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.]]
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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.
Pages
¶The 10. Proposition. The side of an Icosahedron, is the meane proportionall betwene the side of the Cube circumscribed about the Icosahedron, and the side of the Dode∣cahedron inscribed in the same Cube.
SVppose that there be a cube ABFD, in which let there be inscribed an icosahedron CL∣IGOR, by the 14. of the fiuetenth.* 1.1 Let also the Dodecahedron inscribed in the same be EDMNPS, by the 13. of the same. Now forasmuch as CL the side of the Icosahedron is the greater segmēt of AB the side of the cube circumscribed about it, by the 3. Corolla∣ry of the 14. of the fiuetenth:* 1.2 and the side ED of the
[illustration]
Dodecahedrō inscribed in thesame cube is the lesse segmēt of the same side AB of the cube, by the 2. Corollary of the 13. of the fiuetenth: it followeth that AB the side of the cube be∣ing diuided by an extreme and meane proportion, maketh the greater segment CL the side of the Icosahedron inscribed in it, and the lesse segment ED the side of the Dodecahedron likewise inscrib••d in it. Wherefore as the whole line AB the side of the cube, is to the greater segment CL the side of the Icosahedron, so is the greater segment CL the side of the Icosahedron, to the lesse segment ED•• the side of the Dodecahedron, by the third definition of the sixth. Wherefore the side of an Icosahedron, is the meane proportionall betwene the side of the cube circum∣scribed about the Icosahedron, and the side of the Dodecahe∣dron inscribed in the same cube.