Chapter 7: On the third division of all number

1. Numbers are abstract or concrete. The latter are divided as follows: first, lineal; second, superficial; third, solid. Abstract number is that which is made up of abstract units. For example, III, IV, V, VI, and so on.

2. Concrete number is that which is made up of units that are not abstract, as for example, the number three, if it is understood of magnitude, whether line, superficies, or solid, is called concrete.

4. The number of superficies is that which is constituted not only by length but also by breadth, as triangular, square, pentangular, or circular numbers, and the rest that are contained in a plane surface or superficies.

5. The circular number, when it is multiplied by itself, beginning with itself, ends with itself. For example, _Quinquies quini vicies quinque_.

6. ... The spherical number is that which being multiplied by the circular number begins with itself and ends with itself; for example, five times five are twenty-five, and this circle being multiplied by itself makes a sphere, that is, five times XXV make CXXV.