¶The 3. Theoreme. The 3. Proposition. If two playne superficieces cutte the one the other: their common section is a right line.
SVppose that these two superficieces AB & BC do
[illustration]
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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- Geometry -- Early works to 1800.
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http://name.umdl.umich.edu/A00429.0001.001
- Cite this Item
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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 14, 2024.
Pages
cutte the one the other, and let their common secti∣•••• ••e the line DB. Then I say that DB is a right line. For if not, draw from the poynt D to the point B a right line DFB in the playne superficies AB,* 1.1 and likewise from the same poyntes draw an other right line DEB in the playne superficies BC. Now therfore two right lines DEB and DFB shall ••aue the selfe sa•••• e••de••, and therefore doo include a superficies which (by the last common sentence) is impossible•• Wherefore the lines DEB and DFB are not right lines. In
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like sort also may we proue that no other right line can be drawne from the poynt D to the point B besides the line DB which is the common section of the two superficieces AB and BC. If therefore two playne superficieces cutte the one the other, their common section is a right line: which was required to be demonstrated.
[illustration]
This figure here set, sheweth most playnely not onely this third proposition, but also the demonstra∣tion thereof, if ye eleuate the superficies AB, and so compare it with the demonstration.
Notes
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* 1.1
Demonstra∣tion leading to an impossibi∣litie.