The Mathematical Preface to Euclid

John Dee's 1570 Mathematicall Praeface introduced English readers to a vision of mathematics far broader than calculation alone. Written for Henry Billingsley's first complete English translation of Euclid's Elements and printed in London by John Day, it begins with the status of mathematical objects, moves through number and magnitude, and branches into a wide-ranging catalogue of arts. Optics, astronomy, music, surveying, mechanics, medicine, architecture, navigation, image making, artificial marvels, and Archemastrie all enter Dee's order of knowledge. This edition offers a complete modern-English reading of the Preface and its appended Groundplat. Spelling, punctuation, and difficult syntax have been modernized with documentary restraint. Dee's source order, technical claims, examples, qualifications, and historically consequential terminology remain visible. Statements about astrology, medicine, prophecy, marvels, and national policy are presented as parts of a sixteenth-century argument, with context that neither endorses them as current fact nor dismisses their historical importance. What this edition includes: - Editorial orientation. A concise introduction to Dee, Billingsley, John Day, the 1570 English Euclid, and the intellectual setting in which practical mathematics, Renaissance Platonism, theology, craft, and learned magic could meet. - Selective reader notes. Notes appear only when a source recovery, safety issue, historical category, or material reconstruction would otherwise invite misunderstanding. - The Groundplat, two ways. Originally printed as a large folding tree, it receives two complementary treatments: an original path-only reconstruction for a visual overview, and a complete searchable 72-node hierarchy that preserves every branch in accessible text. - Reference apparatus. A glossary, bibliography, and detailed index support further study. Documented sources. The text is based on the CC0 EEBO Text Creation Partnership transcription A00429. Project Gutenberg ebook 22062 is used only as a named collation aid at explicit gaps in that controlling witness. Substantial restorations are disclosed, and no EEBO page images are reproduced. For readers of Renaissance intellectual history, the history of science, Western esotericism, early modern technology, and the changing boundaries among mathematics, natural philosophy, craft, and wonder. Read this edition to follow Dee's ambitious order of knowledge from its first principles to its practical and marvellous arts.