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

I. D••e.

This figure is answerable to the firste plaine: which, cutting the two Spheres by their common center A, made two concen∣tricall circles (hauing the same center with the two Spheres) namely BCDE, and FG∣H. Vppon which, •• you aptly reare perpen∣dicularly, the second figure contayning two concentricall circles, (to the first e∣quall) and make the pointes noted with like letters to agree, and afterward vppon the se∣cōd figure, set on the third figure being here for the better handling made a semicircle: which vppon the first figure must also be e∣rected perpendicularly: And lastly if you take the little quadrangled figure BOKS, and make euery point to touch, his like: & then reade the construction & wey the de∣monstratiō (twise o•• thrise being red ouer) shall you in this del••••eatiō in apt pastborde, or like ma••ter framed, finde al things in this probleme very euident.

I neede not warne you, that the line AY may easely be imagined, or with a fine thred supplyed: or of the right lines imaginable betwene P and T, and betwene R and V, I neede say nothing, trusting that the great exercise past, by that tyme you are orderly come to this place, will haue made you suf∣ficient perfect to supply any farther thinge herein to be considered.

The little fowercornerd peeces remay¦ning to the semicircle, are to be let through the first ground playne: therby to stay this se¦micircle the better in his apt place and situ∣ation: which it will the more aptly doo, if ye do 〈…〉〈…〉, the contrary arasses of the slitt of it, and of the slitt of the second figure, into which it is to be let: abating thē alike much: a litle will serue. Experience, by aduise, will teach sufficiently.