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 15, 2024.
Pages
An other demonstration after Fl••s••••s.
If it be possible let there be a right line ABG,
[illustration]
whose part AB let be in the ground playne super∣ficies AED;* 1.1 and let the rest therof BG be eleuated on high, that is, without the playne AED. Then I say that ABG is not one right line. For forasmuch as AED is a plaine superficies, produce directly & equally vpon the sayd playne AED the right lyne AB towardes D, which by the 4. definition of the first shall be a right line. And from some one point of the right line ABD, namely, from C, dra•• vnto the point G a right lyne CG. Wherefore in the triangle 〈…〉〈…〉 the outward ang•••• AB•• is eq••••ll to the two inward and opposite angles (by the 32. of the first) and therfore it is lesse then two right angles (by the 17. of the same) Wherfore the lyne ABG forasmuch as it maketh an angle, is not •• right line. Wh••refore that part of a right line should be in a ground playne superficies, and part eleuated vpward is impossible.
If ye marke well the figure before added for the play••er declaration of Euclides demonstration, i•• will not be hard for you to co••••••••e this figure which ••luss••s putteth for his demonst••••tion •• wherein is no difference but onely the draught of the lyne GC.