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.

Admit this round holowe timber logge ABC were to be measured the heigth being 14 foote, the Diameter of the outwarde Circle 7 foote, the Dimetient of the

[illustration]

inwarde Circle 5 foote, the circumfe∣rēce of the bigger 22 foote, the cōtent su∣perficiall or plaine of it 38 ½ the Circū¦ference of the lesse 15 foote and ••/7, hys plaine 19 ••/14. Now multiply 38 ½, in 14,

•• haue ye the crassitude of the whole round peece of Timber which is 539 foote. ••hen augment 19 ••/14 into 14 ryseth 275 foote, whiche subtracted from 539, re∣••ayneth 264, so many foote is in the crassitude aboute that hollow piece of tym∣••er. Or thus ye may bring it to passe: Pul 19 9/14 from 38 ½, that is the one super∣••••ciall content from the other, and the remayne multiplye in the heigth 14, So ••aue ye as afore 264 foote. An other example of tymber hollowed and somewhat ••ashioned lyke vnto a troughe: Suppose it to be DEFG, whose outward bredth DE is 10 foote, the length EF 14 foote, the heigth FG 8 foot, the inward bredth ••f the hollow HI 5 foote, the length HK 7 foote, the heigth as before. Now mul∣••iplie 10 in 14, so haue ye 140. This augmented in 8 ryseth 1120. Then multi∣••lye 7 in 5, that maketh 35, whiche augmented in 8, surmounteth 280, that ••umme by subtraction taken from 1120, leaueth 840, so many foote is the crassi∣••ude of this hollow troughe DEFG, euen thus of all other. By that whiche is ••oken ye may gather howe to get the capacitie of all maner regular vessels, and ••hat is performed in multiplying the playne or content superficiall of the inward ••ase or bottom in the profunditie or heigth. Example 35 the inward bases playn ••ugmented in 8, the heigth produceth 280. So many cubicall feete is in the hol∣••owe vessell. These 280 augmented in 51, bringeth foorth 14280 pints of water, farther diuided by 8 sheweth 1785 gallons. Thus of al other, and that for liquour ••onteyned in any maner vessell.