An Elementary Treatise On Trilinear Co-Ordinates: the Method of Reciprocal ...
An Elementary Treatise On Trilinear Co-Ordinates: the Method of Reciprocal ...
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Trilinear Co-Ordinates: the Method of Reciprocal ... 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 An Elementary Treatise On Trilinear Co-Ordinates: the Method of Reciprocal ...
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9. Since the tangents at the extremity of any diame- ter of a conic are parallel to one another, it follows that the polar of the centre is at an infinite distance, and con- versely, that the line at infinity reciprocates into the centre of the auxiliary conic. Hence it follows tliat parallel lines reciprocate into points lying on a straight line passing through the centre of the auxiliary conic ; and that the asymptotes of any curve, being the tangents drawn to it at the points where it meets ...the line at infinity, reciprocate into the points of contact of the tangents drawn to the reciprocal curve from the centre of the auxiliary conic.
Since the asymptotes of an hyperbola are real, while those of an ellipse are imaginary, it follows that the tangents, drawn from the centre of the auxiliary conic (supposed real) to the reciprocal curve, will be real or imaginary, according as the original curve is an hyperbola or an ellipse. If it be a para- bola, the reciprocal curve will pass through the centre of the conic, which is in accordance with what has already been 8tq,ted, that every parabola touches the line at infinity.
What to read after An Elementary Treatise On Trilinear Co-Ordinates: the Method of Reciprocal ...?
You can find similar books in the "Read Also" column, or choose other free books by Norman Macleod Ferrers to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
9. Since the tangents at the extremity of any diame- ter of a conic are parallel to one another, it follows that the polar of the centre is at an infinite distance, and con- versely, that the line at infinity reciprocates into the centre of the auxiliary conic. Hence it follows tliat parallel lines reciprocate into points lying on a straight line passing through the centre of the auxiliary conic ; and that the asymptotes of any curve, being the tangents drawn to it at the points where it meets ...the line at infinity, reciprocate into the points of contact of the tangents drawn to the reciprocal curve from the centre of the auxiliary conic.
Since the asymptotes of an hyperbola are real, while those of an ellipse are imaginary, it follows that the tangents, drawn from the centre of the auxiliary conic (supposed real) to the reciprocal curve, will be real or imaginary, according as the original curve is an hyperbola or an ellipse. If it be a para- bola, the reciprocal curve will pass through the centre of the conic, which is in accordance with what has already been 8tq,ted, that every parabola touches the line at infinity.
What to read after An Elementary Treatise On Trilinear Co-Ordinates: the Method of Reciprocal ...?
You can find similar books in the "Read Also" column, or choose other free books by Norman Macleod Ferrers to read onlineMoreLess
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