Second Corollary.
A right line ioyning together the centres of the opposite bases of the Octo∣hedron, is sesquialter to the perpendicular line drawen from the angle of the in∣scribed
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.
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http://name.umdl.umich.edu/A00429.0001.001
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"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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pyramis to the base thereof. For forasmuch as the pyramis and the cube which containeth it do in the selfe same pointes end their angles (by the 1. of this booke): therefore they shall both be inclosed in one and the selfe same Octohedron (by the 4. of this booke). But the diame∣ter of the cube ioyneth together the centres of the opposite bases of the Octohedron, and therefore is the diameter of the Sphere which containeth the cube and the pyramis inscribed in the cube (by the 13. and 14. of the thirtenth): which diameter is sesquialter to the perpendicular which is drawen from the angle of the pyramis to the base thereof: for the line which is drawen from the centre of the sphere to the base of the pyramis, is the sixth part of the diameter (by the 3. Corollary of the 13. of the thir∣tenth). Wherefore of what partes the di••meter containeth sixe, of the same partes the perpendicular containeth fower.