German K S N Angle of the Center Angulus Centri Angle du Centre Mittelpunets eck O K N Angle of the Figure Angulus Figurae Angle du Poligone Keelpunct R B F Angle of the Bastion Angulus Prepugnaculi Angle Flancque Bolwercks eck B H D Angle Flancking Angulus Defendens Angle Flanquant Der Schutzwinckel B F L Angle of the Face and Flanck Angulus Faciti Alae Angle du Flancq de la Face Der winckel der Streichen und Gesich-linie 1. From a Pentagone to a Right-line HAving divided the given Base or Exterior Poligone C D in Fig. I. which suppose to be 575 English Feet into two equal parts in E From the Point E raise a Perpendicular E L of a sufficient length This done enter the Number of the Half-Base viz. 575 in the first Column of the Hercotectonick Table over which is D. Base and look what number answers to it in the second Column over which is Perp. and finding it to be 192. take from off your Sector or Scale 192 and set it on the Perpendicular E L where it will terminate in the Point F. And then from either Point D and C of the given Base C D through the Point F draw the Lines C G and D H of a sufficient length In the next place enter the number of the same Half-Base viz. 575 in the third Column of the Table at the head whereof is D. Base to which you will find the Number 351½ answers in the fourth Column over which is the word Face This likewise you must find upon your Sector or Scale and by it determine the two Lines C I and D K. Lastly enter the aforesaid Number 575 in the fifth Column of the Table which you will find answered by 204½ for the Compliment which Compliment or 204 1 â— must determine the two Lines F G and F H. Which done joyn the Points C I H G K D so have you C I and K D for the two Faces H I and G K for the two Flancks and H G for the Curtain of that Fortification And observing the very same method from each Base the Fortification becomes perfectly delineated as in Fig. I. 2. For a Square THE Method for delineating a Fortification upon a Square is the very same with that from a Pentagone to a Right-line only the Proportions and consequently the Numbers expressing those Proportions are different as may be better seen in the second Part of the Hercotectonick Table compared with Fig. II. I. II. But now forasmuch as in Fortifying Cities and other Irregular places it often happens that the Engineer is constrained to make use of the old Walls and Ramparts and consequently the Courtines must be the same with those Walls Therefore the Count de Pagan thought it would be some help to give a Rule to find the Distance between the two Poligones which Distance is also found in the 8th and 16th Columns of the Table For example in Fig. I. E L or the Distance between H G and C D is 257 Feet and four Inches And in Fig. II. M N or the Distance between O P and Q R is 207 Feet and eight Inches But as to this last particular namely of Fortifying from the Interior Poligone the New Method comprised in a MEDALL is much more exact and expeditious LINEAE HERCOTECTONICAE NOVAE Augustisimo Principi CAROLO II Magnae BRITANNIAE c. REGI humillimè oblatae à Samuele Morlando Equite Aurato et Baronetto nec non Camerae Regis Privatae Adjuncto Anno Salutis MDCLXVI Of the Dimensions of the Bastions Ramparts Ditches Half-Moons Counterscarps c. AS concerning the Measures and Dimensions of the Count de Pagan's Bastions Ramparts Ditches Half-Moons Counterscarps c. it would require more time than I can at this present afford and a larger Volumn than I have design'd for this Treatise forasmuch as the Count has given Names to many things quite different from those in other Authors I shall therefore leave the comparing those differences to those who are more at leasure and only content my self to have set down some few of his Proportions which are adjoyned to the opposite Table of Plain-Angles which Table is of Excellent and Universal use The use of the Table of Plain-Angles WHen you would measure an Angle of any Field or Plot of ground As for example let the Angle to be measured be C A B in Fig. C. Take a Chain and measure 30 Links it matters not of what length those Links be so they be equal one to another from A to C and so from A to B. And at B and C stick up two sticks And then measure with the same Chain the distance between C and B and finding it to be 20 seek 20 in the Table in one of the Columns over which is the word Bases and the Number of the next Column answering to it is the true Number of Degrees and Minutes of the Angle sought viz. 40° 00′ After the same manner because the distance between I and K is 55 Links the opposite Angle is 132° 55′ Again suppose you desire to lay out an Angle of 100° 05′ I first stick down two sticks at the two ends or Terms of any given Line F E divided into 30 equal parts in the Points F and E. Then fastening a Chain of 30 Links equal to those 30 equal parts at F and one of 60 Links at E I enter the Table of Angles with 100° 05′ and finding 46 to answer to it where-ever the Chain of 30 Links and 46 of the Chain of 60 meet as in G. thence draw the Line F G and you have what you desire And after the same manner may any Angle be laid out most exactly and expeditiously from 10 Minutes to 180 Degrees â—ES BASTIONS DES RAMPARTS ET DES FOSSEZ Largeur des Ramparts 45 Largeur des Parapets 19 Hauteur de la 3 casematte du fond du sossé 38+ Hauteur des Parapets au dedans 6+ Hauteur des Parapets au dehors 5+ Largeur de Grand Fossé 102 Profondeur du Grand Fossé 19 La largeur du Fossé compris entre le premier et 2 Rampart du Bastion est diverse selon la Fortification le Poligone et sa profondeur 13 Reds ou plus Et la largeur du Flanc retiré 77 Pieds DES DEMI LUNES ET DES CONTRESCARPES 1 Methode Pieds d'Angl Demiegorge de la Demi-Lune 192 Face de la Demi-Lune 320 Largeur de la Grande Contrescarpe 320 Largeur de son Fossé 77 Largeur de la Petite Contrescarpe 26 La Demi-Lune se forme tousiours sur l'Angle Rentrant de la Contrescarpe 2. Methode Pieds d'Angl Largeur de la Grande Contrescarpe 161 Largeur de son Fossé 77 Largeur de la Petite Contrescarpe 26 Demi-gorge de la Demi-Lune 128+ Face de la Demi-Lune 217+ â—es Flanes de la Grande Contrescarpe comprennet Parapets et peuuent ainsi contenir 9 Pieces de Canon LIGNE DES
