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 1, 2024.

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¶ Corollaryes added by Flussas.

First Corollary.

Hereby it is manifest, that the diameter of a Sphere containeth in power the sides both of a pyra∣mis and of a cube inscribed in it.

For the power of the side of the pyramis is two thirdes of the power of the diameter (by the 13. of this booke). And the power of the side of the cube is, by this Proposition, one third of the power of the sayd diameter. Wherefore the diameter of the Sphere contayneth in power the sides of the pyra∣mis and of the cube..

¶ Second Corollary.

All the diameters of a cube cut the one the other into two equall partes in the centre of the sphere which containeth the cube. And moreouer those diameters do in the selfe same point cut into two e∣quall partes the right lines which ioyne together the centres of the opposite bases.

As it is manifest to see by the right line LOF. For the angles LKO, and FIO, are equall, by the 29. of the first: and it is proued, that they are contained vnder equall sides: Wherefore (by the 4. of the first) the bases LO and FO are equall. In like sort may be proued, that the rest of the right lines which ioyne together the centres of the opposite bases do cut the one the other into two equall partes in the centre O.