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" The facility which this mode of expressing points on a cubic of the third class, gives to the management of questions concerning them, renders them nearly as easy to be treated as conic sections. Many theorems, too, are thus suggested, which, though only... "
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 166
by George Salmon - 1852 - 316 pages
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 334 pages
...ju2),~2. We see thus (as we found already, Art. 26) that the 3/> points, •where the curve of the pih degree meets the cubic, are such, that all but one...intersection. The tangents will be 2a2L - 3a2R + M = 0, 2j32L - 3/32R + M = 0, where a + /3 + 7 = 0, and j is known. We eliminate a, |3 thus : first, subtract...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1852 - 329 pages
...be R 3 R We see thus (as we found already, Art. 26) that the op points, where the curve of the p th degree meets the cubic, are such, that all but one...locus of their intersection. The tangents will be 2a 3 L - 3a 2 R + M = 0, 2/3 3 L-3j3 2 Rf M=0, where a + j3 + 7 = 0, and y is known. We eliminate a,...
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A Treatise on Infinitesimal Calculus: Differential calculus. 1857

Bartholomew Price - Calculus - 1857 - 660 pages
...through these several pairs ; and as these lines arc not tangents in the ordinary meaning of the word, the number of tangents which can be drawn to the curve from a given point is to be diminished by three for each cusp. Hence if a curve has K cusps, the number...
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A Treatise on the Analytic Geometry of Three Dimensions

George Salmon - Geometry, Analytic - 1862 - 465 pages
...satisfythat equation. This problem will have a definite number of solutions, and the number will plainly be the number of tangents which can be drawn to the curve from an arbitrary point; that is to say, the class of the curve. For example, the envelope of the line act*...
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A Treatise on the Analytic Geometry of Three Dimensions

George Salmon - Geometry, Analytic - 1862 - 502 pages
...that equation. This problem will have a definite number of solutions, and the number will plainly be the number of tangents which can be drawn to the curve from an arbitrary point; that is to say, the class of the curve. For example, the envelope of the line where...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1879 - 424 pages
...determine indirectly the number of double tangents of a curve of the ęth order. The equation of the system of tangents which can be drawn to the curve from any point x'y'z, may be derived from the equation A=0 by the method used (Conies, Arts. 92, 294). Any point on...
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The Collected Mathematical Papers of Arthur Cayley, Volume 11

Arthur Cayley - Mathematics - 1896 - 663 pages
...number of inflexions, and number of double tangents, — first, as regards the class, this is equal to the number of tangents which can be drawn to the curve from an arbitrary point, or what is the same thing, it is equal to the number of the points of contact of...
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The Collected Mathematical Papers of Arthur Cayley, Volume 11

Arthur Cayley - Mathematics - 1896 - 674 pages
...number of inflexions, and number of double tangents, — first, as regards the class, this is equal to the number of tangents which can be drawn to the curve from an arbitrary point, or what is the same thing, it is equal to the number of the points of contact of...
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Principles of Geometry: Vol. 2. Plane Geometry

H. F. Baker - 1954 - 270 pages
...the curve (other than at the multiple points), no one of which is common to all of them. Also that the number of tangents which can be drawn to the curve from an arbitrary point is 2m + 2p — 2. We have also shewn that the theory, for a curve whose multiple...
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