deducted from D F the distance between the second and fourth there remains H F your Divisor which measured I admit 50 Halberds lengths the distance between G E 30 Halberds lengths the space between D F 100 Halberds length now 100 multiplyed in 30 produceth 3000 which divided by 50 leaveth in the Quotient 60. I conclude therefore the distance between A and B to be 60 Pikes lengths This one thing is to be taken notice of especially that whatsoever you mete the space G E withall that you use the same in measuring H F and as for D F it matters not what you measure it withall for your Quotient shall bear the same denomination Preciseness is to be used in placing of your Triangle and in measuring E G and H F otherwise error may ensue especially if D F be but a small distance and the Angle at B very sharp There needeth in this matter no further admonition small Practice will resolve all doubts CHAP. IX To measure the distance between any two Forts Castles or other places howsoever they be scituated though there be Rivers or such like Impediments between that you cannot approach nigh any of them and that without an Instrument also LEt your Angles as before hath been said be prepared of any three Staves c. you shall first at pleasure set up one Staff and applying thereunto your Angle in such sort that the one containing side lye directly to one of the Marks which here for distinction sake I will call the first go backwards too and fro until you find your second Mark precisely covered with your Staff noting what part of the line or side subtending the Angle it cuts by your line visual and there make a fine notch or mark upon that subtending Staff which done you shall go sidewise from the first erected Staff as the other containing side of your Triangle will direct you so far as you list and then set up your second Staff yet pass on from thence in a right line with that containing side of your Angle that riseth from your Staves and cometh somewhat toward the Mark and go so far until you spy your self justly between your third Staff and your first mark there set up your fourth Staff then resort to your Angle again and standing behind the second Staff note whether a right line from the Angle to that notch before made on the subtendent Staff or side of the Triangle will direct you for that way precisely shall you go on until you come in a right line with the second and third Staff and erect there the fifth Staff this done measure the distance between the second and third Staff reserving that for a Divisor then multiply your distance between the first and third Staff by the distance between the fourth and fifth Staff the product divide by your reserved Divisor and it yieldeth in the Quotient the true distance between the two marks Example Let A B be the distance I would know C my first Station where the first Staff is erected I my Triangle made of three Staves and placed at the Station and directed with one of the containing sides to A which is the first mark as you may see in the Figure and with the other side to D and E the second and third Staves H is the notch or mark upon the side subtended to the Angle where the line visual from ☽ passeth to the second mark B my Triangle now I scituate at D as it was before at C the one contained side lying even with the erected Staves the other directed to my fourth Staff F placed in a right line with E the third Staff and A the first mark Again my line visual proceeding from D to H the notch in the subtended side of the Angle is extended to my fifth Staff G scituated exactly between E the third Staff and B the other mark This done I measure the distance between my second and third Staff finding it 20 foot likewise between the fourth and fifth Staff and find it 72 foot finally between the first and third Staff 65 paces so that according to the Rule before given multiplying 65 by 72 I have 4680. which divided by 20 yieldeth in the Quotient 234 and so many paces is there between A and B. I have not set out the Figures in just proportions answering to these numbers for that is not requisite but in such form as may best open and make manifest the scituation of the Staves and Triangle wherein consists all the difficulty of this Practice CHAP. X. How you may readily find out the distance to any Tower Castle Forts c. by help of the former Quadrant LEt the Quadrant be made upon a square Board as is there marked A D B Q. Let D B be divided into 90 Degrees or equal parts and instead of the 12 equal parts or right and contrary shadows g m and h m let the two sides D Q and B Q be divided each into 1200 equal parts or as many as you please and marked from the Center A and have a Ruler or Index to be moved round upon the Center A having two sights upon it set just upon the feducial line of the Index and let it be divided into such equal parts as the Lymb B Q or D Q. Let this Instrument thus fitted be handsomly placed upon its Staff or otherwise lay the feducial of your Index upon the beginning of the Degrees of the Quadrant and turn your whole Instrument the Index not moved till you may espy through the sight your mark then remove your Index to the contrary side of the Quadrant placing the line feducial on the side line where the degrees end and look through the sights and in that very line set up a mark a certain distance the farther the better this done take away your Instrument and set up a Staff there and remove the Instrument to the mark you espyed set your Index on the beginning of the Degrees moving your whole Instrument till you find through the Sights the Staff at the first Station then remove your Index your Quadrant keeping its place till you may again espy through the Sights your mark which done note the Degrees cut by the line feducial and then work thus upon some even smooth Superficies whether it be Board Plate or Paper Draw first a streight line and open your Compasses to some small distance call that space a score and make so many such divisions upon your Line as there is scores between your Stations then upon the end of your line raise a perpendicular and fixing one foot of your Compasses at the other end opening it to what wideness you please draw an Arch rising from the same line that represents your Stationary distance and dividing it into 90 equal parts or Degrees as you was taught in the making your Quadrant extend from the Center to the number of Degrees cut by your feducial line a right line until it concur with
labour and honour may be equally divided By the way you may observe whereas the Serjants of every company are to be assistant to the Serjant-Major of that particular Regiment for the dividing of their several Corporalships or squadrons files or half files for the making up of any body form or figure according to directions c. So the Serjant-Majors of Regiments are to assist the Serjant-Major of an Army to bring in what divisions or bodies soever shall be called for and the Serjant-Major General is so to do to the Martial of the Field And that his duty may be performed with all careful severity the Serjant-Major is allowed his Hakney to speed it from Company to Company to see that every Company be in his true form and not to suffer any man whatever through Pride Stubborness Neglect Covetousness of Pillage or by any other dilitory and weak excuse to break out of his rank or to disproportion any part of the body by any rude or uncomely posture but severely to rebuke the same and compel a speedy reformation But out of an Army both in field or otherwise then the office both of a Serjant-Major and Marshal shall be in himself he shall summon Courts of War with the assistance of his Captains to proceed to trial against offenders he shall proportion all allodgments encampings and with his best skill fortifie the same and shall upon fight draw the battel yet with this limitation to take directions from his superior Officer c. And as you see he is to take care of all Watches and Guards about that Regiment so if there be no