A geometrical practise, named Pantometria diuided into three bookes, longimetra, planimetra, and stereometria, containing rules manifolde for mensuration of all lines, superficies and solides: with sundry straunge conclusions both by instrument and without, and also by perspectiue glasses, to set forth the true description or exact plat of an whole region: framed by Leonard Digges gentleman, lately finished by Thomas Digges his sonne. Who hathe also thereunto adioyned a mathematicall treatise of the fiue regulare Platonicall bodies, and their Metamorphosis or transformation into fiue other equilater vniforme solides Geometricall, of his owne inuention, hitherto not mentioned of by any geometricians.

Example.

Considering of Solides called Prismata, there are two kindes, the one directe •• vpright, whose Paralelogrammes are Perpendiculare to their Base, the other ••••lique or declining, whose Paralelogrammes are obliquely situate on their bases. ••f either I minde to propound an example, although one rule suffise them bothe. ••dmit therfore ABCDEF a direct or vpright Triangular Prisma, hauing 〈◊〉〈◊〉 three sides of his base ED 3, DC 4, EC ••, his altitude AD 10, so that by 〈◊〉〈◊〉 rules geuen in Planimetra I finde the Area of either Triangle or base 6, the Paralelogrammes AFED 30, ABCD 40 FBCE 50, all these ioyned toge∣ther,

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make 132, the Superficies of that Prisma. Likewise for the superficies of the declining solide IKLMNO, by the preceptes geuē in Planimetra I finde the Area of the right angled Paralelogrammes or bases either of them 18, the Area of the other Pa∣ralelogrammes IGNO 39, IGLK 72, KLMP 39, OPNM 72. and these ioyned ••••gether yeldeth 258, that is the content superficiall therof.

For the Crassitude I search the altitude of either Solide, which in the vpright Prisma is, the ereared side of any of his Paralelogrammes, as AD, BC, or FE. ••or they are all equall, euery one of them being 10, but the altitude of the declining Quadrangular Prisma is the Perpendicular OR, falling from O the top of the Prisma perpendicularly on MR a line drawne in the plaine wheron the body re∣••••eth, 10 therfore multiplied in 6, produceth 60, the Solide quantitie of that Pris∣••a: Also the altitude OC being founde by mensuration 12. multiplied in 18 the ••ase, bringeth 216, and that is the Solide capacitie of the declining Prisma IKLMNO.

Although these common péeces. K.L. are moten as is tofore taught, yet 〈◊〉〈◊〉 may readely thus measure them, multiplye the length with the bredth, ••nd the Product in the thicknesse, so haue ye the content or Crassitude.

Beholde the Figure.

The content of K 216 Cubicall foote, the Crassitude of L 216 square foote.

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