Etymologiae, Book III, chapters 9-12: Quot numeri infiniti existunt to De figuris geometriae
Chapter IX. How many numbers are infinite That numbers are infinite is most certain, since at whatever number you may think an end should be made, that same number, I do not say by one added is increased, but however great it be, and containing however vast a multitude, in the very reckoning and science of numbers can not only be doubled but also multiplied. Yet each number is so bounded by its own properties that none of them can be equal to any other. Therefore they are both unequal among themselves and different, and each single one is finite, and all are infinite.
Chapter X. On the inventors of geometry and its name The discipline of Geometry is said to have been first discovered by the Egyptians, because, when the Nile overflowed and covered the possessions of all with silt, the beginning of dividing the land by lines and measures gave the name to the art. Which afterwards, advancing further by the keenness of the wise, measure also the spaces of sea and sky and air. For, provoked by zeal, they began thus after the measuring of the earth to inquire into the spaces of the sky: at what interval the moon was from the earth, the sun itself from the moon, and how great a measure extended to the vertex of the sky, and so they distinguished the intervals of the sky itself and the compass of the orb by a number of stadia, with probable reasoning. But because this discipline began from the measurement of the earth, it also preserved from its beginning the name. For geometry is named from earth and measure. For earth in Greek is called gē, measure metra. The art of this discipline contains in itself lines, intervals, magnitudes and figures, and in figures dimensions and numbers.
Chapter XI. On the fourfold division of geometry The division of geometry is fourfold: into the plane, into numerable magnitude, into rational magnitude, and into solid figures. Plane figures are those which are contained by length and breadth, which are, according to Plato, five in number. Numerable magnitude is that which can be divided by the numbers of arithmetic. Rational magnitudes are those whose measure we can know; irrational, those whose quantity of measure is not known.
Chapter XII. On the figures of geometry Solid figures are those which are contained by length, breadth and height, as the cube, whose species are five in the plane. Of which the first is the circle, a plane figure, which is called “drawn around”; in whose middle is a point, to which all converge, which they call the centre of geometry; the Latins call it the point of the circle. The quadrilateral is a figure in the plane, square; which lies under four straight lines. _Diametros_, a plane figure. Orthogonium, that is, right-angled, a plane figure. For it is a triangle and has a right angle. Isopleuros is a plane figure, straight and set beneath. The sphere is a figure formed in a round, equal in all its parts. The cube is a proper solid figure, which is contained by length, breadth and height. The cylinder is a square figure, having above a semicircle. The cone is a figure that ends from broad to narrow, like the orthogonium. The pyramid is a figure that rises from broad to a point in the manner of fire; for fire among the Greeks is called pyr. As all number is within ten, so within this circle the compass of all figures is enclosed. The first figure of this art is the point, of which there is no part. The second the line, length without breadth. A straight line is that which lies evenly in its points. A surface is that which has only lengths and breadths. The ends of a surface are lines, whose forms are not put among the above ten figures because they are found among them.