apiece. Her long flanks are 100 yards apiece, and her short flanks of 50 yards apiece, and the faces of her Avant Guards, are uniform to her long flanks, whereby they are also of 100 yards apiece. And by these dimensions, it is apparent that this Superficie is a compact and complete Fortification because all her Faces, Flanks, Courtines, and Angles, can be easily defended by the Musket shot; her line of defence is taken from the middle of the Courtine, and by this means of 160 yards.  
Yet let me inform the reader, that if he had occasion to fortify a town that might be reduced into this Triangle for me, although her sides were from 520 yards apiece, to 750 yards apiece, that he may boldly fortify the same after this manner, so he divide his three sides into 8 equal parts; and doth proportion his Flanks, Faces, Breasts, Courtines, and line of defence, after this extent: for notwithstanding this addition of 230 yards to every side of the Triangle, all the dimensions of his fortification, will be defensible by the Musket shot.  
Now to set out this Superficie in the field, you are to make choice of your Centre, and to knock in a stake; and after to set the sight of your Demi-circle upon 60 degrees, and to follow the same directions given you in plate 9 for the setting out of a Triangle fortified by bastions. And because these sides are as long again as they were, I refer you to the directions given you in chap. 19 for the straining of a long line by knocking in at every hundred yards of it a stake. But if it be an erected town that you are to fortify, after this manner, go up to the end of the town where you intent the North Angle of the Triangle shall be, and turn your face South; and with your Demi-circle, when the sight of it is set upon the ray of 60 degrees, set out the Southeast Angle of the Triangle, cau●ing the man with lines to strain a line from the North Anglestake where you stand, to follow the ray of your Demi-circle; the man with stak s knocking at every hundred yards a stake, and by this plurality of stakes you may lengthen your line as you please, twisting the same always of one and the same side of the stake, till he come to the just distance of your side of the Triangle, whether it be five hundred and twenty yards, or 720 yards; and at the side of the distance, knock in a stake, and that last stake will represent the Southeast Angle of the Triangle, than set out after this manner the Southeast Angle, and knock in a stake at the same distance, that it may represent the South-West Angle; then measure with a line of 100 yards, whether the distance between the Southeast and South-West Angle stake, is equal with the two other sides; and finding it to be equal, then is the Superficie of the Triangle perfected, that you are presently to have traced, by many Pioniers; but if there be any error, you are to amend the same by your Demi-circle and your lines.  
The Superficie of the Triangle being traced, you are to divide the sides into 8 parts, and at every division to knock 8 stakes; knocking in also a stake in the middle of every side, for it will serve to set out the faces of the Avant guards, and the lines of defence, allowing two parts to every Courtine, and two parts to the two breasts of the Avant guards; and at every third stake of every side, you are to fasten a line of 32 yards and ½, and to strain it first on the right hand along the side traced; and at the side of the line you are to knock in a stake, and then you are to wind the same line on the left hand, and to strain it along the side traced; and at the end of the line you are to knock in a stake, and these two stakes will represent the breadth of the breast of the Avant Guards; the exterior stake toward the Angles of the Triangle, representing the beginning of the long flank, and the inward stake toward the middle of the side, representing the beginning of the short flank, and as you have set out this first breast of the Avant Guard, you are to set out the other five after the same manner. That being done, you are to fasten a line of one hundred 
* If you can strain a line from the middle stake of the side of 320 yards, that is the just distance; from the side opposite to every long flank, it would ●e the better; if not, this way will serve turn, so you stand with your Demi-circle. At the middle stake of the side ●o guide the end of the line of 100 yards, to the very out most Point or Angle of the Avant Guard.  yards to every one of the stakes that represent the beginning of the long flank, and to strain the same into the field upon a Diagonal line, taken from the midst of the Courtine or side opposite to it; and at the end of the line knock in a stake, and six of these stakes will represent all the utmost parts of the long flank, and set out the sides of them that are to be traced as you set them out: then fasten a line of fifty yards to every inward stake that represents the inward parts of the breast, and the beginning of the short flank, and strain the same into the field, parallel with the line of the long flank, and at the end of a line knock in a stake, and these six stakes will bond and set out all the short flanks that are to be also traced, as you remove the line from one stake to another. Then you are to fasten a line of one hundred and threescore yards to every one of the middle stakes of the side, and to strain and fasten the ●●me one after another to the utmost stakes that represent the Angles or Points of the Avant Guards; and they will set out all the faces of the Avant Guards and the lines of defence; for they will out the line of the short flanks, and end at the point of the long flanks, and these faces are also to be traced before you remove this line from one stake to another: and these being all traced, you are to set out all the ditches, according to the dimensions described in the 17 chap. of this abstract. And when all the ditches and inward works are finished, you are to set out the small ditch called La cunette out of the great ditch, and with the earth of it to erect the brest-work of the Country escarpe, as it is described in chap. 17.  
Here followeth the Itchnographie of this method of Fortification, but specially of the fortifications of this equilateral Triangle. The letter A. represents the Market place, that contains in extent one hundred yards on every side.  

B. Represents the breast of the Avant guards that are in this figure, out 65 yard's bread.  
C. Represents the Courtines that are in this figure, but 130. yards.  
D. Represents the ditches that are 10 yards broad, and 5 yards deep, besides the small ditch called La cunette, that is 16 foot broad, and nine foot deep.  
L. F. Represents the long flanks, that are 100 yards long.  
S. F. Represents the short flanks, that are 50 yards long.  
F. Represents the faces of the Avant guards, that are in extent 100 yards.  
G. Represents the broad street that goes round about the Rampiars, and from the Rampiars to the Market place, that are to be 30 foot broad.  
H. Represents the places for the lodgings and the small streets, that are to be 15 foot broad.  
I. Represents the middle of the South Courtine where the gate and the drawbridge is to be placed.  
K. Represents the brest-works with his five footsteps, that is 34 foot in the bottom, with the five footsteps, and twenty foot at top; 12 foot high within side, and 9 foot without side, with a slope at top, from twelve to nine that is a yard; the five footsteps are two foot broad, and eighteen inches high apiece.    

CHAP. XXII. Of the Fortifications of the square, fortified by Avant Guards, and Outguards, demonstrated in Plate 16.  
THe four sides of this square contains 400 yards apiece, and by consequence the circumference of it is of 1600 yards, that is almost an English mile; the Angle of his Centre is of 90 degrees; I will omit his continent, for it is fit to fortify a compact Market town, that may be reduced to this form, then for a Fort; it is to be set out after the manner as hath been described in Plate 10. And therefore I will only here insert some directions how you are to set out the Avant Guards, and Outguards, by which it is fortified.  
The square being set out and traced, you are to knock four stakes in the midst of the four sides of it, than you are to fasten a line one after another to these four stakes of 125 yards, and to strain the same upon a straight perpendicular line from the Centre stake, 125 yards into the field, and at every end of the line to knock in a stake, and these four stakes will represent the middle of the faces of the four Avant Guards; than you are to fasten a line of 41 yard's ⅔. to the very same stakes whereon the line of 100 yards was fastened to; that is, to be removed and put by: and this line of 41 yards, and ⅔. is to be strained first on the right hand, and then on the left hand; upon the traced sides of the squares, and at every end of the line you are to knock a stake; and having done so to all the four sides one after another, these eight stakes will represent the breadth of the breast of the four Avantguards: that is of 83 yards, ⅓. for the Avaunt Guards are to be one third part longer than they are broad; than you are to fasten to every one of these last stakes, the former line of one hundred yards one after another, and to strain the same parallel wise to the stakes that represent the middle of the face of the Avant Guards; and at the end of every line you are to knock a stake, and to trace that flank of the Avant Guards, before you remove the line to the other flanks stake; and having done so round, and knocked in eight stakes, all the flanks will be set out and traced: than you are to remove the line of 100 yards, and lay it by, and to fasten the former line of 41 yards, 1/5. to the utmost middle stakes, that represent the middle of the faces of the Avant Guards, and to strain and fasten the same first to the right hand stake, and then to the left hand stake that represents the utmost Angles of the Avant Guards; but before you wind the line from the right hand, to the left hand stake, have that moiety of the face of the Avant Guard traced, then wind the line on the left hand, and trace the other moiety of the face; and as you have set out and traced that face of the Avant Guard, do all the rest after this manner: which being done, your four Avaunt Guards will be perfectly fet out and traced.  
Then you are to set out all your ditches after the same dimensions described in chap. 17. and to cast all the earth inward; to erect your brest-works and their footsteps, of that height and breadth mentioned in the said Chapter. And when all the ditches, brest-works, and footsteps are finished, than you are to set out the small ditch called La cunette, out of the great ditch; end with the earth that is taken from it, you are to erect the brest-work with the foot-step of it of your Country escarpe, four yards beyond the brim of the great ditch. Before you set out any of your Outguards, that are not to be undertaken before the brest-work and the slope of it belonging to the Country esearpe, be fully finished; only you are to leave a gate of 12 soot broad against the places where you are to erect your out-gtards, and these gates are to be made up by so many strong and sufficient Turn-Pikes, well ironed, with iron pikes, and good hasps and locks: for by these you are to relieve your Outguards, or make your retreat, if you be driven from the Outguards: all this being finished, you are to set out the Outguards after this manner.  
The four Outguards against the four Angles of the square, are four equilater all Triangies or Holfe-moones of one hundred yards on all sides, two of the sides are to have a di●ch of nine foot broad, and six foot deep; and their brest-works of six foot high with a foot-step, and the brest-work at cop is to be six foot thick, and in the bottom nine foot with the foot-step. And the other side towards the Angle of the square is to be open, that the assailants may be discovered if they should possess themselves of these Outguards; he Points of these Triangles that are towards the Angles of the square, are to be 16 foot distant from the brim of the ditch.  
The four smaller Triangles have their Base 13 yards longer than their two sides that are to have ditches and brestworks that are to be of the very same dimensions of their former Triangles; their base is of 83. and their fortified sides of 70 yards; the first defend the Angles of the square and the flanks of the Avant Guards, and the last defends the faces of the Avant Guards; so that this fortification is complete, strong, and of great defence: the coming in is to be in the middle of the South Avant Guards, for the gate and the drawbridge are flanked, and covered by one of the Halfe-moons.   

CHAP. XXIII. Of the Fortifications of the Pentagon fortified by Avant Guards, and Outguards, demonstrated in Plate 17.  
I Have formerly shown in Plate 11, how to set out the Pentagon in the field; to omit repetitions, I will only give you some directions how to set out the Avant Guards, and the Outguards of this Pentagon, because this Fortification differs from the other. The Angle of the Pentagon is of 75 degrees, his five sides are of 240 yards apiece, ten yards less than the former; the circumference of it is 1200 yards, that is almost three quarters of an English mile, a very convenient form for a Royal Fort for the continent of it: it differs little from the other, because the circumference of it is but 50 yards less, and therefore I will refer you to Plate 11. only I will inform you that if the circumference of it were a quarter of a mile greater than it is, that it might be defended, being fortified after this method by a smaller number of men than the other could be, that is fortified by bastions, with orillons.  
When the Superficie of the Pentagon is fully set out and traced, you are to divide his five sides, into three 
* Note by this that the breast of the Avant Guard is 80 yards broad.  equal parts, that will be of 80 yards apiece, and you are to knock in stakes in all their divisions; than you are to divide the middle division in two parts, that there may be a stake knocked in to represent the middle of every side. Then you are to fasten a line of 80 yards 
* Note that the greatest slanks of the Parliament Guards advance 80 yards into the field.  to the Southeast Angle stake, and to strain the same full East upon a straight line agreeing with the side, and at the end of the line knock in a stake; then remove that line and fasten the same to the North and by East Angle stake, and to strain it as before, and to knock in a stake; then remove that line, and fasten the same to the North and by West Angle stake, and strain it as before, and knock in a stake; then remove the line and do the like, to the West and by North Angle, and as much to the West and by South stake, straining the line as is said before; and at every fide of the line knock in a stake, and these five stakes will represent the five out-most Angles or Points of the five Avant Guards. Then remove that line, and fasten a shorter line of 
* The short slank is sorcy yards.  40 yards to the second stake of the South side, on the left hand South West; and strain the same into the field perpendiculary wise, and knock in a stake at the end of the line, and this line will represent the short flank of the South-West Avaunt Guard: and as you have set out this short frank, set out the other four, and knock stakes at every end of the line, and these five stakes will represent the five short flanks. Then fasten the former line of 80 yards to every one of these last stakes, one after another; and first of all to the South-West short flank, and strain the same Diagonal wise, fastening the same to the stakes that represent the out-most Point of the Avant Guard: and before the line be removed, set Pioniers to trace the same, and it will set out the face 
* The line of defence is taken from the midale of the side or Courtine that is in this figure of 240 yards.  of the South-West Avaunt Guard; and as you have set out this face, set out the other four, after the same manner. You are to observe, that if a line of four hundred yards could be strained from the Southeast Angle of the side of the Pentagon, and fastened to the outmost Point stake of the South-West Avaunt Guard, that this Diagona line that represents and sets out the face, would be more perfect, for it would cut the end of the short flank, and terminate itself at the end or point of the long flank; but this cannot be done conveniently: only when you set out these faces, stand with your Demi-circle at every Angle stake of the side opposite to the face you set out, and by the Diagonal ray of your circle, you may guide the line of the faces, to be set out as perfectly, as if a line of 400 yards had been strained.  
Now when you have thus set out and traced the five Avant Guards, with their faces, long and short flanks; you are to set out all your ditches, after the dimensions described in chap. 17. Casting the earth of them inward, to erect the brest-works and their five footsteps of that height, breadth, and thickness, there described. And when all your inward works, and the great ditch is finished, you are to set out the Cunette or small ditch out of the great ditch, and to erect with the earth that is taken out of it, the Country escarpe brest-work, distant from the orim of the great ditch four yards, observing the rules and dimensions described in chap. 17. and also five places of twelve foot apiece to be left open in the brest-work of the Country escarpe; to set five Turn-Pikes right against these five Halfmoons here demonstrated, which Halfmoons you are to set out after your Country escarpe brest-work is finished, placing the open side of them within 16 foot distance of the slope of your Country escarpe, that there may be a clear passage for horse and foot to come to the Halfmoons, without spoiling of the slope of the Country escarpe, that the French call glasis.  
The five Outguards of this figure are five Halfmoons, that have one side longer than the other by twenty yards; 
* And this must of necessity be observed that the Ling side of the Halt-moones, may cover the slanks of the Avant Guards.  the long side is of 80 yards, and the short side of 60 yards; their ditch is to be nine foot broad, and fix foot deep; their brest-work is to be 9 foot broad in the botteme, with the foot-step; and six foot thick at top, having a foot slope; and their height six foot from the ground, and four foot and a half from the footstep. The gate and drawbridge of this Fort is to be in the middle of the South side, that it may be defended with the South-West flank, and covered with the South Halfmoon, marked with the letter A.   

