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 6, 2024.
Pages
¶An assumpt.
If there be three right lines hauing betwene them selues any proportion: as the first is to the third, so is the parallelograme contained vnder the first and the second, to the parallelograme contained vnder the second and the third.
Suppose that these three lines AB, B
[illustration]
C, and CD be in some certayne proporti∣on. Then I say that as the line AB is to the line CD, so is the parallelograme contay∣ned vnder the lines AB and BC to the parallelograme contayned vnder the lines BC and CD.* 1.1 From the point A raise vp vnto the line AB a perpendicular line AE, and let AE be equall to the line BC: and by the poynt E draw vnto the line AD a pa∣rallel line EK: and by euery one of the poyntes B, C, and D draw vnto the line AE parallel lines BF, CH, and DK. And for that as the line AB is to the line BC so is the parallelo∣grame AF to the parallelograme BH (by the first of the sixt):* 1.2 and as the line BC is to the
descriptionPage 255
lin••CD, so is the parallelograme BH to the parallelograme CK. Wherefore of equalitie as the line AB is to the line CD, so is the parallelograme AF to the parallelograme CK. But the parallelograme AF is that which is contayned vnder the lines AB and BC, for the line AE is put equall to the line BC. And the parallelograme CK is that which is contained vnder the lines BC and CD, for the line BC is equal to the line CH, for that the line CH is equall to the line AE (by the 34. of the first). If therefore there be three right lines ha∣uing betwene them selues any proportion: as the first is to the third, so is the parallelograme contained vnder the first and the second, to the parallelogramme cōtained vnder the second and the third: which was required to be demonstrated.