The elements of geometrie of the most auncient philosopher Euclide 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 scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed

The Translator to the Reader.

THere is (gentle Reader) nothing (the word of God onely set apart) which so much beautifieth and a∣dorneth the soule and minde of mā, as doth the knowledge of good artes and sciences: as the know∣ledge of naturall and morall Phi∣losophie. The one setteth before our eyes, the creatures of God, both in the heauens aboue, and in the earth beneath: in which as in a glasse, we beholde the exceding maiestie and wisedome of God, in adorning and beautifying them as we see: in geuing vn∣to them such wonderfull and manifolde proprieties, and naturall workinges, and that so diuersly and in such varietie: farther in maintaining and conseruing them continually, whereby to praise and adore him, as by S. Paule we are taught. The other tea∣cheth vs rules and preceptes of vertue, how, in common life a∣mongest men, we ought to walke vprightly: what dueties per∣taine to our selues, what pertaine to the gouernment or good or∣der both of an housholde, and also of a citie or common wealth. The reading likewise of histories, conduceth not a litle, to the ad∣orning of the soule & minde of man, a studie of all men cōmen∣ded: by it are seene and knowen the artes and doinges of infinite wise men gone before vs. In histories are contained infinite ex∣amples of heroicall vertues to be of vs followed, and horrible ex∣amples of vices to be of vs eschewed. Many other artes also there are which beautifie the minde of man: but of all other none do more garnishe & beautifie it, then those artes which are cal∣led Mathematicall. Vnto the knowledge of which no man can attaine, without the perfecte knowledge and instruction of the principles, groundes, and Elementes of Geometrie. But per∣fectly

to be instructed in them, requireth diligent studie and rea∣ding of olde auncient authors. Amongest which, none for a be∣ginner is to be preferred before the most auncient Philosopher Euclide of Megara. For of all others he hath in a true me∣thode and iuste order, gathered together whatsoeuer any before him had of these Elementes written: inuenting also and adding many thinges of his owne: wherby he hath in due forme accom∣plished the arte: first geuing definitions, principles, & groundes, wherof he deduceth his Propositions or conclusions, in such won∣derfull wise, that that which goeth before, is of necessitie requi∣red to the proufe of that which followeth. So that without the diligent studie of Euclides Elementes, it is impossible to attaine vnto the perfecte knowledge of Geometrie, and consequently of any of the other Mathematicall sciences. Wherefore conside∣ring the want & lacke of such good authors hitherto in our Eng∣lishe tounge, lamenting also the negligence, and lacke of zeale to their countrey in those of our nation, to whom God hath geuen both knowledge, & also abilitie to translate into our tounge, and to publishe abroad such good authors, and bookes (the chiefe in∣strumentes of all learninges): seing moreouer that many good wittes both of gentlemen and of others of all degrees, much de∣sirous and studious of these artes, and seeking for them as much as they can, sparing no paines, and yet frustrate of their intent, by no meanes attaining to that which they seeke: I haue for their sakes, with some charge & great trauaile, faithfully tran∣slated into our vulgare toūge, & set abroad in Print, this booke of Euclide. Whereunto I haue added easie and plaine decla∣rations and examples by figures, of the definitions. In which booke also ye shall in due place finde manifolde additions, Scho∣lies, Annotations, and Inuentions: which I haue gathered out of many of the most famous & chiefe Mathematicies, both of old time, and in our age: as by diligent reading it in course, ye shall

well perceaue. The fruite and gaine which I require for these my paines and trauaile, shall be nothing els, but onely that thou gentle reader, will gratefully accept the same: and that thou mayest thereby receaue some profite: and moreouer to excite and stirre vp others learned, to do the like, & to take paines in that behalfe. By meanes wherof, our Englishe tounge shall no lesse be enriched with good Authors, then are other straunge tounges: as the Dutch, French, Italian, and Spanishe: in which are red all good authors in a manner, found amongest the Grekes or Latines. Which is the chiefest cause, that amongest thē do flo∣rishe so many cunning and skilfull men, in the inuentions of straunge and wonderfull thinges, as in these our daies we see there do. Which fruite and gaine if I attaine vnto, it shall encourage me hereafter, in such like sort to translate, and set abroad some other good authors, both pertaining to religion (as partly I haue already done) and also pertaining to the Mathe∣maticall Artes. Thus gentle reader farewell.