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
descriptionPage 157
¶ Here also Flussates addeth a Corollary.
If a line parallel to one of the sides of a triangle do cut the triangle, it shall cut of from the whole triangle a triangle like to the whole triangle.* 1.1 For as it hath bene proued it deui∣deth the sides proportionally. So that as EC is to EA, so is BD to DA, wherfore by the 18. of the fifth, as AC is to AE, so is AB to AD. Wherfore alternately by the 16. of the fifth as AC is to AB, so is AE to AD: wherefore in the two trian∣gles EAD and CAB the sides about the common angle A are proportional. The sayd triangles also are equiangle. For forasmuch as the right lynes AEC and ADB do fall vpon the parallel lynes ED and CB, therefore by the 29. of the firs•• they make the angles AED and ADE in the triangle ADE equall to the angles ACB and ABC in the triangle ACB. Wherefore by the first definition of this booke the whole triangle ABC is like vnto the triangle cut of ADE.