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 14, 2024.
Pages
¶ The fourth Proposition.
If there be foure quantities, and if the proportion of the first and the second to the second be greater then the proportion of the third and fourth to the fourth: then by diuision also the proportion of the first to the second, shall be greater th••n the proportion of the thirde to the fourth.
Suppose that the proportion of AB to B be greater then the proportion of CD to D.* 1.1 Then I say that by diuision also the proportion of A to B is greater then the pro∣portion of C to D. For it cannot be the same. For then by composition AB should be to B as CD is to D. Neither also can it be lesse:
[illustration]
for if the proportion of C to D be greater then the proportion of A to B, then by the former proposition, the proportion of CD to D should be greater then the proportion of AB to B: which is contrary also to the suppositiō. Wher∣fore the proportion of A to B is neither one and the same with the proportion of C to D,〈…〉〈…〉 it: Wherefore it is greater then it: which was required to be proued.
descriptionPage [unnumbered]
* 1.2The same may also be proued affirmatiuely. Suppose that EB be vnto B as CD is to D. Now then (by the first part of the 10. of
[illustration]
the fifth) EB shall be lesse then AB: and there∣fore by the common sentence, E is lesse then A, wherfore by the first part of the 8. of this booke, the proportion of E to B, is lesse then the propor∣tion of A to B, but as E is to B, so is C to D: wher∣fore the proportion of C to D, is lesse then the proportion of A to B. Wherfore the pro¦portion of A to B is greater then the proportion of C to D: which was required to be proued.