¶The 25. Theoreme. The 27. Proposition. If two numbers be prime the one to the other, that which is produced of the one into him selfe, is prime to the other.
SVppose that there be two numbers prime the one to the other,
[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
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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
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- Euclid.
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- Imprinted at London :: By Iohn Daye,
- [1570 (3 Feb.]]
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- Geometry -- Early works to 1800.
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http://name.umdl.umich.edu/A00429.0001.001
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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.
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A and B, and let A multiplieng himselfe produce C. Then I say that B and C are prime the one to the other. For put vn∣to A an equall number,* 1.1 namely, D. And forasmuch as A & B are prime the one to the other, and A is equall vnto D: therefore D and B also are prime the one to the other. Wherfore either of these numbers D and A is prime to B. Wherfore that which is produced of D into A is prime vnto B by the former proposition. But that number which is produced of D into A is the number C. Wherefore C and B are prime numbers the one to the other: which was required to be proued.
Notes
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* 1.1
Demonstra∣tion.