Edward Bernard, Gregory's predecessor in the Savilian Chair of Astronomy, had conceived of an edition of the ancient geometers, beginning with Apollonius, whose "Sectio Rationis" he found in Arabic among the Selden manuscripts at Oxford. He attempted a translation into Latin. This item is the result of that attempt (minus pages 1 and 2), along with a fair copy made by Gregory (see also Item 21) at the request of Henry Aldrich, Dean of Christ Church and collaborator on the project. Bernard had abandoned the translation because of defects in the original manuscript. Gregory's fair copy is the one Edmund Halley later used as a key to teach himself enough Arabic to complete the translation that Bernard had started.