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" ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. "
The Principles of Analytical Geometry: Designed for the Use of Students - Strona 115
autor: Henry Parr Hamilton - 1826 - Liczba stron: 326
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A Treatise on Analytical Geometry

Benedict Sestini - 1852 - Liczba stron: 246
...be the diameter of the system of chords parallel to that line 126 Proposition VI., .The difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes 128 Properties of the equilateral hyperbola 129 Proposition VII....
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Elements of Geometry and Conic Sections

Elias Loomis - 1858 - Liczba stron: 256
...CH'. By composition, CB' : CA' : : EH' : CA'+CH' or CG". Hence CA" : CB' : : CG" : EH". The difference of the squares of any two conjugate diameters, is equal to the difference of the squares of the axes. Let DD', EE' be any two conjugate diameters ; then we shall...
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Conic Sections and Analytical Geometry: Theoretically and Practically ...

Horatio Nelson Robinson - 1862 - Liczba stron: 356
...4J/2— 4.B'2=4^L?— 4.B2, which equation shows this general geometrical truth : That the difference of the squares of any two conjugate- diameters is equal to the difference of the squares of the axes. Hence, there can be no equal conjugate diameters unless A=JB,...
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Conic Sections and Analytical Geometry: Theoretically and Practically ...

Horatio Nelson Robinson - 1863 - Liczba stron: 362
...have Or 4J.'2— 4B'2=4A} which equation shows this general geometrical truth : That the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. Hence, there can be no equal conjugate diameters unless A=B,...
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Sixteenth (Twenty-fifth) annual report

St. Louis Mo, board of directors of the publ. sch - 1871 - Liczba stron: 354
...equation of the ellipse, referred to its center and conjugate diameters. 13. Prove that the difference of the squares of any two conjugate diameters, is equal to the difference of the squares of the axes. 14. Deduce the equation of the hyperbola, referred to its center...
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Elements of Analytical Geometry, and of the Differential and Integral Calculus

Gerardus Beekman Docharty - 1865 - Liczba stron: 328
...diameters is equal to the sum of the squares of the axes. (100.) But in an hyperbola, the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. Let D'D and E'E be any two conjugate diameters, a;', y' the...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - Liczba stron: 458
...drawn, we shall have Hence CG x GT : Cg Xfft : : DG* : dg\ PROPOSITION . XVII. THEOREM. The difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. Let DD', EE' be any two conjugate diameters ; then we shall...
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The Elementary Geometry of Conics

Charles Taylor - 1883 - Liczba stron: 164
...CB : CA, and CN* + CR* = CA* ; and therefore PN* + DR* = CB\ By addition, CP* + CD* = CA* + Cff, or the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axes of the ellipse*. (ii) In the hyperbola, as will be proved in Art. 52 -f% CP* ~...
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Plane and Solid Analytic Geometry: An Elementary Textbook

Charles Hamilton Ashton - 1900 - Liczba stron: 294
...conjugate diameters of the equilateral hyperbola Xy = k ? 82. Theorems concerning diameters. — 1. In the ellipse the sum of the squares of any two conjugate semi-diameters is equal to the sum of the squares of the semi-axes. In Fig. 81, let GP1= a' and CP2=...
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