Algebraic Geometry; a New Treatise On Analytical Conic Sections
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In our eReader you can find the full English version of the book. Read Algebraic Geometry; a New Treatise On Analytical Conic Sections Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Algebraic Geometry; a New Treatise On Analytical Conic Sections
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To quickly assess the difficulty of the text, read a short excerpt:
If the diameter y = 'mx meets the hyperbola -g -72^ ^ *** ''^^^ 'points, its conjugate diameter y = m'x meets the curve in imaginary points.
hety = mx meet the curve at the point (aij, ^j), and y==m'x at the point (x^, y^.
ART. 279.] CONJUGATE HYPERBOLA. 257 Where y = 'mx meets the curve, we have by substitution, ' 2/^1 "^^ 1 Similarly where y — mix meets the curve.
*2 —) ft4m2 for mm =-2 «*m2 x,\ x„^ J2-a2m2- Hence, if x-^ is real, x^ is imaginary. This proves the proposition.
If 2a is the len...gth of a diameter of a hyperbola, and 2/S the length of the conjugate diameter cut off by the conjugate h3a>erbola, 2a and 2/3 are often called the lengths of these two conjugate diameters of the original hyperbola.
278. If a hyperbola has its centre at the origin, its equation contains no terms of the first degree.
See Art. 213.
*279. To find the equation of a hyperbola referred to two conjugate diameters as axes of co-ordinates. (Oblique.) The origin being at the centre of the curve, if (x, y) lies on the curve, {-X, -,y) also lies on the curve.
What to read after Algebraic Geometry; a New Treatise On Analytical Conic Sections?
You can find similar books in the "Read Also" column, or choose other free books by Baker, W. M to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
If the diameter y = 'mx meets the hyperbola -g -72^ ^ *** ''^^^ 'points, its conjugate diameter y = m'x meets the curve in imaginary points.
hety = mx meet the curve at the point (aij, ^j), and y==m'x at the point (x^, y^.
ART. 279.] CONJUGATE HYPERBOLA. 257 Where y = 'mx meets the curve, we have by substitution, ' 2/^1 "^^ 1 Similarly where y — mix meets the curve.
*2 —) ft4m2 for mm =-2 «*m2 x,\ x„^ J2-a2m2- Hence, if x-^ is real, x^ is imaginary. This proves the proposition.
If 2a is the len...gth of a diameter of a hyperbola, and 2/S the length of the conjugate diameter cut off by the conjugate h3a>erbola, 2a and 2/3 are often called the lengths of these two conjugate diameters of the original hyperbola.
278. If a hyperbola has its centre at the origin, its equation contains no terms of the first degree.
See Art. 213.
*279. To find the equation of a hyperbola referred to two conjugate diameters as axes of co-ordinates. (Oblique.) The origin being at the centre of the curve, if (x, y) lies on the curve, {-X, -,y) also lies on the curve.
What to read after Algebraic Geometry; a New Treatise On Analytical Conic Sections?
You can find similar books in the "Read Also" column, or choose other free books by Baker, W. M to read onlineMoreLess
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