| 1836
...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 - 112 páginas
...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 ;... | |
| John Hymers - 1837 - 130 páginas
...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... | |
| 1840
.... 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
...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, M.A., - 1847
...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 - 324 páginas
...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 each... | |
| WILLIAM WALTON, M.A., - 1851
...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... | |
| Sholto Percy - 1857
...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... | |
| Bartholomew Price - 1862
...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... | |
| |