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

5 VVhen a right line falling vpon ••wo right lines, doth make ••n one & the selfe same syde, the two inwarde angles lesse then two right angles, then shal these two right lines beyng produced 〈◊〉〈◊〉 length concurre on that part, in which are the two angles lesse then two right angles.

As if the right line AB, fall vpon two right lines,

[illustration]

namely, CD and EF, so that it make the two inward angles on the one side, as the angles DHI & FIH, lesse then two right angles (as in the example they do) the said two lines CD, and EF, being drawen forth in lēgth on that part, wheron the two angles being less•• 〈◊〉〈◊〉 ••wo right angle•• consist, shal 〈◊〉〈◊〉 lēgth concurre and meete together: as in the point D, as it is easie to see. For the partes of the lines towardes DF, are more enclined the one to

the other, then the partes of the lines towardes CE are. Wherfore the more these parts are produced, the more they shall approch neare and neare, till at length they shal mete in one point. Contrariwise the same lines drawn in lēgth on the other side, for that the angles on that side, namely, the angle CHB, and the angle EIA, are greater then two right angles, so much as the other two angles are lesse th••n two right angles, shall ne∣uer mete, but the further they are drawen, the further they shalbe distant the one from the other.