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 14, 2024.
Pages
¶ An other demonstration after Flussates, which proueth this proposition affirmatiuely.
From the parallelogramme ABGD let there be taken away the parallelogramme AEZK like and in like sorte situate with the whole parallelogramme ABGD, and ha∣uing also the angle A common with the whole parallelogramme.* 1.1 Then I say that both their diameters, namely, AZ and AZG do make one and the selfe same right line. De∣uide the sides AB and B•• into two equall partes in the pointes C and F (by the 10. of
descriptionPage [unnumbered]
the first.) And drawe a line from C to F.
[illustration]
Wherefore the line CF is a parallel to the right line AG (by the corollary added by Campane after the 29. of the first) Wher∣fore the angles BAG and BCF are equall (by the 29. of the first): but the angle EA∣Z is equall vnto the angle BAG (by reasō the parallelogrammes are supposed to be like) wherefore the same angle EAZ is e∣quall to the angle BCF, namely, the out∣ward angle to the inward and opposite an∣gle. Wherfore (by the 28. of the first) the lines AZ and CF are parallel lynes. Now then the lines AZ and AG being parallels to one and the selfe same lyne, namely, to CF do concurre in the point A. Wherefore they are set directly the one to the other, so that they both make one right line (by that which was added in the ende of the 30. proposition of the first) wherfore the parallelo∣grammes ABGD, and AEZK are about one and the selfe fame dimetient: which was required to be proued.