...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...

...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...

...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...

...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...

...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,...

...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...

...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...

...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...

...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,...

...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...