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.

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Or, thus it may be demonstrated.

Forasmuch as the square, DN is quin••uple to the square GF, (I meane the square of DB the line geuē, to the square o•• DC the segmēt). And the same square DN, is equall to the parallelogrāme vnder AB, CB, with the square made of the line DC: by the sixth of the second: (for vnto the line AC, equally deuided: the line, CB, is, as it were adioyned). Wherefore the parallelogramme vnder AB, CB, toge∣ther with the square of DC, which is GF, is quintuple to

[illustration]

the square GF, made o•• th•• line DC. Taking then, that square GF, ••rom the parallelogramme vnder AB, CB: that parallelogramme (vnder AB, CB) remayning alone, is but quadruple to the sayd square of the line DC. But, (by the 4. of the second, or the second Corollary of the 20. of the sixth) RS, ••he square of the line AC, is quadrupla to the same square GF•• Wherfore by the 7. of the fifth, the square of the line AC, is equall to the parallelogramme vnder A∣B, CB, and so, by the second part of the 16. of the sixth: A∣B, AC, and CB, are three lines in continuall proportion. And seing AB is greater thē AC, the same AC, the double of the line DC, shall be greater then the part BC, remay∣ning: Wherfore by the 3. definition of the sixth, AB, (com∣posed or made of the double of DC, and the other part of DB remaining) is deuided by an extreme and middel pro∣portion: and also his greater segment is AC the double of the segment DC. Wherfore, If a right line be quintuple in power &c. as in the proposition•• which was to be demonstrated.