The substance of Isidore’s _De Geometria_ comes with little change from Cassiodorus. It is noteworthy that these two writers have nothing that does not go with the subject according to the modern conception of it, and do not follow the example of their predecessor Martianus Capella,[251] in whose account of the seven liberal arts the void caused by the loss of the proper content of geometry is filled with geography. [251] _Cf._ Martianus Capella’s definition: “Geometria vocor quod permeatam crebro admensamque tellurem eiusque figuram, magnitudinem, locum, partes et stadia possim cum suis rationibus explicare neque ulla sit in totius terrae diversitate partitio quam non memoris cursu descriptionis absolvam.” Eyssenhardt, 198, 30. TRANSLATION[252] [252] The whole of Isidore’s _De Geometria_ is here given, with the exception of a few passages that are untranslatable. It is given as a whole to enforce attention to the loss of the traditional content, partial or complete, which was so striking a feature of all the members of the quadrivium in early medieval times. Book III, Chapter 10. On the inventors of geometry and its name. 1. The science of geometry is said to have been discovered first by the Egyptians, because when the Nile overflowed and all their lands were overspread with mud, its origin in the division of the land by lines and measurements gave the name to the art. And later, being carried further by the keenness of the philosophers, it measured the spaces of the sea, the heavens, and the air. 2. For, having their attention aroused, students began to search into the spaces of the heavens, after measuring the earth; how far the moon was from the earth, the sun itself from the moon, and how great a measure extended to the summit of the sky; and thus they laid off in numbers of stades with probable reason the very distances of the sky and the circuit of the earth. 3. But since this science arose from the measuring of the earth, it took its name also from its beginning. For _geometria_ is so named from the earth and measuring. For the earth is called γῆ in Greek, and measuring, μέτρον. The art[253] of this science embraces lines, intervals, magnitudes, and figures, and in figures, dimensions and numbers. [253] _Hujus ars disciplinae_. _Ars_ may be equal to ‘hand-book’ here. Chapter 11. On the four-fold division of geometry. 1. The four-fold division of geometry is into plane figures, numerical magnitude, rational magnitude, and solid figures. 2. Plane figures are those which are contained by length and breadth. Numerical magnitude is that which can be divided by the numbers of arithmetic. 3. Rational magnitudes are those whose measures we can know, and irrational, those the amount of whose measurement is not known. 4. Solid figures are those that are contained by length, breadth, and thickness, which are five in number, according to Plato. Chapter 12. On the figures of geometry.