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" ... from it by the theory of reciprocal polars (or that of geometrical duality), viz. we do not demonstrate the first theorem and deduce from it the other, but we do at one and the same time demonstrate the two theorems; our (a:, y, e) instead of meaning... "
The Collected Mathematical Papers of Arthur Cayley - Page 468
by Arthur Cayley - 1896 - 664 pages
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon, Arthur Cayley - Curves, Algebraic - 1873 - 379 pages
...polars (or lhat of geometrical duality) : viz. we do not demonstrate the first theorem and deduce ^frorn it the other, but we do at one and the same time demonstrate the two theorems: our (a:, y^ z) instead of meaning point-coordinates may mean line-coordinates, and the demonstration is...
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Monthly Notices of the Royal Astronomical Society, Volume 39

Royal Astronomical Society - Astronomy - 1879 - 598 pages
...reciprocal polars (or that of geometrical duality) : viz., we do not demonstrate the first theorem and deduce from it the other, but we do at one and the...same time demonstrate the two theorems : our (x, y, ••) instead of meaning point coordinates may mean line coordinates, and the demonstration is in...
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Monthly Notices of the Royal Astronomical Society, Volume 39

Royal Astronomical Society - Astronomy - 1879 - 602 pages
...reciprocal polars (or that of geometrical duality) : viz., we do not demonstrate the first theorem and deduce from it the other, but we do at one and the same time demonstrate the two theorems : our (a;, y, z) instead of meaning point coordinates may mean line coordinates, and the demonstration is...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1879 - 426 pages
...reciprocal polars (or that of geometrical duality), vijs. we do not demonstrate the first theorem and deduce from it the other, but we do at one and the same time demonstrate the two theorems; our (ar, y, z) instead of meaning point-coordinates may mean line-coordinates, and the demonstration is...
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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
...reciprocal polars (or that of geometrical duality), viz. we do not demonstrate the first theorem and deduce from it the other, but we do at one and the same time demonstrate the two theorems; our (a:, y, e) instead of meaning point-coordinates may mean line-coordinates, and the demonstration is...
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Monthly Notices of the Royal Astronomical Society, Volume 39

Royal Astronomical Society - Astronomy - 1879 - 594 pages
...geometrical duality) : viz., we do not demonstrate the first theorem and deduce from it the other, bnt we do at one and the same time demonstrate the two theorems : our (x, y, 2) instead of meaning point coordinates may mean line coordinates, and the demonstration is in every...
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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
...deduce from it the other, but we do at one and the same time demonstrate the two theorems; our (or, y, z) instead of meaning point-coordinates may mean line-coordinates, and the demonstration is in every step thereof a demonstration of the correlative theorem. 23. And in like manner when any theorem...
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The Collected Mathematical Papers of Arthur Cayley, Volume 11

Arthur Cayley - Mathematics - 1896 - 676 pages
...line-equation (»$f, 17, f)" = 0 is the relation which is satisfied by the line-coordinates (f, 17, f) of each line (tangent) of the curve. There is in...according to a cross division, are Proper. Improper. , ... (1. The stationary point, 2. The double point, or node; romt-smgulanties — •( -, I cusp,...
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The Collected Mathematical Papers of Arthur Cayley, Volume 11

Arthur Cayley - Mathematics - 1896 - 676 pages
...deduce from it the other, but we do at one and the same time demonstrate the two theorems ; our (a;, y, z) instead of meaning point-coordinates may mean...according to a cross division, are Proper. Improper. -. . , (1. The stationary point, 2. The double point, or node; roint-singularities — i . , I cusp,...
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