greater Officer than himself there to give the word and to appoint the Court of guard and Sentinels but if there be a superior Officer then the Serjant-Major shall receive it from him and so give it to the Captains and other such inferior Officers as shall have the guard that night In short a Serjant-Major ought to be dutiful to all his Superiours by whom he is to be directed he ought to be an experienced Souldier and of a valiant and undaunted behaviour 4. The Office of a Quarter-master 1. He shall in all changing of lodging attend the Quartermaster General and take the place assigned by him for the quartering of the Regiment in such form as the Quarter-master General shall direct him and there he shall appoint lodgings to the Colonel and the Officers according to their places that they are to take in the Regiment both in town and field 2. He shall lodge suttlers of that Regiment in the hindermost part of the quarter at such distance as the Quartermaster General shall appoint 3. His place is to lodge on the back side of the Quarter behind the lodgings of the Lieutenant-Colonel 4. The Office of the Provost 1. He shall see all Proclamations Orders or Decrees that shall be published by the Provost-Martial of the Army likewise to be published in the Regiment whereof he is Provost 2. Also he shall keep all the Prisoners committed to him and once a week give notice to the Provost-Martial-General of all the Prisoners within his charge and of the cause of their committance 3. Furthermore He shall oversee all the Victuallers of the Regiment that they shall neither at unreasonable prices nor at unlawful hours sell their victuals and shall on the other side be watchful that no wrong be done and if any be that forthwith the party doing wrong shall be brought before some officer that hath Authority to yield redress and to that end he shall go about the Quarters once every forenoon once in the afternoon and once in the dead time in the night if it may be conveniently performed 4. He shall have an accompt given him every night of the Victualer what victual is in the quarter and he shall carry the notes thereof to the Provost-martial of the Army 5. He shall when preys or booties are brought in after the Provost-martial general hath divided them to the Regiments divide them to the several Companies he is Provost-martial of 6. He is to see the quarters kept clean and sweet all garbage and filth buried nothing that may annoy the quarters suffered to be at such a distance as shall be appointed by the Provost-martial of the Army 7. He shall lodge in the midst of the Victuallers of the Regiment 8. He shall come to the Carriage-master for directions where the baggage of that Regiment shall march where they shall assemble and what wayes they shall go which directions he shall perform and after he hath given the first place to the Colonels baggage he shall place by turn the rest as the Companies do march 9. Also he shall see the wayes made for the Carriages accompanied with men sufficient and with instruments to help and amend every thing that is amiss in the wayes or Carriages and if any carriages be unable to go he shall provide that it may be no hindrance to the rest The Officers of a Foot Company 1 The Office of a Captain 1. He hath proportionably the same Command over his Company as a Colonel hath over his Regiment and so also all his Officers and Souldiers are to obey him 2. When he receiveth his Company and his Arms he is to chose his men and to sort them to his Armes as he thinks fit c. 3. He shall chose his Officers such as either have had the like place before or are of Experience and good government or such as have made themselves known to be fit for the like 4. He shall divide his Company into Corporalships 5. He shall take care and labour to teach all his Souldiers the carriage and use of their Armes to keep their order in marchings and imbattailings and to understand all manner of motions and the beat of the drum and to this end he shall have usual times of Exercising which shall be once a day at least till his men be perfect 6. In the marching of his Company alone he shall be in the head of his Company going toward the Enemy and in the Reer-ward coming from an Ennemy 7. In Marching with the Regiment he is to receive his directions from the the Serjant-major of the Regiment and to carry the several sorts of weapons as shall be by him directed and to every one of the divisions of his Company appoint such an officer as the Serjeant-major shall direct and for his place it shall be where the Serjeant-major shall assign 8. In imbattailing he is to order his Company as the Serjeant-major shall direct him and to be himself where his Colonel or superiour Officer shall appoint him 9. In lodging he shall take that according to his degree and place in the Regiment and see that be ordered according to direction 10. He shall have his quarter kept sweet for healthfulness for quiet for order especially in the night 11. If his whole company be to march he shall draw off his company and stand in arms attending
ends of the flanque C D those parts of these strait lines F E G E cut off from the Bank-side of the Ditch towards E are the Faces of the Bulworks 1. Another way On the Centers A B the extream points of the Courtine with the distance of the same Courtine describe two Arches intersecting one another in E. 2. Produce the marginal lines of the Ditch φ 1 M L till they meet at the point H then from the ends of the flanques C D draw strait lines to the point E that may cut the marginal lines of the Ditch in F G and F E G H shall be the perfect delineation of the Raveline the faces are F E G E the Gorge Lines are F H G H. 1. Another way bisect the Gorge Lines of the Bulwork A R B Q in the points O P then draw strait lines from the points O P by the ends of the flanques C D till theâ—y meet one another in the point E. 2. Then produce the out-out-lines of the Ditch φ I M L till they meet in H and cut the former lines in F G so shall F E G H be the Ravelin required IV. The Orthographie and Ichnographie or the Profile and Plain This Table following shews the height and breadth of each part The third column shews the Orthographie of the Out-works of Breda The first and fourth shews the Orthographie of the largest The second and fifth of the middle size the sixth shews the least the four last Columns are taken out of Dogen This Table doth not serve only for Ravelins but for all manner of Out-works A Table for the building of Outworks Rhynland feet  Max. Med. Bred. Stab Min. st Temp. The lower breadth of the Ramp 40 36 44 36 24 20 The outward Talu of the Ramp 3 2 6 3 2 2 The inward Talu of the Ramp 6 4 8 6 4 4 The height of the Rampar 6 4 8 6 4 4 The upper thickness of the Ram. 31 30 30 27 18 14 The base of the Brestwork 15 15 16¼ 13 10 8 The outward Talu of the brestw 2 2 3¼ 2 2 2 The inward Talu of the Brestw 1 1 1 1 1 1 The outward height of the Brest 2 2 5 4 4 4 The inward height of the Brestw 6 6 6 6 6 6 The upper thickness of the Brest 15 12 12 10 7 5 The height of the step 1½ 1½ 1½ 1½ 1½ 1½ The breadth of the step 3 3 