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
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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 1, 2024.
Pages
¶A Corollary added by Flussates.
If two nnmbers be in the same proportion the one to the other that a square number is to a square number: those two numbers shall be like superficiall numbers.* 1.1 And if they be in the same propor∣tion the one to the other that a cube number is to a cube number, they shall be like solide nūbers.
First let the number A haue vnto the number B the same proportion, that the square number C hath to the square number D. Then I say, that A and B are like superficiall nūbers. For forasmuch as betwene the square numbers C and D there falleth a meane proportionall (by the 11. of this booke) there shall
[illustration]
also betwene A and B (which haue one and the same proportion with C and D) fall a meane proportio∣nall (by the 8. of this booke). Wherefore A and B are like superficiall nūbers (by the 20. of this booke).
But if A be vnto B, as the cube number C, is to the cube number D. Then are A & B like solide num∣bers. For forasmuch as C and D are cube numbers, there falleth betwene them ••wo meane proportio∣nall
[illustration]
numbers (by the 12. of this booke). And therefore (by the 8. of the same) betwene A and B (which are in the same proportion that C is to D) there falleth also two meane proportionall numbers. Wher∣fore (by the 21. of this booke) A and B are like solide numbers.