Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two Dimensions: An Elementary Treatise
Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two Dimensions: An Elementary Treatise
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(139) The chord of contact of the tangents (whether the coordinates be trilinear or triangular) is l{^ — y) + {m — n) a = 0.
CHAPTER XVI.
CONICS REFEREED TO A CIRCUMSCRIBED TRIANGLE.
202. The equation ZV + m^^'' + wV - 2W2W/37 - Inl^a - 2lma^ = (1) may be written {la, + m^ - njY - Alma^ = 0, and therefore (Art. 161) represents a conic section to which a = and ^ = are tangents, and la + m^ — W7 = 0, the chord of contact.
Similarly, W2/3 + ny — la = 0, is the chord of contact of tangents /8 = and... 7 = 0, and ny+ la — m^ = 0, the chord of contact of tangents 7=0 and a = 0.
Hence the equation ZV + nt"^ + n^i^ - 2mnl3y - 2nlya - 2lmoi/3 = (1 ) represents a conic section, to which the lines of reference are tangents, and — la + ?n/3 + ny = 0, la — m^ + W7 = 0, la + m^ — ny=0, the chords joining the point of contact.
CONICS REFEEEED TO A CIECUMSCRIBED TRIANGLE. 207 203. It should be observed that if we write — I for I, the equation (1) takes the form ZV + w'/3' + -n^rf - 2mn^x + "^^h^ + 2?wayS = (2), and the chords of contact now become loL + m/3 + tvy = 0, loL + on^ — nj = 0, loL — m/3 + ny = 0.
What to read after Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two Dimensions: An Elementary Treatise?
You can find similar books in the "Read Also" column, or choose other free books by William Allen Whitworth to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(139) The chord of contact of the tangents (whether the coordinates be trilinear or triangular) is l{^ — y) + {m — n) a = 0.
CHAPTER XVI.
CONICS REFEREED TO A CIRCUMSCRIBED TRIANGLE.
202. The equation ZV + m^^'' + wV - 2W2W/37 - Inl^a - 2lma^ = (1) may be written {la, + m^ - njY - Alma^ = 0, and therefore (Art. 161) represents a conic section to which a = and ^ = are tangents, and la + m^ — W7 = 0, the chord of contact.
Similarly, W2/3 + ny — la = 0, is the chord of contact of tangents /8 = and... 7 = 0, and ny+ la — m^ = 0, the chord of contact of tangents 7=0 and a = 0.
Hence the equation ZV + nt"^ + n^i^ - 2mnl3y - 2nlya - 2lmoi/3 = (1 ) represents a conic section, to which the lines of reference are tangents, and — la + ?n/3 + ny = 0, la — m^ + W7 = 0, la + m^ — ny=0, the chords joining the point of contact.
CONICS REFEEEED TO A CIECUMSCRIBED TRIANGLE. 207 203. It should be observed that if we write — I for I, the equation (1) takes the form ZV + w'/3' + -n^rf - 2mn^x + "^^h^ + 2?wayS = (2), and the chords of contact now become loL + m/3 + tvy = 0, loL + on^ — nj = 0, loL — m/3 + ny = 0.
What to read after Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two Dimensions: An Elementary Treatise?
You can find similar books in the "Read Also" column, or choose other free books by William Allen Whitworth to read onlineMoreLess
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