CHAP. XXIV. Of the Fortification of the Demi-Sexagon fortified by Avant Guards, and Outguards, demonstrated in Plate 18.  
THis Sexagon is of a large extent, for her sides are of 800 yards apiece, and by consequence her cucumference is of 4800 yards, that is almost two English miles and a half; and therefore fit to fortify a good Corporation, then for a Citadel, or Fort: the Angle of her Centre is of 60 degrees. And the same directions that were given you for to set out the Sexagon demonstrated in Plate 12. fortified by bastions with orillons will suffice, with the observations contained in chap. 19 viz. to knock in stakes at every hundred yards, when sides, or Diametrical, or diagonal lines exceed 250 yards.  
The Superficie of this Sexagon being then set out, and fully traced, as it hath been shown in the foresaid Plate; you are to divide every one of the Bases into three equal parts, that will be of 266 yards, and ⅔. apiece; and to knock in a stake at every division: than you are to fasten a line to the two inward stakes one after another of 60 
* 60 Yards is the just moiety of the breast of the Avant Guards.  yards, and to strain the same first on the right hand; and upon the side traced and the end of the line you are to knock in a stake, than you are to wind the said line about on the left hand, and to strain the same upon a straight line upon the sidetraced: and at the end of the line you are to knock in a stake, than you are to remove the line, and to fasten the same to the other in ward stake of that side, and to do as you did before; and to knock in two stakes at the end of the line, and these four stakes represent the breadth 
* That is of 120 Yards broad.  of the two breasts of these two Avant Guards, and the middle stake represents the Centre of the Avant Guards. Then you are to set out the breast of the other ten Avant Guards of the other five sides, after the very same manner as you did these last.  
And that being done, you are to fasten a line of 120 yards to every one of the exterior stakes that represent the breadth of the breasts of the Avant Gnards, and to strain the same into the field upon a straight diagonal line, derived from the Centre stake of the Sexagon; that you are to guide by the sight of your Demi-circle, standing at the Centre stake, while the man that carrieth your lines, straineth the foresaid line into the field: and at the end of it, the man that carrieth your stakes, is to knock in a stake, and this stake represents the utmost Point of the long flank of your first Avant Guard. And as you have set out this long 
* Note and observe, This course is to be taken, lecause the Demi Diagonal line of this Sexagon, from the Centre stake to the utmost Point of the long flank, is of 680 yards; that is too long a line to be conveniently strained.  flank, set out the other eleven that remain. And that being done, you are to fasten a line of 60 yards to the inward stake of that Avant Guard, that represents the breadth of the breast of it; and to strain the same into the field parallel-wise, to that of the long flank; and at the end of it, you are to knock in a stake, and this stake represents the utmost point of the short flank of that Avaunt Guard. But observe 
* These long flanks, are of 120 yards apiece.  to trace the long and short flanks before you remove the line to another flake, to avoid mistake. And as you have set out this short 
* These short flanks, are of 60 yards apiece  flank, set out the eleven that remain.  
That being done, knock fix stakes in the middle of the six sides of this S xigon, than you are to fasten a line to every one of them one ofter another of 240 yards, and to strain and fasten the same first on the right hand stake that represents the utmost Point of the long flanks, and this line will cut the end of the line of the short flank, and set out the face of that Avant Guard, and withal doth represent the line of defence; 
* The line of defence is taken from the midst of the Courtine, and the extent of it in this figure, is o● 240 yards. And the extent or all the Courtines are o● 186 yard's ⅓. aprece.  but before you remove this line, you are to trace the face of this Avant Guard that extends it selce from the stake of the short flank, to the stake that represents the utmost Point of the long flank. Then you are to wind the very same line about, and to fasten it to the left hand inward stake that represents the utmost Point of that long flank, and to do as you did before to the other on the right hand, and then the two Avant Guards of that fide of the Sexagon will be perfected; and as you have done this side; do the other five sides after the very same manner.  
When the twelve Aven Guards are thus set out and traced, you are to set out all the ditches of it, after the very same dimensions set down in chap. 17. Casting all the earth inward, to erect the brest-works, and their five footsteps; of that height, breadth, and thickness; described in the aforesaid chapter. And when they are all finished, you are then to set out the small ditch called La cunette, out of the great ditch, and with the earth that is taken out of it, you are to erect the brest-werk of of your Country escarpe, with the foot-step of it; the height of which is to be six foot high with the foot-step from the ground, and four foot and a half from the footstep; and the top of it sloped to nothing, and leveled with the firm ground, leaving six places of twelve foot broad to place six Turn-Pikes, right against the middle of the six Halfe-moons, that are to be erected after the brest-works of the Country escarpe are finished; the distance between the brest-work and the brim of the great ditch, is to betwelve foot at the least; and these Turn-Pikes are all of them to be locked in the night, and serve to retreat or relieve the Outguards in time of a siege.  
And when all this is perfected, you are to set out the six Outguards, that are six Halfmoons in the form of six equilateral Triangles, that have all their sides equal, of one handred and forty yards apiece; their Base that lieth towards the Country escarpe is to be open, and the ends of it 20 foot or 24 foot from the slope of the Country escarpe; and the coming to the town and the going out, is to be by the South and North Half-moon, marked by the letter A. For by this means the gate and drawbridge will be secured and covered by the Half-moones; and the Horse, Carts, or Foot that come to town, shall be enforced to wind about the said Halfmoon; and by it exposed if they be enemies, to the musket shot of them that keep the brest-works of the Half-moones. Now to secure these Half-moones from surptises, besides the Sentinel Perdues, there is to be a small Court of Cuard in the midst of them, and strong Pallisadoes, with palisado gates; that extendeth from the Points or Angles, to the very brest-works of the Country escarpe. The ditches of these Halfmoons are to be nine foot broad, and fix foot deep; their brest-work 9 foot broad in the bottom, with their foot-step; and their height fix foot from the ground, and four foot and a half from the foot-step; and their thickness at top six foot, having a foot slope towards the ditch.  
This Garrison thus fortified, and manned with a thousand foot and three hundred horse, and provided with 24 pieces of Ordnance, Arms, Ammunition, Fireworks, and Victuals, and all other necessaries for a siege; will be able to oppose an Army of twelve thousand men for 3 months. For to conclude, this method of Fortification, is as convenient for us in these times of civil distraction as any, for it is not of great charges, and requires less men to man the same; and yet is safer and stronger threefold, than our skare-crow Mounts: small and ill flanked redouts, and winding Angles.   

CHAP. XXV. Of the fourth and last method of Fortification by small Flankers in general.  
THis fourth and last method of Fortification is derived from the first; composed of Flanks, Courtines, and Eastions, without orillon's; for they agree in their form, but disagree in their dimensions: the faces, flanks, and breasts of these flankers, being in a manner half as short again, as those of the Bastions; & the extent of the Courtines of this method by 
* A Flanker is properly a bastard Bastion, without Or●llons.  flankers; longer by forty yards, by reason of the narrowness of their breasts. It was invented to save charges, both in the erection of the works, and in the manning of the Garrisons; for I know no manner of Fortifications that will require less men to defend it, nor smaller charges to erect it, than this method: and therefore the more convenient for us to make use of it in these times of civil distractions, in which we want means and time to erect strong, complete, and permanent Fortifications, and men to man and defend them; yet I will inform the reader of this truth, that if this method of Fortification be set and lined out by a judicious Engineer, and the dimensions of it here described, carefully observed; that it will be threefold as strong again, and as permanent and regulary than the Mounts, weak redoubts, and slight winding Angles, used In these days. And that a valiant and experienced Governor in a Garrison thus fortified, will be able to defend it with twelve hundred foot, and three hundred horse, although it be of three mile and a half circumference; then he could do one that I know, fortified with Mounts and winding Angles; with eighteen hundred foot, and three hundred horse.  
So much availeth the Art and the Method of Fortification in the defence of a corporation, and yet I dare affirm for a truth, that their charges have been greater, then if they they had erected such works as these; with the very same dimensions following.  

1, The extent of the sides or Bases of this Method, are not to exceed two hundred and fifty yards.  
2. The neck of their flankers is neither less, nor exceeds in extent fifty yards.  
3. The breast of their flankers neither more nor less than 60 yards.  
4. The flanks of their flankers neither less nor more than 25 yards.  
5. Nor the faces of their flankers less or more than fifty yards.  
6. The Courtines between two flankers, is not to exceed two hundred yards.  
7. Their line of defence is to be taken in this method from the middle of the Courtine, that it may not exceed one hundred and fifty yards. Nor the exterior Angle of their flanker, be more acute than these are.  
8. The line of their flanks is not to be drawn upon a straight perpendiculary line, as most men use to do; for this way is destructive to the flanks, and they being reduced to dust, the Garrison is lost. But they are drawn one ⅛. part more slope toward the other flank opposite to it, that the shoulders of the flankers may be thicker; and jet or extend so much the more over the ditches, to preserve the flanks.  
9 All the ditches are to be in this methed that hath no Country escarpe, or Outguards, thirty foot broad, and twenty foot deep; the slope of them is to be for every yard a foot on every side, that the very bottom of them may be sixteen foot, and ⅔, broad; for it is a disparagement to make the ditches of Fortifications, and Martial works, like the ditches of enclosed grounds; besides, they are not so safe, because they are sooner filled in a storm: and this manner of ditches savours over much, of the ignorance and self-conceitedness of our country surveyors.  
10. The brest-works are to be twelve foot high within side, and nine foot without side; their inside is to be carried up from the firm ground, as well as the outside; and the five footsteps within side are to be carried up after the brest-work is finished on both sides; they are to be two foot 
* Of the breadth and height of the five footsteps, and of the brest-works.  broad, and eighteen inches high. The slope 
* the slope of brest-work walls.  of the inside wall is to be but a foot in six foot, because the footsteps serve instead of buttresses to that inward side; but the step of the outside wall is to be a foot in three; and a water table is to be left, of eight inches broad (if the earth be good) between the brim of the ditch; and the turf of the outside wall, if the ground be sandy, or a tunning clay, it is to be eighteen inches broad; notwithstanding the chat of ignorant men. The bottom or foundation of the brest-work is to be thirty five foot in the bottom, with the five footsteps; and twenty foot broad at top, that it may be of Cannon proof; and it is to have a slope towards the ditch of three foot: and for that purpose, 
Of the water table of the brest-works. Of the slope of the top of the breast works, and of their thickness.  the outside wall is but nine foot, and the inward twelve foot; that the slope may be from twelve to nine. And observe once for all, that all the Angles of this method where you erect Platforms, are to have another brest-work fix foot higher than the rest, in which you make your Portholes; and that this brest-work is to have a 
* Of the freeze of the Platform.  frise when it is twelve foot from the ground, made of wooden pikes sharp at one and of six foot long, and four inches broad, and three inches thick, that are to be placed eight inches distant one from another; jetting three foot over the ditch, and running a yard into the brast-works.   
These high brest-works are at every four course of turf to be laid with brush, or bavin would well rammed with the earth; if the crectors intent they should be of continuance.  
Having so clearly expressed the dimensions of this method of Fortification, I shall not need hereafter to speak any thing at all of them, because I have observed in these five Superficies following, these proportions related in their Sides, Courtines, Flanks, Breasts, Faces, Gorges, and Lines of defence; and so I come to the method itself.   

