The gentlemans recreation in two parts : the first being an encyclopedy of the arts and sciences ... the second part treats of horsmanship, hawking, hunting, fowling, fishing, and agriculture : with a short treatise of cock-fighting ... : all which are collected from the most authentick authors, and the many gross errors therein corrected, with great enlargements ... : and for the better explanation thereof, great variety of useful sculptures, as nets, traps, engines, &c. are added for the taking of beasts, fowl and fish : not hitherto published by any : the whole illustrated with about an hundred ornamental and useful sculptures engraven in copper, relating to the several subjects.
Blome, Richard, d. 1705.

CHAP. III.

Of Regular Fortification. [ 50]

IN the construction of Regular Figures, and how to Fortify them according to the most modern ways used by the Italians, French and Dutch, with the Methods of some Modern Au∣thors.

Regular Fortification is that which is made upon Equiangular, and Equilateral Figures described in a [ 60] Circle, such as a Triangle, Quadrangle, or four∣square Pentagone, or five-sided Figure to a Do∣decagone, or twelve-sided Figure; the Bastions be∣ing so placed that the Points of them are alike distant, from the Center; the Curtains of one length, and all the other Lines and Angles of one Form, and greatness.

Regular Figures are made by calculating the Angle at the Center, which is by dividing 360, the number of Degrees, a Circle is always di∣vided into, and in which the Regular Figure is described by the number of the sides of any Polygone, or Regular Figure the Fort is to consist of. The Quotient shews the Angle of the Center. As in this Example of a Pentagone, or 5 sided Figure. By the operation the Angle of the Center, is found to be 72 Degrees, and so of any other Figure. Then if with a Protractor, or a Line of Chords you draw a Circle, and set off the Angle at the Center, as in the Example 72 Degrees, it will divide the Circle exactly into 5 equal Parts, on which strait Lines drawn from one Point to another, gives the sides of a Penta∣gone.

The Protractor is described in the Treatise of Geometry, viz. surveying, and is nothing else but a Semicircle made on Brass, or Horn divided in∣to 180 Degrees.

The Line of Chords is the fourth part of a Circle, or 90 Degrees, projected on a strait Line, such as are always upon any plain Scale.

The Radius, or Semidiameter of a Circle, for which this Line shews the Degrees, is always represented by the Brasen Point at 60 Degrees on the same Line, and if with your Compasses you take from the Line of Chords 60 Degrees, and draw a Circle 72 Degrees, taken from off the same Line, will go 5 times exactly round the Cir∣cle, and so of any other Figure.

Of the Italian Method according to P. Sardi.

THis Author being learned, and much ex∣perienced in the Wars in his time, has wrote much, and to good purpose; so that I choose him as the most approved of the Italian Authors. He makes the Interior Polygone 800, Venetian or Geometrical Feet, (which makes 921 of the English,) the Demi-Gorges 150, and the Flanks also 150, so that the Gorges and Flanks are equal, and in English Feet make 172 1/2 for each, which is betwixt a 1/5 and 1/6 part of the Interior Polygone; He raises the Flanks Perpendicular to the Curtain; and to set off the Faces and Angles of the Bastions in a Square and Pentagone, he makes the Line of Defence fall on a 1/10 of the Curtain in the Hexagone, or a 1/4 Part; in a 7, 8, and 9 sided Figures on a 1/3; and in all above on the half. In this Example of a Hex∣agone, divide the Curtain into 4 equal Parts, from N. which is 1/4 of it, draw a Line by the Top of the Flank, until it cut the Radius prolonged in the Point a, so you have the stringent Line of Defence, the Face of the Bastion, and the Angle required, and so a Polygone.

To reduce this construction to the second Maxim, you are to find the particular Measures by the Rule of Proportion, thus.

If 800 Venetian Feet, give 150 for the Gorge, how much will 921 English Feet give? Answer 172. Then again, If 921 English Feet give 172 for the Gorge, how much will 720 give? Answer 134.

