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.
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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 May 2, 2024.
Pages
¶ A Corollary following of the former Propositions.
A binomiall line and the other irrationall lines following it, are neither mediall lines, nor one and the same betwene them selues. For the square of a mediall line applied to a rati∣onall line, maketh the breadth rationall and incommensurale in length to the rationall line, wherunto it is applied (by the 22. of the tenth). The square of a binomiall line applyed to •• rationall line, maketh the breadth a first binomiall line (by the 60. of the tenth). The square of a first bimediall line applied vnto a rationall line, maketh the breadth a second binomiall line (by the 61. of the tenth). The square of a second bimediall line applied vnto a rationall line, maketh the breadth a third binomiall line (by the 62. of the tenth). The square of a greater line applied to a rationall line, maketh the breadth a fourth binomiall line (by the 63. of the tenth). The square of a line containing in power a rationall & a mediall superficies, maketh the breadth a fift binomiall line (by the 64. of the tenth). And the square of a line containing in power two medialls, applied vnto a rationall line, maketh the breadth a sixt binomiall line (by the 65. of the tenth). Seing therefore that these foresaid breadthes differ both from the first breadth, for that it is rationall, and differ also the one from the other, for that they are binomials of diuers orders: it is manifest that those irrationall lines differ also the one from the other.