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 15, 2024.

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¶A Corollary.

A Dodecahedron is double to a Cube inscribed in it, taking away the third part of the lesse segment of the cube, and moreouer the lesse segment of the lesse segment of halfe of that excesse. For if there be geuen a cube, from which is cut of a solide set vpon a third part of the lesse segment of the base and vnder one and the same altitude with the cube: that solide taken away hath to the whole solide the proportion of the section of the base to the base, by the 32. of the eleuenth. Wherefo••e from the cube is taken away a third ••art of the lesse segment. Far∣ther, forasmuch as the residue wanteth of the altitude of the cube, by the lesse segment of the lesse seg∣ment of halfe the altitude or side, and that residue is a parallelipipedon, if it be cut by a plaine superficies parallel to the opposite plaine superficieces, cutting the altitude of the cube by a point, it shall take away from that parallelipipedon a solide, hauing to the whole the proportion of the section to the altitude, by the 3. Corollary of the 25. of the eleuenth. Wherefore the excesse wanteth of the same cube by the thi••d part of the lesse segment, and moreouer by the lesse segment of the lesse segment of halfe of that excesse.