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
The 4. Probleme. The 30. Proposition. To deuide a circumference geuen into two equall partes.
SVppose that the circumference geuen be ADB. It is required to de∣uide the circumference ADB into two equall partes.* 1.1 Draw a right line from A to B. And (by the 10. of the first) deuide the line AB into two equall partes in the point C. And (by the 11. of the first) from the point C rayse vp vnto AB a perpendicular line CD. And draw these right lines AD and DB. And forasmuch as the line AC is equall to the line CB,* 1.2 & the line CD is common to them both, there∣fore
[illustration]
these two lines AC and CD are equall to these two lines BC and CD. And (by the 4. peti••ion) the angle ACD is equall to the angle BCD, for either of them is a right right angle. Wherfore (by the 4. of the first) the base AD is equall to the base DB. But equall right lines do cut away equall circum∣ferences, the greater equall to the greater, & the lesse equall to the lesse (by the 28. of the third) And either of these circum∣ferences AD and DB is lesse then a semicircle. Wherfore the circumference AD is equall to the circumference DB. Wherfore the circumference geuen is deui∣ded into two equall partes: Which was required to be done.