CHAP. XXVI. Of the Fortifications of the Octogon, fortified by small Flankers; demonstrated in Plate 19  
THe eight sides of this Octogon, contains two hundred and fifty yards apiece; and by consequence, the circumference of it is of two thousand yards, that is an English mile; and the ⅕. part of a mile. The Angle of her Centre is of 45 degrees, it is to be set out in the field as the Sexagon, by the Demi-cirle and Lines; as it is described in Plate twelve, and Chapter 15. I will therefore only give you some directions how to set out the small flankers, because it is a new method of Fortification, that we have not as yet given you any directions for.  
When the Superficie of this Octogon hath been set out and fully traced, after the manner you were directed to set out the Sexagon; you are to divide all the sides of it in two equal parts, and to knock in a stake 
* From these middle stakes is the line of defence drawn, that is in this figure of 150. yards; and the Courtine 200 yards.  in every one of their divisions; than you are to fasten a line of twenty five yards to every one of the eight Angle stakes one after another, and to strain that line first on the right hand, and then at the left hand, upon a straight line; upon the sides traced on the left and right hand of that stake, and at the end of the line you are to knock a stake, and these two stakes will represent the two Demi-Gorges 
* The whole Gorge of the flankers is to be 50 yards.  of that flanker; then remove your line to another Angle stake, and do as you did before, till you have set out all the demi-gorges after that manner. Then set by that line, and fasten another line of fifty 
* The Line of fifty yards represent the distance from the centre to the point of the flanker.  yards to every anglestake of the sides, and strain the same into the field upon a straight diagonal line, standing at the center-stake with your demi-circle to guide the same, (because the demi-diagonall line from the center-stake to the utmost point of the flank is of 380 yards in this Figure, and therefore too long to be strained conveniently) and at the end of this line of fifty yards drive in a stake, and this stake will represent the utmost angle or point of the said flanker; and as you have done this, set out the other seven angles of the flankers after this very manner; than you are to fasten a Line of 28 
* 28 yards is the extent of the slope flank.  yards to every one of the sixteen stakes one after another, that represent the Demi-Gorges of the Flankers, and to strain it three yards more slope than upon a straight perpendiculary Line, towards the other Flanker of that side of the Octogon, and at the end of th' Line you are to drive in a stake. The reason why you strain this Line three yards more slope then straight, is to preserve the Flanks from the Enemy's battery, that are otherwise too much exposed to be ruinated by it: when the Line of the Flank is drawn upon a straight perpendiculary Line, you are also to observe that the straight perpendiculary Line of the Flank is but five and twenty yards, and that these three yards are added to it, that the Flanks may be three yards more slope then straight, because a slope line in five and twenty yard's extent, comes to be three yards longer than a strait. And as you have set out this Flank, set out the other sixteen after this manner, and drive in stakes in them all; that being done, you are to fasten a Line of 150 yards to the middle stake of every side, and strain it first on the right hand, and then on the left, and as you strain it, make it touch the Flank-stake, and fasten it to the stakes that represent the utmost point of your Flankers, and this Line doth represent the Line of defence, and the 
* The face of the flanker is to be 25 yards, besides the three yards added to thicken the Angle of the shoulder.  face of that Flanker; and before you remove the Line, have the face traced by the Pioniers, and this face extends itself from the Flank-stake to the stake that represents the utmost angle of the Flanker. And as you have set out this face-stake, set out all the fifteen other; and they being set out and traced, your eight Flankers will be perfected. Then you are to set out all your dikes after the dimensions described in Chap. 25. And these directions for the setting out of the Flankers of all the other ensuing Superficies, shall suffice once for all, to avoid repetitions. This Octogon thus set out, and the proportions of her Flankers thus observed, it will produce a strong, and a very regularie Fortification, fit to fortify a fair Market-town, of a mile and a quarter circumference, that may be reduced to this form.   

CHAP. XXVII. Of the Fortifications of the Paralograme fortified by small Flankers demonstrated in Plate 20.  
THis Paralograme fortified by 18. Flankers hath his broad sides of 1500. yards, and his end sides of 750. yards, for a long Paralograme is to be as long again as broad, and a Demi-Paralograme one third part longer than it is broad; his Circumference is of 4500, yards, that is of two English miles, and one third part of a mile, a large Circumference for so small a Continent, for it contains from out to out but 1125000. square yards, whereas if there had been 750. yards added to his breadth to reduce it to a Square, it had contained 2250000. square yards, that is just as much again; so much availeth in the Art of Fortification, to make choice of compact Towns for a Garrison, when a place of three miles, and two fifth parts of a mile Circumference can be fortified for one quarter part more of charges, than a Town that is smaller by half, and all because of her ill form; yet because there are many Towns in this Kingdom, of this form, I have inserted two different kind of Fortifieations for them in this Abstract; for his Angles if you take the Angle of the Centre, of the end side, from the Centre of one of the two Cirdes of which it is composed, you shall find it of 90 degrees, but if you take it from the Centre of the Paralograme itself, you will find it is but of 45. degrees, and the Angle of his broad sides is of 135. degrees, a very open and obtus Angle. This Superficie is easy to be set out upon paper, as you may see by this Figure; but because it is more difficult to set out in the field, when the broad sides of it are of so large an extent, I will here add some observations to my former direction given in Plate 14.  
The best and the most speedy way to set out so large a Paralograme in the field, is to make choice of your Centre, and to drive in a stake, and to fasten a line to it, of 375. 
* This line of 375 yards is the fourth part of the diametrical line of the long side of the Paralograme.  yards, and to strain it full East, and at the end of it to drive in a stake, than you are to wind that line about and to strain it full West upon a straight line, and at the end of the line drive in a stake, & these two last stakes will represent the two Centres of the two circles, from which this Paralagrame is composed. Then you are to set the sight of your demi-circle upon the ray of 90. degrees, and to stand at the East circle stake, turning your face full East winding your demi-circle on the right hand to set out the Southeast Angle, the man that carrieth your lines following the ray of your demi-circle till he be five hundred and thirty 
* The ray of this line of 530 yards is the diagonal line from the centre of that circle to the angle of the Paralograme.  yards and just against you, and upon the ray, than your man that carrieth the stakes is to drive in a stake at his feet, and with a line of 100 yards, that they are to strain between them, let them cast with it, if there be just 530. yards from that stake to the Centre stake you stand at, if there be just so much, then is that Angle perfectly set out, but if the distance begreater or less, they are to remove the stake, and amend it, you guiding them by the sight of your demi-circle, than you are to wind your demi-circle on the left hand, to set out as you did this the North-East Angle; and that being set out and a stake driven in, you are to remove yourself from that East circle Centre stake, to go to the West circle stake, and to set out with your demi-circle, the South-West and North-West Angles, after the very same manner as you did the former, and two stakes being driven in them, the four Angles of the Paralograme will be perfected. Then you are to stand with your demi-circle at the middle Centre stake of the whole Paralograme, and after you have set the sight of it upon the ray of 135. degrees, you are to turn yourself full South and to try whether your Southeast and North-East Angle stakes are just of 135. degrees, which being so, that broad side is perfected, then return yourself full North, and try whether the North-East and the North-West Angle stakes are just upon 135. degrees, which if they be, then is the Paralograme perfect in all his four Angles, than you are to stand at every Angle stake, one after another, and to fasten a line to them, of 250. 
* This Line of 250 yards is the distance that is to be between the centre of one flanker to the other centre.  yards, and the man with the lines is to strain the same from one Angle stake to another, drive in at every end of the line a stake, till he hath gone round, guiding his stakes with the sight of your demi-circle, that all the stakes may be upon a perfect straight line, than you are to fasten lines as near the ground as may be to these stakes and to set many Pioniers to trace out the whole Superficie of this Paralograme, and that being done you are to set out all the 18 Flankers one after another, as you were directed in the last Chapter.   

CHAP. XXVIII. Of the Fortifications of the Square fortified by small Flankers demonstrated by a Demi-Square in Plate 21.  
THis Square fortified by twenty four small Flanks if of 6000 yard's circumference, that is three English miles and two fifth parts of a mile. It is very convenient to fortify a great Corporation Town that may be redeced to that form, his continent is great, because of the solidity of his body, for it contains 2250000 square yards. The Angle of his Centre is of 90 degrees, and it is to be set out in the field after the very same manner of the end-sides of the Paralograme, described in the last Chapter, and his Flankers are to be set out according to the directions given in Chapt. 26. and therefore to avoid repetitions, I will omit to speak of these things, and will only set forth what number of Ordnance, Foot-soldiers, and Horsemen, will be required to defend a place thus fortified against an Army of twenty thousand men, the circumference of it being so great as it is.  

1 It requires to be provided with forty eight Pieces of Ordnance of all sorts; for there cannot be less than two upon every Flanker, six Demi-Cannons to dismount the Assailants Cannons, if they erect their batteries, twelve Demi-Culverins to hinder their approaches, and twenty four Sacres and six Drakes to clear the Courtines, with Balls and Ammunition sufficient for these, to shoot six thousand shot.  
2 Every Flanker with his Courtine requires to have for their defence fifty men besides the Cannoneers and Matrosses, viz. twenty Musketeers at every Flank, and ten more along the Courtine; for the Flanks are the main defence; for the Flank being of 28 yards, every one of them will have a yards space to manage his Arms, and the Cannoneers eight yards at every side to manage their Ordnance; and after this rate, 1200 Foot with the Inhabitant Trained Bands is sufficient, and a Regiment of three or four hundred Horse, to make sallies, and to bring in contributions and provisions. And I dare maintain, that a place of this extent fortified with mounts and winding Angles, will require as many more men to defend the same, as well as the lesser number before cited can defend it, if it be thus fortified.  
3 It is to be provided with great store of Fireworks, with two hundred Ladders of all sizes, with two hundred wheelbarrows, and two hundred hand-barrows, with two hundred new spades, two hundred shovels, and two hundred pick-axes, all new, besides those of the Inhabitants; and with ropes, flax, poles, and great store of timber, with many wooll-sacks; for all these things serve to repair and to stop breaches suddenly.  
4 It must be carefully provided with Corn, Meal, Malt, Oatmeal, Pease, Oats, and store of Hay and Straw, to fodder and relieve the Horse, with great store of Powder Beef, Pork, Bacon, White Pease, Rise, Butter and Cheese, and of all these such a competent proportion, according to the number of the Inhabitants, and Soldiers there in the Garrison, to serve them three months, for otherwise it availeth little to fortify Towns.    

CHAP. XXIX. Of the Fortifications of the 24 Angle Poligon, fortified by small Flankers, demonstrated in Plate 22 by a Demi-Poligon of twelve Angles.  
BEcause the scale of this demi-Polligon is smaller than that of the last square, some will suppose his sides the Circumference, and Contment of it, to be less than those of the last Figure, but it is not so, for their sides and circumference are equal, and the Continent of this last is so much greater, as the circulary form doth contain more than the square, which I could easily calculate if it did any wise concern to be informed of it, but it concerns not, because this large Superficie is fitter to fortify a great Corporation already built then for a new-erected City, and therefore I do omit the calculation of it.  
To acquaint you, that the demi-diametricall and diagonal lines of this superficie are of a thousand yards, and the whole as much more, that is an English mile, and the one tenth part of a mile, and therefore very difficult to set, by any other way then by the demi-circle; the Angle of his Centre is of 15. degrees, and it is composed of 24 Isocele Triangles that have three sides four times as long as their Bases, the Base containing 250. yards, and their sides 1000 yards: the best and the most speedy way then to set the same out in the field, is to drive in a stake in the Centre of it, and to set out first of all these four Angles, viz. the South, North, East, and West Angles, for those being perfectly set out, all the rest will be the easier to be set out, by dividing every quarter into five equal parts: Now how you are to set out these four Angles, it would be superfluous to relate, because I have formerly given so many directions for it, and therefore I will refer you to the precedent Instructions set down in Plate 12. and 19 I will then acquaint you, that if this Corporation or City that you are to fortify after this manner hath no streets nor gates, that are seated, or run straight South, North, East and West, that you are in stead of a stake to set up a very high pole, in the Centre of the Town, in manner of a maypole, having a small slag or a bush at the top, except there be near the Centre of the Town a high steeple, that you may stake by it your Angles from without the town, and having set out and traced the superficie of it, you are then to set out and trace one quarter of the Flankers, one after another, to avoid confusion or mistake, and then you are to set out all the dikes after that manner described in Chapter 17. and of the very same breadth and depth, and having done so, and your work being fully finished, you are to provide this Garrison with the like number of Ordnance, Footmen and Horsemen, Ammunition, Victuals, and all other necessaries for a siege mentioned in the last Chapter, and so it will be able having a valiant and experienced Governor to oppose (by God's favour) an Army of twenty thousand men for three months.   

