The questions to be considered in this chapter overlap with those of Chapter 10, but we shall take a slightly different angle of approach. There we based our discussion on what Ptolemy says about his instruments; here we shall concentrate on his account of what we are to do with them when we have got them. Broadly speaking, his comments fall under three headings. Some are concerned with the preparation of the data, that is, with the way in which propositions to be assessed must be expressed, if their content is to be ‘displayed to perception’ on an instrument's strings. Others relate to the procedures by which attunements are to be set up in practice on the instruments themselves, and by which the constructions of reason are actually to be made accessible to perceptual judgement. Finally there are passages that make statements or carry implications about the criteria according to which such judgements can be made. The thesis that they are made ‘by perception’ or ‘by the ear’ is altogether too vague, and we must see what efforts Ptolemy makes to sharpen it up.

The relevant passages are of course not separated out under these headings in the text. In reviewing them there are several important questions that we shall be seeking to answer. More or less tentative answers to some of them have been proposed in Chapter 10, and in these cases we shall be looking for further evidence that might bear on these provisional conclusions.