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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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
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 15, 2024.
Pages
¶The 14. Theoreme. The 16. Proposition. If two numbers multiplying them selues the one into the other, produce any numbers: the numbers produced shall be equall the one into the other.
SVppose that there be two numbers A and B: and let A multiplying B produce C, and let B multiplying A produce D. Th••n I say, that the number C•• equall vn∣to the n••mber D.* 1.1Take any vnitie, namely•• E. And forasmuch as A multiplying B produced C, therefore B measureth C by the vnities which are in A. And vni∣tie E measureth the number A by those vnities which are in the number
[illustration]
A. VVhere••ore vnitie E so many times measureth A, as B measureth C. VVherefore alternately (by the 15. of the seuenth) vnitie E measureth the number B so many times as A measureth C. Againe, for that B mul∣tiplying A produced D, therefore A measureth D by th•• vnities which are in B. And vnitie E measureth B by the vnities which are in B. VVherefore vnitie E so many times measureth the number B, as A mea∣sureth D. But vnitie E so many times measureth the number B, as A measureth C. VVhere∣fore A measureth either of these numbers C and D a like. VVherefore (by the 3. common s••ntence of this booke) C is equall vnto D: which was required to be demonstrated.