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too complicated to be written here. Click on the link to download a text file. |
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X(2), X(67), X(524), X(625), X(40341), X(40342), X(40343) (these last three points are labelled Q1, Q2, Q3 in the figure) other points below |
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Geometric properties : |
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Osiris cubics are introduced in Table 75. K1167 is the only circular cubic of the net. Its singular focus is F = X(40340), the midpoint of X(5), X(126). K1167 meets the Droussent cubic K008 at three infinite points (X524, circular points) and six finite points (A, B, C, G (twice), X67). The tangent at G to both cubics passes through X(625) which is the tangential of G in K1167. K1167 meets the Steiner ellipse (S) at A, B, C and three other points S1, S2, S3 also on pK(G, X625). K1167 meets the medians again at A1, B1, C1 on the ellipse (S'), the image of (S) under the homothety h(G, –5/4). |