Theophrastus, Sextus and Vitruvius: the differentiae indexed to the senses, Diodorus’s partless bodies, and the voice as spreading waves

Companion source

Source: three works in one excerpt file, each with its own edition recorded there; retrieved and verified 2026-09-18. Rights: all three editions are public domain. Stratton 1917 and Gwilt 1826 are translations out of copyright; Mutschmann 1912 is the Teubner Greek. The Sextus text is archive.org OCR of Greek, so accents and breathings are unreliable and the passage is kept as served; the sense is not in doubt but the orthography is a verification target.

What each supplies

Theophrastus, De sensibus, the Democritus section, c. 320 BCE. This is where Democritus’s differentiae appear indexed to sensory qualities, and it is the text from which any parallel with the Laozi triad would have to be argued rather than from Metaphysics A.4:

Democritus has no uniform account of all <the sensory objects>: some he distinguishes by the size <of their atoms>, others by the shape, and a few by the <atomic> order and position.

Stratton’s introduction adds that Democritus “would in general explain the effect of a sensory stimulus by the shape of its constituent atoms; but … he is also found explaining the effect by their size, or their position”, which is Theophrastus’s complaint against him. So the differentiae are not a fixed triad mapped onto the senses; they are applied unevenly, and Theophrastus’s objection is precisely that the mapping is inconsistent. That weakens rather than strengthens a term-by-term comparison with Laozi 14, and it does so from the Greek side, independently of the Chinese recension swap recorded there.

Sextus Empiricus, Pyrrhoneion Hypotyposeis III.32, c. 200 CE. In the doxography of material principles: Διόδωρος δὲ ὁ ἐπικληθεὶς Κρόνος ἐλάχιστα καὶ ἀμερῆ σώματα, “Diodorus surnamed Cronus [posits] least and partless bodies”, listed between the atoms of Democritus and Epicurus and the unjointed masses of Heraclides and Asclepiades. Diodorus is the Greek author whose denial of motion rests on minima, and he is the twin of Vasubandhu’s na gatiḥ three centuries earlier. This passage certifies the minima; the motion argument itself, “a thing never is moving but it has moved”, is at Adversus Mathematicos X.85–120 and is not verified here, volume II of Mutschmann being unavailable through the routes tried.

Vitruvius, De architectura V.3.6–7, c. 25 BCE. The Roman statement of the wave model, with a point the Greek and Indian versions do not make:

The voice arises from flowing breath, sensible to the hearing through its percussion on the air. It is propelled by an infinite number of circles similar to those generated in standing water when a stone is cast therein … But, whereas the circles in water only spread horizontally, the voice, on the contrary, extends vertically as well as horizontally.

So the same water-ring image that carries the Stoic account in Diogenes Laertius VII.158 and Praśastapāda’s vīcī-santāna is here corrected into a spherical wave, and the correction is argued from the disanalogy with water rather than asserted. Vitruvius also notes that obstruction to the first undulation disturbs all that follow, which is the propagation chain again.

Passage anchors

Coverage and limits

Reading level passage for the three locations; metadata for the rest of each work. Three related items are cited but not verified here and should not be treated as readings: Diodorus’s motion argument at Sextus AM X.85–120; Boethius, De institutione musica I.14, which repeats the water-ring image at almost exactly the 500 CE boundary; and Lucretius, De rerum natura IV, on the speed of the simulacra.