After this manner all the rest of the Parts are found out.

Page  174

Now to the Construction. Plate 1. Figure 3.

IN the Hexagone drawn as before taught on the side mark't P. Sardi, divide the side P, P, into 720 Parts, at 134, or cc, make a Mark for the Demi-Gorges, set up Perpendicular to the Curtain; the same Measure for the Flanks c, f, and draw the Faces as before. These parts may be taken off from any Sector, or Joynt Ruler, or [ 10] from any Diagonal Scale of an Inch, or 1/2 an Inch divided into 100 Parts.

In a Book of Military Architecture entituled Corona Imperialis written by this Author, he sets Cazemats and Orillons on the Flanks; Of which in their place.

Of the French Method as it is by Manesson Mallet Author of the Travaux de Mars. Plate 1. Figure 3. [ 20]

THis Author observes the same Rules for the construction of all the Regular Figures, as are here given in this Example of a Hexa∣gone.

Having drawn the Polygone PP, extend the Semidiameters by the extremities of the side of the Polygone marked M. Mallet; divide the side P, P, into 3 equal parts; set one of these parts, on the extended Semidiameter or Radius from [ 30] P, to A, for the Capitals; take a fifth part of the Polygone, for the Demi-Gorges, set it from P, to C, to make the Faces and Flanks draw the Strin∣gent Line of Defence, from the Capital to the extremity of the Gorge, and raise the Flanks at an Angle of 98, or 100 Degrees with the Cur∣tain; where they cut the Line of Defence deter∣mines the length of the Flanks and Faces, as c, f, and f, A; With the length of this Face you may compleat a Polygone all round by Transfer∣ing [ 40] it to the other Lines of Defence.

This Author hath no second Flank, he makes the Stringent Line of Defence, 120 Toises, or Fathoms (allowing 6 Feet to a Fathom) which is 720 Feet.

See Travaux de Mars by this Author of de Ville, and Furnier's Method. Plate 1. Figure 3.

THey Divide the Interior Polygone into 6 e∣qual [ 50] parts, and take one of them for the Demi-Gorge and Flanks Pc, cf, both being e∣qual, and at right Angles to the Curtain, for draw∣ing the Faces of the square, and Pentagone, lay a Ruler from the extremity of the Gorge C, by the Top of the Flank f, until it cut the Capital in A; These have no Flanks.

For the Hexagone, and all Figures above it, joyn ff, by a Line; the Capital will divide it into two equal parts at e, as a Center draw the [ 60] Circle f, A, f, at the Distance af, where it cuts the Capital at A, draw af, for the Faces.

These Authors make their Interior Polygone or Line of Defence 150 Toises, or 960 English Feet.

This Method is to be reduced to the second Maxim by the former Rules.

See De Ville's Ingenieur Perfail, and Furniers Architecture Military.

Of the Dutch Method, as it is abridged by the Emperor Ferdinand the Third; with an Account of the Construction of the Fortifications at the Grave in Holland. Plate 1 Figure 3.

THe Dutch have been as famous for their experience in Fortification, as their Coun∣trey at present is for their fortifyed Towns; and by their Engineers, as Dogen, Marolois, &c. have filled the World full of their Books, and ways of Fortifying; altho they might have saved them∣selves the trouble, and laborious pains in cal∣culating Triangles, and other Mathematical Learning, more for curiosity than use in this mat∣ter. For which reason the Emperor Ferdinand the Third found out Rules approved of, by turn∣ing their Fortifications out of the way of calcula∣ting Angles into Lines. He sets down this univer∣sal way of drawing the Lines of any Fort.

'Tis to be taken as a Rule, That if the Interior Polygone be 66 of any Measure, the Gorge must be 15, the Flank 12, and the Capital 24.

