Kummers Quartic Surface
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In our eReader you can find the full English version of the book. Read Kummers Quartic Surface 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 Kummers Quartic Surface
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This has been integrated when f is quadratic but not when, as in the general case, / is cubic*.
b c ca ab showing that the intersections of the normal with the planes of reference and perpendicular central plane form a range of constant cross ratio.
The line element is given by AM dX2, alcd ^ 4:ds 2 = - -- h -o, . .
A V fJ^(ufJi) 67. ASYMPTOTIC LINES.
The differential equation of asymptotic lines is dxdl + dydm + dzdn = 0, d\ adp / du dv ^A, / \ ap \ / u v \ or zlx r -- 1 -. -- -, ) (- --i --- ...= 0; \X a u(fji a)J \u a v aj , , 7 (X - a) (u a) be (^ -a)(v- a) further Ix = ; -- ^ -- ( = \- ^ -- ( . (a b)(a c) pv (a o)(a c) The coefficients of d\du and dfidv are 0, and the equation reduces to jjb(^-u) d\dv + v (v X) dfidu = 0.
This equation is unaltered if X, /^, u, v are replaced by tr 1, u~\ /A- 1, X" 1, respectively, illustrating the fact that asymptotic lines are re ciprocated into asymptotic lines.
* Darboux, Comptes Eendus, xcn, 446; xcvn, 1133.
66-67] ASYMPTOTIC LINES 111 When expressed in terms of u and X only, this equation takes the form _ du?
What to read after Kummers Quartic Surface?
You can find similar books in the "Read Also" column, or choose other free books by R W H T Ronald William Henry Turnbull Hudson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
This has been integrated when f is quadratic but not when, as in the general case, / is cubic*.
b c ca ab showing that the intersections of the normal with the planes of reference and perpendicular central plane form a range of constant cross ratio.
The line element is given by AM dX2, alcd ^ 4:ds 2 = - -- h -o, . .
A V fJ^(ufJi) 67. ASYMPTOTIC LINES.
The differential equation of asymptotic lines is dxdl + dydm + dzdn = 0, d\ adp / du dv ^A, / \ ap \ / u v \ or zlx r -- 1 -. -- -, ) (- --i --- ...= 0; \X a u(fji a)J \u a v aj , , 7 (X - a) (u a) be (^ -a)(v- a) further Ix = ; -- ^ -- ( = \- ^ -- ( . (a b)(a c) pv (a o)(a c) The coefficients of d\du and dfidv are 0, and the equation reduces to jjb(^-u) d\dv + v (v X) dfidu = 0.
This equation is unaltered if X, /^, u, v are replaced by tr 1, u~\ /A- 1, X" 1, respectively, illustrating the fact that asymptotic lines are re ciprocated into asymptotic lines.
* Darboux, Comptes Eendus, xcn, 446; xcvn, 1133.
66-67] ASYMPTOTIC LINES 111 When expressed in terms of u and X only, this equation takes the form _ du?
What to read after Kummers Quartic Surface?
You can find similar books in the "Read Also" column, or choose other free books by R W H T Ronald William Henry Turnbull Hudson to read onlineMoreLess
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