¶ An addition of Pelitarius.
If in a circle be inscribed a rectangle triangle, the side opposite vnto the right angle shall be the diameter of the circle.
* 1.1Suppose that in the circle ABC be inscribed a
[illustration]
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
About this Item
- 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
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http://name.umdl.umich.edu/A00429.0001.001
- Cite this Item
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"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.
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rectangle triangle ABC, whose angle at the point B let be a right angle. Then I say, that the side AC is the diameter of the circle. For if not, then shall the centre be without the line AC, as in the point E.* 1.2 And draw a line from the poynt A to the point E, & produce it to the circumference to the point D: and let AED be the diameter: and draw a line from the point B to the point D. Now (by this 31. Propositiō) the angle ABD shall be a right angle, and therefore shall be equall to the right angle ABC, namely, the part to the whole: which is ab∣surde. Euen so may we proue, that the centre is in no other where but in the line AC. Wherfore AC is the diameter of the circle: which was required to be proued.
Notes
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* 1.1
An addition of P••litarius.
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* 1.2
Demonstra∣tion lea••ing to an absurdi∣t••••.