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 14, 2024.

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¶ The 23. Theoreme. The 25. Proposition. If two numbers be in the same proportion the one to the other, that a cube number is to a cube number, and if the first be a cube number, the second al∣so shall be a cube number.

SVppose that two numbers A and B be in the same proportiō the one to the other, that the cube nūber C is vnto the cube number D. And let A be a cube number. Then I say that B also is a cube nūber. For forasmuch as C, D, are cube nūbers, therfore C,* 1.1 D are like solide numbers, wherfore (by the 19. of the eight) betwene

[illustration]

C and D there are two proportionall numbers. But how many numbers fall in continual pro∣portion betwene C and D, so many (by the 8. of the eight) fal there betwene the numbers that haue the same proportion with them. Wherefore betwene A and B there are two meane pro∣portionall numbers which let be E and F. And forasmuch as there are foure numbers in con∣tinuall proportion, namely, A, E, F, B, and A is a cube number, therefore (by the 2••. of the eight) B also is a cube number: which was required to be demonstrated.

A Corollary added by Flussates.

* 1.2Betwene a square number and a number that is not a square number, falleth not the proportion of one square number to an other. For if the first be a square number, the second also should be a square number which is contrary to the supposition. Likewis•• betwene a cube number, and a number that is no cube number falleth not the propor∣tion of one cube number to an other. For if the first be a cube number, the second also should be a cube number, which is contrary to the supposition, & therfore impossible.

Notes

* 1.1

Demonstra∣tion.

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* 1.2

A Corollary added by Flussates.

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