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.

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Title: 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.
Author: Digges, Leonard, d. 1571?
Publication: Imprinted at London :: By Henrie Bynneman,; Anno. 1571.
Rights/Permissions: To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
Subject terms: Mensuration -- Early works to 1800.; Geometry -- Early works to 1800.; Surveying -- Early works to 1800.
Link to this Item: http://name.umdl.umich.edu/A20458.0001.001
Cite this Item: "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." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A20458.0001.001. University of Michigan Library Digital Collections. Accessed May 22, 2025.

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Example.

Tetraedrons side supposed, Octaedrons side is ½, √{powerof2}½ his Diameter, vvhose square diuided by 12 bringeth 1/24, the roote being √{powerof2}1/24, is the Oc∣taedrons Axis. Likevvise for Icosaedron the medietie of Tetraedrons side diuided in extreame and meane proportion by the first Probleme, maketh the lesser portion ••/4—√{powerof2}5/16, the square hereof doubled, hath for his roote √{powerof2} vni. 14/8—√{powerof2}180/64, so much is the inscribed Icosaedrons side. Agayne, the difference of Tetraedrons sides medieties Portions diuided by ex∣treame and meane proportion is √{powerof2}20/16—1, the square of halfe this diffe∣rence is 9/16—√{powerof2}80/256, vvhich added to the square of Octaedrons sides me∣dietie, produceth ⅝—√{powerof2}5/16, the roote thereof doubled, is √{powerof2} v. 5/2—√{powerof2}5 the true quātitie of Icosaedrōs dimetiēt. Novv by subtracting 7/12—√{powerof2}45/144 the third parte of Icosaedrons sides square, from ⅝—√{powerof2}5/16, the laste pro∣ducte vvhose roote ye doubled to make the Diameter youre remainder vvil be this number 1/24+√{powerof2}45/144—√{powerof2}5/16, vvhose roote vniuersall is the inscri∣bed Icosaedrons Axis.

The con∣tayning Tetrae∣drons side 1

...Tetraedrons
- Diameter. √{powerof2}3/2
- Axis, √{powerof2}1/24
...The inscribed Octaedrons
- Syde ½
- Diameter √{powerof2}½
- Axis, √{powerof2}1/24
...The cōtayned Icosaedrons
- Syde √{powerof2} vni. 7/4—√{powerof2}45/16
- Diameter √{powerof2} vni. 5/2—√{powerof2}5
- Axis, √{powerof2}1/24.