Projective Geometry
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In our eReader you can find the full English version of the book. Read Projective 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 Projective Geometry
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The quadrangle QOPR is then inscribed in the curve. The tangents at and R must meet on the line ST (Art. 57). Thus ST is parallel to OY. Also SP and TQ are parallel lines. Hence, x'OD'LO'WLO ^^^ and yi_EQ_LS_DP_j_ xi~ OE" LO" W^ LO ^^^ Eliminating LO from (1) and (2) we have X Xi The ratio y^/x is, therefore, the same for all points on the parabola.
Hence: The equation of a parabolay referred to any diameter and the tangent at its extremity as coordinate axes, is y^ = kx, where k is a constant....
The parabola is completely determined by three fixed points 0, Of R and the tangents at and R; and is generated by project- ively related sheaves of rays with centers at and R, correspond- ing rays meeting in the various positions of P. This remark furnishes an easy construction for the parabola.
The results of this article establish completely the identity of the curves of second order with the conies of analytic geometry.
Exercises 1. Construct an ellipse according to the suggestions made in 2 of the preceding article.
What to read after Projective Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Dowling, L. Wayland (Linnaeus Wayland), B. 1867 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The quadrangle QOPR is then inscribed in the curve. The tangents at and R must meet on the line ST (Art. 57). Thus ST is parallel to OY. Also SP and TQ are parallel lines. Hence, x'OD'LO'WLO ^^^ and yi_EQ_LS_DP_j_ xi~ OE" LO" W^ LO ^^^ Eliminating LO from (1) and (2) we have X Xi The ratio y^/x is, therefore, the same for all points on the parabola.
Hence: The equation of a parabolay referred to any diameter and the tangent at its extremity as coordinate axes, is y^ = kx, where k is a constant....
The parabola is completely determined by three fixed points 0, Of R and the tangents at and R; and is generated by project- ively related sheaves of rays with centers at and R, correspond- ing rays meeting in the various positions of P. This remark furnishes an easy construction for the parabola.
The results of this article establish completely the identity of the curves of second order with the conies of analytic geometry.
Exercises 1. Construct an ellipse according to the suggestions made in 2 of the preceding article.
What to read after Projective Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Dowling, L. Wayland (Linnaeus Wayland), B. 1867 to read onlineMoreLess
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