OF THE PRINCIPLES OF FORTIFICATION.

To make a Star, three things must be given: First, the figure, which may be a Square, a Pentagon, or a Hexagon. Secondly, the side, which is taken as in the Redoubt, and we shall hold to the middle ground, taking it at one hundred feet. Thirdly, the interior flanking angle, which is always fifteen degrees.

EIGHTH PROPOSITION.

First, the figure shall be made, of which the Sides shall be taken of the same length, as you see the figure H I E A is made—a Square, of which each side carries a length of one hundred feet. From point A, with an opening of the compass taken at discretion (provided it is somewhat larger than half of the given side), an arc shall be made inside the figure, such as C B; and with the same opening A C, choosing the center C, cut C B; then such an arc will be the sixth part of its circle, and consequently it will comprise three score degreesoriginal: "trois vingts degrés"; sixty degrees.. Divide it then into four equal parts, of which each will contain fifteen degrees, and one shall be C D. Draw D A and you will have the angle D A C of fifteen degrees, as is required. At the midpoint of A E, raise the Perpendicular F G, which cuts D A at G; take the length G A, and with such an opening, placing it at each angle of the figure, make the crossed arcs K, L, M; finally draw E G, K E, H K, H L, L I, I M, and M A. And the Design of the Star will be completed.

NINTH PROPOSITION.

It is first necessary to pay heed to the Points, Lines, and Angles, and to learn their names.
A, is the point of the Center. B, C, D, E, are the points of the figure.
F, the point of Defense. G, the point of the perpendicular.
Regarding the lines: C F and H C shall be called the Faces. F G, the minor perpendicular. A G, the major perpendicular. C D, the side. A C and A D, the Radiioriginal: "Raids"; Goldman uses this term to refer to the lines radiating from the center to the vertices of the polygon.. A F, the small Radius.
The angle of the center, C A D. The angle of the figure, B C D. The interior flanking angle of fifteen degrees, F C G. The exterior flanking angle, C F D, of which the half is G F C. The flanked angle, H C F.
This being well learned, we shall find the rest, given: first, the Square figure; second, the side of 100 This symbol indicates feet.; and finally, the interior flanking angle of fifteen degrees.

RULES FOR THE CALCULATION.

1. The angle of the center is found by dividing the entire circle, that is to say, three hundred and sixty degrees, by the number of sides of the figure.

2. The angle of the figure is found by subtracting the angle of the center from two right angles, or one hundred and eighty degrees.

3. The interior flanking angle, which is given as fifteen degrees, must be subtracted from 90 degrees—that is to say, from the sum of the angles FCG and GFC—then only GFC will remain.

4. The preceding angle shall be doubled to have the sum of two angles of the same magni-