The Fortifications

DEFINITION IV.

The Angle is called that part where two lines come to join together, that is, the IH, HK, which join at H, where they form the angle in that part.

An acute angle formed by two line segments meeting at point H. The outer ends of the lines are labeled I and k.

DEFINITION V.

The diversity of angles can be in three ways, that is, the acute by L, the obtuse by M, and the remainder by N, where the perpendicular line makes one and the other right angle NN, and the acute L will be smaller than the right, the obtuse M, the larger.

A diagram showing a horizontal line intersected by a vertical line, creating two right angles labeled N. A third oblique line passes through the intersection, creating an acute angle labeled L and an obtuse angle labeled M.

DEFINITION VI.

Since the right angle is that which is formed by two lines, one of which stands on the plane and the other falls perpendicular to it, and this alone is a determined and perfect angle in all buildings. Its construction is described in this way: that is, let AB be the line on the plane, which must be divided into two parts BDA, noting the point D where one wishes to form the angle. And then, having fixed the point of the compass at A, and with the other extending itself up to B, one will draw the semicircle BH, and similarly from the side B, the other semicircle AF, and where these two lines will come to intersect together (that is, in C), there will make the beginning of the straight line that will fall perpendicular over point D, so that the part CB will always be equal to CA. And thus the right angle BDC, to the ADC, which we presume to demonstrate.

A geometric construction diagram for a perpendicular line. A base line is labeled B, D, A. Two arcs intersect at point C. A vertical line CD is drawn perpendicular to the base line. One arc endpoint is labeled H.

DEFINITION VII.

The circle is a plane figure, contained by one single line, called the circumference, in the middle of which is the point C, from which all the straight lines that go to the circumference AB are equal among themselves, and that point is said to be the center of the circle.

A circle with a center point C. Several diameters and radii are drawn, with the vertical diameter endpoints labeled A and B.

DEFINITION VIII.

The equilateral triangle is formed with three equal lines, which join at their heads NMO, closing the surface P.

A diagram of an equilateral triangle with vertices labeled N, M, and O. The internal area is marked with the letter P.