The Cardioide And Some of Its Related Curves: Inaugural Dissertation Der ...
The Cardioide And Some of Its Related Curves: Inaugural Dissertation Der ...
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The theorem was first published by TsCHmNHAUSEN, A, E. Nov. Iti82, p. 364-Hfio but was kno%Yn to bim still earlier (17. April, 1(>81) as we see ia one of his letters to LeIBKITZ (V^L Afu(h. Schriften t\ Letbnit^ herausff. v, Gerhartif IV 484, 1859), The curve was further studied^ and for the first time drawn in its completeness by TsCHlRXHAUSEX A. K April \m^\ p. 169472: Feb. 1690, p. m-13.
Digitized by Google - 9 - 15. If Fj be the foot of the perpendicular from the cusp S of the cardioide on ...its tangent at any point P, the locus of Fj is the first postftre mspidal pedal of the cardioide. I have named this curve a Catfletj Sextic, for rea^rions which will appt^r later; it will evidently be tangent to the cardioide at its vertex, will pass thro its cusp, and have a double point where the double tangent of the cardioide meets its axis produced.
Suppose now that S Fi be produced to F' so that SF, = FiF'; it is not hard to show, on making use of our introductory theorem, that F' P is normal at F' to the curve traced by V* ; and is, moreover the direction of the reflection from the cardioide of any ray SP emanating from S, But the locus of F', is simply the above Oayley Sextic doubled in its linear dimensions.
What to read after The Cardioide And Some of Its Related Curves: Inaugural Dissertation Der ...?
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To quickly assess the difficulty of the text, read a short excerpt:
The theorem was first published by TsCHmNHAUSEN, A, E. Nov. Iti82, p. 364-Hfio but was kno%Yn to bim still earlier (17. April, 1(>81) as we see ia one of his letters to LeIBKITZ (V^L Afu(h. Schriften t\ Letbnit^ herausff. v, Gerhartif IV 484, 1859), The curve was further studied^ and for the first time drawn in its completeness by TsCHlRXHAUSEX A. K April \m^\ p. 169472: Feb. 1690, p. m-13.
Digitized by Google - 9 - 15. If Fj be the foot of the perpendicular from the cusp S of the cardioide on ...its tangent at any point P, the locus of Fj is the first postftre mspidal pedal of the cardioide. I have named this curve a Catfletj Sextic, for rea^rions which will appt^r later; it will evidently be tangent to the cardioide at its vertex, will pass thro its cusp, and have a double point where the double tangent of the cardioide meets its axis produced.
Suppose now that S Fi be produced to F' so that SF, = FiF'; it is not hard to show, on making use of our introductory theorem, that F' P is normal at F' to the curve traced by V* ; and is, moreover the direction of the reflection from the cardioide of any ray SP emanating from S, But the locus of F', is simply the above Oayley Sextic doubled in its linear dimensions.
What to read after The Cardioide And Some of Its Related Curves: Inaugural Dissertation Der ...?
You can find similar books in the "Read Also" column, or choose other free books by Raymond Clare Archibald to read onlineMoreLess
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