1. Here the property of being ‘visual and auditory’ is called an attribute {pathos); at 302c it was called an essential property (ousia). The fact that these two terms are used interchangeably {pace Euthyphro 11a) need not lead us to regard the dialogue as not a genuine Platonic composition.

2. That is, a visual pleasure is not visual-and-auditory (‘caused by both the senses together’); only visual and auditory pleasures are caused by both the senses together.

3. 300e-301a.

4. It has been universally denied by the commentators that the sum of two irrationals is ever rational, and various explanations have been given for Plato’s confident statement, of which the most plausible are that ‘irrational’ was a wider term in his day; or that he has suddenly switched from talking of sums to talking of products; or simply that he is making a mistake. But in fact, for example, the sum of (√2–1), which is irrational, and (3-√2), which is also irrational, is the rational number 2 (my thanks to Peter Thomas).