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 eight proposition.

If a number be deuided into two numbers, the superficiall number produced of the multiplication of the whole into one of the partes foure tymes, together with the square of the other parte, is equall to the square of the number composed of the whole number and the foresayd part.

Suppose that the number AB be deuided into two numbers AC and CB. Then I say that the superficiall number produced of the multiplication of the number AB in to the number CB foure tymes together with the square of the number AC, is equall to the square of the number composed of the numbers AB & CB. For vnto the num∣ber BC let the number BD be equall. Now forasmuch as the square of the

[illustration]

number AD is equal to the squares of the numbers AB and BD, & to the superficiall number produced of the multiplication of the numbers AB & BD the one into the other twise (by the 4. of this booke) And the number BD is equall to the number BC: therefore the square of the number AD is equall to the squares of the numbers AB and BC, and to the superficiall number produced of the multiplication of the numbers AB and BC the one into the other twise. But the squares of the numbers AB and BC are e∣quall vnto the superficiall number produced of the multiplication of the numbers AB and BC the one into the other twise, and to the square of AC (by the former proposition) Wherfore the square of the number AD is equall to the superficial number produced of the multiplication of the nū∣bers AB and BC the one into the other foure tymes, and to the square of the number AC. But the square of the number AD is the square of the number composed of the numbers AB and BC: for the number BD is e∣qual to the number BC. Wherfore the square of the number composed of the numbers AB and BC is equall to the superficiall number produced of the multiplication of the numbers AB and BC the one into the other foure tymes, & to the square of the num∣ber AC. If therfore a number be deuided into two numbers, &c.

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