Selected quad for the lemma: reason_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
reason_n	angle_n	equal_a	line_n	4,117	5	11.1250	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A39333	The compleat body of the art military in three books : I. The postures of the pike and musket ..., II. Twelve exercises ..., III. The drawing up and exercising of regiments after the manner of private companies ... : also, the duties of all souldiers and officers ... / by Richard Elton ... ; to which is added a supplement comprehending these particulars, I. the duties and qualifications of all officers belonging to an army .., formerly written by Capt. Tho. Rudd ...	Elton, Richard, fl. 1650.; Rudd, Thomas, 1584?-1656.	1668 (1668)	Wing E655	278,856	257

the setting of the Angles both which Scales may be upon one and the same Ruler First Take from your Scale of equal parts 484 which you shall find under V in the line of Semi-diameters and with the length describe the Circle A F B E then take from the same Scale 569 which is under V in the Line of the interior Polygon and this will reach in the Circle from B to B and will divide it into five equal parts according to the number of Sides of the Fort. Secondly Set off from the Point B B I equal to 104 which shall be the Gorge and Neck from the point I erect two Penpendiculars I G H and I H to the line B B making I H 87 parts of the Scale which is in the line under V belonging to the first Wing Lastly Make B G 207 which is your Capital Line and draw H G compleating your Bulwark And in this manner may you finish all the several Bastions of this or any other Fort working according to the Measures belonging to that Polygon you are to fortify But it may so fall out sometimes that you cannot readily find the Centre of your Figure by reason some House or other obstacle may stand in the way so that you will be troubled to draw the Line A G upon which your Capital line is taken nor perhaps know what Angle it makes with the Polygon interior continued though in truth that Angle is always equal to half your Angle of Circumference you may make use of your Table and find the quantity of the Angle contained between the Wing continued and the Face namely the Angle G H F in the Figure which in this Example will be found to be 70 degrees 30 minutes This being set off on both sides you may finish your Bastion without help of the Capital Line This done draw lines parallel to the Face of your Bastion delineate your Ditch which is to be made round about your Fort as you see in the second Figure which is the side of a Pentagon fortified Concerning the farther strengthning of your Fort by Half-Moons Horn-works Redoubts c. YOur Fort thus finished you may farther strengthen it with Half-Moons Ravelines Horn-works Redoubts and such like according as the place shall require and the number of Souldiers you have for defence will permit I. Of the Half-Moon A Half-Moon hath either relation to the Curtain or Bastion and in the second Figure are marked with ☽ that which hath relation to the Curtain is properly called a Raveline and that at the point of the Bastion a Half-Moon How to delineate a Raveline Divide the Curtain into two equal parts by the perpendicular n o from p the middle of your Wing draw p o p o and from o their intersection set off o q equal to the Wing of your Bastion H I or thereabouts but this is left to the discretion of the Enginier as also at what distance they shall be made from the Curtain or Bastion But he must not make the Angle of the Raveline too acute but so to proportion the distance that the Angle may be neer or equal to the Angle of the Bastion The Half-Moon is alike with the Raveline but that it hath relation to the Bastion and is drawn after the same manner all which is plain in the second Figure where the Half-Moons are marked with ☽ II. Of the Horn-work The Horn-work is most conveniently defended from the face of your Bastion which if you intend to do make H F equal or neer equal to G L your line of defence and draw F F which shall be equal to I I your Curtain and let M L the Curtain of your Horn-work be about one third part of I I but somewhat more viz. 130 such parts as your Curtain is 360 or more if you please to 150 and from n the middle of F F set off n o n o equal to 65 of your Scale and draw o m o l right Angles at o. Then set off the Angles F K S each of them 65 deg as you would have the Angle of your Horn-work contain Draw the Lines F S and F S and bisect the Angles S F F which shall cut off F K equal to M L the Curtain of your Horn-work of which k m k l shall be the Wings Of Irregular Fortifications TOuching Irregular Fortifications I can give no new Precept only in the general it is best if possible to reduce them to regular Forms but if the place will not permit it take first the Plot of the place and observe what Angles are made between every two sides thereof Then look in the Table in the cell of the Angles of Polygons and see what Polygon the observed Angle comes neerest to and make that Bastion according to the measures belonging to that Polygon and so of the rest so shall you have unequal Bastions but alike defensible Wherein likewise it is be noted that if the two sides of your interior Polygon be of unequal length the Bastion is best framed according to the measures taken upon the shorter side Example Let it be required to draw Bastions to the side of an inordinate Pentagon whose Angles are as they are marked in the third Figure First I observe 134 the Angle comprehended between two of the sides comes neerest to the Angle of an Octagon in the Cell of the Angles of Polygons I conclude therefore that Bastion is to be drawn according to the measures belonging to an Octagon taking the measures from the shortest side A B. Now because the measures of the Polygon interior belong to an Octagon is 614 you must make a Scale of which 614 parts shall be equal to A B then set off the Neck or Gorge A E B E 127 such parts as A B is 614 then measure 106 for the Wing Lastly because the Center of the Figure is not known by which the measure of the Capital line should be taken I take the Angle between the Wing prolonged and the Face and take off 240 such parts as the Curtain is 360 and so finish the Bastion belonging to the Angle 134 The next Angle 113 which is neerest to a Hexagon therefore that Bastion must be framed from the shorter side according to the measures of a Hexagon and so must all the Angles be fortified by those measures which come neerest to the Angle comprehended between the sides thereof But in all Irregular Fortifications much is attributed to the judgment of the Enginier either to increase or diminish the Angles as he finds most convenient but in such manner as the line of defence may scoure the face of the Bastion and that one part thereof may defend and be defended by the other It now remains to treat of the manner of making of Ditches about Forts of the quantity of earth required to make a Fort with Walls of any determined breadth and height as also what inclinations they ought to have both on the inside

