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
About this Item
- 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
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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 1, 2024.
Pages
Page [unnumbered]
SVppose that the right line EF falling vppon these two right lines AB and CD, do make the alternate angles, namely, the angles AEF & EFD equall the one to the other. Then I say that AB is a parallel line to CD. For if not, then these lines produced shall
mete together, either on the side of B and D, or on the syde of A & C.* 1.1 Let them be produced therfore, and let them mete if it be possible on the syde of B and D, in the point G. VVherfore in the triangle GEF, the outward angle AEF is equal to the in∣ward and opposite angle EFG, which (by the 16. proposition) is impossible. VVherfore the lines AB and CD beyng produced on the side of B and D, shall not meete. In like sorte also may it be proued that they shall not mete on the syde of A and C. But lines whiche being produced on no syde meete together, are parrallell lines (by the last definition:) wherfore AB is a parrallel line to CD. If therfore a right line falling vpon two right lines, do make the alternate angles equall the one to the other: those two right lines are parrallels the one to the o∣ther: which was required to be demonstrated.[illustration]
* 1.2This worde alternate is of Euclide in diuers places diuersly taken: somtimes for a kind of situation in place, and somtime for an order in proportion, in which signification he vseth it in the v. booke, and in his bokes of numbers. And in the first signification he vseth it here in this place, and generally in all hys other bokes,* 1.3 h••uing to do with lines & figures. And those two angles he calleth alter∣nate, which beyng both contayned within two parallel or equidistant lynes are neither angles in order, nor are on the one and selfe same side, but are seperated the one from the other by the line which falleth on the two lines: the one angle beyng aboue, and the other beneath.
Notes
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* 1.1
Demo••stration ••eading to an absurditie.
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* 1.2
〈1 paragraph〉〈1 paragraph〉
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* 1.3
〈1 paragraph〉〈1 paragraph〉