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 6. Theoreme. The 6. Proposition. If two magnitudes be ••quemultiplices to two magnitudes, & any par••es taken away of them also, be aequemultiplices to the same magnitudes: the residues also of them shal vnto the same magnitudes be either equall, or equemultiplices.
SVppose that there be two magnitudes AB and CD equemultiplices to two magnitudes E and F, and let the partes takē away of the mag∣nitudes AB and CD, namely, AG and CH be equemultiplices to the same magnitudes E and F.* 1.1 Then I say that the residues GB and HD, are vnto the selfe same magnitudes E and F either equall, or els eque∣multiplices.
* 1.2Suppose first that GB be equall vnto E. Then I say that
[illustration]
HD is equall vnto F.* 1.3 Vnto F put an equall magnitude CK.
And forasmuch as AG is equemultiplex vnto E, as CH is vnto F:* 1.4 but GB is equall vnto E, & KC vnto F: therfore AB is equemultiplex to E, as KH is to F. But AB is put eque¦multiplex vnto E, as CD is to F. Wherfore KH is equimul¦tiplex vnto F, as CD is to F. And forasmuch as either of these KH and CD are equimultiplices vnto F, therfore (by the 1 common sentence) KH is equall vnto CD. Take away CH which is common to them both. Wherefore the residue KC is equal vnto the residue HD. But KC is equal vnto F, wher∣fore HD is equall vnto F. Wherfore if GB be equal vnto E, DH also shall be equall vnto F.
And in like sort may we proue, yt if GB be multiplex to E, HD also shal be so multiplex vnto F. If therfore there be two magnitudes equemultiplices to two magnitudes,* 1.5 and any parts taken away of them be also equemultiplices to ye same magnitudes: the residues also of them shall vnto the same magnitudes be either equall, or equemultiplices: which was required to be proued.