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" THEOREM. The parameter of any diameter is equal to four times the distance from the vertex of that diameter to the directrix, or four times the distance from the vertex to the focus. Y... "
Elements of Analytical Geometry, and of the Differential and Integral Calculus - Page 42
by Gerardus Beekman Docharty - 1865 - 306 pages
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The Elements of Analytical Geometry: Comprehending the Doctrine of the Conic ...

John Radford Young - Conic sections - 1830 - 342 pages
...employed, is called the parameter of that diameter, which is taken for the axis of x, so that generally the parameter of any diameter is equal to four times the distance of its vertex from the focus. By equation (5) the parameter is always equal to the double ordinate,...
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The Elements of Analytical Geometry: Comprehending the Doctrine of the Conic ...

John Radford Young - Conic sections - 1830 - 390 pages
...employed, is called the parameter of that diameter, which is taken for the axis of x, so that generally the parameter of any diameter is equal to four times the distance of its vertex from the focus. By equation (5) the parameter is always equal to the double ordinate,...
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An Analytical System of Conic Sections: Designed for the Use of Students

Henry Parr Hamilton - Mathematics - 1834 - 272 pages
...passing through the' focus is called the parameter of the corresponding diameter ; hence 80. COR. 2. The parameter of any diameter is equal to four times the distance of its vertex from the focus. 81. COR. 3. Hence also, the square of the ordinate to any diameter is...
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An Analytical System of Conic Sections: Designed for the Use of Students ...

Henry Parr Hamilton - Conic sections - 1834 - 240 pages
...passing through the focus is called the parameter of the corresponding diameter ; hence 80. COE. 2. The parameter of any diameter is equal to four times the distance of its vertex from the focus. 81. COR. 3. Hence also, the square of the ordinate to any diameter is...
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The Elements of Analytical Geometry ...

John Radford Young - Geometry, Analytic - 1835 - 298 pages
...employed, is called the parameter of that diameter, which is taken for the axis of x, so that generally the parameter of any diameter is equal to four times the distance of its vertex from the focus. By equation (5) the parameter is always equal to the double ordinate,...
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Elements of Analytical Geometry: Embracing the Equations of the Point, the ...

Charles Davies - Geometry, Analytic - 1836 - 370 pages
...new diameter A'X'. PROPOSITION VII. THEOREM. The parameter of any diameter is equal to four times ike distance from the vertex of that diameter to the directrix,...four times the distance from the vertex to the focus. Y' We have, from the last scholium, But the equation which determined the direction of the new axis...
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A Treatise on the Construction, Properties, and Analogies of the Three Conic ...

Bewick Bridge - Conic sections - 1836 - 148 pages
...(22) eg" =4SP XP#=4SP XSP = 4SP3. Hence 46c3=4SP=, and J6c =2SP, or be =4SP; that is, the parameter to any diameter is equal to four times the distance from the vertex of that diameter to the focus. (25.) COR. Hence QV3=(4SPxPV=)6cxPV; and since be is constant with respect to the same diameter,...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...terminated both ways by the curve ; or every diameter bisects its double ordinales. 8. The parameter to any diameter is equal to four times the distance from the vertex of that diameter to the focus. COR. The square of the ordinate is equal to the parameter into the abscissa.. 9. If a diameter...
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Mechanics of Fluids for Practical Men: Comprising Hydrostatics, Descriptive ...

Alexander Jamieson - Fluid mechanics - 1837 - 516 pages
...curve, we have D p = \p ; therefore, by addition, it is But since by the property of the parabola, the parameter of any diameter, is equal to four times the distance between the vertex of that diameter and the focus, we have P and by the equation to the curve, it is...
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Elements of Analytical Geometry: Embracing the Equations of the Point, the ...

Charles Davies - Geometry, Analytic - 1838 - 366 pages
...-fji or its equal 2p', is called the parameter of the new diameter A'X!. PROPOSITION VII. THEOREM. The parameter of any diameter is equal to four times...four times the distance from the vertex to the focus. Y' We have, from the last scholium, But the equation which determined the direction of the new axis...
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