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 15. Theoreme. The 21. Proposition. Rectiline figures which are like vnto one and the same recti∣line figure, are also like the one to the other.
SVppose there be two rectiline figures A and B like vnto the rectiline figure C. Then I say that the figure A is also like vnto the figure B. For forasmuch as the figure A is like vnto the figure C,* 1.1 it is also equi∣angle vnto it (by the conuersion of the first definition of the sixth) & the sides including the equall angles
[illustration]
shall be proportionall. Agayne foras∣much as the figure B is like vnto the figure C, it is also (by the same defini∣tion) equiangle vnto it, and the sides about the equall angles are proportio∣nall. Wherfore both these figures A and B are equiangle vnto the figure C, and the sides about the equall angles are proportionall. Wherfore (by the first common sentence) the figure A is equiangle vnto the figure B, and the sides a∣bout the equall angles are proportionall, wherfore the figure B is like vnto the figure A, which was required to be proued.