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 15, 2024.
Pages
The 5. Theoreme. The 5. Proposition. If a magnitude be equemultiplex to a magnitude, as a parte taken away of the one, is to a part taken away from the other: the residue also of the one, to the residue of the other, shal be e∣quemultiplex, as the whole is to the whole.
SVppose that the whole magnitude AB be vnto the whole magnitude CD equemultiplex, as the part taken away of the one, namely, AE, is to the part taken away of the other, namely, CF. Then I say that the resi∣duē of the one, namely, EB, is to the residue of the other, namely, DF equemul∣tiplex as the whole AB is to the whole CD. How multiplex AE is to CF, so multiplex make EB to CG.* 1.1 And forasmuch as (by ye first of the fifth) AE is to GF equemultiplex, as AB is to GF:* 1.2 but AE is to CF equemulti∣plex, as AB is to CD. Wherfore AB is equemultiplex to either
[illustration]
of these GF and CD. Wherfore GF is equall vnto CD. Take a∣way CF which is common to them both. Wherfore that which re∣mayneth namely, GC, is equall vnto that which remayneth name∣ly, DF. And forasmuch as AE is to CF equemultiplex as EB is to GC, but GC is equall vnto DE, therefore AE is to CF eque∣multiplex as EB is to FD. But AE is put to be equemultiplex to CF, as AB is to CD, wherfore EB is to FD equemultiplex, as AB is to CD. Wherfore the residue EB is to the residue FD e∣quemultiplex, as the whole AB is to the whole CD. If therfore a
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magnitude be equemultiplex to a magnitude, as a part taken away of the one is to a parte taken away of the other: the residue of the one also to the residue of the other, shalbe equemultiplex as the whole is to the whole: which was required to be proued.