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

Note.

Many wayes, these two Theoremes, may be demonstrated: which I leaue to the exercise of young studentes. But vtterly to want these two Theoremes, and their demonstrations: in so principall a line, or rather the chiefe piller of Euclides Geometricall pallace,* 1.1 was hetherto, (and so would remayne) a great disgrace. Also I thinke it good to note vnto you, what we meant, by one onely poynt. We m••••••••, that the quantities of the two segmentes, can not be altered, the whole line being once geuen. And though, from either end of the whole line, the greater segment may begin:* 1.2 And so as it were the point of secti∣on may seeme to be altered: yet with vs, that is no alteration: forasmuch as the quantities of the seg∣mentes, remayne all one. I meane, the quantitie of the greater segment, is all one: at which end so euer it be taken: And therefore, likewise the quantitie of the lesse segment is all one, &c. The like confidera∣tion may be had in Euclides tenth booke, in the Binomiall lines. &c.

Io••n Dee. 1569. Decemb. 18.

Notes

• * 1.1

  The chie••e line in all Euclides Geometrie.
• * 1.2

  What is ment here by, A secti∣on in one onely poi••t.