Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

SECT. VII. Of some Maxims or Rules necessary to be known in Irregular Fortification.

IRregular Fortifications is when any Town or Place is to be fortified, which lieth in an Irregular form; i. e. whose Sides and Angles are unequal in the forti∣fying of Irregular Fi∣gures* 1.1. I shall here say very little, only I shall lay down some Precepts that are of immediate concern in fortifying of Irregular Figures, and shall refer you to peruse Marlois, Dogen, Fritach, Taurnier, Dilichius, &c. which will greatly satisfie and help you: To this end know,

1. That the same Laws and Maxims for Re∣gular Fortifications stand and be in force for Irregular; i. e. that the line of Defence must not exceed the Port of a Musquet, nor the Angles of the Bastion be less than 60°, nor much above 90°, &c.

2. That no inward Angle of the Place be less than 90°, if it be so it must be altered, and that point may be made the outward point of a Bastion.

3. That between Regular and Irregular For∣tifications, there is no other difference, but by rectifying the sides that are too short, or too long, and altering the Angles that are too little; as for the sides, if they be above 500, and un∣der 1000 Feet, they may be fortified by Ba∣stions placed according to the usual manner, at the extreme points thereof; But if the sides be between 1000 and 1700 Feet, then in the midst you may place a Plat Bastion, and at the Extreme Points, place two Bastions, as before: But if the line be less than 500 Feet, you may lengthen it, by producing it into the Plane: As for the Angles, they are made greater or lesser according as occasion requireth. For the Raising the Rampires, Parapets, and other Out∣works, they are to be as in the Regular, and the Out-work may be placed before the Cur∣tains as was before mentioned.

4. That the Capital, in any Regular or Irre∣gular Bastion, is found by dividing the Angle of the Polygon into two equal parts (by prop. 7. §. 1. chap. 4.) and by producing the line of Angular Division or Separation, on which the due length of the Capital must be placed, which observe for a general Rule.

Notes

• * 1.1

  The Inginier must first form a Map of the Town or Place, with all the Ways, Passages, Old Walls, Rivers, Pools, Enclosures, and all o∣ther matters fit to be known in the draught, and then he is to design what Works he findeth most agreeing to the place to be Fortified.