Diotimos Reading Desk

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← ExitStobaeus, Volume I

Reading language

On arithmetic

1 Aeschylus, from Prometheus

They had no certain sign of winter, of blossoming spring, or fruit-bearing summer; they did everything without understanding, until I showed them the rising of the stars and their courses, so difficult to discern, discovering number, foremost of inventions.⁷

1a [The same author, from Palamedes]

Then I set in order the life of all Greece and her allies, which before was confused and like the life of beasts. First I discovered all-wise number, foremost of inventions. …⁸

2 ⟨Plutarch⟩

Homer also understood the study of numbers. He calls enemies and men at war “discordant”:

“and all the harm hostile men had done upon the land”;

but a kindly and friendly man he calls “in accord”:

“he afflicted the Thesprotians, who were at peace with us”;

and again:

“They fought indeed in strife that devours the heart,

but parted again in friendship, reconciled.”

He regards enmity as a lack of harmony and friendship as harmony; for “in accord” means “harmonious,” since every harmony has its origin in numerical ratios.⁹

2 continued

Timaeus of Locri calls the monad a generative principle, because it governs the generation of numbers.¹⁰

Aristotle declared the One to be the primary and indivisible form of the odd and indivisible principle. The monad, acquiring its distinctive character through the activity of this One, is the beginning and element of numbers.¹¹

3 Philolaus

We must consider the workings and essence of number in the light of the power contained in the decad. For great, all-completing, and all-accomplishing is the power of the decad: it participates in divine, heavenly, and human life as a beginning and guide … . Without it, all things are unlimited, unclear, and unseen.¹²

3 continued

For the nature of number gives a rule, a guide, and instruction to everyone about everything that is puzzling or unknown. Without number and its essence, nothing whatsoever would be clear to anyone, whether things in themselves or one thing in relation to another. As it is, number, bringing all things into harmony with perception within the soul, makes them knowable and mutually commensurable, in the manner of a gnomon: it gives body to the ratios of things and separates them individually, both those of the unlimited things and those of the things that impose limit.¹³

3 continued

You may see the nature and power of number at work not only in supernatural and divine things, but everywhere in all human deeds and words, in every skilled craft, and in music.

The nature of number admits no falsehood, nor does harmony; falsehood is foreign to both.

Falsehood and envy belong to the nature of the unlimited, the unintelligent, and the irrational. Falsehood never enters number, for it is hostile and inimical to number’s nature; truth, however, is native to and inseparable from the race of number.¹⁴

3 continued

And the bodies within the sphere are five: those within the sphere, fire, water, earth, and air; and fifth, the vessel of the sphere.¹⁵

4 From the discourses of Archytas

In relation to the other branches of knowledge, the art of calculation seems greatly to surpass the other arts, and to handle its chosen subjects more clearly even than geometry. The proofs that geometry in turn leaves incomplete, calculation completes. And likewise, if indeed the inquiry concerns forms, it also concerns the things that fall under those forms.¹⁶

5 Boutheros, On Numbers

Number is composed of monads … which is the beginning of existing things and the measure of ⟨intelligible things⟩, uncompounded, ungenerated, eternal, alone, and unmixed.

The ⟨One⟩ is apart from the other things, itself by itself, a beginning and primary nature; and ⟨it is possible⟩ to know it without defining ⟨anything⟩ else.

… it alone is unmixed, itself disclosing ⟨itself too⟩.¹⁷

5 continued

Odd number is more complete than even number. The former has a beginning, an end, and a middle; the latter lacks the middle. And when they are generated proportionally and in relation to units, the former fills with its own areas the areas enclosed by the lines. The latter, when it comes to be in its own area, is never bounded; but when it comes to be in an odd one, it is itself bounded and has a side possessing a ratio.¹⁸

5 continued

The One is being, nature, mind, and disclosure: for it has a beginning, a middle, and an end. The other things that exist and are thought have also partaken of it; through its nature each is distinguished from the others, becoming an image and likenesses of the One.¹⁹

6 From Aristoxenus, On Arithmetic

Pythagoras seems to have honored the study of numbers more than anyone else and to have advanced it, taking it beyond the needs of merchants and likening all things to numbers. For number embraces the other things, and all numbers stand in a ratio to one another. The Egyptians say that it was an invention of Hermes, whom they call Thoth; others say that it was conceived from the divine revolutions.²⁰

The monad, then, is the beginning of number, and number is a multitude composed of monads. Of numbers, the even are those divided into equal parts, the odd those divided into unequal parts and possessing a middle. Thus the crises and changes of illnesses are thought to occur on odd days, because odd number has a beginning, an end, and a middle, corresponding to onset, culmination, and decline.²¹

7 Plato, from Book V of the Laws

And, speaking generally, one should recognize that the powers and varied combinations of numbers are useful for everything: both the variations numbers display in themselves and the patterns they produce in lengths and depths, and also in sounds ⟨and motions⟩, whether in the straight course of upward and downward movement ⟨or in circular revolution⟩. With all this in view, the lawgiver must direct every citizen, as far as each is able, to keep pace with this ordered study.

