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Book I Chapter 14

Chapter 14: Bodies and their division

On bodies, on their division, and on the smallest.

1a ⟨Aëtius, Opinions⟩: Body

A body is what has three dimensions: breadth, depth, and length; or a bulk that offers resistance, so far as depends on itself.⁴⁰²

1a ⟨Aëtius, Opinions⟩: Plato

Plato held that nothing is by nature either heavy or light when it is in its own place. When it comes to be in a place foreign to it, however, it then acquires an inclination, and from this inclination a tendency toward either heaviness or lightness.⁴⁰³

1a ⟨Aëtius, Opinions⟩: Aristotle

Aristotle held earth to be the heaviest and fire the lightest, while air and water are now one way, now the other.⁴⁰⁴

1b ⟨Aëtius: Aristotle⟩

And bodies can be divided without limit potentially, but by no means actually.⁴⁰⁵

1c ⟨Arius Didymus: Aristotle⟩, part 1

The qualities of simple bodies are simple. Magnitudes and things possessing magnitude are divisible without limit; these are also called continuous. The magnitudes are length, breadth, and depth; and there are six things possessing magnitude: body, place, surface, line, motion, and time.⁴⁰⁶

1c ⟨Arius Didymus: Aristotle⟩, part 2

A surface is the boundary of a body, defined by two dimensions; a line is the boundary of a surface in one dimension. A body, then, is ⟨that which⟩ has the three dimensions. Since these also apply to place, one must add that a body offers resistance and does not admit another [body] into the same place. For a body fills a place, just as a place receives a body.⁴⁰⁷

1c ⟨Arius Didymus: Aristotle⟩, part 3

Bodies act and are acted upon through incorporeal powers; for the natures of things capable of acting and of things capable of being acted upon are constituted according to the differences in these powers.⁴⁰⁸

1d ⟨Aëtius: Aristotle⟩

No fire moves naturally in a circle; only the fifth body does so.⁴⁰⁹

1e ⟨Aëtius, Opinions⟩: Chrysippus

Chrysippus said that bodies are divisible without limit, as are things resembling bodies, such as surface, line, place, void, and time. Yet although these are divisible without limit, a body is not composed of infinitely many bodies, nor is a surface, a line, or a place ⟨or void or time⟩ so composed.⁴¹⁰

1f ⟨Aëtius, Opinions⟩: The Stoics

The Stoics held two of the four elements to be light, fire and air, and two heavy, water and earth. For what inclines away from its own center is light by nature, while what inclines toward the center is heavy. Light near the earth moves in a straight line; light in the aether moves in a circle.⁴¹¹

1f ⟨Aëtius, Opinions⟩: Epicurus

Epicurus held ⟨atomic⟩ bodies to be imperceptible. The primary bodies, moreover, are simple; and the compounds formed from them have weight.⁴¹² The atoms move sometimes along a plumb line, sometimes by a swerve; those that move upward do so through impact and rebound.⁴¹³

1f ⟨Aëtius, Opinions⟩: Democritus

Democritus says that the primary bodies (these were the solid bodies) have no weight, ⟨but⟩ move through collisions with one another in the infinite. It is possible for an atom to be as large as a world.⁴¹⁴

1g ⟨Aëtius, Opinions⟩: Democritus

The same thinker said that division stops at things without parts.⁴¹⁵

1h ⟨Aëtius, Opinions⟩: Strato

Strato held that bodies possess natural weight, but that the lighter float above the heavier, as though squeezed out like fruit stones.⁴¹⁶

1i ⟨Aëtius, Opinions⟩: Thales and Pythagoras

The followers of Thales and Pythagoras held ⟨the⟩ bodies to be capable of being affected and divisible without limit, and likewise all continuous things: line, surface, solid body, place, and time.⁴¹⁷

Subsection heading

On the smallest.⁴¹⁸

1k ⟨Aëtius, Opinions⟩: Empedocles and Heraclitus

Empedocles said that before the four elements there are smallest fragments, as it were elements before the elements, with parts of the same kind.⁴¹⁹

Heraclitus seems to some to leave filings prior to the One.⁴²⁰

1k ⟨Aëtius, Opinions⟩: Other accounts

Xenocrates and Diodorus defined the smallest things as without parts.

Heraclides defined them as fragments.⁴²¹

1l ⟨Arius Didymus: The Stoics⟩, part 1

A body is what has three dimensions: breadth, depth, and length. These terms are used in more than one way. Sometimes length is said to be the greatest extent of a body, sometimes only its extent from below upward; and breadth is sometimes ⟨on the one hand⟩ the second extent, sometimes the extent to right and left; and depth is sometimes its inward extent, sometimes the extent forward and backward.⁴²²

1l ⟨Arius Didymus: The Stoics⟩, part 2

According to the first account, neither spheres nor square bodies and similar things have any of these extents; according to the second, every body has the three dimensions, since in every position it falls under this account.⁴²³

2 Parmenides

From every side like the bulk of a well-rounded sphere, equally balanced from the center in every direction; for it must be neither any greater nor any smaller here or there.⁴²⁴

402.The two definitions emphasize extension and resistance respectively. Antitypos describes resistance to penetration. The qualification “so far as depends on itself” belongs to the second definition. Wachsmuth supplies the attribution to Aëtius, as he does for the other excerpts so labeled in this chapter.

