Skip to main content
main-content
Top

About this book

The seventh book of Pappus's Collection, his commentary on the Domain (or Treasury) of Analysis, figures prominently in the history of both ancient and modern mathematics: as our chief source of information concerning several lost works of the Greek geometers Euclid and Apollonius, and as a book that inspired later mathematicians, among them Viete, Newton, and Chasles, to original discoveries in their pursuit of the lost science of antiquity. This presentation of it is concerned solely with recovering what can be learned from Pappus about Greek mathematics. The main part of it comprises a new edition of Book 7; a literal translation; and a commentary on textual, historical, and mathematical aspects of the book. It proved to be convenient to divide the commentary into two parts, the notes to the text and translation, and essays about the lost works that Pappus discusses. The first function of an edition of this kind is, not to expose new discoveries, but to present a reliable text and organize the accumulated knowledge about it for the reader's convenience. Nevertheless there are novelties here. The text is based on a fresh transcription of Vat. gr. 218, the archetype of all extant manuscripts, and in it I have adopted numerous readings, on manuscript authority or by emendation, that differ from those of the old edition of Hultsch. Moreover, many difficult parts of the work have received little or no commentary hitherto.

Table of Contents

Frontmatter

Part 1

Frontmatter

Pappus and the Collection

Abstract
In the later Hellenistic period, after several hundred years of progress, the main stream of Greek mathematics, synthetic geometry, experienced a deep and permanent decline. The subject did not stop being studied and taught, but original discoveries became less and less frequent and important. The causes and even the date of this decadence are obscured by the fewness of our sources for the period between Apollonius, about 200 B.C, and the fourth century A.D. But although the conditions under which ancient books were transmitted to us naturally favored (if we except a few ‘classics’ by the great Hellenistic geometers) later texts over earlier ones, we learn from reports at second hand that authors such as Geminus, Menelaus, and Heron in the first century A.D. were already excerpting, reediting, and commenting on older works.
Alexander Jones

Introduction to Book 7

Abstract
Book 7 of the Collection is a companion to several geometrical treatises, which by Pappus’s time were alotted to a special branch of mathematics, the άναλνόμενος τόπος, or ‘Domain of Analysis’.162 These books were supposed to equip the geometer with a “special resource” enabling him to solve geometrical problems. More precisely, they were to help him in a particular kind of mathematical argument called ‘analysis’. The nature of Greek geometrical analysis has been the subject of an enormous philosophical and metamathematical literature, to which I am reluctant to add.163 The following remarks are meant only as a description of analysis as it actually occurs in Pappus and other ancient texts, and to show the application of the “Domain of Analysis” to it.
Alexander Jones

Editorial Principles

Abstract
The Greek text. The text is based on a transcription made from photographs of the Vaticanus, subsequently collated with Hultsch’s text, Commandino’s translation, and the partial editions. Some passages, where moisture had long ago made the manuscript difficult to read, were collated again with the Vaticanus itself; personal inspection revealed that much of the text in these places could be read from the impression of the scribe’s pen. In a small number of passages the original text is practically illegible; these have been enclosed in half-brackets (“⌈”, “⌉”) in this edition.
Alexander Jones

Abbreviations Used in the Apparatus

Without Abstract
Alexander Jones

Text and Translation

Frontmatter

Pappus of Alexandria The Collection Book 7

Which contains lemmas of the Domain of Analysis
Abstract
That which is called the Domain of Analysis, my son Hermodorus, is, taken as a whole, a special resource that was prepared, after the composition of the Common Elements, for those who want to acquire a power in geometry that is capable of solving problems set to them; and it is useful for this alone. It was written by three men: Euclid the Elementarist, Appollonius of Perge, and Aristaeus the elder, and its approach is by analysis and synthesis.
Alexander Jones

Backmatter

Additional information