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.
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 6. Probleme. The 6. Proposition. In a circle geuen, to describe a square.
SVppose that the circle geuen be ABCD. It is required in the circle ABCD to describe a square. Draw in the circle ABCD two diameters making right angles,* 1.1 and let the same be AC and BD, and drawe right lines from A to B, from B to C, from C to D,
[illustration]
and from D to A. And forasmuch as the line BE is equall vnto the line ED (by the 15. definition of the first) for the point E is the centre.* 1.2 And the line EA is common to them both, making on eche side a right angle: ther∣fore (by the 4. of the first) the base AB is e∣quall vnto the base AD. And by the same reason also either of these lines BC and CD is equall to either of these lines AB and AD: wherefore ABCD is a figure of foure equal sides. I say also that it is a rectangle figure. For forasmuch as the right line BD is the diameter of the circle ABCD, therfore the angle BAD beyng in the se∣micircle is a right angle (by the 31. of the third) And by the same reason euery one of these angles ABC, BCD and CDA is a right angle. Wherfore the foure sided figure ABCD is a rectangle figure, and it is proued that it consisteth of equall sides. Wherfore (by the 30. definition of the first) it is a square, and it is described in the circle ABCD: which was required to be done.