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.]]
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Subject terms
Geometry -- Early works to 1800.
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http://name.umdl.umich.edu/A00429.0001.001
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"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 1, 2024.
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descriptionPage [unnumbered]
An other Corollary added also by Flussates.
If a number multiplying a square number, produce not a square number: the sayd number multiplying shall b•• no square number.* 1.1 For if it should be a square number, then should it and the number multiplied being like superficiall numbers (by reason they are square numbers) haue a meane proportionall (by the 18. of thys booke). And the number produced of the sayd meane should be equall to the number contayned vnder the extremes, which are square numbers (by the 20. of the seuenth). Wherefore the number produced of the extremes being equall to the square num∣ber produced of the meane, should be a square number. But the sayd number by supposition, is no square number. Wherefore neither is the number multiplying the square number, a square number.
The first part of the first Corollary is the conuerse of the 26. Proposition of this booke, and hath some vse in the tenth booke. The second part of the same also is the conuerse of the 27. Proposi∣tion of the same.