An other more briefe demonstration of the same after Campane.
Suppose that A be a greater line, vnto which let the line B be
[illustration]
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.
- 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 May 2, 2024.
Pages
commēsurable, either in length and power, or in power onely. And take a rational line CD. And vpon it apply the superficies C•• equall to the square of the line A: and also vpō the line FE (which is equall to the rationall line CD) apply the parallelogramme FG equall to the square of the line B. And forasmuch as the squares of the two lines A and •• are commensurable by supposition, the superficies C••, shalbe commensurable vnto the superficies FG: and therefore by the first of the sixt and tenth of this booke, the line DE is commen∣surable in length to the line GB. And forasmuch as (by the ••3. of this booke) the line DE is a fourth binomiall line, therefore by the ••6. of this booke the line GE is also a fourth binomiall line: where∣fore by the 57. of this booke the line B which contayneth in power the superficies FG is a greater line.
Notes
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An other de∣monstration after Campane.