Edmond Halley and Apollonius: second-order historical knowledge in mathematics education

In the present paper I look at Edmond Halley’s reconstruction of Book VIII of Apollonius’s Conic as an example of a second-order historical text. Such texts constitute a particular class of original works whose distinction is that they present mathematicians of the past engaging with texts from their own past, as we do when we look at historical material in classrooms. Hence, texts of this kind provide us with an opportunity not so much for gaining a historical understanding of a concept, method, or theorem but for viewing another reader of mathematical texts, and, therefore, they provide teachers and students with an opportunity to reflect on themselves as readers. This, in effect, is a matter of reflecting on one’s relationship to the past. In the case of Halley, I characterize his particular relationship as ‘a moderator’ between past and present. But I also stress that his is not the only possible relationship to the mathematical past. The case of Halley, however, serves to bring out some of the alternatives. Bearing in mind this variety of relationships to the past will help teachers give shape to their own reflections and, more importantly, help guide their students’ reflections as readers of historical texts.