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" Fig. 83,84. conjugate diameters is equal to the sum of the squares of the... "
The Principles of Analytical Geometry: Designed for the Use of Students - Strona 120
autor: Henry Parr Hamilton - 1826 - Liczba stron: 326
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A Treatise on Fluxions: In Two Volumes, Tom 2

Colin MacLaurin - 1801
...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...
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A Course of Mathematics ...: Designed for the Use of the Officers and ..., Tom 2

Isaac Dalby - 1806
...parallelogram SN, consequently vlC . 2lZ or the rcctang. CG. ZB = the parallelogram SN. 279. The sum of the squares of any two conjugate diameters, is equal to the sum of the squares rf the, two axes. Tliut is, PK '• + HV = CG2 -1- ZB3 : (see the preceding fig.)...
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Elements of the Conic Sections

Robert Simson - 1809 - Liczba stron: 177
...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 ;...
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Elements of the Conic Sections

Robert Simson - 1817 - Liczba stron: 253
...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...
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Elements of conic sections deduced from the cone

Abram Robertson - 1818 - Liczba stron: 125
...any two Fig. 83,84. 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...diameters is equal to the difference of the squares of the axes. For the rest remaining, as in the last two articles, let AB, DE be the axes, and then the angles...
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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...
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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...
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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
...if the angles 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, is equal to the sum...
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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
...within the acute 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,...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - Liczba stron: 575
...PM'*=ft». Fourth, 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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