8470 



Special Transcendental Curves 



8470 



8470 Special transcendental curves. 



(For cycloids, epicycloids and tro- 

 choids see 8420.) 



Catenary. Hill, T. Gould As. J. 2 (1852) 10-. 

 , areas and volumes related to. Wasteels, 



C. E. Mathesis 16 (1896) 241-. 



.centrifrugal. Webb,J.B. Am. As. P. (1889) 



76. 

 , constants. Loffler, A. Grunert Arch. 36 



(1861) 323-. 

 , construction, graphic method. Palmer, 



W. K. Kan. Un. Q. 7 (1898) 211-. 



of equal strength, involute. Azzarelli, M. 

 Palomba Eac. 4 (1848) 9-, 17-, 35-, 57-. 



-, , identity of tractrix with. 

 Calegari, P. (vn) Bologna Opusc. Sc. N. 

 Col. (1824) 233-. 



and other transcendental curves, 



properties. Masetti, G. Bologna Opusc. Sc. 



4 (1823) 179-. 

 , evolute (Huygens' problem). Egger, E. 



A. Mt. 6 (1864) 19-. 

 , mechanical description. Robillier, . 



Angers Mm. S. Ag. 1 (1831) 41-. 

 , by parabolic trigonometry. Booth, J. R. 



S. P. 8 (1856-57) 443-. 



problem, Huygens' solution. Korteweg, 



D. J. Bb. Mth. 1 (1900) 97-. 



, spherical. Greenhill, A. G. [1894] L. Mth. 

 S. P. 27 (1896) 123-. 



on surface of revolution. Molins, H. Toul. 

 Mm. Ac. 5 (1849) 261-. 



, vertical force on elements and distance of 



elements from horizontal plane. Molins, H. 



Toul. Mm. Ac. 4 (1848) 221-. 

 Closed class of transcendental curves. Schicer- 



ing, K. Z. Mth. Ps. 20 (1875) 457-. 

 Curve of elliptic functions of 1st kind. 



Serdobinskij, V. E. [1893] Rec. Mth. 



(Moscou) 17 (1895) 337-; Fschr. Mth. (1893- 



94) 1158. 



logarithmic sines. Barbour, L. G. Des 

 Moines Anal. 4 (1877) 114-. 



, evolute. Barbour, L. G. Des 



Moines Anal. 4 (1877) 169-. 



second sines and its variations. Sang, 



E. [1874] Edinb. R. S. P. 8 (1875) 356-. 



r = - . Fontana, G. Verona S. It. Mm. 



2 (1784) 123-. 



Differential curve of parabola, foci. Hochheim, 

 A. [1875] Arch. Mth. Ps. 58 (1876) 278-. 



Elastic curve. Halphen, G. Par. EC. Pol. J. 

 54 (1884) 183-. 



. Ise, E. Nap. Ac. Pont. At. 18 (1888) 



203-. 



. Tedone, 0. Rm. R. Ac. Line. Rd. 



3 (1894) (Sem. 1) 265-. 



, intrinsic equation. Greenhill, A. G. 

 Mess. Mth. 8 (1879) 82. 



Evolutes of circular arcs. Poinsot, L. Par. 



EC. Pol. Cor. 1 (1804-08) 245-. 

 Exponential curve. Church, I. P. Des Moines 



Anal. 1 (1874) 84-. 



Helices. Tissot, A. N. A. Mth. 11 (1852) 



454-. 

 , characteristic property. Appell, P. Arch. 



Mth. Ps. 64 (1879) 19-. 



and helicoidal surfaces. Richardson, J. M. 

 Franklin I. J. 33 (1857) 231-. 



, problem. Cesaro, E. G. Mt. 24 (1886) 46-. 



, theory. Tos y Feitto, J. de. [1898] Barcel. 

 Ac. Mm. 2 (1892-1900) 307-. 



, , general. Schoelcher, (le col.) . As. 

 Fr. C. R. (1891) (Pt. 1) 160. 



, of Torricelli. Ferroni, P. Mod. S. It. 

 Mm. 15 (1811) 60-. 



Helix, only curve with ratio of curvatures con- 

 stant. Bertrand, J. Liouv. J. Mth. 13 

 (1848) 423-. 



, cylindrical, lines connected with. Piron- 

 dini, G. Crelle J. Mth. 121 (1900) 245-. 



projected into cycloid. Olivier, T. Par. 

 S. Phlm. PV. (1847) 106-. 



, property. Reye, T. Z. Mth. Ps. 15 (1870) 



, sense. Anon, (vi 889) N. A. Mth. 14 



(1855) 175-. 

 Hirundo. Hill, (Rev.) T. Am. As. P. (1886) 



67. 

 Hypergeometric curves. Multedo, . Genova 



Mm. Ac. 3 (1814) 328-. 

 Involute of circle, Bakewell, T. W. Franklin 



I. J. 7 (1831) 99-. 

 . Crofton, M. W. [1864] Mess. Mth. 



3 (1866) 93-. 

 . D'Auria, L. Franklin I. J. 80 



(1880) 45-. 

 . Skinner, J. J. Franklin I. J. 80 



(1880) 105-. 

 Involutes of circle. Hill, T. Am. As. P. 19 



(1870) 21-. 

 depending on Diophantine equation. 



Sylvester, J. J. L. Mth. S. P. 2 (1869) 137-. 

 and their relation to analytic functions. 



Thoman, F. C. R. 26 (1848) 498-. 



, successive. Sylvester, J. J. Ph. 

 Mg. 36 (1868) 295-, 459-. 



Kumaids. (Plane curves becoming ellipses on 

 cylinder.) Vieth, G. U. A. Gilbert A. 54 

 (1816) 311-. 



Logarithmic curve', researches of Torricelli. 

 Loria, G. Bb. Mth. 1 (1900) 75-. 



exponential curves. Vincent, A. J. H. 

 Gergonne A. Mth. 15 (1824-25) 1-; 16 (1825- 

 26) 92-. 



parabola. Booth, J. Camb. and Dubl. 

 Mth. J. 7 (1852) 35-. 



Logocyclic curve. Booth, J. R. S. P. 9 (1857- 

 59) 256-; QJ. Mth. 3 (1860) 38-, 127-. 



. or strophoid. Gilnther, A. W. S. (xn) 



Mathesis 1 (1881) 81-. 



Loxodromes of cone. Piccioli, H. N. A. Mth. 

 18 (1899) 508-. 



Mechanical properties of some curves. Heulen, 

 J. van. N. Arch. Wisk. 7 (*1881) 33-. 



Normals to several mechanical curves, con- 

 struction. Chasles, M. [1829] (ix) Par. 

 S. Mth. Bll. 6 (1878) 208-. 



Plane curves, Roberval's method. Geer, P. 

 van. N. Arch. Wisk. 11 (1884) 28-; Fschr. 

 Ps. (1884) (Ab. 1) 217-. 



631 



