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

10 A Pyramis is a solide figure contained vnder many playne superficieces set vpon one playne superficies, and gathered together to one point.* 1.1

Two superficieces raysed vpon any ground can not make a Pyramis, for that two superficiall angles ioyned together in the toppe, cannot (as before is sayd) make a solide angle. Wherfore whē thre, foure, fiue, or moe (how many soeuer) superficieces are raised vp frō one superficies being the ground, or base, and euer ascēding diminish their breadth, till at the lēgth all their angles cōcurre in one point, making there a solide angle: the solide inclosed, bounded, and terminated by these superficieces is called a Py∣ramis, as ye see in a taper of foure sides, and in a spire of a towre which containeth many sides, either of which is a Pyramis.

And because that all the superficieces of euery Pyramis ascend from one playne superficies as from the base, and tende to one poynt, it must of necessitie come to passe; that all the superficieces of a Pyra∣mis are trianguler, except the base, which may be of any forme or figure except a circle. For if the base be a circle, then it ascendeth not with sides, or diuers superficieces, but with one round superficies, and hath not the name of a Pyramis, but is called (as hereafter shall appeare) a Cone.

Of Pyramid, there are diuers kindes. For according to the varietie of the base is brought forth the varietie and diuersitie of kindes of Pyramids. If the base of a Pyramis be a triangle, then is it called a triangled Pyramis. If the base be a figure of fower angles, it is called a quadrangled Pyramis. If the base be a Pentagon, then is it a Pentagonall or fiue angled Pyramis. And so forth according to the increase of the angles of the base infinitely. Although the fi∣gure

[illustration]

of a Pyramis can not be well expressed in a playne superficies, yet may ye sufficiently conceaue of it both by the figure before set in the de••inition of a solide angle, and by the figure here set, if ye ima∣gine the point A together with the lines AB, AC, and AD, to be eleuated on high. And yet that the reader may more clerely see the forme of a Pyramis, I haue h••re set two sundry Pyramids which will appeare bodilike, if ye erecte the papers wherin are drawen the trian∣gular sides of eche Pyramis, in such sort that the pointes of the angles F of ech triangle may in euery Pyramis concurre in one point, and make a solide angle: one of which hath to his base a fower sided fi∣gure, and the other a fiue sided figure. T〈◊〉〈◊〉me of a triangled Pyra∣mis ye may before beholde in the examp〈◊〉〈◊〉 solide angle. And by these may ye conceaue of all other kindes o•• ••yramids.

Notes

• * 1.1

  Tenth diffini∣tion.