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
¶An other demonstration of the same after Campane.
Suppose that A and B be plaine numbers: and let the sides of A be the numbers C and D: and let the numbers E and F be the sides of the number B. And let D multiplying E produce the number G. Thē I say that the proportiō of
[illustration]
A to B is cōposed of the propor¦tiōs of C to E & D to F that is, of the sides of the superficial nū¦ber A to the sides of the super∣ficiall number B. For forasmuch as D multiplying E produced G, and multiplying C it produced A, therefore by (the 17. of the seuenth) A is to G as C is to E: agayne forasmuch as E multiplying D produced G and multiplying F it produ∣ceth B, therefore by the same G is to B as D is to F. Wherefore the proportions of the sides namely, of C to E and of D to F are one and the same with the proportions of A to G and G to B. But (by the fifth definition of the sixth) the proportion of the extremes A to B is composed of the proportions of the meanes, namely, of A to G and G to B, which are proued to be one and the same with the proportions of the sides C to E, and D to F. Wherefore the proportion of the superficiall numbers A to B is cōposed of the proportions of the sides C to E, and D to F. Wherefore pla••ne. &c. which was required to be proued.