An addition of Pelitarius.
To deuide a triangle geuen into two equall partes.
Suppose that the triangle geuen to be deuided in to two
[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 7, 2024.
Pages
equall partes be ABC.* 1.1 Deuide one of the sides therof, namely, BC into two equall partes (by the 10. propo∣sition) in the point D. And draw a line from the point D to the point A. Thē I say that the two triangles ABD & ACD, are equal, which is easy to proue (by the 38. pro∣position) if by the point A we drawe vnto the line BC a paral••el line (by the 31. proposition), which let by HK: for so the triangles AB D and ADC, consisting vppon equal bases BD & DC, and being in the selfe same paral∣lel lines HK and BC are of necessitie equall. The selfe
Page [unnumbered]
same thing also wil happen if the side BA be deuided into two equall parts in the point E, and so be drawen a right line from the point E, to the point C. Or if the side AC be deuided into two equall partes in the point F, and so be drawen a right line from the point F to the point B: which is in like manner proued by drawing parallel lines by the pointes B, and C, to the lines BA and AC,
* 1.2And so by this you may deuide any triangle into so many partes as are sig∣nified by any number that is euenly euen: as into 14.16.32.64. &c.
Notes
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* 1.1
An addition of Pelitarius, to deuide a trian∣gle into two e∣quall partes.
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* 1.2
Note.