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.

Pages

Composition of the first Theoreme.

Now forasmuch as the square of the line AB is quadruple to the square of the line AD, but the square of the line AB, is that which is contayned vnder the lines AB, and AC, toge∣ther with that, which is contayned vnder the lines BA, and BC. Wherefore that which is contayned vnder the lines BA, and AC, together with that which is contayned vnder the lines BA, and BC is quadruple to the square of the line AD. But that which is contayned vnder the lines BA, and AC, is equall to that which is contayned vnder the lines DA, and AC twise (by the 1. of the sixth), and that which is contayned vnder the lines AB, and ••C is equall to the square of the line AC, by the definition of a line diuided by extreme and meane proportion. Wherefore the square of the line AC, together with that, which is contay∣ned vnder the lines DA, and AC twise, is quaduple to the square of the line DA. Wherfore that which is composed of the squares of the lines DA, and AC, together with that which is contayned vnder the lines DA, and AC, twise, is quintuple to the square of the line DA. But that which is composed of the squares of the lines DA, and AC, together with that which is contayned vnder the lines DA, and AC twise, is equall to the square of the line CD (by the 4. of the second). Wherefore the square of the line CD is quintuple to the square of the line AD: which was required to be demonstrated.