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 other addition of Pelitarius.
* 1.1Two vnequall lines being geuen, to know how much the square of the one is greater then the square of the other.
Suppose that there be two vnequal lines AB and BC: of which let AB be the grea∣ter. It is required to search out how much the square of AB excedeth the square of BC. That is I wil finde out the square, which with the square of the line BC shalbe equal to the square of the line AB. Put the lines A
[illustration]
B and BC directly, that they make both one right line: and making the centre the point B, and the space BA describe a circle ADE. And produce the line AC to the circumference, and let it concurre with it in the point E. And vpon the lyne AE and frō the point C erect (by the 11. proposition) a perpendiculer line CD, which produce till it concurre with the circumference in the point D: & draw a line from B to D. Then I say, that the square of the line CD, is the excesse of the square of the line AB aboue the square of the line BC. For for∣asmuch as in the triangle BCD, the angle at the point C is a right angle, the square of the base BD is equall to the squares of the two sides BC and CD (by this 47. proposition). Wherefore also the square of the line AB is equall to the selfe same squares of the lines BC and CD. Wherefore the square of the line BC is so much lesse then the square of the line AB, as is the square of the line CD: which was required to search out.