Now in proportion according to the second Maxim, If the Polygone be 720 Feet, the Capital will be 261 Feet, 9 Inches, the Gorge 163 Feet 7 Inches, the Flank 130 Feet 10 Inches, which is to be set at right Angles with the Curtain; thus by taking of these proportions from the Sector, you may fortify any Figure according to this Method.

This is an abridgment or Epitomy of all the Dutch Fortifications, except the Square, which hath no second Flank.

See Schottus Edition of Amussis Ferdinandea.

The construction of the Fortification of the Grave according to Monsieur Storf.

HAving drawn the Exterior Polygone AB, of 94 Rods, and divided it into two equal parts in C, let fall the Perpendicular CD, of 15 2/3 Rods, which is 1/6 of the Exterior Polygone; then from the Points AB, draw the Lines of Defence ae, and BY, through D, infinitely; divide the Perpendicular CD, into two equal parts at F, by which draw FG, Parallel to AB, cutting the Line of Defence in the Point G, which determines the Face AG. Then for the Point F, at the interval FG, describe the Arch IH, and from the Point G, at the distance of 15 Rods des∣cribe IL, cutting the other in the Point I, which shall be the extremity of the Curtain, and of the Line of Defence BI; To trace the Circular Flanks and Oreillons, divide the Flank GI, into 3 equal parts, one of which is for the Oreillon, and the other two the length of the lower Flank. Let also BN, be 1/3 of the Face BZ, and draw NO, infinitely, by the Points N and M, on which take MP, of 2 Rods; then draw IP, with the distance IP; From the Points P and I, describe 2 Arches cutting one another in Q▪ which shall be the Center of the low and high Circular Flanks; let the Interval of them be a Rod; draw RV, Parallel to MO, and at the Interval QP, or QI, draw the Arch R, S, I; and having taken ST, of 5 Rods draw the Arch VX, make X Y, 2 Rods;Page  [unnumbered]

[illustration]
The Ichnographicall and Scenographicall Lines of a FORT. Plate 1.
Page  [unnumbered]Page  175 so you have traced the two Circular Flanks. For the Oreillon find the Center W, which is the half of GM, and describing the Arch of a Circle, at the distance WM, it comes to touch the Face prolonged in the Point 2.
[illustration]
[ 10]

Or the Construction may be more short thus: Having drawn as before the Exterior Polygone, the Perpendicular, and the two Lines of Defence, take for every one of 69 Rods 3 feet; take for the Face 25 Rods, and having drawn the Flanks at the [ 20] exetremity of the Lines of Defence to the extre∣mity of the Face, the rest you will find as be∣fore, or insensibly near.

The Method according to Count Pagen. Plate 1. Figure 3.

THis Author in his retirement after having been unfortunately Shot in the Eye at the Siege of Arras, wrote a great many good things [ 30] on this Subject.

He takes a Method quite contrary to any that wrote before him; he works by the outward, or Exterior Polygone, and sets his Flanks Perpendi∣cularly to the Lines of Defence; he divides Forts into Royal, Mean, and small Royal.

Royal, when the Exterior Polygone is 200 Fa∣thoms, or 1200 Feet. Mean, when the Exterior Polygone is 180 Fathoms. And small Royal, when the Exterior Polygone is 160 Fathoms. [ 40]

The Example shall be for a great Royal. The Con∣struction is as followeth.

DIvide the Exterior Polygone AA, into two equal parts at M, each being 600 Feet; on M,aise a Perpendicular MM, take 180 Feet, or 30 Fathoms, and set it on the Perpendicular from M to T; then draw A, T, C, for the Lines of Defence, from A, set at AF, 60 Fathoms, or [ 50] 360 Feet; from f, let fall a Perpendicular on the Line of Defence at c, or from T, set of 222 Feet; joyn cc, for the Curtain, upon the Points aa, set at the half of the Angle of the Figure aoa, as in the Hexagone 60 Degrees, that will determin the Centero; set of the Gorge PC, and the Capital Pa, which you may Measure on the same Scale with the rest, and know the length of them in Feet.

