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Caption: Mathematical Models by Arnold Emch - Series 4 (1928)
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30 Mathematical Models Fig. 19 of a singularity. This method, already used by Newton,a more fully by D e Gua,b and later systematically developed by G. Cramer,0 consists in writing the possible terms of an n-ic, in homogeneous coordinates x, y, z; xay0zy, a + /3 + 7 = n\ at the vertices of a triangular latice-work, as indicated in Fig. 19, in case of a quartic. Those terms which are missing in the equation (coefficient Aa$y = 0) are left out in the places otherwise assigned to them in the triangle. Then we connect the extreme existing and marked terms to the left and right and below by a convex polygon. The sum of the terms of the polygonal line nearest to I, or II, or III, with the proper coefficients of the equation, set equal to zero are approximation curves of the given curve i the latter passes through one, two, or three of f the vertices of the coordinate triangle. The application of this method is shown in a number of examples in some of the following slides. For this see Theorie der ebenen algebraischen Kurven hoherer Ordnung by Dr. H. Wieleitner, pp. 83-118. 43. Assortment of Quartic Curves. including Quartic with 28 real double tangents. 44. Rational Quartics. 45. Quintics and Sextics. *Enumeralio linearum tertii or dint.—London 1704, see complete reference above. bP. Sauerbeck. Einleitung in die analytische Geometrie der hoheren algebraischen Kurven. Nach den Methoden von Jean Paul De Gua De Malves. Teubner, 1902. ^Introduction a VAnalyse des Lignes courbes algebriques, Geneve, 1750.
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