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

¶ The 11. Theoreme. The 11. Proposition. If from vnitie be numbers in continuall proportion how many soeuer, the lesse measureth the greater by some one of them which are before in the said proportionall numbers.

SVppose that from vnitie A be these numbers in continuall proportion B, C, D, E. Then I say that of these numbers B, C, D, •••• E being the lesse, measureth E the grea¦ter by one of these numbers C or D. For for that as vnitie A is vnto the number B, so is D to E,* 1.1 therfore how many times vnitie A measureth

[illustration]

the number B, so many times D measureth E•• wherefore alternately (by the 15. of the seuenth) how many times vni∣ti•• A measureth the number D, so many times •• mea∣sureth E. But vnitie A measureth D by those vnities which are in D. Wherefore B also measureth E by those vnities which are in D. Wherefore •• the lesse, measu∣reth. E the greater by some one of the numbers which went before E in the proportionall numbers. And so likewise may we proue that E measureth D by some one of the numbers ••, C, D, namely, by C. And so of the rest. If therfore from vnitie &c. Which was required to be proued.

Notes

* 1.1

Demonstra∣tion.

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