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 Assumpt.

If there be two right lines hauing betwene them selues any proportion: as the one right line is to the other, so is the parallelograme contained vnder both the right lines to the square of the lesse of those two lines.

Suppose that these two right AB and BC be

[illustration]
in some certaine proportion.* 1.1 Then I say that as the line AB is to the line BC, so is the parallelograme contained vnder AB and BC to the square of BC. Describe the square of the line BC and let the same be CD, and make perfect the parallelograme AD now it is manifest that as the line AB is to the line BC, so is the parallelograme AD to the parallelograme or square BE (by the first of the sixt). But the parallelograme AD is that which is bontained vnder the lines AB and BC, for the line BC is equall to the line BD and the parallelograme BE is the square of the line BC. Wherefore as the line AB is to the line BC so is the parallelograme coutained vnder the lines AB and BC to the square of the line BC, which was required to be proued.

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