CHAP. XXX. Of the Fortifications of the mixed Superficie, fortified by small Flankers, and three Redouts, demonstrated in Plate 23.  
THis Superficie hath six of her Angles regulary, and the other irregulary; the regulary are of 75. degrees, the irregulary sides whose point terminates itself in the midst of the Paralograme Redoubt, are reduced to the form of a recteligne Triangle whose base is of greater extent than her sides, the three Redoubts are so placed, to blind the deformity that doth always ensue upon the conjunction of regulary and irregulary lines, and for divers other considerations, the whole circumference of it is of three English miles, and a half, and will require 1600. foot, and 300. horse, and 54. pieces of Ordnance, with all other necessaries for a siege, mentioned in Chapter 28. for to enable the same to oppose an Army of twenty thousand men for three months.  
It is to be set out not from the Centre, but with the demi-circle, standing one hundred yards in the field beyond the walls, to take in all the Allows that are near to the walls: The steeple serving naturally as for the Centre; having then set your demi-circle upon the ray of 75. degrees, you are to set out the six regularie Angles after the very same manner, as you have been directed to set out the Sexagon and the Octogon, in Plate 12, and 19 and in the midst of the Southeast and South-West sides you are to set out the two square Redoubts, that will require for their defence two pieces of Ordnance, and 100 men a piece; and from the South Angles of those two sides, you are to draw two diagonal lines, that may terminate in the Centre stake of the Paralograme Redoubt, turning the rod after a winding manner, as it is set out by the prick lines, this Redoubt will require two pieces of Ordnance, and two hundred men for her defence, and every flanker fifty men, for the defence of it and his courtine, these flankers are to be set out, after you have divided the eight sides into three equal parts, according to the directions given in Chapter 26. and where the Platforms are erected in the Angles of the Redoubts, you are to erect your Brest-work six foot higher than the other Brest-works, that have five footsteps, because the Platform is to be level with the inside Brest-worke, that is to be twelve foot high, whereby the Brest-workes of the Platforms will be eighteen foct high from the ground, observing in all Angles where you erect a platform, to place upon the last row of turf that reducett your Brest-works to be 12 foot high, a 
* How the Freeze of a platform is to be placed, and of the distance between the pikes.  freeze of sharp square wooden pikes of six foot long, and of four inches one way, and of three inches the other way, jetting out a yard over the dike, and running a yard into the Brest-works, and these pikes are to be but eight inches distant one from another; now if this Garrison were thus fortified, and provided, it would be one of the strongest and one of the most complete Garrisons in this Kingdom.  
PLANS & SUPERFICIES  
plate: 1:   diagrams 
PLANS & SUPERFICIES  
Equilateral  
Isosele  
Recteligne  
Scalene  
Oxig●ne  
Obtus  
scale 10 yards for everi ⅛ part of an inch  
plate: 2:   diagrams 
PLANS & SUPERFPCIES  
plate 3   diagram 
V: REDOUTES (The scale js for everi ⅛ part of an jnch: 10: yards  
plate: 4:   diagrams of redoubts 
The scale of this Equilatirall Triangle is for every ⅛ part of an jnch 15 yard's  
plate: 5:   diagram 
A TRIANGLE  
The scale is for every ⅛ part of an jnch 15 yard's  
plate: 9:   diagram 
The scale of this Squaire is an ⅛ part of an jnch for 15 yard's  
plate: 6:   diagram 
A SQVAIRE  
The scale js 〈◊〉 ⅛ part of an jnch for 15 yard's  
plate: 10:   diagram 
A PENTAGON  
The scale js for everi ⅛ part of an jnch: 20: yards  
plate: 7:   diagram 
A PENTAGON  
The scale js for every ⅛ part of an jnch 20 yard's  
plate: 11:   diagram 
AN OVAL  
Fortified with Bastions the scale js for ⅛ part of an jnch 20 yard's  
plate: 8:   diagram 
A SEXAGON  
The scale is for every ⅛ part of an jnch 20 yard's  
plate: 12:   diagram 
A Fort in the form of a Cross fortified with 8 half moons, the scale 30 yards for ⅛ parts of an jnch  
plate: 13:   diagram of a fort 
A LONG SQVAIRE fortified with avant guards, the scale is for everi ⅛ part of an jnch: 30: yards  
plate 14   diagram of a fort 
A TRIANGLE Fortified by Avaunt guards the scale js 20 yards for everi ⅛ part of an jnch  
plate. 15.   diagram of a fort 
A SQVAIRE fortified with avaunt guards and out guards  
The scale is for everi ⅛ part of an jnch 2● yards  
plate. 16.   diagram of a fort 
A PENTAGON fortified with avant guards and out guards  
The scale is for everi ⅛ part of an jnch: 20: yards  
plate 17.   diagram of a fort 
A ½ SEXAGON fortified with avaunt guards and out guards The scale is 40 yards for every ⅛ part of an jnch  
plate. 18.   diagram of a fort 
AN OXOGON Fortified with small Flankers  
The scale is for every ⅛ part of an jnch 20. yard's  
plate. 19   diagram of a fort 
A PARALLOGRAME fortified with: 18: small flankers; the scale js for everi: 8: part of an jnch. 46. yards and ⅓  
plate. 20.   diagram of a fort 
A DEMY SQVAIRE fortified with 24: small flankers, the scale js for everi ⅛ part of an jnch. 25. yard's  
plate. 21.   diagram of a fort 
A DEMY FIGURE OF: 24: ANGLES fortified with. 24. small flankers; the scale 40 yards for everi. ⅛. part of an jnch  
plate. 22.   diagram of a fort 
NORTHAMPTON RIGHTLY Fortified Tae scale is for every ⅛ part of an jnch: 50. yards   diagram of a fort 
A GARRISON BESIEGED By an Entrenched Army the scale is for every ⅛ part of an jnch 100 yards   diagram of a garrison 
A GARRISON UNDERMINED AND Battered with Tenn Cannons the scale of the Sexagon is for every ⅛ part of an jnch 15 yards  
The scale of the Mine Work is for every 8 part of an inch one 〈◊〉   diagram of a garrison  

OF THE ART OF ASSAILING IN GENERAL.  
AS there is diversity of 
* 1 Cor. 12.4.  gifts in the spiritual Function, among those that God hath set apart from their mother's womb, to be the Messengers of the blessed tidings of the Gospel of Christ: Even so God out of his admirable wisdom, doth also bestow different gifts to men of one and the same profession: But this wise dispensation of his gifts is more apparently seen in the variety of parts that he is pleased to bestow upon the most eminent Commanders, that have anciently, and do at this day exercise themselves in the Art of war: For among all the ancient and modern Commanders, there was never any but Caesar, that did attain to the perfection of this Art; all the other having only received different gifts, to excel others in some of the most essential parts of it, but not in all. For some have excelled in the field, some in stratagems of war, some in the Art of assailing, and reducing of Towns, and some in the Art of preserving of them: And some have been very successful in the field, and yet very unhappy in sieges. 
* See Plutarch in his life.  Nicias Generalissimo of the Athenians, lost his life and the reputation he had obtained in Arms, by the besieging of Syracuse. And the Emperor Charles the fifth was always victorious in 
* See sleidan's Histories.  field, and always foiled in his sieges; for he lost the former reputation that he had obtained by Arms, and threescore thousand men, by the sieges of Marseilles and Mests. We read that Alexander 
* See Plutarch in their lives.  the Great, Scipio, and Sylla, were prosperous in the field; Aratus, 
* See Tacitus.  Hannibal, and Sertorius, successful in stratagems of war; 
* See josephus  Marcellus, Carbulo, and 
* See the French History.  Titus, happy in their singes, and excelling in the Art of assailing, and of reducing of strong holds. And among our modern Commanders, Heary the fourth King of France, and the last King of Sweden, were always victorious in the field; Scanderbag, 
* See the Sweden Soldier.  Mont Luc, and Mondragon, prosperous in their stratagems; the Duke 
* See his Commentary.  de Parma, the 
* See the Turkish History.  marquis Spinola, the two Princes of Orange, Maurice and Henry, and the Marshal Gastion, wonderfully successful in their sieges. And in the Art of defending of Towns, Monsieur de la Valette, great Master of Malta, the Duke of Guise, 
* See Demetrius' History of the Netherlands.  Sir Francis Vere, and of late Colonel Massey. But, as I have said before, there never was any perfect and successful in all the essential parts of the Art of war, but Caesar; for he hath excelled all others in the field, 
* See the French History.  in the Art of fortification, defending, and assailing, in his stratagems of war, in his admittable activity, in his prudent forecast, in his entrenched 
* See the siege of Malta.  Camps, in his military discipline, and in taking the opportunities of war by the forelock, to advance his designs. 
* See the French History.  And therefore the Duke de Rouen, in his Perfect Captain, doth affirm, that all the most famous exploits of all these forenamed modern Commanders, 
* See the siege of Ostend.  were but weak imitations of the noble and unparallelled actions that he did execute and perform at the siege of Alexie in France, 
* See his Commentary.  as the masterpiece of this admirable Soldier.  
Now if any should presume to inquire the reasons why God was pleased to be larger in dispensation of his gifts to Caesar, then to any of the greatest Christian Commanders, he being but a Heathen.  
I answer; That it was his free will and pleasure, and that it is not for us to dive into his private and unrevealed will; yet we may suppose in all humility, that it was his pleasure to enrich Caesar with these unparallelled parts of the Art of war, to make him the instrument of the greatest revolution that ever happened in the world; for the three former revolutions of the three Monarchies of the Chaldeans, Persians, and the Greeks, were nothing in comparison of this last revolution, that Caesar was the main instrument of, to reduce the greatest and most powerful Commonweal that ever was, under the absolute command of one man: And by this means to accomplish the Prophecies of the Prophet Daniel, that prophesied many hundred years before, 
See Daniel chap. 7. ver. 17  that the Roman Monarchy should excel the other in might and power. We may conjecture that he was pleased to have the instrument of so great a work to excel all others in the Art of war, as this last revolution did excel the former. And we may also collect by the Commentaries of Caesar, that the finger of the admirable Providence of God had the ruling of all his actions; for it is beyond humane reason or belief, that fifty thousand men should pen up fourscore thousand in Alexie, and rout and defeat one hundred and fourscore thousand more that came to their relief: Or overcome with a handful of men (as he did) the great Kingdom of Egypt, and defeat so many great Commanders joined together in Africa and Spain.  
To conclude the point, God under Caesar was the Author of all the segreat actions, and so he is of all our modern Commanders exploits, yet wisdom, valour, activity, and experience in Arms, are the secondary causes of their great achievements; and these rare qualities are as much required to be in a Commander in chief, that will excel others in this Art of Assailing, that we are to speak of, as in any other essential part of the Art of war.  
Now since the erecting of strong and well-lined works are but a part of the Art of defence, that will avail little, except the Governor of a Garrison thus fortified be provident, valiant, and experienced in the practical Art of war, to make the better use of these works; I will in the next Chapter set out the charge of a prudent Governor, before I come to the particulars of the Art of Assailing: Because this Art, and the Art of Defence, are like two inseparable twins, that are to go hand in hand together; for it is impossible to assail judiciously, except the Assailant be experienced in the Art of Defence; or for a Defendant to defend a place as he ought, except he be versed in the mysteries of the Art of Assailing, to prevent in either of them, what may be done by the Assailants or Defendants.   

