...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...

...center is С and radius equal to v a2 + W. 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 the center, whose equation is y = mx ; then...

...center 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...

...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...

...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...

...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) —...

...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...

...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...between an hyperbola and the conjugate hyperbola. Let two conjugate diameters be taken as axes of coordinates, the axis of y being parallel to the chords....

...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...

...tangent lines parallel to a is = 0. XXVII. To study the nature of the surface more closely, let us find the locus of the middle points of a system of parallel chords. Let them be parallel to a, then, if ts be the vector of the middle point of one of them, ts + xa. and...