403.The report makes heaviness and lightness depend on a body’s relation to its proper place. Neusis, “inclination,” and rhopē, “tendency,” describe its directed movement. Wachsmuth refers to Plato, Timaeus 62 and following; this is a summary, not a direct quotation from that dialogue.

404.Air and water occupy an intermediate position: the same element may be light in relation to one and heavy in relation to another. The terse “now one way, now the other” preserves the contrast in the report.

405.“Potentially” means that division can always be carried farther; “actually” would mean an infinite division already accomplished. The contrast does not deny that particular divisions can occur.

406.The report distinguishes magnitude from what possesses it. Its list includes motion and time as continua as well as spatial things. The attribution to Arius Didymus and identification of Aristotle as the subject are supplied in the base edition.

407.Three dimensions alone do not distinguish body from place in this account; resistance and exclusion of another body are added. Wachsmuth supplies the article rendered “that which” and brackets the later “body” as a dispensable addition. The English moves that bracketed noun beside “another” for intelligibility.

408.The powers are expressly called incorporeal. This belongs to the report about Aristotle; it should not be merged with the Stoic account of bodily causes in the preceding chapter. “Being acted upon” renders paschein, which need not involve pain.

409.The “fifth body” is distinguished from the four elements. Wachsmuth points out that Aristotle himself calls the celestial substance the “first body”; “fifth” is the reporter’s designation, retained here.

410.The contrast is between endless divisibility and composition from an already infinite collection. In the compressed second clause, the corresponding constituents of surfaces, lines, and the rest are left implicit. Wachsmuth prints “or void or time” as a supplement, while noting an alternative of deleting these two items from the earlier list.

411.“Light” first renders kouphon, the opposite of heavy; in the final sentence it renders phōs, luminous light. The Greek changes words. The distinction between straight and circular movement belongs to the ancient account of earthly and celestial regions.

412.Aperilēpta, literally “not to be grasped,” is taken here in a perceptual sense. “Atomic” is supplied in the base edition. The following sentence is textually troubled, as Wachsmuth’s apparatus records; this translation follows his printed punctuation and takes “simple” as a predicate. The syntax does not securely establish how the primary bodies are connected to the statement about weight. Compare Aëtius I.12.5, collected as Epicurus, fragment 275 Usener.

413.A stathmē is a measuring line, here a plumb line marking straight downward movement. Parenklisis names the swerve away from that course; upward movement is separately assigned to a blow and rebound.

414.Nasta means solid or compact bodies. The startling claim of a world-sized atom distinguishes indivisibility from smallness: “atom” need not mean a tiny object in this report. The denial of weight is also retained as reported, without harmonizing it with other ancient accounts.

415.“The same thinker” refers to Democritus. Wachsmuth adopts tamerē, “things without parts,” in place of the manuscripts’ ta merē, “the parts.” The contrast is with the unlimited division asserted elsewhere in this chapter.

416.Ekpyrēnizomena evokes the expulsion of a fruit’s stone or kernel. The image explains the rise of lighter bodies by their being forced out by heavier ones; it does not require them to lack weight.

417.Pathēta means capable of undergoing an affection or change. The attribution groups together “those from” Thales and Pythagoras; it should be read as the reporter’s classification, rather than a quotation of either founder.

418.Wachsmuth places this transmitted phrase here as a subsection title. Elachiston is “the smallest” or “minimum”; the reports that follow ask what the smallest constituents are and whether they have parts.

419.Homoiomerē means having like parts. The report posits fragments prior to the four elements, without explaining whether this priority is temporal or structural. Its unusual formulation is retained rather than assimilated to another account of Empedocles.

420.Psēgmata are scrapings or filings. “Seems to some” explicitly marks this as an interpretation of Heraclitus; the text does not directly quote him or identify the interpreters.

421.“Without parts” translates amerē, as in the preceding report of Democritus. The final Greek is only a name and “fragments”; the English supplies the governing words from the preceding sentence. The passage offers classifications, not their supporting arguments.

422.The first usage begins by ranking extents; the second names directions. “Inward extent” follows Wachsmuth’s to eis heauto diastēma, a difficult phrase. His apparatus records Usener’s alternative “the smallest extent,” which would complete the ranking explicitly. The facing Greek retains the printed reading and the supplied men, rendered “on the one hand.”

423.The first usage cannot distinguish a uniquely greatest and second extent in such symmetrical bodies. The claim is therefore about the applicability of the dimensional names under that definition, not a denial that spheres have spatial extension. Tetragōna, literally “square things,” is rendered “square bodies” in this three-dimensional context.

424.These verses compare what-is to a sphere, emphasizing balance and the absence of greater or lesser being in different directions. The comparison should not by itself be turned into a statement about the shape of the earth. Wachsmuth also cites Plato, Sophist 244e, for the transmission of this passage; the Greek here follows the supplied scan.