CHAP. XXXII. Of the charge and qualities of a prudent and experienced Governor.  
1 HE is to be well-affected to the party he stands for, his own interest rather inducing him to it, than otherwise, and faithful and diligent in his place, for upon his fidelity, valour, and experience in Arms, 
Of the parts of a Governor.  depends the safety of a County; nay, sometimes the welfare of a Kingdom, for the loss of a well-seated Garrison endangers a State, more than the loss of an Army, and therefore it behoveth a Prince or a State to be very circumspect in the choice of a Governor, if the place assigned to him, be a frontier Garrison, 
Of the choice of a Governor.  it matters not if he be of great descent, and allied with great families, for when they are such, upon the least discontent, they are apt to foment civil discords; neither is he to be of a low descent, but a Gentleman by birth, and by merit, whose valour and fidelity makes him to deserve such a place: he is to be of competent means, borne in the same County, and allied to men of repute, and abilities, and trained from his youth in Arms, and such a man is reputed amongst Statesmen the fittest for such a place.  
2 He is to be of an approved conversation, 
Of his manners and disposition.  honourably inclined, no swaggerer, nor a vaunting rover, but temperate in all his actions, not over young to be seduced or miss, nor over old to avoid heaviness, fear, and apprehensions, infirmities, incident to old men, but in the flower of his age from forty to threescore, that he may be active, provident, and vigilant, and well acquainted with all things that appertain to his charge.  
3 He is to be well versed in Histories, and to be adorned besides his natural parts, with divers acquired virtues and qualities, but above all, he is to have a practical knowledge, of all the essential parts of the Art of War, that he may know how to assail and to defend places, how to Martial his men both horse, and foot, how to advance and how to retreat, for if he hath not been present in great battles, in famous sieges, in routs, in great batteries, in storms, and assaults, he will be terrified or astonished, upon any unexpected accident.  
4 He is to be free from avarice, oppression, drunkenness, licentiousness, and from all impiety, 
He is to be free from vices and adorned with virtue.  and adorned with the opposite virtues to these vices, sincere in Religion, and rather fervent then of the Laodicean temper; temperate and moderate, frugal and yet charitable, punctual in his promises, cherishing valour, and punishing cowardice, a loving father to his soldiers, relieving them in their need, rather than to detain or deprive them of their pay, by wiles or collusions.  
5 He is to be acquainted with the ancient and the modern Military Laws, and with the Civil and Politic Statutes, 
He is to be learned, and versed in the Military and Politic Laws.  and Ordinances, to decide all controversies, that may happen between the soldiers of his Garrisons, and the Countrypeople, or the Inhabitants of it, he is also to love as his own life, the place where he hath been assigned, and to procure the good and the welfare of the Inhabitants, and of all honest and religious people that sojourn there; and to have especial care of the preservation of it, having always in mind, that his life, honour and reputation, depends upon the safety of it.  
6 He is to provide his Garrison of all necessaries for a siege, 
He is to be provident in the repair of the works of his garrison.  and to repair the Works of it in due and in convenient time, not delaying from day to day, but pressing the effecting of it, to the utmost of his power; although there be no likelihood of a siege, for when an enemy is at hand, it is too late to go about such employments, neither is it a sufficient excuse for a Governor to say who would have thought the enemy had a design upon this place?  
7 He is to be acquainted with all the principles of the Mathematics, and especially with the essential parts of the Art of Fortification, that he may be able to control the ignorance of self-conceited men, that take upon them to set out ridiculous and destructive works, 
He is to be skilful in the Art of fortification and assailing.  improper for the defence of the place where they live, with whom he is by no means to combine, as some do for private or politic respects, because such deformed and ill flanked Works indenger his own life, and will one time or other blemish his honour, and reputation; and therefore he is to be skilful in the Art of Fortification and assailing. For if the town be lost by these defects, the blame will only be laid upon him, and not upon the contrivers of these works: now because the safety of the Town is entrusted to his care, he ought not to endure that ignorant Shopkeepers be chosen Sub-Committees of the Works of a Garrison, for these places belong more properly to the wise, and prudent Gentlemen of the County, and to the most experienced Officers of the Garrison, then to such men as these that will precipitate their own ruin, rather than they will be crossed in their destructive ways.  
8 He is to dispose of all the Functions of War, 
He is to dispose of all the functions of war, and not to meddle with politic affairs.  and to command absolutely over Horse and Foot, or otherwise, he is but a titulary Governor, and it is no wonder if divers of our Counties are plundered daily, by the incursions of the Enemy's Garrisons, since he that should send out parties to curb and restrain these disorders, hath his hands tied. In all things, without order, nothing can be successful: for a Governor to anticipate upon the prerogative of Committees, and be meddling in civil and politic affairs, it is to go against order; or for Committees to anticipate and be meddling with those things that belong properly to a Governors' place, as to command over a Colonel of Horse, 
Committees are not to meddle in warlike affairs, only in civil and politic affairs.  and to send out parties at random; it is against order, and against the rules of war; for Committees should not be answerable for the defects, errors, and omissions of martial designs; nor the Governor be answerable for any dismeanour committed, or duty omitted, in civil or politic affairs; but every one should be answerable for such things that belong to their places. Therefore if a County be daily molested by the incursions of the Enemy's Garrisons, the Governor should be answerable to the State for his neglect and carelessness in this case, because the protection and preservation of the whole County depends upon his charge. On the other side, if the men of war of such a County be not duly paid, and notwithstanding the County is oppressed, the Committees are answerable to the State for this omission and dismeniour. But by the common disorder there is in the greater part of our Counties, between the Committees and the Governors of the head Garrisons, by the anticipation they do upon one another's charges, the State knows not whom to call to account for divers gross abuses that are daily committed, under which divers Counties groan, and become desolate. In a word, there is no wisdom nor policy to suffer the Committee to manage, or to dispose of the designs of war; or to suffer the Governors to raise contributions for their own Garrisons pay, or to meddle in any manner of way in civil or politic affairs, except it be to decide some differences that may befall between some Soldiers, and some of the Inhabitants.  
9 He is to observe an austere military discipline, and to suffer none of the Inhabitants to be wronged and abused by any of the Soldiers of the Garrison; for if he give them an inch this way, they will take a foot; and of the two, he is rather to take the part of the Inhabitants then of the Soldiers, because the Soldiers are most commonly the first Aggressours: 
He is to be austere in the Military Discipline, and just in his judgement.  Yet for fear this rule should not be general, he is to examine the case, and to distribute justice impartially. He is also to train his Soldiers every week, and withal to command the Sergeant of every Company to instruct them daily, when their Company enters in guard, and especially the youngest and rawest Soldiers, how they should manage their muskets and pikes, that they may be the more perfect when they train before him, in the handling of their Arms. And for the Horse, when they are at home, once a fortnight he is to appoint their Colonel a place in the field near the walls, where he is to be himself, to see them exercise, by dividing their Regiment in two equal parts; 
He is to be careful and present at all military exercises.  the Colonel commanding one party, and the Lieutenant-colonell the other; the one being the Assailants, and the other the Defendants. And in all these exercises the Governor is to take exact notice both of the Horse and Foot, that are defective in their horses, arms, and apparel, and to censure them severely for the first time, and to panish them the next training day if these defects be not amended.  
10 He is to be active and vigilant, that Sentinels be placed and relieved punctually at their hours, and to oversee the Courts of Guards every night, not relying altogether upon his Major, for two eye-witnesses are better than one; the French, whose Garrisons are not ordinarily above one English mile, and half circumference, 
Of the number of the Courts of Guard.  content themselves with six Courts of Guards, the greatest in the Marketplace of 120. men, four more at the four gates of 60. men a piece, and one before the Governors' lodging of twenty men. and by this calculation there is to be in that Garrison 1140. Foot-soldiers, of which 380. are so enter into guard every night, that they might have two day's respite in three. Their Sentinels or Sentries are relieved in the night time every hour, and in the day time every two hours, and they place at every 200. yard's distance a Sentry, 
Of the number of Sentinels.  if their Garrisons be fortified by Bastions, they place besides the abovesaid Sentries, three upon every Bastion, one at the point of it, and two at the two ends of the faces, next to the flanks, so that this place of so small a Circumference is to have forty Sentries relieved every hour in the night times, besides them that are to make the Rounds, that are to be done three times every night, besides a private Round called by the French La Patronille, every Round is to have a principal 
* The Governor is sometimes to go the Rounds, but the day & hour of his going is to be kept private. Of the Rounds, and of the French Patronille.  Officer, their number is commonly of 12. and this private Round of as many, it marcheth commonly in the dead time of the night, that is an hour before day, the most dangerous time for surprises. By this calculation the Reader may see that the greater part of our Garrisons are not half manned as they should be; for I know some of three English miles and half circumference, that have not a thousand Foot-soldiers, and a place of this extent should have at least ten or twelve Courts of Guards, whether it hath so many gates or no; for where the distance between two gates are over great, there is a Court of Guard to be erected in the midst, to prevent a surprise by scaling.  
11 He is to have care to see his Garrison provided with Ordnance, Arms, Balls, Ammunition, Fireworks, some ready made, and store of materials ready to make more, 
Of the Ordnance and Ammunition of a Garrison.  and with all manner of Engines of war, as Manttlelets and Ladders, Tortoises, Pioniers tools, store of timber, of wooll-pacles, pitch, oil, Brimstone, coal for powder, pit-coale, and wood for sewell; and hay, straw, oats, and pease for the Horse.  
If I should here relate the number and quantity of these necessaries, that the Italians, French, and Hollanders use to provide their Garrisons withal, it would seem to many a false, or an incredible relation; and therefore I will pass them over, and will only speak of a very mean proportion, fitted according to our ability, after I have given you a hint of the store of the Citadel of Milan. The Citadel of Milan is a perfect Sexagon, fortified by six Bastions with orillon's, as in Plate 12. The Circumference of it cannot be at the most above an English mile and a quarter, and yet it had in my time 160 Cannons and Demi-Cannons in the Magazines, besides those that were placed in the paints, faces, and Flanks of the Bastions, that were above 90 in number, and in all 250 at the least, and fifty thousand iron bullets of all sorts, and two hundred thousand weight of powder, and victualied for a year for three thousand men, and with Arms and other necessaries proportionable, and such provisions will seem (as I have said) incredible.  
But the meanest proportion allowed for foreign Garrisons is of fifty Pieces of Ordnance, for a Town of two English miles circumference, of these sorts, six Cannons, six Demi-Cannons, six long 
* If it be a Sea-towne you are to double the number of the long Culverins, and to de●●lk the same from the Sacres.  Culverins, twenty Sacres, and twelve Drakes, and one hundred thousand weight of powder, that is a thousand barrels of powder. But it were well if one of our Garrisons of three or four mile's circumference were thus provided: for Arms there are to be of all sorts as many in the Magizines, as there is Soldiers in the Garrison; and for balls, the least number that can be provided, is for Cannon-balls, Demi-Cannons, and long Culverins, six hundred a piece, that is 1800 of these three sorts, and 2000 balls for the Secres, and 1200 for the Drakes, and fifty new Carriages of all sorts in the Magazine, that if any Piece of Ordnance be dismouned, it may presently be let up again; and twenty lie thousand weight of match, five hundred Granado's, and 100 great oves for Masterpieces, and as many materials to make twice as many more, and of all other necessaries spoken of before proportionably.  
12 He is to have a provident forecast to provide in due season his Garrison with all manner of victuals, and malt, for otherwise the strong Works of the Garrison, the number nor the valour of the Soldiers, nor this store of Cannons, Ammunition, and Arms, Granades, and other necessaries will avail nothing, if the Garrison be distressed for want of victuals, for all these things will but enrich the Enemy, when by famine the Town shall be enforced to yield to the Enemy's mercy.  
The two most necessary provisions, 
He is to provide his Garrison with all manner of provisions and victuals.  are bread and beer, and therefore the Governor is to take an exact account of the number of men, women and children, there is in his Garrison, I mean with the Foot and Horsemen of the Garrison, that I will suppose to be ten thousand living souls. The least allowance of bread and beer that can be given, is of a pound of bread and a pottle of beer a day, now every strike, or bushel of Corn, will yield, 56. pound weight of bread, and this will amount to 188 strike a day, and in three months to 16920. strike of wheat, that is 2115. quarters of wheat. And as for beer, every barrel of beer contains 36. gallons, and every quarter of malt will make eight barrels of small beer, that contains 576 pottles of beer; so that after this rate there will be spent 17. quarters and half of malt in a day, but we will allow 18 quarters for the soldier's mornings-draught, that will amount in three months to 1620. quarters of malt.  
The salt is the next, for without salt a Garrison cannot subsist, and therefore one hundred quarters of salt is the least that can be provided for three months. Butter and Cheese are the next, and ten thousand weight of each is of the least, and a thousand barrels of Pork, and of salt Beef, is little enough, besides a thousand fliches of Bacon, five hundred quarters of white Pease, two thousand weight of Rice, twenty tun of Vinegar, for it is useful to cool the pieces of Ordnance when they are overheated; three or four tun of oil, great store of timber and fuel, and especially of brush bavins, for to repair breaches, good store of sugar, and spices, but specially all manner of Physical drugs, for sick and wounded men, and store of Chirurgeons to dress the wounded soldiers: All these things and many more, a provident Governor will have a care to provide his Garrison withal, if he intent to make a noble resistance, and to preserve his Garrrison, life, honour, and reputation. But divers will object, that the providing of these things belongeth to the Committees, and not to the Governors. I answer, that it belongeth to the Governors in foreign parts, and that he is bound by his place, after he hath twice or thrice admonished them, to provide these things, and they do it not, to protest against them, and to acquaint the State of their neglect, and omission of it, otherwise if the Town be lost by the want of any of these things, the blame will be imputed only to the improvidency of the Governor. Moreover 
* The duty of a Governor to prevent surprises and scaling.  he is to be very vigilant, to prevent surprises, by Ambushes, that may lie undiscovered in allows near to a gate, that may of a sudden slay the Centeries, force a Court of Guard, and take a town; or by scaling in the night time, for it is a thing easy to be done, to scale Works that are so low as ours. To prevent these surprises, and scaling, the Governor is to send out every night 24. horse divided into four parties of six a piece, and these parties must range all the principal roads that lead to his Garrison, for the distance of seven or eight mile every way, as South, North, East and West, and to cause at the break of day all hollows, and old walls about the town to be viewed by two soldiers of every gate, that are to be put forth at the Sally-ports, and to come in again before the gates be open, and their drawbridge put down, and by these two means the Governor will preselve his Garrison from scaling and surprises.   

