On the in And Circumscribed Triangles of the Plane Rational Quartic Curve By J
On the in And Circumscribed Triangles of the Plane Rational Quartic Curve By J
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The resulting curve is of order 10-3-2-2 = 3, t * W. F. Meyer: "Apolaritat und Rationale Curven, " Chap, i, p. 3. T Ibid. , Chap, ii, p. 184.
JR. Sturm: "Die Lehre von dem Geometrischen Verwandtschaften, " Vol. Iv, p. 44.
14 In-(nid-Circiimsc)ihed Triangles of Qitartic Curve having points of tangency on the sides 1'3' and 2'3' of the singular triangle in the transformed plane; also a branch of the curve goes through the vertex 3', since there is one extra intersection on the side 12 of the orig...inal triangle.
The original quintic had a third cusp, which in the transforma- tion remains a cusp. Hence the new curve is a cuspidal cubic, and therefore of the third class. That is, from a point of the curve, but one tangent, excluding the one at the point itself, may be drawn.
But this curve would be on the vertex 3' and have as tangents the sides 1'3' and 2'3', which is clearly an impossibility. I\ccordingly, the three cusped rational quintic cannot have a triple point.
The Quadratic Transformation t-ai If the quintic xi = ^^_ ' (i = 1, 2, 3) be subjected to the quadratic transformation Xi = - (i— 1, 2, 3), the resulting curve is t—ai or yi = {t-^i)Ht-a2)(t-as) y2 = {t-^2)-{t-a^){t-a{) yz = {t-^^y{t-a, ){t-a.^.
What to read after On the in And Circumscribed Triangles of the Plane Rational Quartic Curve By J?
You can find similar books in the "Read Also" column, or choose other free books by Joseph Nelson Rice to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The resulting curve is of order 10-3-2-2 = 3, t * W. F. Meyer: "Apolaritat und Rationale Curven, " Chap, i, p. 3. T Ibid. , Chap, ii, p. 184.
JR. Sturm: "Die Lehre von dem Geometrischen Verwandtschaften, " Vol. Iv, p. 44.
14 In-(nid-Circiimsc)ihed Triangles of Qitartic Curve having points of tangency on the sides 1'3' and 2'3' of the singular triangle in the transformed plane; also a branch of the curve goes through the vertex 3', since there is one extra intersection on the side 12 of the orig...inal triangle.
The original quintic had a third cusp, which in the transforma- tion remains a cusp. Hence the new curve is a cuspidal cubic, and therefore of the third class. That is, from a point of the curve, but one tangent, excluding the one at the point itself, may be drawn.
But this curve would be on the vertex 3' and have as tangents the sides 1'3' and 2'3', which is clearly an impossibility. I\ccordingly, the three cusped rational quintic cannot have a triple point.
The Quadratic Transformation t-ai If the quintic xi = ^^_ ' (i = 1, 2, 3) be subjected to the quadratic transformation Xi = - (i— 1, 2, 3), the resulting curve is t—ai or yi = {t-^i)Ht-a2)(t-as) y2 = {t-^2)-{t-a^){t-a{) yz = {t-^^y{t-a, ){t-a.^.
What to read after On the in And Circumscribed Triangles of the Plane Rational Quartic Curve By J?
You can find similar books in the "Read Also" column, or choose other free books by Joseph Nelson Rice to read onlineMoreLess
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