Diotimos Reading Desk

Tap the page, move to the top or bottom edge, swipe down, or press Tab to reveal reading controls. Use the arrow keys or swipe sideways to turn pages.

← ExitStobaeus, Volume I

Reading language

On arithmetic

8 From Moderatus the Pythagorean

Number, to give a general description, is a system of monads, or the forward progression of a multitude beginning from a monad and a backward progression ending in a monad. Monads set a limit to quantity: as the multitude is diminished by subtraction, this quantity, stripped of every number, reaches a state of rest and stands still. For the monad cannot move backward any farther along the scale of quantity. It was therefore reasonably called a “monad,” either because it stands still and remains unchanged, always in the same condition, or because it has been separated from the multitude and left altogether alone.²³

9 ⟨The same author⟩

Some declared the monad to be the beginning of numbers, but the One the beginning of things that are numbered. The latter is a body divisible without limit; thus things that are numbered differ from numbers in the same way that bodies differ from incorporeal things. We should also know that, as principles of numbers, later thinkers introduced the monad and the dyad, whereas the Pythagoreans introduced the successive setting out of all the terms through which even and odd are understood.²⁴

10 ⟨Plutarch⟩

Pythagoras devoted the greatest care to numbers, referring both the generation of living beings and the revolutions of the stars to them. He also named numbers by likening them to the gods: the monad was Apollo, the dyad Artemis … the number six Marriage and Aphrodite, seven the Opportune Moment and Athena, eight Poseidon the Steadfast, and ten All-Completeness.²⁵

10 continued

As for number itself, he declared the even incomplete, but the odd full and complete. For when odd is combined with even, it always makes the odd result prevail; and when added to itself, it generates even, whereas even never generates odd, since it is neither fertile nor endowed with the power of a beginning. Thus, when divided in two, many even numbers resolve into odd numbers, such as six and ten; but no odd number resolves into even numbers. For the beginning and element cannot be divided into other things; all the other things, however, resolve into the same constituents.²⁶

10 continued

Moreover, when successive odd gnomons are placed around the monad, the number produced is always square. When even gnomons are placed around it in the same way, all the resulting figures are oblong and unequal-sided; none is an equal number taken an equal number of times. And when the numbers are divided into two equal groups, an odd number has a monad left over in the middle; in an even number the middle is left empty, unoccupied, and unnumbered, as though the number were deficient and incomplete. This is how he sets out the general account of numbers.²⁷

23.The opening of the definition reads “monads set a limit to quantity,” the plural construction printed by Wachsmuth on Usener’s correction. The following relative clause refers to quantity; the passage then returns to the singular monad. Number is treated as a plurality of units, with the monad as the boundary beyond which subtraction of whole units cannot proceed. The explanation of monas plays on remaining and being alone.

24.“Things that are numbered” translates arithmēta and keeps them distinct from arithmoi, numbers. The “One” in this particular report is a bodily unit; the passage does not license importing that meaning into every occurrence of the One elsewhere. Wachsmuth prints the editorial author-heading in Latin as “Eiusdem”; it is rendered in Greek opposite for consistency.

25.The attribution to Plutarch is supplied by Wachsmuth, as in excerpt 2. The printed gap follows Artemis; no missing assignments have been invented. Kairos is the fitting or opportune moment. Asphaleios is an epithet of Poseidon associated with stability; Panteleia means complete fulfillment.

26.The arithmetic behind the first claim is odd + even = odd, odd + odd = even, and even + even = even. Halving six or ten gives three or five. These relations are used to support evaluative language about completeness and fertility; they do not themselves prove that evaluation. The final sentence about beginning and element is terse and has been left at the same level of generality as the Greek.

27.The odd construction gives 1, 1 + 3 = 4, 1 + 3 + 5 = 9, and so on. The standard even construction gives oblongs such as 2, 2 + 4 = 6, and 2 + 4 + 6 = 12. The phrase “in the same way” leaves its starting figure implicit; the text has not been silently changed to specify one. For the last comparison, picture an odd row as two equal groups with one central counter, an even row as two equal groups separated by a gap.