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

¶ A Corollary.

A Pyramis exceedeth the double of an Icosahedron inscribed in it, by a so∣lide, set vpon the square of the side of the Icosahedron inscribed in it, and hauing to his altitude that whole line of which the side of the Icosahedron is the greater segmēt. For it is manifest by the 19. of the fiuetēth, that an octohedrō & an Icosahedrō inscribed in it are inscribed in one & the self same pyramis. It hath moreouer bene proued in the 26. of this boke, that a pyramis is double to an octohedrō inscribed in it. Wherfore the two excesses of the two octohedrons (vnto which the pyramis is equal) aboue the two Icosahedrons (inscribed in the said two octohedrons) being brought into an solide, the said solide shalbe set vpon the selfe same square of the side of the Ico∣sahedron, and shall haue to his altitude the perpendicular KO doubled: whose double coupling the opposite sides HK and XM maketh the greater segment the same side of the Icosahedron, by the first and second corollary of the 14. of the fiu••••en••h.