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 second Corollary.

Hereby also it is manifest, that if there be three right lines proportionall,* 1.1 as the first is to the third, so is the figure descri∣bed vppon the first to the figure described vpon the second, so that the sayd figures be like and in like sort described.

For it is proued, that the proportion of the Poligonon figure ABCDE to the Poligonon figure FGHKL is double to y^e proportion of the side AB to the side FG. And if (by the 11. of the sixt) vnto the lines AB and FG we take a third line in proportion, namely, MN, the first line, namely, AB shall haue vnto the third line, namely, to MN, double proportion that it hath to the second line, namely, to FG (by the 10. definition of the fift). Wherfore as y^e line AB is to the line MN, so is the rectiline figure ABC to the rectiline figure FGH, the sayd rectiline figures being like & in like sort described.

Notes

• * 1.1

  The second Corollary.