CHAP. XXXIII. Of six different ways, how strong Holds may be reduced.  
Antigonus' King of Macedonia was wont to say, that the strongest Hold in the world might be reduced, if by the gate of it a Mule laden with gold might enter therein, meaning that strong Holds that were by nature or by art impregnable, might be won by the infidelity of the Governor, if he was inclined to Avarice and greedy of money, whereby we may collect that concussion and bribery was as familiar in those days as they are in ours: 
The first way attempted by the Spaniard is bribery.  And this is one of the first means that Philip the second King of spain did attempt to reduce the strongest Garrisons of his Enemies, for by these means he obtained Cambray and Calais, in the reign of Henry the fourth King of France; a good Caution for a Prince or State, to make choice of trusty and faith full Governors, that may be free of Avarice and Concussion.  
The second way is more noble and generous, and that is by Stratagems of War, 
The second waie is stratagems of war.  as the great City of 
* See the History of the civil wars of France.  Amiens was taken by Montdragon, by four and twenty soldiers, hidden under four wagons laden with hay, and a disguised soldier that was upon the last load, that tumbled down wittingly a basket of apples, and walnuts, when he saw the waggon under the Portcallice, whereupon the Sentries and all the soldiers of the Court of Guard being over eager about the taking of them up, were all slain by the 24. armed soldiers, that came out of the wagons, and the gate made good, till a thousand horsemen with as many Dragoones behind them, entered the town and took it without little or no opposition at all; or as 
* See the History of the Netherlands.  Breda was taken by a French Captain, with twenty soldiers hidden in a ship laden with turf that was let in at the Port, and in the night time sallied out, killed the Round, and put to the sword all the Soldiers of the Court of Guard that were next to the gate, where a thousand Horse and five hundred Foot of their party lay inambusc●do, and so took that strong Hold, without much loss for opposition. But the two next Stratagems are worthy of admiration; in the civil warres* of France a young Gentleman and a royalist, did oftentimes repair to a strong Garrison of the League, to fee a kinsman of his, that was a Commander of the Garrison, and having noted that the soldiers of that Court of Guard next to the gate that he was used to come in, kept but an indifferent watch, persuaded five young Gentlemen of his acquaintance, that had no more hair on their faces then he had himself, to attempt the taking of that Garrison, they embraced the motion and disguised then selves in Gentlewoman's apparel, riding behind six Gentlemen, that lived near that Garrison, every horseman having at his side a young valiant soldier, disguised like Lacquie's that made up eighteen in all, having pistols in their pockets, and coming to the gate of the Garrison, he that rid foremost carried behind him the undertaker disguised like a Gentlewoman, the Set jeant of the Court of Guard began to examine where they went: we come (saith the first horseman) to be merry in the Town, with these Gentlewomen our kinswomen, whereupon he let them pass, but being come between the two gates, where the Portcullis was, the first Gentlewoman feigned to be ready to swoon, and called to some of the Court of guard for help, they as officious men came all to assist the sick Gentlewoman, whereupon they all lighted, and the Lacquies did instantly run to the Court of guard, and brought all the Partisans and Halberds they could lay hold on, and the Gentlemen and Gentlewomen drew out their pistols, and slew every one of them a fouldier of the Court of guard, and made good the gate till their Ambuscado that was within a musket-shot of the town in a hollow came to their relief, and so took this garrison that was strong and of great concernment. The last Stratagem is known of all men, for it is the surprising of Hereford, that was as neatly carried as any of the former, for he that played the Constable's part, was certainly a valiant Gentleman, for it was a great attempt to venture upon so strong and so well manned a garrison as that was; 
The third way is by policy.  The third way was used by the Parthians to famish Crassus' 
* See Plutarch in Crassus' life.  Army in Armenia the great, and by the Duke 
* See Du Belluy his Commentaries.  de Montmorency, in the days of Francis the first King of France, to famish the Emperor Charles the fifth's Army, that was coming to besiege Marseilles; for he persuaded the King three weeks before the coming of the Emperor's Army, to publish a Proclamation that all the Inhabitants of what degree soever, that lived within twenty mile's compass of the City of Marseilles, should upon pain of death, remove all their Cattles, Wine, Corn, and Movables, and bring them to his Camp where they should have money for their corn and wine, and lodging for themselves in the adjacent towns, with pasture for their cattles, at free cost, till the war was over: and those that did not obey this Proclamation, within fifteen days, were enforced to obey the same by a party of 2000, horse that were sent by the King to see the execution of it, whereby the Emperor was reduced within a month after, to such extreme want of victuals, and of provender for his horses, that he was enforced to raise his siege with the loss of his former reputation, and of 30000. of his men that perished by famine, and by the sword upon their retreat into Italy.  
This policy may be used also to reduce the strongest Garrison that can be, if the party be master of the field, or lie in an entrenched Camp some twenty miles off, that he may day and night scour all the roads with strong parties of Horse, as the Deke de Montmorency did; for after the favour of God, it was the secondary cause of the preservation of the Kingdom of Frances for if the French King had enforced the Emperor to a pitched battle, and that he had been routed, the Emperor's Army had advinced without opposition to the very gates of Paris, because there was not in those days any strong hold between Marseilles and Paris. But by this means the French King did not hazard his Kingdom upon the casual event of a battle, and yet preserved the same, and did utterly waste and reduce to nothing, the greatest Army that ever this Emperor was Master of, and that was led by the most experienced Commanders in Christendom. 
The fourth way is by scaling in the night time.   
The fourth way is by scaling in the night time, as Geneva was likely to have been taken by the Lord D'Aulbigny, General for the Duke of Savoy in Henry the fourth's days; 
* The best way for a Governor to prevent these surprises by stratagems of War and scaling, is set out in Chap. 32.  for there were above five hundred men gotten up upon the Rampires before they were discovered; and had it not been by the favour of God, that one of the first Inhabitants that was alarmed, did run to the lower Flanks of one of their Bastions, that had two Cannons mounted, pointed and charged with case and chain-shot, and presently fired them, whereby all the Assailants scaling ladders were broken, and cast into the dike, the City had been taken; but the Soldiers and the Inhabitants being assured by this means, that no greater number than was entered could annoy them, took courage, and put the greater part of them to the sword, some Lords excepted, that they caused to be beheaded the same day.  
And this is the reason that I have pressed so much in my former discourses of the practical Art of Fortification, the necessity there is to erect upper and lower Flanks, as the only means to preserve a strong hold from scaling in the night time, and from casting of galleries over the mote or dike, to prevent a general assault; for these Flanks (under God) were the cause, not only of the preservation of Geneva, but of Casal in Italy some certain years since; for the French 
* He was the very same that was Governor of the Isle of Ree, called Monsieur de Thorax.  Governor that was entrusted by the Duke of Mantua to defend that strong hold against an Army of thirty thousand men, commanded by the Marquis Spinola, did make such use of the lower Flanks of the Bastions of that Garrison, that he broke three times one after another, the strong galleries that the said Marquis did cast over the mote, and hindered him by that means to come to a general assault, and so enforced him to raise his siege, which disgrace struck such a deep impression in the heart of the Marquis, that he died shortly after, more of grief then by the violence of his disease, holding and reputing that it was a great blemish to his former reputation, to be beaten off by so young a Governor, from a siege, when he had been reputed the most experienced Commander in Christendom, in the Art of Assailing.  
The fifth way is by the blocking up of a Garrison at a certain distance, by strong Forts, or strong houses, seated and erected by, 
* The fifth way is by the blocking up of a Garrison at a certain distance.  or near the said Garrison. This way is tedious and uncertain, because such ancient houses are rarely seated in the most convenient places, or at an equal distance for that purpose, and by these defects, the reducing of the Garrison is much retarded; for the besieged receive ordinarily some relief from the adjacent villages. It were therefore safer for a General, if he be resolved to reduce a Garrison this way, to erect four new Forts, on the South, North, East, and West of that Town, upon the most convenient seats that can be found, within no longer distance than a mile, of all sides from that Garrison; and are to be seated where they may most conveniently command and block up the roads that lead to that Garrison. The continent of these Forts are to contain four hundred Foot, and two hundred Horse, and from 
* The lodgings of these Forts are to be low and slight, so they be kept dry, for it matters not so they may last half a year.  Fort to Fort, a small Line of Communication is to be drawn, with a dike of six foot deep, and nine foot broad. And if there be a River running thorough, or by one side of that Garrison, two wooden bridges are to be erected, either with boats, or with piles, and two good Redouts erected to defend these bridges. And all this may be done in less than a month's time, by an Army that is eight thousand Foot strong, and two thousand Horse, so it be Master of the field: And this course being taken about the latter end of October, this Garrison will be in such straits for victuals and Ammunition before March, that it will be enforced to yield to the mercy of the Assailants: for it cannot be relieved, but by a greater party by half then are billetted in these four Forts and two Redouts, because they relieve and join one with another upon all occasions.  
The sixth and the most certain and method-like way, 
The sixth and the surest way is by a do able entrenched Camp.  is by an entrenched Camp used in Caesar's days, and at this time in Flanders by the French and Hollanders; because if all the five former ways having been attempted and fail, this will assuredly carry away the Garrison, either by storm or famine. But before I come to the particulars of it, I will relate the judgements of the most experienced Commanders, both ancient and modern, whether the sallies of the Defendants are profitable to them, or necessary to be done, to hinder the Assailants to incamp themselves, and to make their approaches.   

CHAP. XXXIV. Of the opinions of experienced Commanders, concerning sallies made by the Defendants at the beginning of a Siege.  
ALL our modern Commanders do not agree in this point, for some would have no 
* Whether it be best to sally, or not to sally, in the beginning of a Siege.  sallies at all, till the Assailant begin to pierce the Counterscarp with their secret approaches, because they would maintain the soldiers of the Garrison in their full number and strength, for the most urgent occasion of defence, that is, when the enemies do indervour to cast their galleries over the mote, and to make their Mines for to come to a general assault: their reasons are these. 1. All the sallies of a Garrison say they, cannot hinder an Assailant Army to perform eight of the ten operations, that shall be spoken of in the next Chapter. 2. If it be never so well manned, the Assailants are always sieve to one at least, and sometime ten for one; and therefore if the Defendants in these sallies lose one man, their loss is greater, then if the Assailants lose five; nay, more than ten, because they may be supplied and recruted: but the Defendants cannot, but by the coming of a great Army to their relief. 3. When the Defendants sally so fare from their Rampiars, as to endeavour to impede the encamping of the Assailants, or the making of their first approaches; it is ten to one say they, if they be not beaten and driven in again with loss. 
* Forces that sally out are subject to be routed, if a party of the Assailants horse goeth between them and the town.  Nay, they may be utterly routed, and their retreat into the town stopped; if a good party of horse of the Assailants, can get between their Rampiars and them: which if they do, as it hath been oftentimes effected; the strength and the courage of the Defendants is much weakened, and the town in a manner half reduced. Therefore say they, it is safer, and a part of greater wisdom for a Governor to keep in his men till the Assailants are near the Country escarpe, that their retreat may be secured by their musket shot, from the Country escarpe, and from the Ordnance of the Bastions and rampiars. But if in case the Garrison is not strongly manned, they are not say they, to make any sallies at all; but only to discharge now and then some Culverings shot when some of the Assailants horse are in a body, and in the reach of the shot; or to discharge a Drake or two when they see some Commander of quality come near to view their Outworks: for such expenses are not always cast away, for many great Commanders have been slain after this manner; and among the rest the King of Sweden 
* See the Sweden soldier.  scaped narrowly, for his horse was killed under him, and the hinder part carried a way by the shot of a Sacre, as he was viewing the works of the Castle of English-State in Bavier. On the other side, some other Commanders maintain, 

1. That if a Garrison do keep within their Rampiars, and make no sallies at all, that the Assailants are encouraged by it; and suppose the town to be weakly manned, or ill provided of Ammunition, if they be not lavish of their powder, in shooting daily their Culverins, to hinder with shot the assailants approaches.  
2. They say that if the Defendants do not endeavour to impede by sallies their approaches, before they come to pierce their Contreescarpe; that their sallies will be then to little purpose, because they may be so suddenly begerted, that they will not then be able to sally forth at all.  
3. That to gain time, which is more precious in sieges then to any other occasions of war, because they hope to be relieved by some party of theirs, if they can hold out but a certain time, that the defendants are by their daily sallies, to hinder the Assailants approaches; and to the utmost of their power, to impede them, to break through their Country escarpe: for if they can but busy them three weeks or a month's time, about these operations, it will much dishearten the common sculdiers, and discourage the Commanders of the Assailants Army.    
Now to decide this point I leave it to the judicious Reader, yet I will inform him that the Duke De 
* See his perfect Captain.  Rouen, Sir Authoine 
* See his Treaty de la charge dun Governeur. Of the charge of a Governor.  De Ville, 
* See his Military Architecture.  Petro Sardy, and the greater part of the Italian and French Commanders, side in their judgement, with the first opinion here related; and that I conceive it also to be the safest way, and especially in this civil war of ours; in which, our Garrisons are so ill manned, and so ill provided with Ordnance and Ammunition. And also, because we have neither Outworks, nor Country escarpe, and not so much as any lower flunks to scour our Courtines, or ditches; and therefore our works being so weak and deformed, as the greater part are, we are to keep our men fresh and in heart, for the defence of a general assault. Besides, raw, and unexperienced soldiers, that never were in besieged Towns, are mightily astonished and amazed, at the first approach of a great Army before their Rampiars; but when they have been wont to look the enemy in the face, their courage and resolution is increased, and dare better attempt such sallies than they could at the first coming. And to prevent this Panic fear, 
* See Plutarc. in Marius' life.  Marius a great Commander of the ancient Romans, being appointed by the Senate to raise an Army to hinder the Cymbers, a barbarous nation, that was coming into Italy, to pass the Alpelins' Mounts, for they were already entered in Lombardia; he seeing that the greater part of his Army did consist of raw soldiers, he caused them to lie in an entrenched Camp every night, but when he came in sight of the enemy, their multitude, their grim countenance, their high stature, and barbarous carriage, and apparel, did so affright his soldiers, that he could hardly make them defend the Rampiars of their Camp; whereupon he gave charge to his Officers, to make one Regiment after another, to be day and night upon the Rampiars, that they might be wont to see without fear, this barbarous and grim nation; and lay purposely near a month, in one and the same entrenched Camp, suffering the enemies to approach sometimes to the very brim of the ditch, till he saw his soldiers freed of this Panic fear; and till they came and entreated him to issue forth of their Camp, to give the enemy battle, which he granted with much ado, reproving them for their former fear and cowardice. And by this wise Policy obtained a famous victory, for there remained slain in that battle, fourscore thousand in the field of the Cymbers, and very few of the Romans. But had he set upon them at the first, when his Army was amazed, he had undoubtedly been routed; and had cast the City of Rome into a great danger, for they had then no other Army ready to oppose them.  
To conclude this point, it is most certain that the Assailants in this unnatural war of ours, are to come to a storm the very next day that their Army hath faced a Garrison, if the works of it be not regulary, or have no lower flanks; and their brest-work not above nine foot high, and six or seven foot thick, with a graft of some nine foot deep, and twenty foot broad; for if they have but courage, they will undoubtedly take the same. And for the Defendants, they are not to waste their men, and Ammunition, in ridiculous sallies, but to be watchful, and valiant to oppose the assailants in a general storm: for if they can beat them off twice or thrice, they will free themselves from their ●ury. But if the works of a Garrison be regulary, and lined out according to Art, and well flanked with upper and lower flanks, having the Rampiars and Brest-works of Cannon proof, and twenty or thirty foot high, with a graft of twenty foot deep, and forty foot broad, besides the small ditch called La cunette: with a good Country escarpe: having a brest-work of six foot high, with a foot-step going round about the inward work, and well manned and provided with Ordnance and Ammunition; then is the General or Commander in chief that undertakes to besiege such a Garrison, to entrench himself in such an entrenched Camp, that is demonstrated in Plate 24. and by degrees to make his approaches both open and private, to break into the Country escarpe; and to beat to dust the defendants flanks by his batteries, that he may cast his Galleries over the mote: and set his Miners at work, to blow up by Mines, the Point, or Faces of the Bastions, to come to a general assault; for otherwise he will but spin out the time, and at last, come off with little honour and reputation.   

