An other demonstration after Campane.
Suppose that A be a mediall residuall line, vnto
[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.
- Link to this Item
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http://name.umdl.umich.edu/A00429.0001.001
- 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 June 14, 2024.
Pages
whome let the line B be commensurable in length, or in power onely. And take a rationall line CD, vnto which apply the parallelogramme CE equall to the square of the line A,* 1.1 and vnto the line FE (which is equall to the line CD) apply the parallelogramme F•• equall to the square of the line B. Now then the parallelogrammes CE and FG shall be commensurable,* 1.2 for that the lines A, B are commensurable in power: wherefore by the 1. of the sixth and 10. of this booke, th•• lines DE and FG are commensurable in length. Now then if A be a first mediall residuall line, then is the line DE a second resi∣duall line by the 98. of this booke: and if the line A be a s••cond mediall residuall line, then is the line •••• a third residuall line by the 99. of this booke. But if DE be a se∣cond residuall line, G•• also shall be a second residuall line (by the ••03. of this boke). And if DE be a third re∣siduall
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line, GE also shall (by the same) be also a third residuall line. Wherefore it followeth by the 9•• and 93. of this booke, that B is either a first medial residuall line or a second mediall residuall line, accor¦ding as the line A is supposed to be: which was required to be proued.
Notes
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* 1.1
Construction.
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* 1.2
Demonstra∣tion.