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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 119
autor: Henry Parr Hamilton - 1826 - Liczba stron: 326
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A Treatise on Fluxions: In Two Volumes, Tom 2

Colin MacLaurin - 1801
...cp*+cqx, or ca1, as CA* + caz to ca1; consequently CtP + CL1 is equal toCAx+c«% or CA^ + CD1; that is, the sum of the squares of any two conjugate diameters is equal to the sum of the squaresof theaxis ABaod DE. 617. Any rectangle gh/k (Jig. 273) in the plane of the circle that is contained...
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A Course of Mathematics ...: Designed for the Use of the Officers and ..., Tom 2

Isaac Dalby - 1806
...arc bisected at the points of contact H, K, V, P, as iu the ellipse (art. 278). 288. The difference of the squares of any two conjugate diameters, is equal to the difference of the squares of the two axes : That is, HV — PK" = CC' — ZBJ. In the ellipse their...
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Elements of the Conic Sections

Robert Simson - 1809 - Liczba stron: 177
...of CF, together with the rectangle EFD, that is, to the (5. 2. Elem.) square of CD. •CoR. 3. Hence the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axes. Let CD, CL be the semi-axis, and CA, C1J conjugate semi-diameters ; let AF, BG...
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Elements of the Conic Sections

Robert Simson - 1817 - Liczba stron: 253
...square of CF, together with the rectangle EFD, that is, to the (5. 2. Elem.) square of CD. COR. 3. Hence the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axis. Let CD, CL be (he semiaxes, and CA, CB conjugate semidiameters ; let AF, BG be...
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Elements of conic sections deduced from the cone

Abram Robertson - 1818 - Liczba stron: 125
...conjugate diameters is equal to the sum of the squares of the axes ; 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. For the rest remaining, as in the last two articles, let AB,...
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British Encyclopedia: Or, Dictionary of Arts and Sciences, Comprising ..., Tom 5

William Nicholson - 1819
...semi-diameter, which is conjugate to that passing through the point of contact. 8. In every ellipsis, the sum of the squares of any two conjugate diameters is equal to the sum of the. squares of the two axes. 9. In every .ellipsis, the angles F GI, /GH, (fig. 1), made by the tangent...
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American Edition of the British Encyclopedia: Or, Dictionary of Arts ..., Tom 5

William Nicholson - 1819
...semi-diameter, which is conjugate to that passing through the point of contact. 8. In every ellipsis, the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the two axes. 9. In every ellipsis, the angles F Gl, /GH, (fig. 1), made by the tangent...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - Liczba stron: 494
...angles, is greater than its conjugate. Cor. In ellipses, the sum, and in hyperbolas, the difference of the squares, of any two conjugate diameters, is equal to the sum or difference, as the case may be, of the squares of any other conjugate diameters, being each, by...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - Liczba stron: 494
...contained by the asymtotes be not right, any two conjugate diameters are unequal; and the difference of the squares of any two conjugate diameters, is equal to the difference of the squares oftheaxes. The sum of the squares of any two conjugate diameters of an ellipse,...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - Liczba stron: 575
...CE=^-MP, cuv Filth, rfJ— fr« ~CP*-f. PM« — DE^— CE-i = CM* — CIK Therefore the difference of the squares of any two conjugate diameters is equal to the dillerence of the squares of the two axes. Hence also in the equilateral hyperbola the conjugate diameters...
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