8450 



Surfaces. Theorems. Curvilinear Coordinates 



8450 



skew, curvature. Weyr, E. Prag Sb. (1870) 



(pt. 2) 29-. 

 , at points of generating straight line. 



Buka, F. Z. Mth. Ps. 26 (1881) 15-. 

 , osculation hyperboloid, construction. Weyr, 



E, Prag Ceske Ak. Fr. Jos. Ez. (Tfida 2) 5 



(1896) Art. 5, 6 pp. ; Fschr. Mth. (1896) 415. 

 , , . Prochdzka, B. Prag CeskS Ak. 



Fr. Jos. Ez. (Tfida 2) 6 (1897) Art. 15, 



38 pp. ; Prag Fr. Jos. Ac. Sc. Bll. (Mth. Nt.) 



4 (1897) (Pt. 1) 14-. 

 , with radii of curvature in certain relation. 



Beltrami, E. A. Mt. 7 (1865) 139-. 

 theory, angle between adjacent normals. 



Lamarle, E. C. E. 60 (1865) 851-. 

 umbilical, 2nd order, properties derived from 



sphere. Booth, J. B.A.Ep. (1858) (^.2)2-. 



Symmetrical investigation of curvature, etc. 



Johnson, A. [1882] (xn) Cn. E. S. P. & 



T. 1 (1883) (Sect. 3) 31-. 

 Tangent-plane. Bedetti, G. Bologna N. Cm. 



5 (1842) 485-. 



Theorems. 



Dim, U. [1869] Mod. S. It. Mm. 2 (1876) 1-. 

 Dupin's, demonstration. Oergonne, J. D. 



Gergonne A. Mth. 4 (1813-14) 368-. 

 , . Cayley, A. QJ. Mth. 12 (1873) 185-. 

 , . Le Pont, H. G. Teix. J. Sc. 7 (1886) 



, . Lichtenfels, 0. von. Mb. Mth. Ps. 



5 (1894) 380-. 

 , and application. Biffignandi, A. G. Mt. 



28 (1890) 202-. 

 , , elementary. Thomson, (Sir) W. Camb. 



Mth. J. 4 (1845) 62-. 

 , generalisation. Cremona, L. Tortolini A. 



3 (1860) 325-. 

 Gauss's. Chelini, D. G. Arcad. 115 (1848) 



257-; 116 (1848) 3-. 

 . Bertrand, J. C. E. 42 (1856) 1088-. 

 , analogue to. Sturm, R. Mth. A. 21 



(1883) 379-. 

 , industrial application. Levy, M. C. E. 



86 (1878) 111-. 

 Meunier's, analogue to. Mannheim, A. [1870] 



(x) Par. S. Phlm. Bll. 7 (1871) 138-. 

 and Bonnet's. Brisse, C. Par. S. Mth. 



Bll. 4 (1876) 96-. 

 , curvature of skew curves. Besant, W. H. 



QJ. Mth. 6 <1863) 140-. 

 , demonstration. Bonnet, 0. Par. S. Phlm. 



PV. (1848) 59-. 

 , generalisation. Mannheim, A. C. E. 74 



(1872) 372-. 



l + l = ^ + ^ + dn lications 



P! p 2 ax ay dz 



E. E. Mess. Mth. 9 (1880) 170-. 



Theory. Bonnet, O. Par. EC. Pol. J. 32" cah. 

 (1848) 1-; C. E. 33 (1851) 89-; 37 (1853) 



. Grunert,J.A. Grunert Arch. 28 (1857)163-. 

 . Lipschitz, E. O. S. Crelle J. Mth. 81 

 (1876) 230-. 



Theory. Salvert, (le vicomte) F. de. (xn) Brux. 



S. Sc. A. 5 (1881) (Pt. 1) 63-, (Pt. 2) 291-. 

 . Lilienthal, E. von. Crelle J. Mth. 104 



(1889) 341-. 



. Voss, A. Mth. A. 39 (1891) 179-. 

 , analytic. Amiot, B. Liouv. J. Mth. 12 



(1847) 129-. 

 , and Dupin's cyclides. Holzmiiller, G. 



Z. Mth. Ps. 44 (1899) 194-. 

 , fundamental formulae. Laguerre, . 



N. A. Mth. 11 (1872) 60-. 

 , Gauss's. Cayley, A. L. Mth. S. P. 12 



(1880-81) 187-. 

 , , principle of least action in relation to 



its foundations. Beke, M. Mth. Tennt. 



fits. 2 (1884) 133- ; Mth. Nt. B. Ung. 2 



(*1883-84) 282-. 

 , general. Beltrami, E. Arch. Mth. Ps. 



42 (1864) 117. 

 , geometrical. Mannheim, A. C. E. 74 



(1872) 598-. 

 , interpretation of quantities of 2nd order. 



Hoppe, E. Arch. Mth. Ps. 60 (1877) 65-. 

 , use of direction cosines of normal. Gilbert, 



P. Brux. S. Sc. A. 18 (1894) (Pt. 2) 1-. 

 Total curvature, and application to double 



definite, integrals. Tortolini, B. Em. At. 



4 (1850-51) 53-. 



of bounded portions of surfaces. Graves, 



C. Ir. Ac. P. 5 (1853) 339-. 

 at edge of regression. Stouff, X. Par. 



EC. Norm. A. 9 (1892) 91-. 

 Transformation to chief axes. Cayley, A. 



QJ. Mth. 12 (1873) 34-. 

 Umbilic, conditions for. Stone, E. J. QJ. 



Mth. 3 (1860) 146-. 



, . Hall, A. A. Mth. 9 (1894-95) 42. 



, lines of curvature near. Frost, P. QJ. 



Mth. 10 (1870) 78-. 

 , (Frost). Cayley, A. QJ. Mth. 



10 (1870) 111-. 

 , through. Bioche, C. Par. S. 



Mth. Bll. 18 (1890) 95-. 

 Umbilics. Bonnet, 0. Par. EC. Pol. J. 30 e cah. 



(1845) 165- ; Liouv. J. Mth. 16 (1851) 191-. 

 . Souillart, C. Crelle J. 65 (1866) 320-. 

 . Catalan, E. Mathesis 5 (1885) 73-. 



and differential equations. Cayley, A. 

 (vn) Ph. Mg. 26 (1863) 373-, 441-. 



, lines of curvature at. Hoppe, E. Arch. 

 Mth. Ps. 70 (1884) 289-. 



of surface of order n, problem comprising 

 determination of number. Berzolari, L. 

 Tor. Ac. Sc. At. 30 (1895) 756-. 



tetrahedral surfaces. Lebon, E. Palermo 



Cir. Mt. Ed. 4 (1890) 115-. 

 Variation in contact transformation of surface. 



Mehmke, E. Ev. Mt. 2 (1892) 159-. 

 /tt s sin 2 ' + i 2 sin 2 i" = a 2 , demonstration. Chasles, 



M. C. E. 22 (1846) 517-. 



CUEVILINEAE COOEDINATES. 



Lame, G. C. E. 6 (1838) 43-; Liouv. J. Mth. 



5 (1840) 313- ; 16 (1851) 171- ; (vra) C. E. 

 49 (1859) 341-. 



Aoust, L. C. E. 48 (1859) 842-; Crelle J. 

 58 (1861) 352-. 



616 



