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 7, 2024.

Pages

An Assumpt.

But now that the angle of an equilater and equiangle pentagon is a right angle and a fi••th par•• more of a right angle, may thus be proued. Suppose that ABCDE be an equilater and equiangle pentagon.* 1.1 And (by the 14. of the fourth) describe about it a circle ABCDE. And take (by the 1. of the third) the center thereof,

[illustration]

and let the same be F. And draw these right lines FA, FB, FC, FD, FE. Wherefore those lines do diuide the angles of the pentagon into two equall partes in the poyntes A, B, C, D, E, by the 4. of the first. And ••orasmuch as the fiue angles that are at the poynt F a••e equall to fower right angles, by the corollary of the 15. of the first, and they are equall the one to the other by the 8. of the first: therfore one of those angles, as ••or example sake, the angle AFB is a fi••th part lesse then a right angle. Wherfore the angles remayning, namely, FAB, & ABF, are one right angle and a fifth part ouer. But the angle F∣AB is equall to the angle FBC. Wherefore the whole angle ABC being one of the an∣gles of the pentagon is a right angle and a fifth part more then a right angle: which was re∣quired to be proued.

Notes

* 1.1

That the angle of an equilater and equiangle Pentagon is one right angle and a 〈◊〉〈◊〉 part 〈◊〉〈◊〉 which thing was also before proued in the 〈◊〉〈◊〉 of the 32. of the ••irst.

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