 | Henry Parr Hamilton - 1843 - 314 pàgines
...substituting in (3) the value of y in (2), and dividing the result by 6a, we have _ « or a 278. !TAe 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 them 'by a and b' respectively,... | |
 | James Devereux Hustler - 1845 - 85 pàgines
...tangents are drawn at A and B, CD coincides with CB, and PF with AC. Hence CDxPF=ACxBC. PROP. XVI. The difference of the squares of any two conjugate...diameters is equal to the difference of the squares of the axes. Draw CZX perpendicular to AB and PD, Then CP2-CD* = PX*-DX* = 4Pixi^(Eucl. 8. n.) But LX : OZ... | |
 | Isaac Wilber Jackson - 1845 - 116 pàgines
...: : AC2 : MO'*, , _,.-, __, BC'xAC* and F'MxFM = MQfa = CN2. (Cor. 1.) PROPOSITION XXIII. THEOREM. The difference of the squares of any two conjugate...diameters, is equal to the difference of the squares of the axes. That is, (Fig. 25,) MM'2 — NN"» = AAra — BB". From the triangles MCF and MCF', we have (Geom... | |
 | Nathan Scholfield - 1845 - 542 pàgines
...CA) (CM+CA). = CM2— CA" CA3 = CM2— Cm* And similarly, CB3 = dmt—PM'. PROPOSITION XV. THEOREM. The difference of the squares of any two conjugate diameters, is equal to the same constant quantity, namely, the difference of the squares of the two axes. That is, if Pp, Dd,... | |
 | Nathan Scholfield - 1845 - 244 pàgines
...CA) (CM+CA). = CM'— CA' CA' = CM'— Cm' And similarly, CB' = dm'— PM'. PROPOSITION XV. THEOREM. The difference of the squares of any two conjugate diameters, is equal to the same constant quantity, namely, the difference of the squares of the two axes. That is, if Pp, Dd,... | |
 | Nathan Scholfield - 1845 - 894 pàgines
...CA) (CM+CA). = CM'— CA' CA'=CM'— Cm' And similarly, CB' = am1— PM1. PROPOSITION XV. THEOREM. The difference of the squares of any two conjugate diameters, is equal to the same constant quantity, namely, the difference of the squares of the two axes. That is, if P/?, T)d,... | |
 | Elias Loomis - 1849 - 252 pàgines
...equal to CA ' —CH ' or AHxHA'; hence CA ' : CB ' : : CG ' : EH ' . PROPOSITION XV. THEOREM. The sum of the squares of any two conjugate diameters, is equal to the sum of ike squares of the axes. Let DD', EE' be any two conjugate diameters; then we shall have DD''+EE"=AA''+BB''.... | |
 | James Hann - 1850 - 146 pàgines
...b'2 = a2 - J2 From equation (3), 4a'6'sin(a' — a)=4a5 (1), (2), (3). (5). Equation (4) shews that the difference of the squares of any two conjugate diameters is equal to the difference of the square of the principal axes. Equation (5) shews that the rectangle described on any system of conjugate... | |
 | Elias Loomis - 1851 - 300 pàgines
...Art. 69, Cor. A 2A1 5, and that of the minor axis to -^-. PROPOSITION XIII. — THEOREM. (88.) 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. Designate the co-ordinates... | |
 | James Haddon - 1851 - 190 pàgines
...¿QCA=<¡,. - . (1) .dp p ab ab ,_ С'-Г' ~ dp,~ ab .. («*)• Hence But since, in an ellipse, the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the major and minor axes, therefore (2л)2 + (25)2=(2г-)2 or et i% з /^Г 3... | |
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Fig. 83,84. conjugate diameters is equal to the sum of the squares of the... 