3 3 3 3 The Walk on the Ramp 12 10 10 1 â— 11 5 3 The rest of the foregoing Table Rhynland feet  Max. Med. Bred. Stab Min. st Temp. The border at the foot of the Ram. 3 3 6 3 3 2 The width of the Ditch 48 30 42 30 24 16 The outward Talu of the Ditch 10 8 7 8 6 4 The inward Talu of the Ditch 10 8 7 8 6 4 The depth of the Ditch 10 8 7 8 6 6 The width of the bottom of the D. 18 14 28 14 12 8 PROP. II. Of the Half-moon or Helmet I. Its definition and place HAlf-moons for the most part do not differ from Ravelins unless it be in bigness perhaps they had this name given them because those which are built before Bulworks are Arch'd in the form of a crescent on that side which lies towards the Bulwork They are placed upon the Covert-way which is beyond the Ditch so that their Capital line produced cuts the Courtine into two equal parts They are built also before the Angle of Bulworks as I said but the greatest use of them is in Irregular Fortification as I shall shew hereafter II. Their Form Let not their Angle be less then 60 degr nor more than 90 degr Let their height be but indifferent and not distant from the Rampar above Musquet-Shot that they may be defended by the Rampar When they are built on the Covert-way their faces must be 25 or 30 paces let the thickness of their Rampar be 15 or 20 feet and they must be so large as to receive 100 or 150 Souldiers III. Their Delineation 1. In the Angle of the Fauss-bray V as in a center with the distance of the breadth of the Ditch V M describe an Arch and produce the Capital line infinitely cutting the Arch in α. 2. On the other side of the Ditch cut off α X from the Capital Line produced which is â…” of the Face of the Bulwork and from the points H and λ where the Gorge lines of the Ravelins intersect one another draw unto λ the lines H X λ X. 3. Produce the faces of the Fauss-bray φ V φ V till they cut the lines H X λ X in 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and the Arch in 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or the Fichant lines of the Fauss-bray continued on 2 V 3 V may determine these Intersections So have you a half-moon delineated placed before a Bulwork whose faces are X ζ X â— and its flanques but open are 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 The delineation of other half-moons is like that of Ravelins The Orthographie and Ichnographie is had out of the foregoing proposition Chap. XIII numb 4. IV. Its Vse and Conveniency 'T is the weakest of all the out-works since it cannot entertain a good quantity of Souldiers to defend it by reason of its straits and is also with more difficulty defended from the Fortification Therefore these half-moons seem to be hurtful to the Fortification unless they be arm'd with these cautions to wit that Ravelins be built on both sides and that they consist only of Faces being altogether without flanques otherwise being possest by the Enemie they cannot be hot from the Ravelins and at last let them be every where within Musquet-Shot Yet if all this were perform'd 't will be still doubtful whether they are useful or not Wherefore they seem not to be built without peculiar necessity PROP. III. Of the Horn-work I. Its Definition and Kinds Fig. 10. THat Outwork that runs farthest into the field with two strait sides objecting to the Enemy two half-Bulworks is called a Horn-work The tenth Figure shews an example of it There are three kinds of Horn-works the first hath its sides inclining to one another towards the Field the second towards the Fortification and the third's are parallel II. Its Place and Form They are built opposite to the Courtine or the Angle of the Bulwork beyond the Out-brestwork Yet they are better defended if they cover the Courtine than if the Bulwork especially if the sides are parallel For when they cover the Bulworks with parallel sides they receive no other defence than from the Courtine and that to little purpose since at so great a distance besides after this manner the work would be too narrow Yet if they are to be placed before Bulworks 't is altogether necessary the sides should incline to one another towards the Bulworks that so they may not take in all the faces but exclude some part of them from which they may be defended
the Siege whose parts I shall briefly expound and every one distinctly by it self CHAP. XIX Of Circumvallation CIrcumvallation consists in Camps Trenches and works of all sorts The very Camps also being a lesser kind of Circumvallaiion doe comprehend the two last to wit Trenches and varietie of Works PROP. I. The disposing of the Camp or Quarters 1. THe Camp is to be form'd in those places that seem most convenient to let in an External Enemy 2. It must not be made in a place that may be drowned 3. Let there be so many that relief may be readily sent from them to all parts of the Circumvallation 4. Let them be above Cannon shot from the Town or at least so far off as that they may fear little dammage from their Guns 5. Let them be placed if you can by a River side 6. The Camp as likewise all the rest of the Circumvallation must be fortified with Trenches that is with a Rampar round about it and several other works PROP. II. Of the Lines commonly called Trenches THese Lines of the Siege are a continual kind of Rampar which surround as wel the Camp as all the rest of the places about the Town besieged Concerning these Observe this 1. Let them be twofold one inward built against the besieg'd to keep them in least with their Sallies they hurt the Besiegers the other outward to keep off any enemy that should attacque the Camp from without Let the outward be stronger than the inward nay when there is but a small Garrison in the Town these inward ones may be spared or at least very slightly built 2. These Trenches especially the outward one must not be extended above 750 feet upon a right Line After every 750 feet they must be fortified with several works cast before and betwixt them These are wont to be used Redoubts or little Turrets Middle or toothed defences outward and inward Angles Little Tonges Stars square Forts with whole Bulworks various Forts with half Bulworks whole plain Bulworks and half ones Ravelins half moons Hornworks Crownworks All this Trade of Works so various and so manifold was used in no time more than in our age nor in no place oftner than in Holland at the Siege of Hartogen Bosch at both the Sieges of Breda Mastricht and many others most of those are already delivered in the foregoing propositions we will expound those that remain in the following 3. The Profiles and Ichnography of these Trenches is various in respect of their place and danger I 'le give you three sorts of them used at the siege of Hartogen Bosch The Base of the Brestwork 7½ 7. The outward Sloap or Talu 2½ 3. The inward Sloap 1. 1. The inward height 6. 6. The outward height 5. 5. The upper part 4. 3. The width of the Step. 3. 3. The heighth of the Step. ½ ½ The Border or footing on the outside 3. 3. The width of the Ditch 12. 8. The outward Talu or Sloap of the Ditch 4. 2. The inward Sloap of the Ditch 4. 2. The depth of the Ditch 5. 