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

¶ Certaine most profitable Corollaries, Annotations, Theo∣remes, and Problemes, with other practises, Logisticall, and Mechanicall, partly vpon this 33. and partly vpon the 34. 36. and other following, added by Master Iohn Dee. ¶ A Corollary. 1.

1. Hereby it is manifest, that two right lines may be found, which shall haue that proportion, the one to the other, that any two like Parallelipi∣pedons, and in like sort described, geuen, haue the one to the other.

Suppose Q and X to be two like Parallelipipedons, and in like sort described. Of Q take any of the three lines, of which it is produced: as namely, RG. Of X, take that right line of his production, which line ••s aunswerable to R G in proportion (which most aptly, after the Greke name, may be

called Omologall to RG) &

[illustration]

let that be TV. By the 11. of the sixth, to RG and TV, let the third line in propor∣tion with them be founde, and let that be Y. By the same 11. of the sixth, to TV and Y, let the thirde right line be foūd, in the sayd pro¦portion of TV to Y: & let that be Z. I say now that RG hath that proportion to Z, which Q hath to X. For by construction, we haue fower right lines in continuall pro∣piotion, namely, RG, TV, Y, and Z. Wherfore by Euclides Corollary, here before, RG is to Z, as Q is to X. Where∣fore we haue foūd two right lines hauing that proportion the one to the other, which any two like Parallelipipedons of like descrip∣tion, geuen, haue the one to the other: which was required to be done.