CHAP. XXXV. Of the entrenched Camp demonstrated in Plate 24.  
TO besiege such a strong hold to some purpose, marked in this figure by the letter A. that the General or Commander in chief of an Army, that undertakes such a siege, may come off with honour; he is in the first place to entrench himself in four 
* The first operation of the ten that are to be done in a siege.  large quarters, of a continent, convenient and proportionable to his Army: if it exceed not four thousand horse, and twelve thousand foot, the dimensions of these four quarters marked in this figure by the letter B. will as I conceive be sufficient, if it be greater or less; his Engineers are to increase or to diminish the Continent of it. For we have found by experience, in this unnatural civil war of ours, that to besiege strong holds, without an entrenched Camp, 
* One of the causes of the spining out of this unnatural war.  is wittingly and wilfully to spin out this war, because it is an easy thing for an experienced and active Commander to beat up and put to rout a quarter of our Armies, as they lie open, and that are at so great a distance one from another, as ours commonly do; it hath been the overthrow of divers of our forces before Newark, Pomfret, Dennington, Banbury, and Dudley Castle; and the tedious spinning out of the reducing of Basin, and Latham house. Besides, they exhaust the means of the Kingdom; for a Garrison begerted with a circulary entrenchment, will be sooner reduced in a month, than another will be in six that is besieged; as we have done hitherto. For instance, How had it been possible for 
* See Caesar's Commentaries of the wars of Gaul. lib 7.  Caesar to have penned in fourscore thousand fight men in the great city of Alexie, and to defeat an Army of one hundred and fourscore thousand more that came to their relief, with his small Army of fifty thousand men at the most, if he had not doubly entrenched himself against the town, and against the great Army that came to raise the siege? And yet some will maintain that we excel in these days, the ancient Romans in the Art of war; But it is not so, for the French, or Gauls, were then a Warlike Nation, and their General Vercingentorix was a very resolved and valiant Commander, but it was by the Art of Fortification, and the excellent military discipline of the Roman soldiers, with the great activity, and the experience in Arms of 
* Caesar's works and Carriage before Alexie in Erance.  Caesar, that brought to pass in so short a time, such incredible things; for he enclosed Alexie, with a double entrenched Camp, with a ditch of twenty foot broad, and twenty foot deep, without a slope; and erected a Rampiar of twelve foot high, and twenty foot thick, beside a brest-work having at every fourscore paces a distance: high wooden Towers to secure his Archers, and to discharge his Balisters against the Assailants, and the exterior of these entrenchments, was at the least twelve English miles compass, and the inward entrenchment could not be less than eight English miles circumference, as may be supposed by the Continent of the city of Alexie, 
You may see how much it availeth, to be in a double entrenched camp.  since it was able to billet fourscore thousand fight men, besides her own inhabitants. And all these works were erected and perfected in less than a month; for he was not in all six weeks before it, so that it may be supposed, that the interior entrenchment, or the circulary line that did begert the city round, was done in eight or ten days; and so sufficiently made, and so vigilantly guarded, that the besieged could never break through these works, to join with them that came to their relief: Nor that great Army could not also go over these works, but tired themselves in endeavouring to break through. And being thus overtired, Caesar made a sally with his fresh Army, and by these means routed them, and obtained the city, that yielded to his mercy, being not able to hold out for want of victuals. By this unparallelled example it is apparent, that there is no way to this to reduce a strong hold, and to be able to oppose a potent Army that cometh purposely to relieve it, when it is besieged.  
But to return where I left, these four quarters being set out and finished, and the Huts or Tents being set up, and the horse and foot with the Carriages, and the Train of Artillery being placed, and the General's Tents being erected in the midst of one of the best seated quarters, a double line 
* The second operation.  of Communication marked C. is to be lined and taken in hand; having in every side small flankers as it is demonstrated, to secure the covered way, made between the two Rampiars, marked by the letter M. whereby one quarter may relieve the other as occasion requires, without danger. Now if a deep and unfordable river run in the midst, or on the side of this Garrison, two bridges 
(a) The third operation.  are to be erected over the same, in the two broad sides quarters of this entrenched Camp; for in that place they will be secured without any other works, and seated conveniently to relieve from both sides the river, any of the quarters, if any of them were assailed by the besieged, or any party that should come to their relief. These bridges 
* Four kind of bridges, and how they are to be erected; the first sort being the best, and soon erected  are to be made with Barges, or great flat bottom boats, well linked together with iron chains, and fastened to pills droven in the midst, and on both sides of the river, that the stream may not drive them down; and these Barges or Boats, are to be covered with planks of three inches thick, and then with gravel; that Carriages and the Train of Artillery, may pass over without fear. But if such flat Boats nor Barges cannot be found, than they are to be erected with Pills, and covered over with such thick planks, or gravel. Or if seasoned Pills could not also be had, then long timber trees are to be felled, and the bark and branches being he wed away and squared, they are to be bound fast together as flotts of timber that are driven down a shallow river, where Barges cannot go for want of water; and five or six of these flotts well bound together, will make a strong bridge, so it be covered with the aforesaid planks and gravel, and fastened in the midst and in the sides to Pills, driven with violence into the ground. Another kind of bridge may be made suddenly, with two double rows of empty Sack-pipes, Hogsheads, or Beer-barrels, well hooped, 
See Philip the Commin. Commentaries.  and close botomed, bound together and fastened to Pills driven in the midst, and in the sides of the river. As Charles the last Duke of Burgundi, did erect one (over the river, the Seine that runneth through the midst of Paris) some three miles from the city, and this bridge was erected in one night: And all the Duke's Army, with his Train of Artillery, bag and baggage, passed the river before eight of the clock in the morning; upon which unexpected tidings, Lewis the eleventh, the great Politician, was greatly amazed.  
This double line of communication, and these bridges being finished, the Enginiers are to line out their approaches 
(b) The fourth operation.  after any of these two ways demonstrated in this Plate by the letter D. erecting at every return an Angle flanker, where Musquettiers are placed to secure the approaches, having a Court of Guard in every one of them, of forty or fifty men; these flankers serve also for Carriages or horsemen to retreat, when other Carriages or horsemen are discovered coming in the next approaches, if in case the General will have them so narrow, that two Carriages cannot pass close together, for he hath the disposing of it: some therefore will have them but 12 foot broad, and 4 foot deep, and some twenty foot broad, and five foot deep; but very flat in the bottom: the slope of the sides is not to be above a foot. The principal care of the Engineer that lines them out, is to set out their Angles so fare into the field on the right, and on the left hand, that they may not be as the French term it (Enfillees) that is, 
* Of the true setting out of approaches.  that any Cannon or Culverin shot, placed upon the the Angle or Point of any of the Bastions of the Garrison besieged, may not upon a straight line beat in any of the approaches; for if they may, the approaches are not safe, nor lined out as they should be, but will be destructive to the Assailants; for such a shot may endanger the lives of twenty horsemen, or footmen, at a time.  
These approaches marked by the leetter F. being finished, and brought within one hundred yards of the Country escarpe of the besieged; the Plat-forms 
(c) The fist operation.  are to be raised, marked by the letters E. and 4 or 6 Demi-Cannons to be placed and pointed against the flanks of the Bastions, and the brest-works of the Rampiars; to batter to dust all the brest-works of the Flanks, and Rampiars. And while this is a doing, some of the Pioniers are to work day and night in the private approaches under ground, 
(d) The sixth operation.  to break into the Country escarp; and some other Pioniers in the night time are to work about the begerting circulary trenches, (but if the Army be provided with mantlets, they may also work about this trench in the day time) that is, to go round about the Garrison, marked by the letter O. that is, to have spaces left to place Turn-pikes to sally forth, when the secret approaches are almost finished, to assail the Country escarpe, while these that are in the approaches under ground, break into the Country escarpe, and by a furious onset insorce the Defendants to retreat into the Garrison, and to forsake the Country escarpe.  
The Country escarpe being won, and the circulary 
(e) When this circulary line is finished, the defendants can by no means sally for th' any more.  trench finished, the Pieces or Demi-Cannons, that were appointed to beat down the brest-works of the Flanks and Rampiars, are to be removed as soon as other Plateforms 
(f) The seventh operation.  are raised upon the Country escarp, to place and point some of them against the Points of the Bastions that are intended to be stormed; and the other against the flanks that may be repaired that way, that they may erect their 
(g) The erecting of Galleries, is the eight operation.  Galleries over the Mote, if it be full of water: or if it be dry, to fill the same in a night with Bavins, that the Pioniers may begin their Mines, to blow up some part of the Bastions; but because the ensuing operations are demonstrated in the next plate, I will here describe the Ichnography of this entrenched Camp with the dimensions of all the parts of it, and will refer you for the rest to the next Chapter.  

The Ichnography of the 24 Plate.  
A. Represents the Garrison besieged of a Sexagon form fortified by six Bastions, with orillon's; after the best Italian Method, as may be seen in the next Plate.  
B. Represents the four quarters of the Army, that contain in their circumference a mile and a half, and may contain three thousand Foot and a thousand Horse a piece.  
C. Represents the double Line of Communication that conjoin the four quarters one with another; the circumference of the whole Camp, with the sour quarters, is in all of eight English miles; and the distance from the end-side of the Camp to the Country escarpe of the Defendants, is of five eight parts of a mile; and the distance from the broad side of the Camp is of seven eight parts of an English mile, and thereby free in all parts from the besieged Garrison Cannon shot.  
D. R presents the winding approaches that run to the begirting trench, the earth of which is cast toward the Town, to serve as a b●●ast-work to the assailants, to cover them from the Musket shot of the Defendants that are in the Country escarpe; the earth of the winding approaches is cast some at the right hand, and some at the left hand, the better to preserve them that go, or are in them; their ditches are represented by the white lines, and their banks by the thatched lines; their banks are so high, that neither Foot nor Horsemen can be in danger of the Cannon or Musket shot of the Defendants. The breast of their flanks placed upon every winding angle, are of seventy yards broad apiece; that they may contain 40 or 50 Musquetiers apiece, if need require.  
E. Represents the sour first platforms for to raise Battery; these batteries are to be raised according to the s●at of the place; if it be to batter the upper flanks of the brest-works of the Rampiars, they need not to be above two yards high; if it be to batter the lower flanks, and the faces or p●●●●s of the Bastions, and the foot of the Rampiar, they are to be 4, paras high, and sometimes more. They are always to be entrenched round, but in one 〈◊〉, 〈…〉 barrier is placed with a good ditch, and a brest-work 〈◊〉 flanked, and to contain between 60 or 100 Musqueteer 〈…〉, and Hollandaise,, to preserve the Pe●ces, if in case the D●●e●●ants made a gr●●● and strong 〈◊〉.  
F. Represents ●he Flankers 〈…〉 the approaches; their breast is from 70 yards to 80, and may contain 40 or 50 Musquetiers.  
G. Represents the diagonal approaches of the broad sides of the Camp, that cross one another like a traverse, of which we have not spoken at all, because the batteries were not of that side; but what hath been said of the other, will also serve for them.  
H. Represents all the flanks of the diagonal approaches of the broad sides of the Camp.  
I. Represents the upper traverse of the diagonal approaches, and a small half moon that defends the coming in of the said traverse.  
K. Represents the lower traverse of the diagonal approaches; and the little half moons that defend the coming in and going out of the two great quarters of the two broad sides of the Camp.  
L. Represents the four small half moons that defence the coming in and the going out of the four great quarters of the Camp, towards the fields. The sides of these half moons are of 6● yards a piece.  
M. Represents the road or covered way, that leadeth from one quarter to another, between the Lines of Communication: it is of 16 yards broad, besides the thickness of the two breast-works, and of their five footsteps that are in the bottom eighteen foot, and at top ten foot, and of nine foot high _____, the ditches are eighteen foot broad and nine foot deep.  
N. Represents the two platforms erected by the diagonal approaches on the broad sides of the Camp.  
O. Represents the begitting trench, and her flanks or breast-works.  
P. Represents the turne-pikes and issues to go to assail the Defendants Country escarpe.   
Some will object, that to erect such a Camp, it will be a tedious and a chargeable piece of work. But I answer, That an Army consisting of twelve thousand Foot, will finish such a Camp, and erect two such bridges over a River, as broad as the Trent is before Newarke, in less than a fortnight's time, so the Army be provided, as it should always be, with six thousand pick-axes, spades, and shovels, and with four hundred wheel, and hand-barrows, and as many scuttles, and with store of Carpenters. And for Pioniers there need none, so the General be pleased to allow four pence a day to the Foot Soldiers of his Army, that will work when they are out of guard, over and above their pay. And these charcges would be recovered one hundred fold, by the speedy reducing of the Garrison that is consumed by the pay of an Army, that spins out the time in other methods of Sieges; and which is of more value, many hundred men's lives will be preserved by this method of Sieges.   

