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.

ABC is the triangle whose sides are knowen, AB 24, BC 40, AC 32, the perpendicular founde, a•• is tofore declared, is 19 ⅕, which diuided at I, in suche

sorte that DI to IA retayne the

[illustration]

proportion of BC to DA, DI shall bee the side of the greatest square that may be made within that Triangle: but too finde the length of DI, you muste multi∣plie 40 the base BC in 19 ⅕ the perpendiculare, so haue you 3840/5 which diuided by 206/5 the perpē∣diculare and Base ioyned togi∣ther, yeldeth 12 36/37, the line ID. Likewise, if ye square the perpendicular, the mounting summe will be 9216/25 which diuided by 196/5 the former diuisor bringeth in the quotient 6 ••2/185, which deducted fro 19 ⅕ the perpendicular, there remayneth 12 180/185, the side of the greatest square agreeing with the former operation. In like manner if ye diuide BD, whose longitude you were taught by the laste Chapter to finde, and also AB, the left side of the Triangle in such sorte, that the greater sections to the lesser retayne the same proportion, that the base doth to the perpen∣dicular, the squares of the two greater sections one deducted from the other le∣ueth the Area of the greatest square that maye be described within that Tri∣angle. Also, if ye diuide any of the two lesser sides in two partes retayning the fo∣resayd proportion of the perpendiculare to the Base, the lesser of those Portions augmented by the base and the product diuided by the side bringeth in the quoti∣ent that greatest squares side. Thus also an other way, you maye attayne the same: Diuide both the Casus, that is ••o say, BD, and DC the distance of ey∣ther Angle from the perpendicular, in like manner as hath been said of the Per∣pendicular, then adde both the smaller sections togither, the resulting summe is the squares side: Euery of these wayes working, ye may resolue this question, great pleasure shall the Arithmetrician (especially if he be seene in surde and radi∣call numbers) receyue, when he shall perceyue so diuerse intricate and different o∣perations alwaye in fine to produce the selfe same certayntie.