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Book I Chapter 15

Chapter 15: Shapes

On shapes.

1 Homer, Iliad 8.16

As far beneath Hades as heaven is from earth.⁴²⁵

2a ⟨An unidentified poet⟩

But it, ⟨being⟩ equal on every side and wholly boundless.⁴²⁶

2b ⟨Empedocles⟩

a rounded Sphere, rejoicing in surrounding solitude.⁴²⁷

3a Surviving attribution

From Porphyry.⁴²⁸

3b ⟨Aëtius, Opinions⟩

A shape is the surface, outline, and boundary of a body.⁴²⁹

4 Plato, Timaeus 33b

Plato said that the world is spherical. For he says in the Timaeus: “He gave it the shape fitting and akin to it. For a living creature destined to contain all living creatures within itself, the fitting shape would be one containing within itself all the shapes there are. So he turned it into a rounded sphere, equidistant from the center to its extremities in every direction, the most complete of all shapes and the most like itself; for he judged likeness immeasurably more beautiful than unlikeness.”⁴³⁰

5 Plato, Timaeus 62d-63a, part 1

For since the whole heaven is spherical, all the extremities that lie at an equal distance from the center must be alike in their character as extremities; and the center, equally distant from the extremities, must be understood to lie directly opposite all of them. Since the world is constituted in this way, if someone designates any of these as “up” or “down,” will he [not] not rightly be thought to use a wholly unsuitable name?⁴³¹

5 Plato, Timaeus 62d-63a, part 2

For its central region cannot properly be called naturally either down or up, but simply in the middle. The surrounding region is not the middle, and no part of it differs from another in its relation to the center or to any of the parts opposite. When something is alike in every direction, what contrary names could someone apply to it, and on what grounds could he consider himself to be speaking correctly?⁴³²

5 Plato, Timaeus 62d-63a, part 3

For even if a solid body were evenly balanced at the center of the whole, it would never move toward any of the extremities, because they are alike in every direction. Yet if someone were to travel in a circle around that same body, repeatedly taking a position with his feet pointing the opposite way, he would call the same part of it both down and up. For since the whole is spherical, as was just said, no sensible person would say that it has one region below and another above.⁴³³

6a ⟨Aëtius, Opinions⟩: The Pythagoreans

The followers of Pythagoras held [the world] the shapes of the four elements to be spherical; only the uppermost fire is conical.⁴³⁴

6a ⟨Aëtius, Opinions⟩: Anaxagoras and Leucippus

Anaxagoras held the things with like parts to have many shapes.

The followers of Leucippus held the atoms to have many shapes.⁴³⁵

6a ⟨Aëtius, Opinions⟩: Cleanthes and Zeno

Cleanthes alone among the Stoics declared fire to be conical.

Zeno said that fire moves in a straight line.⁴³⁶

6b ⟨Aëtius, Opinions⟩: The world’s shape

The Stoics declared the world to be spherical.

Leucippus and Democritus held the world to be spherical.⁴³⁷

6c ⟨Aëtius, Opinions⟩: Diogenes and Anaxagoras

Diogenes and Anaxagoras said that, after the world had formed and brought living creatures out of the earth, the world somehow tilted of its own accord toward its southern part, perhaps through providence, so that some regions of the world would become uninhabitable and others habitable, according to cold, scorching heat, and a temperate mixture.⁴³⁸

6d ⟨Aëtius, Opinions⟩: Empedocles, part 1

Empedocles said that the regions of the elements are not always fixed or bounded, but share in one another in every way.⁴³⁹

6d ⟨Aëtius, Opinions⟩: Empedocles, part 2

When the air yielded to the sun’s impetus, the Bears tilted, the northern regions rose, and the southern regions sank; the whole world was correspondingly inclined.⁴⁴⁰

Its right-hand regions are those along the summer tropic, and its left-hand regions those along the winter tropic.⁴⁴¹

6e ⟨Aëtius, Opinions⟩: Right and left

Pythagoras, Plato, and Aristotle held the eastern regions of the world to be its right side, from which motion begins [because of the risings], and the western regions its left.⁴⁴²

6e ⟨Aëtius, Opinions⟩: Height and depth

They say that the world has neither height nor depth, in the sense in which height means extension from below upward, and depth extension from above downward. For none of the extensions so named applies to the world, because it is constituted around its own center, from which it extends in every direction and toward which it is the same from every side.⁴⁴³

7 Philolaus, Bacchae, part 1

The world is one. It began to come into being as far as the middle; and from the middle upward, through the same things as below, are the things above the middle, lying opposite those below.⁴⁴⁴

7 Philolaus, Bacchae, part 2

For those below, what is lowest is great, just as what is highest is; and the rest likewise. For both stand in the same relation to the middle, insofar as they have not been displaced.⁴⁴⁵

425.The line describes Tartarus in Zeus’s threat to the other gods at the beginning of Iliad 8. Stobaeus extracts the comparison of distances; the name Tartarus belongs to the surrounding Homeric passage.

