8430 



Applications of Calculus to Plane Curves 



8430 



Boundary relations, and formula for radius of 

 curvature. Voller, . Grunert Arch. 32 

 (1859) 97- ; 33 (1859) 350-. 



Caustics, construction. Cornu, A. N. A. Mth. 



2 (1863) 311-. 



identical with pedals. Weyr, E. Z. Mth. 

 Ps. 14 (1869) 376-. 



, plane, application of coordinate system to. 



Habich, E. A. Mt. 2 (1868-69) 134-. 

 Centre of curvature. Ocagne, M. d'. Par. S. 



Mth. fill. 19 (1891) 31-. 



, graphic construction. Anon, (vi 

 541) Gergonne A. Mth. 12 (1821-22) 135-. 



, . Gergonne, J. D. Gergonne 



A. Mth. 12 (1821-22) 137-. 

 of locus of points, distances of which 



from 2 given curves are in constant ratio. 



Mannheim, A. Tortolini A. 1 (1858) 364-. 



and normal of polytropic curves. 

 Kosch, E. Z. Mth. Ps. 45 (1900) 161-. 



with polar coordinates. Husquin de 



Rheville, . N. A. Mth. 10 (1891) 411-. 

 . of certain spiral curves. Rulf, W. 



Mh. Mth. Ps. 3 (1892) 211-. 

 Centres of curvature of integral curve. Ma- 



chovec, F. Casopis 19 (1890) 67- ; Fschr. 



Mth. (1890) 703. 

 isogonal curves. Seiliger, D. N. 



N. Bs. S. Nt. Mm. (Mth.) 14 (1892) 155- ; 



Fschr. Mth. (1892) 582. 

 , successive. Haton de la Goupilliere, 



J. N. C. B. 46 (1858) 930- ; Liouv. J. Mth. 



4 (1859) 183-. 

 of y n =a r x n ~ r . Machovec, F. Prag 



Sb. (1885) '(Mth.-Nt.) 386-. 



\x n + /j.y n = d n . Machovec, F. 

 Prag Sb. (1891) (Mth.-Nt.) 83-. 



Circles of curvature. Schellbach, C. H. Crelle 



J. 45 (1853) 263-. 

 . Tait, P. G. Edinb. Mth. S. P. 14 



(1896) 26. 



and asymptotes. Laisant, C. A. 

 Par. S. Mth. Bll. 23 (1895) 95-. 



complex quantities. Petersen, J. 



Sk. Nf. F. (1892) 354; Fschr. Mth. (1892) 



of conies. Weiler, A. Ziir. Vjschr. 



33 (1888) 119-. 

 ellipse. Cesdro, E. Mathesis 5 



(1885) 7-. 

 family of curves. Allegret, [A.] 



N. A. Mth. 9 (1870) 30-. 

 nodal cubic. Janisch, E. Mh. 



Mth. Ps. 7 (1896) 142-. 

 at point of curve of 4th degree with 



3 double points, of which 2 are circular 

 points at infinity. Saltel, L. Brux. Ac. 

 Bll. 34 (1872) 51-. 



, radii. Pagani, G. M. Brux. Ac. 



Bll. 14 (1847) 185-. 

 , relation to curve at point of contact. 



Mack, L. Arch. Mth. Ps. 64 (1879) 182-. 



having double contact with conic, point 

 transformations in elliptic coordinates. 

 Lovett, E. 0. Am. J. Mth. 20 (1898) 242-. 



Cochleoid. Falkenburg, C. Arch. Mth. Ps. 

 70 (1884) 259-. 



Cochleoid, properties. Benthem, A. N. Arch. 



Wisk. 10 (1884) 76-. 

 Conies having higher order of contact with 



given curve. Ocagne, M. d'. N. A. Mth. 16 



(1897) 252-. 



osculating curves of 3rd degree. Gent, E. 

 Z. Mth. Ps. 17 (1872) 476-. 



, systems, differential equations. Roberts, 

 R. A. [1895] N. Y. Am. Mth. S. Bll. 2 

 (1896) 11-. 



touching curves of any degree. Cayley, A. 

 C. B. 59 (1864) 224-. 



Contact. Christie, A. S. Smiths. Misc. Col. 

 33 (1888) Art. 1, 157-. (Wash. Ph. S. Bll. 

 6 (1884).) 



with conies or curves of 3rd degree. Hal- 

 phen, G. H. [1875] Par. S. Mth. Bll. 4 

 (1876) 59-. 



and curvature, theory. Grunert, J. A. 

 Grunert Arch. 30 (1858) 361-. 



of 2 curves, ratio of curvatures at point of. 

 Wolffing, E. Z. Mth. Ps. 38 (1893) 237-. 



lines, successive intersections. Desmarest, E. 

 N. A. Mth. 3 (1844) 220-. 



of given order, of conic with curve, conditions. 

 Painvin, L. C. B. 78 (1874) 55-. 



5th order, of conic with curve, conditions. 



Painvin, L. C. B. 78 (1874) 436-, 835-. 



with parabola. Schell, W. Marb. Schr. 8 

 (1857) 135-. 



of plane cubic with curve of any degree, 

 positions where closest. Disteli, M. Z. 

 Mth. Ps. 38 (1893) 257-. 



, 6-point, of curves of 3rd degree with conic, 



27 points of. Steiner, J. Berl. B. (1845 

 386-. 



points of parallel tangent lines or planes, 

 centre of mean distances. Liouville, J. 

 Liouv. J. Mth. 6 (1841) 345-; C. B. 13 

 (1841) 412-. 



, theory. Poselger, F. T. Berl. Ab. (1836) 



55-. 

 , , point in. Halphen, G. H. Par. S. 



Mth. Bll. 2 (1874) 94-. 

 Coordinates in plane, Watson's. Hill. T. 



Am. As. P. 22 (1873) 27-. 

 , , problems. Hill, T. Am. As. P. 



(1875) (Pt. 1) 41-. 

 Cubic parabolas, property. Cellerier, G. Arch. 



Sc. Ps. Nt. 11 (1884) 408-. 

 Curvature. Gergonne, J. D. Gergonne A. 



Mth. 21 (1830-31) 1-. 

 . Zimmermann, H. E. M. 0. Z. Mth. Ps. 



28 (1883) 115-. 



. Demoulin, A. Brux. Mm. Cour. 8, 44 

 (1891) No. 5, 48 pp. 



conies. Berg, F. J. van den. Amst. Ak. 

 Vs. M. 9 (1892) 85-; Fschr. Mth. (1892) 

 654-. 



curve of basis point of pencil of curves of 

 nth degree. Zahradnik, K. Prag Sb. (1878) 

 250-. 



at cusp. Anon, (xi 52) N. A. Mth. 10 

 (1871) 318-. 



double point. Cayley, A. QJ. Mth. 3 



(1860) 322-. 



formula. Torry, A. F. Mess. Mth. 2 

 (1863) 81-. 



599 



