 | Benedict Sestini - Geometry, Analytic - 1852 - 246 pages
...2а we have also a« b* С a = Ca"-f- Ce = a* + b* and 4."Co3+ 4.CTe'i= 4.a2 + 4.6s that is, the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axes. PROPOSITION V. The parallelogram on the conjugates is equal to the... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...EH'— CB' : 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 have DD''-EE''=AA''— BB''. Draw... | |
 | Horatio Nelson Robinson - Conic sections - 1862 - 356 pages
...A'2—B'2=A2—B2. Or 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, and then every diameter will be... | |
 | Horatio Nelson Robinson - Conic sections - 1863 - 362 pages
...properties. SCHOLIUM 1. — By adding eqs. (1) and (2) we find Or 44'3+4£'='=4ul='+4.B1. That is, the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axes. SCHOLIUM 2.— Equation eq. (3) or (5) will give us m when n is given... | |
 | St. Louis Mo, board of directors of the publ. sch - 1871 - 354 pages
...Deduce the 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 and asymptotes. ASTRONOMY. 1.... | |
 | Gerardus Beekman Docharty - Calculus - 1865 - 328 pages
...signs belong to the ellipse, the lower to the hyperbola. PROPOSITION X. (99.) In an ellipse, the sum of the squares of any two conjugate 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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
..."c dtl>c drawn, we shall have Hence CG.GT : Cg.gt : : DG2 : dg\ PROPOSITION' XVII. THEOREM. The sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axes. Let DD', EE' be any two conjugate diameters; then we shall have DD'2+EE'2=AA'2+BB'2.... | |
 | De Volson Wood - Geometry, Analytic - 1882 - 360 pages
...be found from the preceding equation. Changing V to — b", and b' ~ to — b' ~ gives that is : For the hyperbola the difference of the squares of any two conjugate diameters, equals the difference of the squares of the axes. Because the axes are conjugate, we must have, (Art.... | |
 | Education, Higher - 1882 - 498 pages
...distances of any point is equal to the square on the corresponding semi-conjugate diameter. 9. Prove that in the hyperbola the difference of the squares of any two semi-conjugate diameters is equal to the difference of the squares of the semi-axes. 10. Shew how to... | |
 | Charles Taylor - Conic sections - 1883 - 164 pages
...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... | |
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Fig. 83,84. conjugate diameters is equal to the sum of the squares of the... 
