BİRİNCİ FEN · BİRİNCİ BÂB · DÖRDÜNCÜ FASIL · Üçüncü Madde
Third Article
It concisely describes geometric shapes such as the cube (mik’ab), cylinder (üstüvâne), cone (mahrût), and sphere, along with their centers, circumferences, areas, poles, axes, movements, circular movements, orbits, and their swift and slow motions.
O esteemed one! It is known that geometers have said: That which is encompassed by one or more surfaces occupying space is called a solid (şekl-i mücessem). If it is surrounded by six equal square faces, it is called a cube (müka‘‘ab). And if a region between two parallel and equal circles is joined by a flat surface to encompass a body, it is called a cylinder (üstüvâne). The two parallel circles are the bases of the cylinder. The line connecting the centers of these two bases is the axis of the cylinder; if this axis is perpendicular to the bases, it is called a right cylinder (üstüvâne-u kaime); otherwise, it is called an oblique cylinder (üstüvâne-i mâyile). And if a circle narrows and rises from its circumference, joining at a point to encompass a body, it is called a cone (şekl-i mahrût) [28/a], this circle being the base of the cone. The line rising from the center of the aforementioned circle to the apex of the cone is the axis of that cone. If the axis is perpendicular to the base, it is called a right cone; otherwise, an oblique cone.
The point imagined in the middle of a solid, connecting to the surface by straight lines, if all those line segments are equal, then this shape is a sphere, and its surface is called the circumference and circular surface (müstedîr) of the sphere. The point assumed is the center of the sphere, and the lines are the radii (ensâf-ı aktâr-ı küre) of the sphere. If a plane divides a sphere, a circle emerges; if this plane passes through the center of the sphere, it is called the greatest circle, while the others are called lesser circles. Every point existing on the surface of the sphere completes its revolution by turning once around it, drawing a circle.
However, there are two reciprocal points, called the poles of the sphere or movement poles, which remain stationary. The line connecting these two poles is called the axis (mihver). Of those circles, the one whose pole is the same as the pole of the sphere and whose center is the same as the center of the sphere is called the zone of the sphere (mıntıka-i küre). Since this circle divides the sphere into two, it is the greatest of all the circles facing it. There are also imaginary linear orbits, which are small circles present on both sides, and each pair of circles equidistant from the zone are equal. The two poles of the sphere are the poles of these orbits.
Therefore, it is certain that if a sphere were to rotate around its own axis at a specific speed, the movement of the zonal line upon it would be swift, while the movement on the small circles outside the zone would be slower than the movement in the circle within the zone. The movement of the circles closest to the poles would be slower than the movement of those close to the zone.
While the entire sphere continues to rotate around itself and its movement proceeds as described above, it is inevitable that the slowness or swiftness of the movements of its parts will differ greatly. Indeed, this difference in speed is constant and valid for the spheres and their movements. The movement of a sphere can be simple or complex. The simple movement of a sphere is called uniform circular motion (hareket-i müteşâbihe). This movement means that every point on or below the sphere moves with that same movement, travels equal distances in equal time intervals around the circumference of the sphere, and forms equal angles at the center of the sphere in equal times.
For example, the ninth sphere, which is the greatest planet, completes its revolution around the center of the universe in a period close to one day and night. A point assumed on that sphere covers the same distance in the same time interval. It creates equal angles at the center of the universe at equal times. That is, the equator of the aforementioned sphere is divided into three hundred sixty equal degrees, and a point on the equator travels fifteen degrees with this movement – measured by a star hour. The arc drawn by that point in the first hour is equal to the arc it draws in the second hour. By moving in this way while revolving around the center of the universe, the angle formed at the center in the first hour is equal to the angle formed at the center in the second hour.
Measurements for other hours can be known by analogy with these. [28/b] This is called uniform circular motion (hareket-i müteşâbihe) because it rotates around its own center. If the movement is not like this, it is not uniform circular motion.
Complex circular motions (hareket-i muhtelife) are precisely the opposite of this. The movement of a sphere can be simple or composite. A simple movement is one originating from a single sphere. A composite movement is that which arises from multiple spheres. Every simple movement is simple, but not every simple movement is simple. Every non-linear movement is composite, but not every composite movement is non-linear.