Forasmuch as, AD is to AC: as AB, is to AC (because AD is equall to AB, by construction): but as AB is to AC, so is AC to CB: by supposition. Therefore by the 11. of the fifth, as AC, is to CB, so is AD to AC. * 1.1 Wherefore, as AC, and CB, (which is AB) is to CB: so is AD, and AC (which is DC) to AC. Therefore, euersedly, as AB, is to AC: so is DC to AD. And it is proued, AD, to be to AC: as AC is to CB. Wherefore as AB is to AC, and AC, to CB: so is DC, to AD, and AD, to AC. But AB, AC, and CB are in continuall proportion, by supposition: Wherfore DC, AD, and AC, are in continuall proportion. Wherefore, by the 3. definition of the sixth booke, DC, is deuided by extreme and middell proportion, and his greatest segment, is AD. Which was to be demonstrated. Note from the marke * 1.2, how this hath two demonstrations. One I haue set in the margent by.
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.
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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 15, 2024.
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Notes
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* 1.1
Therefore, by my second The∣oreme added v∣pon the second proposition, DC is deuided by ex¦treame and meane proporti∣on in the point A. And because AC is bigger then CB: ther∣fore DA is greater then A∣C: wherefore if a right line &c. as in the propo∣sition. Which was to be de∣monstrated.
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* 1.2
Therefore, by my second The∣oreme added v∣pon the second proposition, DC is deuided by ex¦treame and meane proporti∣on in the point A. And because AC is bigger then CB: ther∣fore DA is greater then A∣C: wherefore if a right line &c. as in the propo∣sition. Which was to be de∣monstrated.