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 7, 2024.
Pages
¶The 34. Theoreme. The 39. Proposition. If a number measure any number: the number measured shall haue a part after the denomination of the number measuring.
SVppose that there be a number B, which let measure the number A. Then I say, that A hath a part taking his denomination of the number B. For how often B measureth A, so many vnities let there be in C. And let D be vnitie. And foras∣much as B measureth A, by those vnities which are in C, and vnitie D measu∣reth C by those vnities which are in C, therefore vnitie D, so
[illustration]
many times measureth the number C, as B doth measure A.* 1.1 Wherefore alternately (by the 15. of the seuenth) vnitie D, so many times measureth B, as C doth measure A. Wherfore what part vnitie D is of the number B, the same part is C of A. But vnitie D is a part of B hauing his denomination of B. VVher∣fore C also is a part of A hauing his denomination of B. VVherfore A hath C as a part taking his denomination of B: which was required to be proued.
The meaning of this Proposition is, that if three measure any number, that number hath a third part, and if foure measure any number the sayd number hath a fourth part. And so forth.