 | 1836 - 798 sider
...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... | |
 | John Hymers - 1837 - 486 sider
...is С and radius equal to ^/a* + b3. The Ellipse referred to its conjugate Diameters. 138. To find the locus of the middle points of a system of parallel chords. Let the chords be parallel to a line CD (fig. 45) through fhe center, whose equation is y = mx; then... | |
 | Michel Chasles - 1837 - 564 sider
...consequently HP=2a + r, we have . 2а + r The Hyperbola referred to its Conjugate Diameters. 187- To find the locus of the middle points of a system of parallel chords. Let the chords be parallel to a line CW through the center (fig. 57), whose equation is y — mx ;... | |
 | 1840 - 468 sider
.... 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... | |
 | 1840 - 528 sider
...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... | |
 | Thomas Gaskin - 1847 - 301 sider
...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 sider
...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 sider
...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 sider
...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 entirely... | |
 | Bartholomew Price - 1862 - 614 sider
...from another property of surfaces of the second degree. I shall in the first place demonstrate that the locus of the middle points of a system of parallel chords is a plane. Let us take (28) to be the equation to the surface ; and let the equations to one of a system... | |
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The locus of the middle points of a system of parallel chords is the diameter perpendicular to them. 