CHAP. XXXVI. Of the Batteries erected, and of the Mines to be sprung against a besieged Garrison, demonstrated in Plate 25.  
Upon these last operations, depends the honour or disparagement of the Assailants, and the preservation or desolation of the defendants, if they behave themselves like men of War, or be daunted or dismayed by the roaring of the Cannons, and of the furious storms of the Assailants. Now to describe these effects that are the most dangerous and terrifying actions of the Art of War, I will in the first place set forth the Assailants duty, and secondly, the Defendants opposition.  
The new batteries erected upon the Country escarpe, that we spoke of in the last Chapter, marked with the letter V in this Plate, appointed to beat, to ruin the two points of two Bastions, are to have six whole Cannons mounted upon them, and pointed against the side of the face of the Bastions, within twenty yards of the point, as the most convenient place, to make a speedy breach, for to fill with the ruins of it the mote or ditch, these six Cannons are to be pointed, discharged, and fired at one and the same instance of time, by six Cannoneers, and not one after another, allowing some intermission of time, between the fitting of them, as we commonly use to do, but all at one clap, because six Cannon shot coming at once against a Bulwark, Rampiar, or Stone Tower, is more powerful to shake and ruin the same, than forty single Cannon shot, that are fired between some intermission of time: And as soon as the six Cannons of one Battery have been fired, the other six Cannons of the other Battery pointed against the other face of the other bulwark is to be fired, that there may be a continual roaring of the Cannons, that the besieged may be the more amazed and perplexed, to which of these two breaches they shall first repair, or bring materials to repair them.  
The other two batteries also, marked by the letter R. are to have three or four whole Culverings upon them, that are to be pointed against the flanks of these two bastions, that are also to be fired one after another from every several battery, but the four culverins upon every one of them are to be discharged and fired at one instant of time, as hath been formerly said of the six Cannons. And so by these four batteries, if they be well ordered, there will be a continual Roaring of th● Cannon, with little or no intermission at all; And these batteries are to continue till the breaches be sufficient, and at the least twenty yards broad, and level with the ground, that twenty men may come out abrest, as close together as may be, and all the night time the assaillants from the Country escarpe intrenchments, that they have made as near the brim of the mote as may be, are to hinder (with fresh companies of Musquetiers that are to be relieved at every change of the Sentries) the defendants to repair the breaches, that the general assault may be given the next morning.  
But before these Batteries begin, the two 
(i) The ninth operation.  Mines marked by the letter O. are to be brought to such a pass, as they may be ready to spring just in the midst of these four Cannon batteries, that there may be four breaches in three of the bastions of this Sexagon Garrison, all at one time, to make a diversion of the Defendants forces; by which diversion, their forces must of necessity be divided: and by consequence weakened and disenabled to make so strong an opposition as they might do, if there were but two breaches.  
The best way to guide covered approaches or mines, to that very place you purpose to do, is to have a perfect Sea-compasse with you, that you may note upon your Table-book, upon what point or degree the place you intent to come to, standeth; from the mouth, or opening of the covered approaches, or mine.  
This mouth or opening, is to be made eight or nine foot square, and the bottom as deep as you intent to go with your Mine, 
(k) The true way how to begin a Mine.  than you are to set your Sea-compasse 
(l) Sea-compasse is of necessity to be used in the setting out of Mines.  upon the point or degree noted before, and to order the Pioniers to mine just upon the ray of the degree; their way is not to be, if the ground permit above four, or four foot and a half broad, and not above five, or five foot and a half high, that two men may conveniently pass with 
* These hods are great baskets pointed in the bottom, and two foot broad at top, flat against the backs, and round without side; wherein a man may carry three times as much earth as in a Scuttell.  hoddes on their backs full of the earth of the mine; that is, to be brought up from the mouth of the ours with a Ladder, and placed some sixteen foot from the brim of the mouth; in manner of a square brest-work, as it is demonstrated in this Plate by the letter N. the letter M. representing the mouth of the mine. But this method is to be only observed, if in case the mouth be in the field, as the mouth of all covered approaches are; but if the mouth of the mine doth begin beyond the mote, than the earth is to be bestowed to raise the banks of the small entrenchment that are made along the wall of the Rampiar.  
Now when the Pioniers have entered the mine some four foot, you are to set up at the entrance of it such a strong door case, as is marked by the letter T. having two strong ledges nailed two inches and a half lower than the very top; and at every six foot of the way of the mine, 
(m) How to hold up the earth of a Mine from calving in.  you are to place such another doore-case, and to set planks of two inches and a half thick upon these ledges spoken of before; and this must of necessity be done, where you find the earth to be apt to calve: but where it is sound, this charge may be spared.  
And when the way of the Mine is come so fare under the face of the Bastion, as you desire; you are then to wind the way of your Mine ten yards on the right hand, and ten yards on the left hand; in the manner of a T. as it is demonstrated in this Plate, and to make two round Ovens of that capacity, to contain six or seven barrels of powder apiece; as it is demonstrated by the letter P. and when these barrels are placed in both Ovens, the mouth of them is to be stopped (after the Train of powder to them, hath been laid upon boards) with 
(n) All other kind of stopping the ovens mouth, is nothing to bricks and lime.  bricks and lime, with a hole in the bottom of four inches square, for the Train to be brought along the way of the Mine to the very mouth of it. Others make use of a copper pipe made like a T. in which they put a fine tinder match; the burning of which, they have made experience of, to know the just time that it will require to burn, to set the Train close to the powder barrels on fire, and do set the other end towards the mouth of the Mine on fire, so many hours before the time they intent to spring the Mine; the other way by a Train upon boards to the very mouth of the Mine is to be fired with a lighted match, fastened to the end of a long kane; and he that fireth the same, is to run aside as fare as he can, to avoid the danger of the splits of the Mine.  
These two Mines being sprung at the same time, that the breaches of the Cannon batteries are ready for a general assault, will produce a great amazement, or a panic fear among the Defendants. And upon this amazement, the Regiments that are appointed to attempt every one of these several breaches, are to be ready, and to advance furiously 
(o) The tenth and last operation of the Assailants, to obtain and reduce a Garrison Town.  forward to enter the breach; for to crown their heads with the Crown of Laurel, due to the Victors. But because most of our soldiers go not armed as they should, for such a dangerous and desperate attempt, I will here describe the Arms, that a wise General, that holds the lives of his soldiers more precious to him then his own, should have always ready to preserve such valorous soldiers, that lead the way to such a Feast; he is I say to have always one hundred of brest-plates, and one hundred of head-pieces, and one hundred of Roudaches, or broad Targets of musket proof, to dispose among those that undertake to lead the Front of the three first ranks that enter these breaches, and this would preserve many men's lives, and make them go on more boldly to so dangerous a fight.  
In the next place we are to suppose that the Assailants by their valour have entered the breaches, and obtained the points of the Bastions, and other the top of the Rampiars; and yet cannot enter the town, because of the provident forecast of the Defendants, that have entrenched themselves between the town and their Rampiars, and overthwart the breast of the Bastions: yet the Assailants are not to be discouraged, but presently cast up some small trenches upon the Rampiars, and the points of the Bastions they have taken, till their smallest Sacres and Drakes be drawn up upon the Rampiars, and the points of the Bastions, that will speedily beat the Defendants from their weak intrenchments, and enforce them to a parley, having then no other means left to preserve their lives but that; for if they be forced by another storm, they are like to suffer all the miseries that a provoked and incensed enemy, will be able to inflict upon them.  
But suppose that the Assailants be repulsed with great loss from the first and second Assault, yet if the General can bear these losses patiently, being entrenched in such a manner as is afore said; he may reduce in few days this obstinate Garrison, and obtain the Crown of Laurel, due to such as are constant in their warlike attempts, by famine, that enforceth the greatest resolution, to an accommodation. For if he can but endure the irksome and tedious labour of a long siege, this Garrison notwithstanding this great resolution, can hope for no relief. For if a greater Army than his come to endeavour to raise the siege, it cannot force this entrenched Camp, nor enforce him to battle, except he list himself, or that some apparent occasion of prevailing should be offered; as the weariness of the Gauls, did induce Caesar to sally out of his entrenched Camp, after they had tired themselves upon their vain attempt, 
See Caesar's Commentaties lib. 7.  so break through his strong Rampiars and intrenchments, otherwise it would be no wisdom for a General to embrace an uncertain enterprise, for a certain victory, that cannot be taken out of his hands, if he continue in his entrenched Camp; for at last that Garrison will be enforced to yield to his mercy, as the City of Alexie was constrained to submit to Caesar's clemency.  
Having fully shown the endeavonrs and the valour of the Assailants, it remains for the conclusion of this point, and of this abstract, to show also the endeavours that a valiant and prudent Governor is to perform, to discharge with a good conscience the great trust that hath been reposed upon him, for the defence of such a Garrison. First, as the Assailants erect their batteries, and point their Cannons to beat down the brest-works of the flanks, and of the Rampiars; he is to endeavour to hinder the raising of these batteries, or to does ount their Cannons by placing the greatest pieces he hath, upon the Mounts or Cavaliers that are erected near to the middle of the Courtines of his Garrison.  
2. He is to have great care to cause the brest-works of the Flanks, or of the Rampiars, that have been beaten down in the day time to be repaired in the night; causing women and children to bring earth in the day near unto the places of the greatest breaches, 
The ten operations for opposition.  that may with the more speed be repaired, having always many hops and woolsacks in a readiness to serve as brest-works upon the breaches of the Rampiars, and of the Bulwarks.  
3. He is to charge the Inhabitants to bring store of sewel and their greatest Caldrons, or Kittles to the houses adjacent, to the Rampiars, and to command that store of oil, and water may be in a readiness: that in the time of the general assault, sires may be kindled near to the Rampiars; and oil and water heated boiling hot in these Cauldrons and K●ttles, to be thrown by the women upon the Assailants that endeavour to scale the Rampiars.  
4. He is to have great store of all manner of fireworks ready to cast upon those that endeavour to enter the breaches, to dismay and offend the assailants, placing many musketeers on both sides of the breaches, that may g●ll the assailants in the flanks.  
5. He is to have in the Magazine of his Garrison, one hundred of Sea-Muskets, that the French call Harquebus à Groch, that carry a bullet three times as great as an ordinary Musket, and longer than they by half a yard, and one hundred of Roudaches, or iron targets of Musket proof, and one hundred of Partisans, and as many good Halberds, with a hundred of breastplates, and as many headpieces, all of them of Musket shot proof: and all these are to be disposed to the most valiant soldiers of the Garrison, that dare undertake to defend the breaches.  
6. As soon as he perceiveth that the assailants erect their batteries, he may presently guess where they intent to make the breaches; then is he to take order, to erect by times new intrenchments, for it is too late to go about them, when the assailants have gotten the rampiars, and the points of the Bulwarks.  
7. When the Assailants begin their Mines, he is diligently to search the place where they intent to carry their mine; and because they seem sometime to go one way, when they intent to go another, to delude the defendants, he is to try in all places that he may mistrust they intent to go with their Mines, these conclusions:  
Let a very thin Barber's basin be set to that place that is suspected, full of clear water; If the Assailants mine in that place, at every stroke of their pick-axes, the water in the basin will frizzle into small round circles, as if a small stone were cast in a pail of water.  
Or let a drum be set down to the place, and some very round white pease be set upon the top of the drum, and these pease will leap at every stroke of the assailants pick-axes, if they be mining in that place. And if any of these symptoms appear, then is he suddenly to set Pioniers at work, to countermine, and to give air or vent to the assailants mines; and when the defendants Pioniers come near their Mine, let them proceed no farther, but let the Sentries that are near the place, where the mouth of the assailants mine is, give intelligence from time to time, if any barrels of powder be brought into the ovens of the Assailants mine; for before they can sire the same, the defendants may if they be vigilant, deprive them of their powder, and all's under one, give vent to their Mine. This stratagem hath been successful to divers defendants.  
8. When the assailants endeavour to carry over their galleries over the mote, he is then to spare no pains to place Musquetiers on their flanks to impede them; but if in case they are covered from the Musket shot by mantlets, he is then to have the Demy-cannons placed in the lower flanks of the bastions, to be suddenly charged with iron balls, (and the case-shot wherewith they were charged before, removed, that as soon as the assailants galleries are almost brought over) the shot of these two Demi-cannons may break them to pieces.  
9 The Demi-cannons that are placed in the upper flanks, are to be charged with chain shot, that is, with two iron balls linked together by an iron chain, that when the general assault is given, if in case the assailants should attempt to scale the Rampiars, the said chained balls might cast down all their scaling ladders.  
10. And lastly, the Governor during the siege is to double his Courts of Guards, and Sentries, and to go the Rounds oftentimes himself, and in the day of a general assault, he is to go to all places, and to view the defects, and to apply remedies to them, sending sudden relief to those breaches that are in most danger to be entered, and to have always about him, some three score of the most valiant soldiers of the Garrison, being in the head of them, to relieve the most distressed place of the Garrison: and by these and such like endeavours of valour and fidelity, he is to discharge the trust reposed upon him, and preserve his Garrison, if it be possible.  

Here followeth the Ichnegraphie of the dimensions of the Fortifications of the Garrison besieged, demonstrated in Plate 25.  
A. Represents the Garrison reduced into a Sexagon form; the sides of it are according to the best Italian Method; divided first into ten equal parts; four of which are allowed for the two demi gorges, and the other six for the Courtine, and these sides are of 250 yards apiece.  
B. Represents the whole gorge, that is of 100 yards.  
C. Represents the demi-gorge, that is of 50 yards.  
D. Represents the distance from the centre of the Bastion, to the utmost point or angle of it, that is of 100 yards.  
E. Represents the face of the bastion that is of 120 yards.  
G. Represents the circulary compass of the orillon's that jet beyond the shoulder 20 yards.  
H. Represents the breast of the Bastion that is of 120 yards.  
K. Represents the Courtine that is of 150 yards, that is divided into 8 equal parts; from the first part of which, the line of Defence is taken, according to the Italian method, that is, 14 yards nearer the flanks, than the Hollanders take it.  
L. Represents the line of defence that is of ●40 yards.  
M. Represents the mouth of the Mine.  
N. Represents the earth of the Mine, placed in the manner of a breast-work.  
O. Represents the way of the Mine underground.  
P. Represents the two ovens of the Mine.  
Q. Represents the Copper-pipe, in which they set the tinder, match, where with the train of the Mine is fired.  
R. Represents the two smallest platforms.  
S. Represents the winding approaches, whereby they come to the smaller platforms.  
T. Represents the two door-caser, to support the earth of the mine  
V Represents the two great platforms.    
FINIS.   

ERRATA.  
Page 4. line 2. for higher read highest. p. 9 l. 32. for another, r. by another method. p. 25. l. 4. for square, r. base or side. p. 25. l. 11. for set out, r. set it out. p. 32. l. 17. for but one, r. but of one, etc. p. 61. l. 5. for slope nothing, r. slope to nothing. p. 75. l. 15. for step, r. slope. p. 87. l. 4. for stake r. take. p. 88 l. 12. for rod, r. road. p. 92. l. 28. for rover. r. roarer. p. 101. in the Annotations, for du Belluy, r. du Belay. p. 110. l. 33. for Planks or gravel, r. and gravel. p. 111. l. 7. for bottomed, r. bomed.