 | 1836 - 798 pàgines
...usually done ; and then deduce Rules for finding the logarithms of numbers. (5G). QUESTION VI. By . Def. A diameter of a curve is the locus of the middle points of a system of parallel chords. Find the equations of the diameters of the curves represented by the general... | |
 | 1856 - 410 pàgines
...after performing the operation <td , dd ^«i -j -- r- az-j— •' 153. Mr. Fen-wick. Assuming that the diameter of a curve is the " locus of the middle points of a series of parallel chords," it is required to prove that all diameters of the Witch of Agnesi (the principal axis excepted) are... | |
 | 1850 - 418 pàgines
...be written for au a.. .(in, after performing the operation ddd 153. Mr. Fenreick. Assuming that the diameter of a curve is the " locus of the middle points of a series of parallel chords,'1 it \e required to prove that all diameters of the Witch of Agnesi (the principal axis excepted)... | |
 | James Hann - 1850 - 146 pàgines
...the tangent in terms of the angle that it makes with the major axis, is (46.) In the ellipse, to find the locus of the middle points of a series of parallel chords. The equation to the ellipse is AY + B2^ = A'B2 ..................... (1). Let MM' be any right line... | |
 | Royal Military Academy, Woolwich - 1853 - 476 pàgines
...CURVES. 45. To find the equation of a diameter to any curve of the second order. Definition. — The diameter of a curve is the locus of the middle points of a series of parallel chords. Let if = 4 mx ..... (1), be the equation of a parabola, the vertex being the origin (Art. 38), and... | |
 | Robert Potts - 1855 - 1050 pàgines
...find the polar equation to a straight line. 10. Explain what is meant by the diameter of a curve, and find the diameter of a given system of parallel chords in a parabola. If the angle included by the two lines x + y = 0, y = ^3.x be equal to \ir, what is the angle between... | |
 | Isaac Todhunter - 1855 - 332 pàgines
...lengths of the two lines that can be drawn from (x, y') in the given direction to the ellipse. 188. To find the diameter of ^ a given system of parallel chords in an ellipse. (See definition in Art. 148). Let 0 be the inclination of the chords to the major axis... | |
 | Isaac Todhunter - 1862 - 376 pàgines
...parabola, the roots are of the same sign, and the lines are drawn in the same direction. 148. DEF. A diameter of a curve is the locus of the middle points...To find the diameter of a given system of parallel •Jiords in a parabola. Let 0 be the inclination of the chords to the axis of the parabola ; let x',... | |
 | Percival Frost - 1863 - 526 pàgines
...CHAPTER XII. DIAMETRAL SURFACES. DIAMETRAL PLANES. CONJUGATE DIAMETERS. 236. DBF. A diametral surface is the locus of the middle points of a series of parallel chords of a given surface. There are, therefore, for any given surface, an infinite number of corresponding... | |
 | William Allen Whitworth - 1866 - 560 pàgines
...the middle points of any system of parallel chords in a conic section is a straight line. 240. DEP. The locus of the middle points of a series of parallel chords is called a diameter. One of these chords in its limiting and evanescent position will become the tangent... | |
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A diameter of a curve is the locus of the middle points of a series of parallel chords. 
