Etymologiae, Book III, chapter 6: De secunda divisione totius numeri
Chapter VI. On the second division of the whole of number Every number is considered either (1) in itself, or (2) in relation to something. (1) This is divided thus: some are equal, others unequal. (2) This is divided thus: some are greater, some less. The greater are divided thus: multiples, superparticulars, superpartients, multiple superparticulars, multiple superpartients. The less are divided thus: submultiples, subsuperparticulars, subsuperpartients, submultiple subsuperparticulars, submultiple subsuperpartients. A number in itself is one that is spoken of without any relation, as II, III, IV, V, VI, and the rest like them. A number in relation to something is one that is compared relatively with others; for example IV, when compared with II, is called double and multiple, VI to III, VIII to IV, X to V; and again III to one is triple, VI to II, IX to III, and the rest. Equal numbers are those which are equal in quantity, as for example II to II, III to III, X to X, C to C. Unequal numbers are those which, compared with one another, show inequality, as III to II, IV to III, V to IV, X to VI; and universally a greater compared to a less or a less to a greater is, in this way, called unequal. A greater number is one that has in itself that lesser number to which it is compared, and something more; for example the number five is stronger than the number three, because the number five has in itself the number three and two other parts of it, and the rest are such. A lesser number is one that is contained by the greater with which it is compared, with some part of itself, as three to five. For it is contained by it with two parts of itself. A multiple number is one that has in itself the lesser number twice, or thrice, or four times, or many times; for example II to one, when compared, is double; III to one, triple; IV quadruple, and the rest. Conversely a submultiple number is one that is contained within the multiple twice, or thrice, or four times, or many times; for example one is contained by II twice, by III thrice, by IV four times, by V five times, and by others many times. A superparticular number is when the stronger contains within itself the lower number with which it is compared, and likewise one part of it; for example III to II, when compared, contain within themselves another one, which is the half part of two; IV to III, when compared, contain in themselves III and another one, which is the third part of three. Again V to IV, when compared, have in themselves the number four, and another one, which is said to be the fourth part of the number four, and the rest such. A superpartient number is one that contains in itself the lower number whole, and over this other parts of it, II, or III, or IV, or V, or others; for example V to III, when compared, the number five has in itself the number three, and over this two other parts of it; VII to IV, when compared, have in themselves IV, and three other parts of it; IX to V, when compared, have in themselves V, and four other parts of it. A subsuperpartient number is one that is contained in a superpartient number with some parts of itself, two or three or more; for example III is contained by V with other parts of itself; by IX with IV parts of itself. A subsuperparticular number is a lesser that is contained in a stronger number with one other part of itself, either a half, or a third, or a fourth, or a fifth; for example II to III, III to IV, IV to V, and the rest. A multiple superparticular number is one that, when compared with a lower number, contains in itself the whole lower number several times with some part of it; for example V to II, when compared, contain in themselves twice II, IV, and one part of it; IX to IV, when compared, contain in themselves twice IV, VIII, and one part of it. A submultiple subsuperparticular number is one that, when compared with a number stronger than itself, is contained by it several times with one other part of itself; for example II to V, when compared, are contained by it twice with one part of itself. A multiple superpartient number is one that, when compared with a number lower than itself, contains it several times with other parts of it; for example VIII to III, when compared, contain in themselves twice III, with other II parts of it; XIV to VI, when compared, contain within themselves twice VI with other II parts of it; XVI to VII, when compared, contain it twice with other II parts of it; XXI to IX, when compared, contain within themselves twice IX with other III parts of it. A submultiple subsuperpartient number is one that, when compared with a number stronger than itself, is contained by it several times with some parts of itself; for example III to VIII are contained twice with parts of itself; IV to XI are contained twice with III parts of itself.