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
¶ The 9. Theoreme. The 9. Pro〈◊〉〈◊〉 Right lines which are parallels to one and the selfe same right line, and are not in the selfe same superficies that it is in: are also parallels the one to the other.
SVppose that either of these right lines AB and CD be a parallel to the line EF not being in the selfe same superficies with it. Then I say that the line AB is a parallel to the line CD. Take in the line EF a point at all aduentures, and let the same be G.* 1.1 And from the point G raise vp in the superficies wherin are the lines EF and AB, vnto the line EF a perpendiculer line GH, and againe in the superficies wherin are the lines EF and CD, raise vp from the same point G to the line EF a perpen∣diculer line GK.* 1.2 And forasmuch as the line
[illustration]
EF is erected perpendiculerly to either of the lines GH and GK, therfore (by the 4. of the eleuenth) the line EF is erected perpendicu∣larly to the superficies wherein the lines GH and GK are, but the line EF is a parallel line to the line AB. Wherfore (by t••e 8. of the eleuenth) the line AB is erected perpendicu∣larly to the plaine superficies, wherin are the lines GH and GK. And by the same reason al∣so the line CD is erected perpendicularly to the plaine superficies wherin are the lines GH & GK. Wherefore either of these lines AB and CD is erected perpendicularly to the plaine superficies, wherin the lines GH and GK are. But if two right lines be erected perpendicu∣larly to one and the selfe same plaine superficies, those right lines are parallels the one to the other (by the 6. of the eleuenth) Wherfore the line AB is a parallel to the line CD. Wherfore right lines which are parallels to one & the selfe same right line, and are not in the self same superficies with it are also parallels the one to the other: which was required to be proued.
descriptionPage 328
This figure more clearely manifesteth the former propo∣sition
[illustration]
and demonstration, if ye eleuate the superficieces ABEF and CDEF that they may incline and concurre in the lyne EF.