For the Mean Royal work, as before; Take 30 [ 60] Fathoms, or 180 Feet for MF, the Perpendicular, 55 Fathoms for the Faces, 32 Fathoms for Tc, or 192 Feet; the Flanks will be found to be 24 Fathoms.

For the small Royal, Take 30, Fathoms, or 180 Feet for the Perpendicular MT; 50 Fathoms, or 300 Feet for the Faces, 27 Fathoms or 162 Feet for Tc; the Flanks will be found to be 23 Fathoms, or 138 Feet, and are at right Angles, or 90 Degrees with the Line of Defence.

See Fortification de Pagen printed at Paris.

The Method of Monsieur * * * Plate 1. Fi∣gure 3.

HAving shewed the several ways, and Rules for laying the fundamental ground Lines, according to the most considerable Engineers of this last Age, I shall end this Chapter by giving an Account of the Method used by a famous En∣gineer Mounsieur * * * in the building of seve∣ral Fortifications beyond Seas, the which I suppose from the Advantages that attend it will commend it self.

You are to take the Interior Polygone of 720 Feet, or 60 Rods, (allowing 12 Feet to a Rod) according to the second Maxim the Point Blank that a Musket doth Execution; a fifth part of this you are to set off for the Demi-Gorges, which is 12 Rods, or 144 Feet; a sixth part to the Flank, viz. 10 Rods or 120 Feet; these two together, viz. 22 Rods or 264 Feet for the Capital, there remains 36 Rods, or 432 Feet for the Curtain. See the Figure.

The Reason why I give a 1/5 part of the Interior Polygone to the Demi-Gorge, is; First, That the Line of Defence may never exceed the Port of a Musquet, which would happen, if I did but give a 1/6 part. Secondly, The Gorge being too short, the Point of the Bastion would become too sharp, or the Capital too short, and by consequence the Bastion too little: This proportion is the best for the Pentagone, Hexagone, and Heptagone, because by these Figures we cannot have the Flanks greater, or the Defence better. But for the Octo∣gone, 9, 10, 11, and 12 sided Figures, the follow∣ing Method is much better. There is given to the Face 29 Rods, to the Flanks 12, and to the Curtain 36. The Point of the Bastion is 90 De∣grees, then the other parts, viz. the Demi-Gorge, the Capitals, the Polygone interior and exterior are found by calculating and forming Trian∣gles.

This Method for these Figures is much the better, because the Flanks become greater, and the Angle of the Polygon is greater, the Gorges become greater, the interior Polygone longer, and conse∣quently a great deal of more Ground inclosed, than according to the first Method of Fortifying.

The Flanks ought to be perpendicular to the Curtain, or very near it, to the end the Enemy may not make Batteries afar off, but be obliged to make them to rume the Flanks just under the Besiegers Fire, which will cost them much blood and pain; and the reason is evident: For in bring∣ing them to fall perpendicular to the Line of Defence, the Flanks are too much exposed to the Enemy, and so discovered to the Campaign, that the Enemy finds all advantages imaginable to raise many Batteries afar off to batter and ruine the Flanks with their Cannon, which is an Enemies chief Design in a Siege, that they may the easier approach the Town, and pass the Ditch. That the design of the Flanks are chiefly to scour the Page  176Ditch and Counterscarp, to hinder the Enemy to pass their Gallery, and make a Lodgement, the which seems very reasonable, seeing the Guns from the Faces of the Bastions and Curtain, scours the Campaign more directly than the Guns from the Flanks; and tis' found by the account of Sieges that an Enemy advanceth in a little time very securely in their Trenches to the Counterscarp; wherfore if the Guns be still mounted on the Flanks, to discover them at their breaking the [ 10] Scap, and that one or two Batteries at most can be raised to dismount them, and that in so dan∣gerous a Post too, to be under the Besiegers Fire, it is certaily an advantage not to be found when the Flanks fall perpendicular on the Lines of Defence.