2. The width at the bottom of the Ditch 4. 4. At the coming of the Royal Army the Dutch made their Circumvallation stronger they increas'd the Base of their Brestwork to 9 feet making three Steps whose widths added together made 9 feet the height of the brestwork was likewise 9 feet the width of the Ditch was 15 feet PROP. III. To build a Redoubt or Turret IT is a most easie thing since their form is simply square Therefore describe on the earth a Line of 48 feet and on it delineate a square and what you require is done The Ichnographie and Profile is after this manner It s Base 14. or 20. It s width a top 4. or 6. It s height 8. or 10. It s border or footing 2. or 3. The width of its Ditch 15. or 24. The depth of the Ditch 5. or 6. There is usually added to the Brestwork two or three Steps gradually placed over one another PROP. IV. To delineate a Star Fig. 35. To delineate a quadrangular one work after this manner 1. DEscribe on the field a Line of 48 or 50 feet and on it describe a square 2. Bisect the side A B in C and from C raise the perpendicular C D equal to ¼ of A C or 1 ◠of the whole A B. 3. Joyn A D D B if this construction be made round all the sides you 'l have a quadrangular Star Fig. 36. To have a Pentagonal Star work after this manner Describe a Regular Pentagon and from the side A B bisected in C raise the perpendicle C D equal to ⅓ of A C or ⅙ of A B. Joyn A D D B and if you do the same round the figure you will have a Pentagonal Star For a Sexangular one Describe A C E c. a Regular Hexagon Fig. X. let each of its sides A C c. be equal to about 104 paces at the ends of C H c. make the Angles D A C D C A c. 30 degrees each And D A D C will be each about 60 paces Their Ichnographie and Profiles are the same as that of Redoubts Your larger Stars are not in use PROP. V. To delineate a square Fort with half-Bulworks 1. DEscribe the square A B C D whose sides must not be less than 120 feet Fig. 37. nor more than 180. 2. Trisect the sides in E F L M Q S T V. 3. To each of the sides add ⅓ B I DN C O A H but for the Neck-lines take ⅓ in the sides themselves to wit BL D Q C T A E. 4. From the ends of the Neck-lines raise the perpendicular LK QR TX EG each of which must be ⅙ of the side 5. Draw the right lines I K N R O X H G. So have you a Fort with four half-Bulworks PROP. VI. To delineate a Fort on a Rectangular Paralellogram with half-Bulworks 1. TRisect one of the lesser sides A B Fig. 38. and cut off 1 ◠of it from all the sides for the Neck-lines A F BG C O D Q. 2. Add also to each of the sides A K B L CP DS equal to 1 ◠of A B. 3. On the ends of the Neck-lines raise the perpendicles F I G M O N Q R equal to ⅙ of the same A B. 4. Joyn K I LM PN SR I say 't is done PROP. VII To delineate another sort of Quadrilateral Fort with half Bulworks and double Tonges 1. TAke the third part of the sides of the square A B C D Fig. 39. for the Neck-lines CP A M BN RD 2. Add to the side C D on both sides ⅓ C I D K but to the sides C A D B likewise add ⅓ A S B T. 3. From the ends of the Neck-lines raise perpendicles equal to ⅙ P X M L N V R Z and joyn I X S L. T V K Z. 4. Bisect the side C D in E and
thence cut off E G E H equal to ⅓ of the side and thence again raise the perpendicle E F equal also to 1 ◠5. Joyn G F H F you have your purpose Fig. 40. There are built also square Forts with two whole Bulworks and on the opposite side the double Tonges See Fig. 40. PROP. VIII To delineate a three-sided Fort with half Bulworks Fig. 41. 1. DEscribe an equilateral Triangle A B C whose sides must be less than those of a Square 2. Cut off from the sides the third part A I B L C K for the Neck-lines 3. From the end of the Neck-lines raise perpendicularly the sixth part of the sides I H L M K G. 4. Add to the sides of the third part B D C E A F and joyn F H D M E G. you have your purpose The four Forts describ'd in the foregoing Propositions are not to be built promiscuously and for varieties sake but with choise and with respect to the place And although they are much weaker than Forts with whole Bulworks nevertheless they are conveniently made use of As to their Profile and Ichnography you may give them the same as to Redoubts and Stars or if they require a greater you may give them that which was used in the siege of Hartogen Bosch in which the base of the Rampar was 27 feet the height 6 the upper breadth of the Rampar 18 the base of the Brestwork 8 the upper breadth of the Brest-work 4 the height of the Brest-work 6 the width of the Ditch 30 feet CHAP. XX. Of Batteries for great Guns and of the Approaches THe Circumvallation being finish'd which is the first act of the Siege deliver'd in the foregoing Chapter you raise batteries for great Guns in certain places and go towards the Out-brestwork cover'd in oblique Trenches Of these therefore in this present Chapter PROP. I. To build an Offensive and Defensive Battery THere is a twofold Battery offensive and defensive Fig. 42. the last is directed towards the enemy without the first towards the besieged You shall build an Offensive one after this manner 1. Multiply the number of Guns that are to be mounted by 12 the product shall give in feet the length of the Battery for each Gun is distant from another 12. feet and the two at the ends are distant from the Brestwork 6 feet each 2. You 'l have the breadth A D if to the length of a Gun mounted in his carriage you add the space A F ten or twelve feet for the recoiling of the peice and the space F D for traversing and passage 3. Let the plat-form of the Battery be made sloaping downwards towards the Enemy that when the Guns are recoil'd they may with more ease be brought back to their places Let its entry behind be I K the way leading to it must not be very steep but gently rising that the Guns may with more ease be got in 4. That part of the Battery that faces the Enemy must be fortified with a Brest-work whose Base you may make 12 15 or 18 feet its height 6 for the sides A D B E a less width will suffice 5. Let there be so many Ports in the Brestwork as there are Guns let their height be three feet their outward width four their inward two the outward width is more than the inward that the Guns may scowr more of the field 6. Behind the Battery you must describe a space D S N E equal and like the Battery in it make a square hole as M whose side must be ten or twelve feet in which the powder must be kept and you must cover the mouth with leather least any sparks should fall in To conclude as well about the Battery it self A E as the space D N you must make a Ditch eight or ten feet wide six feet deep 7. The first Batteries are wont to be raised at a Musquet-shot from the Town afterwads near the very ditches the general rule may be this that the nearer they are the place they do the greater execution 8. The Defensive Batteries are not so full of work their Brestwork if it be made of earth may be six or seven feet thick the height is sufficient if it cover a Gun in its carriage instead of an earthen Brestwork they use commonly great wicker Baskets fil'd with earth PROP. II. To direct the Lines of