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
-
"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 1, 2024.
Pages
Page [unnumbered]
If there be fower quātities, & if the difference of the first to the second, be as the difference of the third to the fourth, then alternately, as the difference of the first is to the third, so is the difference of the second to the fourth.
This is to be vnderstand of quātities in like sort referred the one to the other, that is if the first be greater then the second,* 1.1 the third ought to be greater then the fourth and if the first be lesse then the se∣cond, the third ought to be lesse then the fourth: and is also to be vnderstand in arithmeticiall propor∣tionality. As for example let the difference of A be vnto B as the difference of C is to D.* 1.2 Then I say that as the difference of A is to C, so is the difference of B to D. For (by this common sētence, the difference of the extreames is composed of the differences of the ex∣treames
[illustration]
Notes
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* 1.1
An Assumpt of Campane.
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* 1.2
I. Dee.
Though Cam∣panes lemma be true, ye•• the maner of de∣monstrating it, (narrowly considered) is not artificiall.