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.

The .4. Probleme. The side of any square knovvne by supputation to attaine the Semidiamiters of his exteriour and interiour Circles, vvith the content of his plaine or Area. (Book 4)

THe halfe of your geuen side is the Semidiameter of the in∣ternall Circle, and if ye double the square of this Semidia∣miter, and from the Product extract a Quadrate roote, that roote is the Semidiameter of the externall Circle. Now for the Area either multiply the side first geuen in it self, or else your lesser Semidiameter in halfe the Perimetry of your square.

Example.

[illustration]

Admit AB the squares side 10, the half being 5 is the Semidimetient of the in∣vvarde Circle, the square thereof doubled is 50, vvhose Quadrate roote is EG, the containing Circles Semidimetient. Novv for the Superficies I augment 10 by it selfe there ariseth 100. Likevvise 5 the in∣ternall Circles Semidiameter multiplied by 20 the squares Semiperimetry yel∣deth also 100, so muche is the Area of the square ABCD.

AB the side of the square 10.

• EG the containing circles Semidiameter √{powerof2}50
• EF the inscribed circles Semidimetient 5
• The Area of the square ABCD 100