8430 Planes Curves (Calculus) 



negative, first, of central conic, properties, de- 

 monstration. Malet, J. G. [1878] Ir. Ac. 

 T. 26 (1879) 431-. 



, theory. Ameseder, A. Arch. Mth. Ps. 64 

 (1879) 164-. 



oblique. Pellet, E. Bll. Sc. Mth. As. 3 (1872) 

 278-. 



any order. Wetzig, F. Schlomilch Z. 4 (1859) 

 319- ; 5 (1860) 1-, 81-. 



and orthogonal trajectories. Hochheim, A. 

 Arch. Mth. Ps. 47 (1867) 121-. 



pedal surfaces. Roberts, W. C. E. 49 



(1859) 742-. 



. Bacaloglo, E. Grunert Arch. 35 



(1860) 41-. 



(Bacaloglo). Magener, A. Grunert 



Arch. 36 (1861) 375-. 

 property. Besant, W. H. [1870] QJ. Mth. 11 



(1871) 38-. 

 . MacMahon, P. A. Mess. Mth. 10 (1881) 



190-. 

 and reciprocal curves, curvature. Steede, B. H. 



[1898] Ir. Ac. P. 5 (1898-1900) 124-. 

 successive. Barisien, E. N. A. Mth. 14 



(1895) 89-, 157-, 207-, 233-, 463-. 

 , radii of curvature. Niewenglowski, B. 



C. B. 84 (1877) 765-. 

 , theory. Roberts, W. N. A. Mth. 3 (1864) 



80-. 

 of system of conies. Amstein, H. Laus. S. Yd. 



Bll. 22 (1887) 87-. 

 tangent constructions for. Janisch, E. Arch. 



Mth. Ps. 9 (1890) 196-, viii. 

 theorem. [Salvatore-~\Dino, N. G. Mt.. 1 



(1863) 217-. 

 theory. Tortolini, B. [1870] Bm. At. N. 



Line. 24 (1871) 63-. 



Plane sections of cones, formula relating to. 



Guimaraes, R. As. Fr. C. B. (1893) (Pt. 2) 



93-. 

 surfaces, curvature. Exner, K. Z. 



Mth. Ps. 17 (1872) 416-. 

 Points of inflexion. Hesse, L. 0. Crelle J. 41 



(1851) 272-. 

 of cubics. Hesse, L. O. Crelle J. 28 



(1844) 97- ; 38 (1849) 257-. 



curve corresponding to plane or 

 skew curve, traced on developable surface. 

 Olivier, T. Par. EC. Pol. J. cah. 22 (1833) 

 78-. 



and cusps. Jeffery, H. M. [1869] 



QJ. Mth. 10 (1870) 232-. 

 in development of plane section of 



cone. Balitrand, F. N. A. Mth. 15 (1896) 



65-. 



, infinitesimal space round. Long- 

 champs, G. de. As. Fr. C. E. (1893) (Pt. 2) 

 277-. 



, symmetrical investigation. Walton, 



W. Camb. Mth. J. 4 (1845) 13-. 



, visible, and curvature at multiple 



points. Walton, W. QJ. Mth. 6 (1863) 

 204-. 



singular curvature. Walker, E. QJ. 

 Mth. 2 (1858) 107-. 



Radii of Curvature 8430 



Polar coordinates, formulae, 



f, , . d (p^sin (n+ 1) o)~l 



tan (u + na)=- r j t ~ l > ,( ( etc. 



L d (p n+l cos (ra + 1) a)J 



Lucas, F. Les Mondes 18 (1868) 611-. 

 Polars of point of curve of nth degree, curva- 

 ture. Servais, C. Brux. Ac. Bll. 21 (1891) 

 362-. 



Radii of curvature. 



Moore, W. Nicholson J. 21 (1808) 256-. 

 Liouville, J. Liouv. J. Mth. 9 (1844) 435. 

 Schellbach, C. H. Crelle J. 45 (1853) 265-. 

 Schlnmilch, O. Schlomilch Z. 2 (1857) 273-. 

 Schlechter, . Grunert Arch. 31 (1858) 



327-. 



Mannheim, A. N. A. Mth. 1 (1862) 123-. 

 Haag, . (x) Par. S. Phlm. Bll. 3 (1866) 



Soufflet, . Les Mondes 17 (1868) 110- ; 24 



(1871) 337-. 



Laisant, C. A. N. A. Mth. 13 (1874) 367-. 

 Wasteels, C. Mathesis 11 (1891) 268-. 

 application of differential calculus. Le Barbier, 



. (vm) Gergonne A. Mth. 22 (1831) 31-. 

 of caustics at cusps. Breton (de Champ), . 



N. A. Mth. 4 (1865) 25-. 

 and centres of curvature. Lamarle, E. Brux. 



Ac. Bll. 2 (1857) 33-, 307-, 528- ; 3 (1857) 



295-; 5 (1858) 5-; 6 (1859) 11-. 



circles of curvature. Schellbach, C. H. 

 N. A. Mth. 12 (1853) 390-. 



of class of curves. Godefroy, R. N. A. Mth. 

 5 (1886) 272-. 



, geometrical determination. 

 Transon, (Prof.) A. Liouv. J. Mth. 10 

 (1845) 147-. 



collinear curves, relation between. Geisen- 

 heimer, L. Z. Mth. Ps. 25 (1880) 214-. 



, reciprocal, and inverse curves, relation 



between. Geisenheimer, L. Z. Mth. Ps. 



25 (1880) 300-. 

 construction for symmetric triangular curves, 



etc. Fouret, G. C. E. 110 (1890) 778-, 



876. 

 of curve and its polar reciprocal, relation. 



Chemin, J. N. A. Mth. 6 (1867) 49-. 

 determination. Laguerre, E. (x) Par. S. 



Phlm. Bll. 4 (1867) 15-. 



in parallel point-coordinates. Ocagne, M. d\ 

 Brux. Ac. Bll. 21 (1891) 220-. 



expression in dipolar coordinates. Frost, W. 



Mess. Mth. 10 (1881) 18-. 

 polar coordinates. Smith, Arch. Camb. 



Mth. J. 2 (1841) 191-. 

 , and curves, equation of which is 



r k =a k sink0. Unferdinger, F. Arch. Mth. 



Ps. 51 (1870) 72-. 



for, in Salmon's Higher Plane Curves, p. 83, 

 reduction by determinants. Story, W. E. 

 [1880] (xn) J. H. Un. Cir. [1] (1882) 35. 



expressions for. Wolfers, J. P. Grunert Arch. 

 9 (1847) 60-. 



in point- and tangential coordinates, 

 relation between. Ocagne, M. d\ Par. S. 

 Mth. Bll. 19 (1891) 26-. 



of Lame's curves. Godefroy, R. Par. S. Mth. 

 Bll. 21 (1893) 20-. 



605 



