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

¶ Corellary.

Hereby it is manifest, that if there be fower right lines in * 1.1 continuall pro∣portion, as the first is to the fourth, so shall the Parallelipipedon described of the first line, be to the Parallelipipedon described of the second, both the Parallelipipedons being like and in like sort described. For the first line is to the fourth in t••eble proportion that it is to the second: and it hath before bene

[illustration]

proued that the Parallelipipedon described of the first, is to the Parallelipipedon described of the second, in the same proportion that the first line is to the fourth.

Because the one of the figures before, described in a plaine, pertayning to the demonstration of this 33. Proposition, is not altogether so easie to a younge begin∣ner to conceaue, I haue here for the same described an other figure, which if ye first drawe vpon pasted paper, and afterward cut the lines & folde the sides accordingly, will agree with the construction & demon∣stration of the sayd Proposition. Howbeit this ye must note that ye must cut the lines OQ & MR on the contrary side ••o that which ye cut the other lines. For the so∣lides which haue to their base the paralle∣logramme LK are set on vpward and the other downward: Ye may if ye thinke good describe after the s••me maner of pasted pa∣per a body equall to the solide CD: though that be easie inough to conceaue by the fi∣gure thereof described in the plaine.

Notes

• * 1.1

  *