Approaches to a place Besieged 1. ABout the distance of a thousand feet from the Town open the Trench 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Fig. 43. which you must carry on obliquely towards the place besieged so that it may not be scowred from any part of it which being continued some space you must dig a new one the other way as 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 with the same obliqueness and so by several turnings you proceed to the Out-brestwork it self where at length the Approaches are finish'd drawing two Trenches 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 longer than ordinary and parallel to the place besieged These two last Lines cover the Besiegers like a Brest-work so that being so near at hand they frighten away the Defendants from guarding their Graft and Rampar 2. Although the Approaches ought so to be carried on that they may never be scowred from the Enemies Rampar yet the Engineer shall take good heed he make them no more obliquer than needs to the loss of time and expences I think with two turnings you may alwayes come to the out-brestwork a far shorter way than if more oblique lines had been made For let there be drawn from the point where you began your Approaches the right line 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which continued may fall a little without the Angle of the brestwork and if another line be produced from β which goes without the Angles of the out-brestwork you will arrive at the out-brestwork in two turnings 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 but why this way of Approaches is less used I think this to be the reason That your long lines of Approach if attempted may be sooner carried and demolish'd by the Enemy than those that are cut in and out with several windings 3. At the end of every Line you must build Redoubts after such a manner that two may be flanqued by one for this is the best situation of Redoubts If one of the Lines be drawn longer than ordinary you may also build Redoubts in the middle for its defence all which the 43 Figure sufficiently expresses 4. The earth which is cast out is thrown towards the Enemy that it may be instead of a Brestwork to the Pioneers Let its Tower width be six feet its upper twelve or fifteen it s least depth must be such that may cover a standing man with the height of its Brestwork joyn'd to it The nearer they advance to the Town tht deeper they must be The width also must be increas'd if there is occasion to bring stuff for the Gallery thorough the Trenches They use frequently to
ANGLES PLANS tousiours compris par deux costez de trente Pieds Angles Bases  1  2  3  4 10 5  6  7  8  9 20 10  11  12  13  14 30 15  16  17  18  19 40 20  21  22    23  24 50 25  26  26  28  29 60 30  31  32  33 70 34  35  36  37  38 80 39  40  41 90 42    43  44  45 100 46  47  48 110 49  50  51 120 52  53 130 54  55   140 56  57 150 58 160 59 170  180 60 The Figure of a most useful Instrument by the help whereof any Poligone from a Square to a Dodecagone which is as much as is required in any Fortification may be described not only with greater expedition but likewise much more exactly than by any Sector Scale or other Instrument or Method whatsoever THE use of this Instrument is only to lay it upon your Paper and holding it fast with your left hand to mark out any Poligone therein conteined with the point of a Needle by its respective Figures and so joyn the Points And if you desire to describe a Poligone larger than the Instrument as is the Dodecagone in this Figure it is easie to continue the Lines from the said Pricks to the Circumference And if it be desired to have a Poligone less than the Instrument the reason is the same ARCHITEC MILIT 1 2 3 4 5 ARCHITEC MILIT 6 7 8 9 ARCHITEC MILIT 10 ARCHITEC MILIT 11 12 13 14 15 16 ARCHITEC MILIT 17 18 19 20 21 22 23 24 ARCHITEC MILIT 25 26 27 28 ARCHITEC MILIT 29 30 31 32 33 34 ARCHITEC MILIT 35 36 X 37 38 39 40 ARCHITEC MILIT 41 42 43 THE Compleat Gunner IN THREE PARTS PART I. Shewing the Art of Founding and Casting Pieces of Ordnance with the composition of Metal thereunto necessary The Composition and Matters of Gunpowders the Several Sorts Colours and Operation PART II. Discovers the necessary Instruments and variety of Instructions to the compleating of a Gunner with a Table of Squares and Cubes serving for the Resolution of Questions of Gunnery and other Arts. AS ALSO The way of taking Heights Distances and Profundities either with or without Instruments PART III. Shews the Nature of Fire-works the manner of Composing many that are Excellent and Useful both for Sea and Land for the defence of our selves as well as the offence of our Enemies Translated out of Casimir Diego Vffano Hexam and other Authors To which is added the Doctrine of Projects applyed to Gunnery by those late famous Authors Galilaeus and Torricellio now rendred into English TOGETHER WITH Some Excellent Observations out of Mersennus and other famous Authors LONDON Printed for Rob. Pawlet Tho. Passinger and Benj. Hurlock 1672. TO THE READER Courteous Reader AMong Arts and Sciences Mathematical Gunnery will not deserve the least respect which has been practised for many years as you may read in the first Chapter of this Book where we treat of its Original and from time to time Necessity and Art together have produced many new Invention so that some may judge it almost impossible to add more unto this Art and are ready to say of this as of other Studies Nil dictum quod non dictum prius But we have not only indeavoured the inquisition into the most knowing Professors of these Arts both German Italian Frenchmen Netherlander c. from whence we have drawn the more Excellent and useful parts which were never before in our English Tongue but may boldly adventure to call some things in it new And finding the great Occasion which these present times do require in the knowledge of these things made me the readier to compose this Work adjudging it a very great injury to our Country-men to be deprived of the knowledge of such things which are of so great importance in this very juncture of time I did therefore incourage my self in this Work hoping my endeavours in the same will shew my willingness to serve my Countrey-men And as it is the part of wise men not to censure any thing without a good consideration and a perfect knowledge of the subject upon which they ought to ground their judgment So also I hope you will not blame my Indeavours when you have judiciously examined the same I have divided it into three Parts endeavouring that it might be imperfect in nothing that is necessary to this Art or useful for a Gunner to know I will assure you that I have no other end in publishing this Treatise than what I have mentioned before I shall only crave your pardon for the faults that may be committed in the Printing as being not there present at the Correction of any part of it my occasions calling me other wayes yet I hope their care was so much that the faults are not material or at most not so much but your Courtesie may supply that defect So I recommend