# Archytas explained — The Lives and Opinions of Eminent Philosophers

> Chapter companion for The Lives and Opinions of Eminent Philosophers by Diogenes Laërtius.

## What happens

This chapter details the life and achievements of Archytas of Tarentum, a Pythagorean philosopher, general, and mathematician. It highlights his rescue of Plato from Dionysius, his unprecedented seven-term generalship, his correspondence with Plato, his pioneering work in mechanics and geometry, and his discovery of the geometrical measure of a cube.

## Themes in this chapter

### Natural Philosophy and Cosmology

Archytas applied mathematical principles to mechanics and geometry, seeking proportional means to double the cube, reflecting Pythagorean interest in the mathematical structure of the cosmos.

### Political Engagement and Tyranny

Archytas's generalship and his intervention to save Plato from Dionysius illustrate the philosopher's role in political affairs and resistance to tyranny.

### Virtue and Self-Sufficiency

Archytas was esteemed for his universal virtue and integrity, holding command without personal ambition, and his correspondence with Plato emphasizes the care of philosophical works.

## Character check-ins

### Archytas

The subject of the chapter; a Pythagorean philosopher, general, and mathematician from Tarentum who saved Plato's life and corresponded with him.

### Plato

Recipient of Archytas's letters and saved by him from execution by Dionysius; exchanged philosophical commentaries with Archytas.

### Aristoxenus

Source for the detail that Archytas was never defeated as general until he gave up his command due to envy.

## Key lines

> He was the first person who applied mathematical principles to mechanics, and reduced them to a system; and the first also who gave a methodical impulse to descriptive geometry in seeking, in the sections of a demicylinder for a proportional mean, which should enable him to find the double of a given cube.

Archytas pioneered the systematic application of mathematics to mechanics and advanced descriptive geometry by using sections of a half-cylinder to find a proportional mean, allowing him to double the volume of a cube.

_Highlights Archytas's foundational contributions to mechanics and geometry._

> He was a man held in very general esteem on account of his universal virtue; and he was seven times appointed general of his countrymen, when no one else had ever held the office for more than one year, as the law forbade it to be held for a longer period.

Archytas was widely respected for his all-around excellence and was elected general seven times, an unprecedented honor since the law normally limited the term to a single year.

_Emphasizes Archytas's exceptional reputation and political career._

## Links

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