And always the Captain ought to march his company after this manner all abrest provided he have ground sufficient for the same And being far more graceful so to do then to march them stragling upon a long march for it doth represent in some kind the manner of marching of a Regiment and at such times the Serjeants are to march upon the Angles as is before described moving to and again sometimes upon the Flanks and causing the Souldiers to keep their Distance of order in File and open order in Rank and to march all even abrest and after to return again unto their places CHAP. XXIV Before I come to make description of a Body I shall shew some further Reasons of the Serjeants places of lesser Companies with the placing of the Drums IT happens many times some Companies falls not out so large as is before set forth and that they have but three Serjeants and therefore it would be known when that they have but one Division of Muskettiers in the Van two Divisions of Pikes and one Division of Muskettiers in the Reer which is the Reer-Guard where then the placing of these three Serjeants and three Drums shall be upon their long March and where to be marching all abrest To which I answer in the first place the youngest Serjeant is always to attend the Captain and having no Division to lead he is to be upon the right Angle of the Front there expecting his Captains pleasure and commands and the second Serjeant is to lead the second Division of Pikes and the eldest Serjeant to lead the last Division of Muskettiers or the Reer-Guard here are their places upon the long march But when they are drawn up and so march even abrest the youngest Serjeants place as is before exprest is to march upon the right Angle in the Front and the eldest upon the left the second Serjeant is to march in the right Angle in the Reer They having their places thus stated are to move sometimes up and down upon the Flanks in their marching causing the Souldiers to keep their due distance of order in File and open order in Rank and to march even abrest and after they may return to their places again But here methinks I meet with some Objector by the way who saith the eldest is much wronged herein for that it is his proper place to be upon the right that when Forlorns are drawn off against an Enemy he is there ready first to lead them on claiming it as his due to give the first on set and therefore far more honour for him to be on the right then on the left and the eldest Serjeant rather placed on the left then on the right As for the second Serjeants place 't is fit he should be in the Reer to assist the Lieutenant there he having none but he to help him if any occasion should require To which I answer that it is the youngest Serjeants place to be upon the right Angle either upon a Stand or upon a March and not the eldest for these reasons following The youngest Serjeant is not placed there for any honour that it is to him for he hath no Division at all to lead upon the March except the Company be very great and if so he is placed so near the Captain to be serviceable to him to carry and convey his pleasures unto all the rest of the Officers As for the leading of the Van-guard upon the March the Captain takes that place unto himself and it is far more honour unto the eldest Serjeant to be a Leader of the Reer-guard or entirely the left Flank then to lead a Subdivision of Pikes And besides that it is properest for his place to be upon the left when they are all drawn up upon a brest for these two reasons as first he is thereupon in readiness to take his due place upon the sub-dividing on the long March and again upon a Stand when they are all drawn up and ready to engage against an Enemy and the Forlorns to be drawn forth equally alike from both Flanks he is then as ready in the Front to execute his Captains Commands the youngest Serjeant being likewise sent to be something helpful to him and attending after for further order from his Captain to send him relief by the second Serjeant as occasion shall require So that in my judgement take it either upon the long March or otherwise when drawn all up even abrest all things are so stated for his due honour and place that he hath no reason to complain nor any of the rest having all their due and proper places which doth belong unto them As for the placing of the Drums upon the long March every Division ought to have his Drums fall between such Ranks as before exprest excepting only the second Division of Pikes which may be excused when they are to beat a March as being all drawn up they are to fall in two to beat even abrest upon the right and one upon the left as is before set down If it should chance further in a Company to be so small to have but three Divisions that is to say one Division of Muskettiers in the Van the Body of Pikes in the midst and another Division of Muskettiers to bring up the Reer-guard and having but two Serjeants and two Drums the youngest Serjeants place will be as before mentioned upon the right in the Front and the eldest Serjeant upon the left and to take his place to lead the last Division of Muskettiers upon the long March and the first Drum to beat in the first Division of Muskettiers and the second to beat and to march along amongst the Pikes I have a little more enlarged my self in this Discourse of placing of the Serjeants then I at first intended but meeting many times with several Souldiers desiring satisfaction in every one of these particulars I shall perhaps undergo here the hard censure of some for this my tedious Discourse but such others which desire to be knowing herein I hope they will have a more favourable opinion of my good meaning unto them And here I shall conclude for the present concerning the particular places of the Serjeants in every private Company and now supposing as by order from the Captain the Serjeants have brought up their Divisions standing again as before expecting something more to be spoken unto them they silently stand to hear what follows CHAP. XXIV A Description of a Body of men throughout with all their several parts and kinds IT is very necessary knowledge to every particular Souldier to be acquainted throughout with all the parts of a Body of men drawn up with their several extents and bounds and with the true understanding of the same Where first note the Description of Files a File is a Sequence of men consisting of Leaders and Followers from the first unto the last the joyning of Files flank-wise maketh Ranks and is the compleating up of a