...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 equation of the second...

...the rules for finding logarithms may be deduced in the asnal way. (56.) <}i ESTÍOS- VI. By - . Def. A diameter of a curve is the locus of the middle points of a system of parallel choids. Find the equations of the diameters of the curves represented by the general equation of the...

...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 ;...

...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...

.... 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...

...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...

...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...

...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...

...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...

...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...