this Work to your good reception and bid you farewell W.T. THE Compleat Gunner CHAP. I. Treating of the Earth necessary in making of Molds for the Casting of Pieces of Ordnance with the manner of Casting c. WE will not dispute of the first Invention of Guns that is whether it came from Archimedes as the Italians do report or from an Englishman or from a Monk for this knowledge matters not much to the Art nor is it of any profitable signification to the Artist especially considering that Authors do not really consent in this thing Our intent is therefore not to trouble the ingenious Students with vain uncertain repetitions but to compose a compleat Piece of Gunnery and therein to discourse from the beginning to the end all that is necessary to be known or learned after the knowledge of common Arithmetick by one that intends to be a perfect Proficient in the said Art We do suppose it therefore necessary for a Master Gunner to know first the making of Molds and casting of Pieces Therefore I shall first begin to discourse of the property and Nature of the Earth fit for casting or making Molds for this is of great moment considering that many or indeed most Earths are not for this purpose for the Earth fit for the casting of Pieces of Ordnance must be such as will not be melted or fuse although it be put into a very great fire but must remain firm and hard and these Earths are generally of a Reddish or Iron-like colour which is well known to many Potters especially such as make Chymical Vessels The Earth being obtained it must be sifted and cast up after the usual manner as men do in the making of Morter then let it be moistned with an Alchalated Water especially such as is made of Niter
be necessary to put planks or some solid thing under the Ghynne and Pins to stay them but this as necessity shall require Now the Ghynne firmly placed and setled the Gunner must get up by the Ladder or some Steps to the head or top of it having the Rope in his hand shall put it through the uppermost truckle of the head and let it fall down to another man again that he may catch it that he may put it through one side of the Piece to fasten it into the Ears of the Piece and so having put it through them he may draw it up until he can give it him that is above and then put it through the other hole of the Truckle and give it to him that is under him who must reach it again to him that is above and so fasten it to the head of the Ghynne giving it some turns until it come under the uppermost Truckle This done he must fasten it with great diligence to the lower Truckle by putting the Ears as through the Ring which is under the said Truckle after this begin to Hoyse your Peice and in the Hoysing put a spar or some such thing into the mouth of the Peice so that thereby it may be governed and may not sway from one side to the other which would be dangerous for if it should strike against the Rouler or any one of the feet of the Gynne it may break all and so spoil both the work and the men tending upon it Therefore I say be sure that those who stand by the Spar be careful in guiding the Piece and keeping it steddy and right until the weight of the Piece is well setled a diligent Eye being had all this while that neither the feet of the Gynne nor Rope give way and be sure every part of the Rope draw equal and that there be no Knicks or that they be not tangled one amongst another and for that purpose when they begin to hoyse the Piece blows must be given upon the Tackling until it be set tort and all bear equal But if you should perceive that the Ghynne or any part give way presently let your Piece sink and underlay and settle well the feet of the Ghynne and that as gently as may be to the end the Cross beam or Rouler may not be disjoyned or broken Then wind it up carefully and very gently by the help of two men onely and in such a manner as when one of the Leavers is brought down it must be held there fast until the other has got purchase and then must this other also be brought down this must be reiterated so often until it be so high that the Carriage may be placed under it so that the Trunions may fall into the Sockets or holes of the Carriage and then Guide the Piece by the Spar so that it fall easily in and so rest it self in the Carriage and then let it be well clasped over and then locked in and fastned with Forelocks and so you may draw away your Piece where you please On board Ships this Ghynne is not of use it being the Boatswains business to fix a Tackle that may be able to hoist up any Piece into its Carriage the Slings one part must come about the Casacabel and the other part about a Billet so made that it may fit in at the Muzzle and by strength of hands or by help of a Windless or Capstain it may be hoysed up so that the Carriage may be brought under so that the Gun being Loared its Trunions may fall into the holes of the Carriage which then clasp over with its Iron Clasps let them be Forelocked and then with Hand-Tackles be brought where you please See the Figure of the Gynne and the Field and Ship-Pieces mounted in the Figure 11. CHAP. VI. The way to draw a Piece of Ordnance with the necessary things thereunto belonging both for Land and Sea SEeing we have discovered the way of Casting a Piece and Mounting it in its Carriage it follows in the next place that in this Chapter we treat of and shew the manner of drawing them from place to place for Service where care must be taken what the way is that you are to pass for if the way be foul moorish and dirty there is then required as many more Horses as in good wayes That is For a whole Cannon of 8000 l. you may use 15 couple of Horses besides the Tyllar For a Demi-Cannon of about 6000 l. you may use 11 couple of Horses besides the Tyllar For a Piece of 4000 l. weight you may use 8 couple of Horses besides the Tyllar For a Field Piece of about 3000 l. use 6 couple of Horses besides the Tyllar For a Saker of 1800 l. weight you may use 4 couple of Horses besides the Tyllar For a Piece of 1500 l. weight you may use 3 couple of Horses besides the Tyllar For a Faucon two couple of Horses besides the Tyllar For a small Drake of about 250 l. one Horse will serve and by the same Rule you may find how many Horses will draw any weight whatsoever Many times when Horses are wanting men are made use of Upon such occasions you must divide your men into three drawing files according to the greatness of the Piece now to the end the Ranks may spread and every man may draw equally alike fasten to the end of the Carriage a Cross beam or bar to which you must fasten the drawing Ropes equally at such distance that one may not impead the other and let there be besure one to steer the Piece when you come to any winding or turning If the drawing Ropes be long 't is necessary to cross it with Ropes or some light peeces of wood like a Ladder with two or more cross peeces let them be made fast for the better and more steady drawing and to every there must be a Neck-line fastned to the Ropes and so to cast over every mans Sholders in manner as is used to draw our Western Barges And you must know your proportion of men fit to draw any Piece of Ordnance and that must be regulated according to the goodness or badness of the way and so more or less men allowing every man to draw about 50 60 or 80 pounds for 't is supposed a man may draw in ordinary way 50 or 60 pounds but in very good way more than 80 pounds however 't is good to have men enough Let the Spunge Ladle c. be made fast along the Piece to the Ring and Britch end Sometimes by reason of the unevenness steepness or other defects of the way it sometimes happens that you may be forc'd to dismount your Piece and remount it again there 't is necessary every Gunner have with him a Ghynne a Wynche and all appurtenances necessary thereunto As to the Sea Gunner on board Ship their occasions require no more than the Wynch and their Piece being mounted according to the
