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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An other demonstration after Flussas.

Suppose that vppon the line AB be described a square

[illustration]

whose diameter let be the line AC. Then I say that the side AB is incommensurable in length vnto the diameter AC. For∣asmuch as the lines AB and BC are equall, therefore the square of the line AC is double to the square of the line AB by the 47. of the first. Take by the 2. of the eight nūbers how many soeuer in continuall proportion frō vnitie, and in the proporti∣on of the squares of the lines AB and AC. Which let be the numbers D, E, F, G. And forasmuch as the first from vnitie name¦ly E is no square number, for that it is a prime number, neither is also any other of the sayd numbers a square number except the third from vnitie and so all the rest leuing one betwene, by the 10. of the ninth. Wherefore D is to E, or E to F, or F to G, in that proportion that a square number is to a number not square. Wherefore by the corrollary of the 25. of the eight, they are not in that proportion the one to the other that a square number is to a square number. Wherefore neither also haue the squares of the lines AB and AC (which are in the same pro∣portion) that porportion that a square number hath to a square number. Wherefore by the 9. of this booke their sides, namely, the side AB and the diameter AC are incommensurable in length the one to the other which was required to be proued.

This demonstration I thought good to adde, for that the former demonstrations seme not so full, and they are thought of some to be none of Theons, as also the proposi∣tion to be none of Euclides.