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
2. ¶An Assumpt.
If a right line be deuided into two vnequall partes: as the greater part is to the lesse,* 1.1 so is the parallelogramme contayned vnder the whole line and the greater part, to the parallelogramme contayned vnder the whole line and the lesse part.
Deuide the right line AB into two vnequall partes in the point E: And let AE be the greater part. Then I say, that as the line AE is to the line EB, so is the parallelogramme contained vnder the lines BA and AE to the parallelogramme contained vnder the lines BA & BE. Describe the square of the line AB, and let the
[illustration]
same be ACDB. And from the point E draw vnto either of these lines AC and DE a parallell line EF. Now it is manifest, that as the line AE is to the line EB, so is the pa∣rallelogramme AF to the parallelogramme BF (by the first of the sixt). But the parallelogramme AF is contayned vn∣der the lines BA and AE (for the line AC is equall to the line AB) and the parallelogramme BF is contained vn∣der the lines AB and BE (for the line DB is equall to the line AB). Wherefore as the line AE is to the line EB, so is the parallelogramme contained vnder the lines BA and AE, to the parallelogramme contained vnder the lines AB and BE: which was requi∣red to be demonstrated.
This Assumpt differeth litle from the first Proposition of the sixt booke.