¶ A Corollary out of Flussates.* 1.1
By this Proposition we may deuide any right line geuen, accordyng to the pro∣portion
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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- 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.
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- Imprinted at London :: By Iohn Daye,
- [1570 (3 Feb.]]
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- 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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of any right lynes geuen. For let those right lynes hauyng proportion be ioyned together directly, that they may make all one right lyne, and then ioyne them to the lyne geuen anglewise. And so proceede as in the proposition, where you see that the right line geuen AB is deuided into the right lynes AF, FG and GB which haue the selfe same proportion that the right lines AD, DE, and EC haue.
By this and the former proposition also may a right line geuen be easily deui∣ded into what partes so euer you will name.* 1.2 As if you will deuide the line AB in∣to three equall partes, let the lyne DE be made equall to the lyne AD, and the lyne EC made equall to the same by the third of the first. And then vsing the selfe same maner of construction that was before: the lyne AB shall be deuided into three equall partes. And so of any kynde of partes whatsoeuer.
Notes
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* 1.1
A Corollary out of Flussates.
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* 1.2
By this and the former propo••ition may a right line be deui∣ded into what partes soeuer you will.