Anharmonic Coordinates
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In our eReader you can find the full English version of the book. Read Anharmonic Coordinates 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 Anharmonic Coordinates
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To quickly assess the difficulty of the text, read a short excerpt:
Then 8x4(l-a;)(17-a;) = 2x4(29-a;)(7~a;), and a;2_ 12a; -45 = 0.
Therefore a; =—3 or 15; L being 3 units to the left, iV 15 units to the right of A.
74 HOMOGRAPHIC DIVISION VeHJication.
and {LANB) = {LA'NB').
12°. Given four fixed points, no three of which are collinear, P^, P^, P^, P^ (fig. 23); to find the locus of a fifth point P = {xyz), subject to the condition P • P^P^^P^P^^ — —F' ' a constant.
Let Pi = i^iVi^i) . . . P4 = (^42/42^4)- ™-'''' -r^^^i / 1 ^yi'^2 1 1 ^Vs^i I + ^ I ^2/2^3 1 1... ^y^^i I = ^> which is evidently an equation of the second degree. The locus of P therefore is a conic, and it passes through P„ P^, P3, P, ; for if we substitute for the variables in this equation the coordinates of any one of the four points, say P3, the second and third matrices vanish and the equa- tion becomes identically, = 0. This theorem shows that a conic must pass through any five arbitrary points, no three of which are collinear. A sixth point, P\ will only lie upon it if equation (a) remains true when the coordinates of P' are substituted in it for those of P.
What to read after Anharmonic Coordinates?
You can find similar books in the "Read Also" column, or choose other free books by H W L Henry William Lovett Hime to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Then 8x4(l-a;)(17-a;) = 2x4(29-a;)(7~a;), and a;2_ 12a; -45 = 0.
Therefore a; =—3 or 15; L being 3 units to the left, iV 15 units to the right of A.
74 HOMOGRAPHIC DIVISION VeHJication.
and {LANB) = {LA'NB').
12°. Given four fixed points, no three of which are collinear, P^, P^, P^, P^ (fig. 23); to find the locus of a fifth point P = {xyz), subject to the condition P • P^P^^P^P^^ — —F' ' a constant.
Let Pi = i^iVi^i) . . . P4 = (^42/42^4)- ™-'''' -r^^^i / 1 ^yi'^2 1 1 ^Vs^i I + ^ I ^2/2^3 1 1... ^y^^i I = ^> which is evidently an equation of the second degree. The locus of P therefore is a conic, and it passes through P„ P^, P3, P, ; for if we substitute for the variables in this equation the coordinates of any one of the four points, say P3, the second and third matrices vanish and the equa- tion becomes identically, = 0. This theorem shows that a conic must pass through any five arbitrary points, no three of which are collinear. A sixth point, P\ will only lie upon it if equation (a) remains true when the coordinates of P' are substituted in it for those of P.
What to read after Anharmonic Coordinates?
You can find similar books in the "Read Also" column, or choose other free books by H W L Henry William Lovett Hime to read onlineMoreLess
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