Non-Euclidean Geometry
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In our eReader you can find the full English version of the book. Read Non-Euclidean Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Non-Euclidean Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
It will lie in the projecting plane OFF'. AB, being perpendicular to FF' and to FK, is perpen- BOUNDARY-SUEFACES 51 dicular to this plane, OFF', and therefore to OF. In the same way we prove that AC is perpendicular to OE. Therefore, ^C is perpendicular to OD (Chap. I, I, 5). But OD is the intersection of the plane ABC with the plane ODD'. Hence, BC is perpendicular to this plane and to DD' (Chap. I, II, 15).
DD' being parallel to BB' lies -in the plane determined by BB' and BC, and in this pla...ne only one perpendicular can be drawn to BC at its middle point. Therefore, if we pass any plane through BB' and from B draw a chord to any other point, C, of its intersection with the surface, the perpendicular in this plane to BC, erected at the middle point of BC, will be parallel to BB'. This proves that the section is a boundary- curve, having BB' for axis, and that the surface can be gener- ated by the revolution of such a boundary -curve around BB'.
Therefore, BB' may be regarded as axis of the surface.
What to read after Non-Euclidean Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Manning, Henry Parker, 1859-1956 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
It will lie in the projecting plane OFF'. AB, being perpendicular to FF' and to FK, is perpen- BOUNDARY-SUEFACES 51 dicular to this plane, OFF', and therefore to OF. In the same way we prove that AC is perpendicular to OE. Therefore, ^C is perpendicular to OD (Chap. I, I, 5). But OD is the intersection of the plane ABC with the plane ODD'. Hence, BC is perpendicular to this plane and to DD' (Chap. I, II, 15).
DD' being parallel to BB' lies -in the plane determined by BB' and BC, and in this pla...ne only one perpendicular can be drawn to BC at its middle point. Therefore, if we pass any plane through BB' and from B draw a chord to any other point, C, of its intersection with the surface, the perpendicular in this plane to BC, erected at the middle point of BC, will be parallel to BB'. This proves that the section is a boundary- curve, having BB' for axis, and that the surface can be gener- ated by the revolution of such a boundary -curve around BB'.
Therefore, BB' may be regarded as axis of the surface.
What to read after Non-Euclidean Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Manning, Henry Parker, 1859-1956 to read onlineMoreLess
Read book Non-Euclidean Geometry for free
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