 | Abram Robertson - Conic sections - 1825 - 180 pages
...ii.)CE*==CD1; but in the hyperbola C P1-C Q1=C P2-DP x PE =s (6. ii.) C D1 =*C Ea. BOOK 200. In an ellipse the sum of the squares of any two .conjugate diameters is equal to the sum of the squares PROP- of the axes ; but in an hyperbola the difference of the Fig. 83, 84. squares of. any... | |
 | Edinburgh encyclopaedia - 1830 - 828 pages
...QG are drawn, is equal to the square of CA, the semidiameter. Fer CE1-r.CG'=CE«+AE.En=CAl. COR. 3. The sum of the squares of any two conjugate diameters, is equal to the sum of the squares of ihe axes. Let Aa, B6 be the axes, and Pp, Qtf any two conjugate diameters ; tlraw PE, QG... | |
 | Ireland commissioners of nat. educ - 1834 - 370 pages
...the squares of the ordinates drawn from the conjugate to the axis. Cor. 5. From this it appears that the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the transverse and conjugate diameters. For AC2+ CD2 = (N02+ Rx2+ Cx2 + С N2 — ) Cor.... | |
 | Henry Parr Hamilton - Mathematics - 1834 - 272 pages
...in (3) the value of y in (2), and dividing the result by 62, we have or a , -y; 234. The difference of the squares of any two conjugate diameters is equal to the difference of the squares of the semiaxes. Let CP, CD be any two semi-conjugate diameters, then denoting... | |
 | Henry Parr Hamilton - Conic sections - 1834 - 240 pages
...Segments of the other 232 SECT. II. On the Properties of Conjugate Diameters, p. 164. The Difference of the Squares of any two Conjugate Diameters is equal to the Difference of the Squares of the Axes 234 The Area of all Parallelograms, whose Sides are parallel... | |
 | 1837 - 136 pages
...ordinates drawn from the vertices of two semi-conjugates to the axis. Cor. 6. From this it appears Chat the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the transverse and conjugate diameters. For Ac2 + cD2 = (N O2 + R X2 + cX2 + с N2 =) cO'... | |
 | A. Bell - Conic sections - 1837 - 180 pages
...are equal to the segments intercepted on CG from C by perpendiculars on it from Q and D. COR. 3. — The sum of the squares of any two conjugate diameters is equal to the sum of the squares of the transverse and conjugate axis. For CD2 + CQ2 = CK2 + KD2 + CN2 + NQ2 = (CK2 + CN2) +... | |
 | William Wallace - Conic sections - 1837 - 248 pages
...diameter. For it has been shown that CE* = CG* + CR*, therefore CE* — CG* = CR*. COR. 3. The difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. Let Rr, Ss be the axes, and Pp, Qq any two conjugate diameters;... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...Ma =(CA+CM)\ (CA-CM) =CA'— CM' .-. CA'=CM'+Cm' And similarly. CB^PW+dm'. PROPOSITION XV. THEOREM. The sum of the squares of any two conjugate diameters, is equal to the same constant quantity, namely, the sum of the squares of the two axis. That is, If Pp, Dd, be any... | |
 | Nathan Scholfield - Conic sections - 1845 - 244 pages
...(CA+CM) . (CA-CM) =CA'— CM' .-. CA'=CM'+C»i' And similarly. CB'=PM.'+dm'. PROPOSITION XV. THEOREM. The sum of the squares of any two conjugate diameters, is equal to the same constant quantity, namely, the sum of the squares of the two axis. That is, If Pp, Dd, be any... | |
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... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. 