426.The subject is not identified within the surviving line. Wachsmuth prints the attribution as anonymous and supplies eōn, “being.” His apparatus discusses attribution to Parmenides or Empedocles, but he does not join this line to the following Empedoclean verse. The English preserves that separation and the unfinished construction.

427.Sphairos, “Sphere,” is the name used in this Empedoclean verse. Moniē denotes solitude or being alone; the adjoining adjective gives it an encompassing quality. Wachsmuth supplies the attribution and adopts several readings from parallel witnesses. This fragment remains a separate quotation from 2a.

428.Only this attribution survives here. Wachsmuth states that the manuscripts retain the name in their margins but no text of the excerpt. It is therefore not used to attribute the following definition to Porphyry.

429.Perigraphē means the outline or circumscription of something. The definition treats shape in terms of the boundary of a body. The attribution to Aëtius is supplied by Wachsmuth, as are the Aëtian attributions in excerpt 6.

430.The maker is the craftsman of the Timaeus; the creature fashioned is the world itself. Etorneusato evokes shaping something on a lathe. The passage relates the sphere’s symmetry and completeness to the world’s inclusion of all living creatures. The comparison concerns likeness within the shape, not a comparison between two separate worlds.

431.The transmitted heading is “In the same work.” The argument concerns whether a spherical whole has an intrinsically upper or lower region. Wachsmuth brackets a duplicated negative before the ordinary rhetorical question. The bracketed “not” should be omitted when reading the continuous English; the question then expects assent.

432.The contrast is between the center and the surrounding boundary. “Up” and “down” would assign contrary directional properties to regions that are alike in relation to the center. The discussion continues the chapter’s concern with symmetry rather than denying differences of position relative to a particular observer.

433.Antipous describes standing with the feet oppositely directed. As the observer changes position around the central body, the same region receives opposite local designations. “Evenly balanced” translates isopales, also used in the Parmenidean verses at the end of chapter 14.

434.“The world” is bracketed for deletion in the base text and has no grammatical role in the resulting sentence. The contrast distinguishes the shapes of the four elements from the form assigned to the uppermost fire. “Conical” means shaped like a cone.

435.Homoiomerē means things whose parts are of the same kind. Wachsmuth exchanges the objects of these two reports: the manuscripts assign atoms to Anaxagoras and things with like parts to Leucippus. His printed correction, followed here, preserves the order of the philosophers.

436.The two statements concern different things: the shape of fire and the direction of its motion. The report singles out Cleanthes within the Stoic school. Compare the statements about fire and circular motion in chapter 14.

437.Kosmos here denotes the ordered world described by each account. The shared predicate “spherical” does not make their accounts of its constituents or formation identical.

438.The report retains both “of its own accord” and “perhaps through providence”; the translation does not resolve their tension. The last three terms concern climatic conditions and habitability. Here ekpyrōsis is rendered “scorching heat,” rather than the destruction of an entire world by fire.

439.The wording describes a mutual occupation of regions rather than permanent, exclusive allotments. “In every way” follows Wachsmuth’s pantachōs; his apparatus records other proposals, including pantachou, “everywhere.” Excerpt 6d gathers three short reports, separated in the base edition.

440.The Bears are the northern constellations. The passage explains a tilt of the heavens through the action of the sun upon the air. Its compressed final clause extends the inclination to the world as a whole.

441.The summer and winter tropics mark the sun’s northern and southern turning circles. This orientation differs from the next report, which assigns right and left to east and west.

442.The motion is described from the side where the heavenly bodies rise. Wachsmuth brackets “because of the risings” as an addition to be omitted; the English retains it within the same editorial signs.

443.The denial is qualified by a particular definition of height and depth. It does not deny the world’s spatial extent. The final phrase is compressed: the translation takes it to describe the same relation to the center from all sides. Compare Plato’s argument in excerpt 5 and the two definitions of dimensions in I.14.1l.

444.The title Bacchae is transmitted with the attribution to Philolaus. The wording of this excerpt is difficult. “As far as” retains Wachsmuth’s achri; “from” (apo) is a proposed correction in his apparatus. The following clause also has disputed wording and punctuation. This deliberately close rendering preserves the printed text’s uncertainty rather than presenting a securely reconstructed account of formation from the center.

445.“Great” renders the printed mega, but the sense of this sentence is not secure. Wachsmuth records conjectures such as mesa, “middle things,” and meros, “part,” as well as deletions, without adopting them. The general comparison is between positions above and below the center; the English does not silently substitute a conjecture for the troublesome word. The final qualification translates the printed mē, “not.”