 | 1836 - 798 pages
...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 equation of the second... | |
 | Michel Chasles - 1837 - 564 pages
...For curves of the second order, since n = 2, the diametral curves can only be straight lines. 237- To find the locus of the middle points of a system of parallel chords of any curve. Let the chords be parallel to a line through the origin whose equation is у = ma?, and... | |
 | John Hymers - 1837 - 486 pages
...For curves of the second order, since n = 2, the diametral curves can only be straight lines. 237. To find the locus of the middle points of a system of parallel chords of any curve. Let the chords be parallel to a line through the origin whose equation is y = mx, and... | |
 | 1840 - 528 pages
...2 ' Sln T~ ' . c AB C . a+b and sin - . cos — — — = sin — . sin -•;;--• m im £i £i 8. Find the locus of the middle points of a system of parallel chords of the curve whose equation is ax* + bxy + cy* + dx -f ey +f = 0. Hence shew that the curve has generally... | |
 | 1840 - 468 pages
...cos - . sin ~~£ 2 2 2 ' c A — BC , o + 4 and sin T..COS.•• = sm — . sm — — ' 9 31 22 8. Find the locus of the middle points of a system of parallel chords of the curve whose equation is aa* + hxy + cy* + dx + ey +/= 0. Heuce show that the curve has generally... | |
 | John Hymers - 1845 - 252 pages
...upon substituting these values there arises an equation of the fourth degree for determining %. 72. To find the locus of the middle points of a system of parallel straight lines, each of which joins two points in two given curves. Let f(x, y) = 0, (f) (x, y) —... | |
 | Thomas Gaskin - 1847 - 301 pages
...draw tangents to the latter. Find the locus of the intersections of the latter pairs of tangents. 15. Find the locus of the middle points of a system of parallel chords drawn between an hyperbola and the conjugate hyperbola. 16. If a pair of conjugate diameters of an... | |
 | John Hymers - 1848 - 368 pages
...proposed equation must be capable of being resolved into two rational factors of the first degree. 136. The locus of the middle points of a system of parallel chords of any proposed surface is called its diametral surface. This surface will have several sheets, if... | |
 | William Walton - 1851 - 446 pages
...hence QR.QR' = Zl'\ Similarly gr.gr' = 26'2. De la Hire : Sectwnes Conicm, lib. IV. prop. 34. 2. To find the locus of the middle points of a system of parallel chords drawn between an hyperbola and the conjugate hyperbola. Let two conjugate diameters be taken as axes... | |
 | Perry Fairfax Nursey - 1857 - 644 pages
...intelligible to the great bulk of students; and that mode of investigation which is made to depend on the locus of the middle points of a system of parallel chords is more unexceptionable, as jhe peculiar difficulties of the doctrine of limits are therein almost... | |
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The locus of the middle points of a system of parallel chords in a parabola is called a diameter. 
