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.

Suppose ABC the triangle from which I would cut off one acre, that is to say 160 rodde by a paralele lyne to the side AB, first therefore I measure the Area of that whole triangle as was before taught in this boke, fynding AB 50 perch, AC 120, BC 130, and so consequentely the Area of that triangle 3000 rodde, the square of AC is 14400, the square of BC is 16900, these augmented by 160, bring 2304000, and 2704000, and these diuided by 3000, produce in the quotientes 768 and 901 ⅓, the roote of 768 perches) being 27 perches 12 foote) I mesure out in the side AC,

[illustration]

beginning from C, admit it ende at D, likewise the roote of 901 ⅓ perches is 30 pear∣ches, and betwene 4 and 9 in∣ches, measuring therefore 30 perches from C in the other side CB I sette vp a marke at E. Nowe if you drawe a streyght lyne from D to E it shall be a paralele to AB, and the peece of grounde, represented by DEC, an exacte acre. But if you desire to laye oute this acre at one of the sides as ye may see in the figure signified by the quadrilater Superficies ABGF, Then must ye deducte the aforesayde 160 roddes fro the Area of that triangle, the re∣mayne is 2840, whiche I multiplye as before in the square of AC, so haue I 40896000, Lykewise the same 2840 augmented by the square of BC produ∣ceth 48016000, these products seuerally deuided by 3000, the Area of the whole triangle will yelde in the quotientes 13632 and 16005 ⅓ theyr quadrate rootes are 116 perches 12 ½ foote, the length of the lyne CF, and 126 perches 8 ½ foote, the lyne GC, Or if yee deducte those rootes from the whole sides AC, and BC there wil remayn 3 rodde 4 foote from A to F, and 3 rodde 8 foote from B to G And thus may you in all Triangular peeces of ground, exactly lay forth an acre,

••r any other quantitie of grounde ye will require, and that either against the side 〈◊〉〈◊〉 Angle, euen as you will desire.