The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed

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Title: The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed
Author: Euclid.
Publication: Imprinted at London :: By Iohn Daye,; [1570 (3 Feb.]]
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: Geometry -- Early works to 1800.
Link to this Item: http://name.umdl.umich.edu/A00429.0001.001
Cite this Item: "The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A00429.0001.001. University of Michigan Library Digital Collections. Accessed June 14, 2024.

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The 35. Proposition. The solide of a Dodecahedron containeth of a Pyramis circumscribed a∣bout it two ninth partes, taking away a third part of one ninth part of the lesse segment (of a line diuided by an extreme and meane proportion) and moreouer the lesse segment of the lesse segment of halfe the residue.

IT hath bene proued that the Dodecahedron, together with the cube inscribed in it is contai∣ned in one and the selfe same pyramis, by the Corollary of the first of this booke. And by the Corollary of the 33. of this booke, it is manifest, that the Dodecahedron is double to the same cube, taking away the third part of the lesse segment, and moreouer the lesse segment of the lesse segment of halfe the residue, or of this excesse. But a pyramis is to the same cube inscribed in it nonecuple, by the 30. of this booke. Wherefore the Dodecahedron inscribed in the pyramis, and con∣taining the same cube twise, taking away the selfe same third of the lesse segment, and moreouer the lesse segment of the lesse segment of halfe the residue, shall containe two ninth partes of the solide of the pyramis (of which ninth partes eche is equall vnto the cube) taking away this selfe same excesse. The solide therefore of a Dodecahedron containeth of a Pyramis circumscribed about it two ninth partes, taking away a third part of one ninth part of the lesse segment (of a line diuided by an extmere and meane proportion) and moreouer the lesse segment of the lesse segment of halfe the residue.