 | Benedict Sestini - 1852 - 246 pàgines
...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 - 1858 - 256 pàgines
...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 - 1862 - 356 pàgines
...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 - 1863 - 362 pàgines
...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 pàgines
...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 - 1865 - 328 pàgines
...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 - 1877 - 458 pàgines
...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 - 1883 - 164 pàgines
...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 - 1900 - 294 pàgines
...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. 
