 | Nathan Scholfield - 1845 - 894 pages
...Ma =(CA+CM)'. (CA-CM) =CA'-CM' .-. CA'=CM'+Cw' And similarly. CB^PM'+dm1. 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 squant of the two axis. That is, If Pp, Dd, be any two... | |
 | Isaac Wilber Jackson - Conic sections - 1845 - 116 pages
...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... | |
 | James Devereux Hustler - Conic sections - 1845 - 85 pages
...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*... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...By composition, CA':CB'::CGxGT:DG'. Cor. 2. By Prop. XII., PROPOSITION XV. 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... | |
 | James Hann - Conic sections - 1850 - 146 pages
...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... | |
 | James Haddon - Differential calculus - 1851 - 180 pages
.... dp p ab ab , -»,s=r, — — = — — -- j rfjo, aft ; , - (aô)* (ai)* Henee 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 (2а)2 + (Щ2=(2г)2 or a2 + b2 a* The form of the evolute... | |
 | Elias Loomis - Calculus - 1851 - 300 pages
...r-, 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 of D by... | |
 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...Prove that such parallelograms have the least area of all which circumscribe the ellipse. 14. In an ellipse the sum of the squares of any two conjugate diameters is invariable. When is the square of their sum least ? 15. Define the asymptotes of an hyperbola. If any... | |
 | Francis James Jameson - Mathematics - 1851 - 144 pages
...tangent with the perpendicular upon it from the focus is the tangent at the vertex. 1848. (A). In an ellipse the sum of the squares of any two conjugate diameters is invariable. (JB). When is the square of their sum least? (CP+ CD)2 = OF* + CD2 + 2CP.CZ), (fig. 20)... | |
 | Elias Loomis - Calculus - 1851 - 296 pages
...that of the A 2A' conjugate axis is equal to -5-. PROPOSITION XII. — THEOREM. (1 14.) 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. Designate 92 the... | |
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... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. 
