 | Benedict Sestini - Geometry, Analytic - 1852 - 246 pages
...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.... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...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... | |
 | Horatio Nelson Robinson - Conic sections - 1862 - 356 pages
...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,... | |
 | Horatio Nelson Robinson - Conic sections - 1863 - 362 pages
...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,... | |
 | St. Louis Mo, board of directors of the publ. sch - 1871 - 354 pages
...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... | |
 | Gerardus Beekman Docharty - Calculus - 1865 - 328 pages
...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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...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... | |
 | Charles Taylor - Conic sections - 1883 - 164 pages
...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* ~... | |
 | Charles Hamilton Ashton - Geometry, Analytic - 1900 - 294 pages
...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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... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. 