For household management, government, and all the arts, no single subject has such great educational power as the study of numbers. Most of all, it awakens the person who is naturally sleepy and slow to learn, making him quick to learn, retentive, and perceptive: through a divine art he advances beyond his own nature.²²

7.Prometheus speaks of the arts he gave to human beings. Wachsmuth identifies the passage with Prometheus Bound 454-459, but the excerpt’s wording differs from the play’s usual text. In particular, this Greek has “courses” (hodous), not “settings,” and joins the discovery of number to the preceding sentence. The translation follows the supplied edition.

8.The bracketed attribution is editorial, not a secure transmitted author-and-title heading. Wachsmuth’s note records competing assignments and identifies Nauck’s placement among anonymous tragic fragments. The fragment should therefore not be treated as certainly from Aeschylus’s Palamedes. The trailing dots are printed in the source.

9.The author heading is supplied by the editor. Wachsmuth associates this piece with a work circulating under Plutarch’s name rather than treating the attribution as secure. The argument turns on the Greek words anarsios, arthmios, and arthmeō, linking hostility and concord with numerical harmony. The quotations are Odyssey 10.459, Odyssey 16.427, and Iliad 7.301-302. Their wording here follows Stobaeus’s excerpt.

10.“Monad” renders monas, a unit considered as a principle of number. “The One” renders to hen. The text places these expressions close together, but later excerpts distinguish them explicitly; they are not automatically interchangeable.

11.This compressed sentence reports a doctrine attributed to Aristotle; it is not presented as a direct quotation from an identified Aristotelian work. Logos here is rendered “principle.” The phrase “through the activity of this One” translates kata de tēn toutou poiēsin; the causal relation is terse in the Greek.

12.The decad is ten understood as a complete numerical order. The Greek is in Doric forms, which are retained opposite. The gap after “guide” corresponds to a lacuna recorded by Wachsmuth after koinōnousa. The syntax surrounding that gap cannot be recovered with confidence; the English preserves the break rather than supplying a missing doctrine.

13.A gnōmōn can be a means of judging or measuring; in arithmetic it also names a figure added around another figure to produce a larger one. The passage combines a claim about knowledge with the language of numerical construction. “Mutually commensurable” interprets potagora allalois as things brought into a relation that number makes intelligible. “Things that impose limit” preserves the active participle perainontōn.

14.“Envy” translates phthonos, the reading retained in Wachsmuth’s text. His apparatus records proposed alternatives; the unusual moral term has not been silently replaced. “Race of number” retains the figurative force of genea.

15.The wording is difficult, including the repetition of “within the sphere.” “Vessel” follows the printed holkas, a word for a ship or carrier. Wachsmuth’s apparatus records several proposed replacements and interpretations. The translation retains this reading without identifying the fifth body more precisely than the excerpt warrants.

16.Logistikē is the art of calculation. The final clause is compressed and its construction uncertain; “concerns the things that fall under those forms” supplies a parallel verb in English. This preserves the printed wording rather than silently rewriting the sentence. The attribution is the heading of the excerpt, not an independent judgment of authorship.

17.Boutheros is the name printed in the source heading. These statements are fragmentary. The gap after “monads” leaves the antecedent of “which” uncertain; the English does not invent a bridge. Wachsmuth supplies several words, shown in angle brackets. “Ungenerated” follows the printed agenēton; the apparatus records a different manuscript reading.

18.This geometrical comparison is obscure in the transmitted wording. “Areas” renders chōrai; “in its own area” and “in an odd one” make the elliptical contrast readable without claiming to reconstruct its diagram. Wachsmuth records uncertainty even over logos (“ratio”) in the last phrase. Compare the more explicit construction with successive odd and even gnomons in excerpt 10 below.

19.“Disclosure” renders mēnyma, the reading adopted by Wachsmuth for the manuscript’s mēnyōma. The final Greek moves from the singular “each” and “image” to a plural participle and “likenesses”; the slightly uneven English retains the movement of the printed text.

20.The “divine revolutions” are the celestial cycles from which counting is said to have been learned. The excerpt offers alternative accounts of arithmetic’s discovery, rather than endorsing only the Pythagorean account.

21.This is an ancient explanation of critical days in disease, reported as part of the numerical doctrine. The order “beginning, end, middle” and then “onset, culmination, decline” is the source’s own order.

22.Laws 747a-b. The excerpt begins in the middle of a construction; the English gives it an independent grammatical opening. The angle-bracketed phrases are supplied in Wachsmuth from the direct tradition of Plato and are absent from the Stobaeus manuscripts cited in his apparatus. “Powers” and “combinations” retain the broad numerical language without restricting it to modern algebraic exponentiation.