The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

Of Irregular Fortification.

IN the seventh Figure following let ABCDE be an Irregular Fort, containing 5 Bastions, or Bulwarks. First we will make a Bastion on the Angle at A, which do thus: Divide the Polygon Angle in half with the Line AF, and draw the Bastion-Angle as formerly, being ⅔ of the Polygon-Angle, as AH, and AI con∣tinued, being the Sides whereon the Fronts must be laid down.

Now upon some spare Paper you shall make the half Polygon-Angle GAF, as you may see underneath this seventh Figure, as LKM: Then make choice of the Ca∣pital Line, as before; let it be of any convenient length (larger than you think your Bastion will be in the seventh Figure) as underneath KN, and from N the Center of the Gorge draw a Parallel to KL, continued to O, as NP; and so proceeding as be∣fore, you shall find the Point of the second Bastion at O: So have you the Propor∣tion of your Bastions, whereby you may gain those in the seventh Figure.

Now to reduce it from the Bastion Point at A, you must take AB the shortest side, and lay it from O unto Q; and from Q draw a Line parallel to the Capital Line KN continued, as QR. Lastly, drawing a Line from N to O, it shall cut QR in the Point S; so is QS the length of the Capital Line sought for, which must be laid down on the seventh Figure from A unto T; so is T the Center of the Gorge. Then for the Front take KV, and lay it on the Capital Line from K to W: so a Ru∣ler being laid from W to O, it shall cut the Line QR in the Point at X; so is QX the length of the Front, to be laid down in the seventh Figure from A unto H and I. Thus shall you finish your Bastion, when you have let fallen your Flanks perpendicular on the ends of your Curtains, as you see. The like Method you are to observe for the other Bastions.

And when you have finished your Fort, you must observe whether your Curtain Lines (that is, from the Centers of the Gorge) be parallel to the outward Sides AB, &c. which if they are not, you must correct them; and by your Judgment, by help of the Lines of Defence, you may as you see occasion widen the Necks of the Gorges, and also the Bastion Angles; but not above 90 Degrees: And so let the Flankers be as neer proportional as the Rules (or Ocular Demonstration directeth) which commonly the Gorge Line to the Flank bears proportion as 7 to 6.

Much more could I write of Irregular Fortification: but my purpose at this time is but to make a small Treatise, or an Epitome thereof.

[illustration] geometrical diagram

The seventh Figure, of an Irregular Fort, containing 5 Bastions; being the Platform of the Royal Fort sometimes on St. Michael's Hill, on the North West Side of the City of Bristol.