[Transcriber’s Note: This e-text includes characters that will only display in UTF-8 (Unicode) text readers, including a few words of Greek: Τακτικὴ [Taktikê] ã ẽ õ ũ [overline or tilde to show following -n or -m] ❧ ☞ [leaf symbol; pointing-finger symbol] ‡ [double-ended dagger, used in size notations (below)] If any of these characters do not display properly-- in particular, if the diacritic does not appear directly above the letter-- or if the quotation marks in this paragraph appear as garbage, make sure your text reader’s “character set” or “file encoding” is set to Unicode (UTF-8). You may also need to change the default font. As a last resort, use the ASCII version of this file instead. Some aspects of the original book had to be modified for all versions of this plain-text file. Superscript letters are shown with ^: y^e, y^t. Marginal quotation marks are shown inline as “ and ”, approximating the beginning and end of the marked passage. In the original text, no quotation marks were printed inline. Paragraphs are broken up for sidenotes, with blank lines before and after. Original paragraph breaks are shown as two blank lines. Brackets within the body text are in the original. All sidenotes except the one beginning “This noble Earle” were printed in italics; markup has been omitted to reduce visual clutter. At least four sizes of text were used, often in combination with _italics_. The variants are shown here as: +‡very large‡+ +larger+ =smaller= Further errors and anomalies are listed at the end of the text, along with those Euclid citations identified by number.] * * * * * * * * * * * * * * THE ELEMENTS OF GEOMETRIE of the most auncient Philosopher _EVCLIDE_ of Megara. _Faithfully (now first) translated into the Englishe toung, by _H. Billingsley_, Citizen of London_. _Whereunto are annexed certaine Scholies, Annotations, and Inuentions, of the best Mathematiciens, both of time past, and in this our age._ _With a very fruitfull Præface made by _M. I. Dee_, specifying the chiefe Mathematicall Sciẽces, what they are, and wherunto commodious: where, also, are disclosed certaine new Secrets Mathematicall and Mechanicall, vntill these our daies, greatly missed._ Imprinted at London by _Iohn Daye_. ❧ The Translator to the Reader.