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 addition of Flussates.
The selfe same also followeth in parallelogrames.* 1.1 For if vpon the base AB be set on one & the same side these equal parallelogrames ABCD & ABGE, they shall of necessitie be in the selfe same parallel lines. For if not, but one of them is
descriptionPage [unnumbered]
set eyther within or without, let the parallelo∣grame
[illustration]
B•• being equall to the parallelograme ABCD be set within the same parallel lines: wherefore the same parallelograme BF beyng e∣quall to the parallelograme ABCD (by the 35. proposition) shall also be equall to the other pa∣rallelograme ABGE (by the first common sen∣tence) For the parallelograme ABGE is by sup∣position equall to the parallelogramme ABCD: whe••fore the parallelograme BF being equall to the parallelograme ABGE, the parte shall bee e∣qual to the whole, which is absurde. The same in∣conuenience also will followe, if it fall without. VVherefore it can neither fall within nor with∣out. VVherfore equall parallelogrames beyng vpon one and the selfe same base and on one and the same side, are also in the selfe same parallel lines.