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 sixt Proposition.
If there be taken three quantities in one order, and as many in an other order, and if the proportion of the first to the second in the first order, be greater then the proportion of the first to the second in the latter order: then also the proportion of the first to the third in the first order, shall be greater then the proportion of the first to the third in the latter order.
Suppose that there be three quātities in one order A, B, C, & as many other quātities in an other order D, E, F. And let the proportion of A to B in the first order be greater then the proportion of D to E in the second order, and let also the proportion of B to C in the first order, be greater then the proportion of E to F in the second order. Then I say that
[illustration]
the pro∣portion of A to C in the first or∣der, is greater thē the propor∣tion of D to F in the second order.* 1.1 For let G be vnto C as E is to F. Now then by the first part of the 10 of this booke G shall be lesse then B. And therefore by the second parte of the 8. of the
descriptionPage 152
••••me, the propor••••on of A to G i•• greater th••n the proport••on of •• to ••. Wh••rfore the proportion of A to G is muche greater th••n the proportion of D to E. Now then let •• be 〈…〉〈…〉D is to E. Wherfore by the first part of the 10•• of the same, A is great••r thē H. And therfore by the first part of the 8. of the same, the proportion of A to C is greater then the proportion of H to C. But by proportion of equality H is to C as D is to F (for H is to G as D i•• to E, and G is to C as E is to F. Wherfore by the 12. of the same A hath to C a greater proportion then hath D to F: which was required to be proued.