the bore and dividing it into two equal parts then with a Plumb line hanging over the mouth of the Piece being guided by the divided stick you shall have good aim where to set your Dispart this being done go to the Base Ring if the Piece be true bored then find which is the highest part and middle of that Ring but if the Piece be not true bored then find which part of the Base Ring is just over the Cylender and take that for your true line when you have found out the dispart and placed it and also found what point in the Base Ring is to answer to it then make some very small mark on the Base Ring in that place hold your head about two foot from the Base Ring and there you may best observe as the Piece is traversing when you are in a direct line with the mark this done give one of your men order to raise and fall the Piece with his Hand-spike as you shall appoint him until you can holding your head two foot from the Britch of the Piece with your eye perceive the mark at the Base Ring and the top of the dispart in a direct line with the mark you must shoot at at that instant stop the motion of the Piece with a Coyn that it may remain as you have directed it then Prime your Piece and give fire Before you place your Dispart you are to take notice whether the ground be Level whereon the Wheels of the Gun stand or if they be not one higher than the other and if the Trunions stand just over the Axeltree of the Wheels or no whether one Trunion lye higher on the Carriage than the other whether the Gun be truely placed in the Carriage or not that is that it be not nearer one side than the other whether the Carriage be truly made according to the direction we have already prescribed in the first part whether the Axeltree be placed just cross the Carriage or not CHAP. XVII How if a Shot do carry to the right or to the left under or over the mark by reason of some known fault to amend it in making the next Shot AFter you have made one Shot and find the Piece carry just over the mark then do all that has been taught again and when your Piece lyes directly against the mark observe how much the last stroak of the Shot is above the mark so much longer make your dispart that the top of it may be just seen from the Britch of the Piece in a direct line with the stroke of the Shot when it is of this length then level your Piece with this new dispart to the assigned mark Give fire and without doubt it will strike the same If the first Shot strike under the mark then bring the Piece in all points as before to pass mark how much of the dispart is over the stroke of the Shot and cut it just so short as being at the Britch you may discern the top of it with the mark on the Base Ring and stroke of the Shot in a just right line and when you perceive it is of such a length level the Piece to the assigned mark as at the first then Prime and Give fire If the first Shot strike on the right hand of the mark to mend it you must level the Piece as formerly you standing behind the Britch of the Piece observe the stroke of the Shot over the dispart and that part of the Base Ring as you at that instant look over in a right line towards the dispart and the stroke of the Shot set up in that place a Pin with a little soft Wax on the Base Ring so this Pin will be in a right line with the dispart and stroke of the Shot This being done level your Piece to the mark assigned by this Pin and the dispart and without question you will make a fair Shot for when you level by the Metal of the Base Ring where the Pin is placed and the mark of the Piece standing at that direction look over the top of the dispart from the notch in the Base Ring and you shall find it to lye just so much to the left as the former Shot struck to the right from the assigned mark which should in all likelyhood now strike the mark But if a Shot be both too wide and too low then you must use both the directions above taught to make the next Shot first regulate the dispart by cutting it shorter according as the Shots mark is lower than the assigned mark when this is done then proceed to my directions to mend shooting wide and these things performed with care and diligence cannot choose but mend a bad Shot CHAP. XVIII Of shooting at Random at a Mark beyond the right line of the Pieces reach or right Range of a Shot and the way of framing a Table of Randoms by help of the Gunners Quadrant FOr the effecting of this matter we must have a Quadrant with a Thread and Plummet which is described in the first Chapter of this second Section to one side of this Quadrant so that one end of the Ruler may go into the Cavity of the Piece and let a Piece of Lead be fastned to the end of the Rule to make it lye close to the bottom of the Metal within the Quadrant hanging without and the plumb-Plumb-line swaying or hanging down from the Center of the Quadrant perpendicular to the Horizontal line for the Quadrant being thus placed you may mount a Piece to what degree you shall find fit to shoot by Now every one that will learn to shoot at Random must draw his Piece on a level ground where first shooting level he must observe that distance in feet or paces then mount his Piece to one degree and mark where that shall graze thus finding the distance of every degree from the level to the tenth degree by these distances make a Table to which annex the degrees against the distance by which Table you may using the Art of Proportions find how far another Piece will convey her Shot from degree to degree and in Loading your Piece for this work you must have your Powder exactly weighed and likewise the Wad and let the Piece cool of it self and this you must do every time and if the Piece be mounted there needs no Wad after the Shot also you must have a special care of the strength of the Powder and let the Powder equally and with the same force and strength be pressed home as near as possible you may CHAP. XIX An effectual way to make a Shot out of a Piece of Ordnance at Random HE that intends to be expert at these things ought principally to endeavour at one time or another to obtain so much liberty of his Superior Commanders as to make two three or more Shot with the Piece he chooseth or intends for most Service then must he measure the distance from the Platform