7210 



Properties of Conies 



Porisms 7210 



Polar groups, construction. Waelsch, E. 



Wien Ak. Sb. 100 (1891) (Ab. 2a) 315- . 

 Pole of given straight line, determination. 



Eeggio, Z. Yen. I. At. 7 (1880-81) 1117-. 

 Poles and polars, theorems. Tychsen, C. Mth. 



Ts. 2 (1860) 19-. 

 Problem. Joachimsthal, F. N. A. Mth. 6 



(1847) 312. 

 Problems. Midy, . N. A. Mth. 1 (1842) 



336-. 

 Eadii vectores and polars, theorem of Chasles. 



Terquem, 0. N. A. Mth. 6 (1847) 162-. 

 Reciprocal polars. Poncelet, J. V. Gergonne 



A. Mth. 8 (1817-18) 201- ; 18 (1827-28) 125- ; 



Crelle J. 4 (1829) 1-. 

 . Terquem, 0. N. A. Mth. 7 (1848) 



308-, 409-. 

 . Elliott, J. W. Mathematician 3 (1850) 



305-. 



, applications, theorems. Godefroy, E. 

 N. A. Mth. 12 (1893) 106-. 



, conies with respect to which 2 conies 



are reciprocal. Euffini, F. P. (xi) Mod. Ac. 



Sc. Mm. 12 (1871) 49- ; 13 (Pt. 1) (1872) 3-. 

 , . Siacci, F. 



Tor. At. Ac. Sc. 7 (1871-72) 758-. 

 , . Battaglini, 



G. Km. At. E. Ac. 25 (1872) 195-. 

 , . Massarini, 



I. G. Mt. 37 (1899) 23-. 



, homologous curves. Ocagne, M. d\ 

 Par. S. Mth. Bll. 13 (1885) 204-. 



, theorems. Euffini, F. P. Bologna Ac. 



Sc. Mm. 6 (1875) 383-. 

 Keciprocation. Hudson, E. W. H. T. Mess. 



Mth. 29 (1900) 191-. 



.cases. Tarry, G. N. A. Mth. 3 (1884) 270- . 

 Eeciprocators of two conies. Eussell, J. W. 



L. Mth. S. P. 26 (1895) 458-. 

 . Jolliffe, A.E. L. Mth. S. P. 26 



(1895) 466-. 

 Successive polars. Bobillier, . Gergonne 



A. Mth. 19 (1828-29) 302-. 

 Triangle and its polar, relation of areas, ex- 

 tension to quadric. Walker, W. F. [1864] 



QJ. Mth. 7 (1866) 119-. 



Polygons related to Conies. 

 (See also 6810.) 



Circum-polygons, product property. Lionville, 



J. Lipuv. J. Mth. 9 (1844) 350-. 

 , theorem. Terquem, 0. N. A. Mth. 12 



(1853) 218-. 

 In- or circum-polygons, semidiameter through 



vertex of. Foscolo, G. Tor. At. Ac. Sc. 7 



(1871-72) 338-. 

 In-polygon, complete, extension of theorems on 



triangle to. Kantor, S. [1877] Wien Ak. 



Sb. 76 (1878) (Ab. 2) 768-. 



with sides through given points, inscription. 

 Battaglini, G. Tortolini A. 2 (1851) 380-. 



, by aid of generating 



circle. Eenshaw, S. A. L. Mth. S. P. 7 



(1875-76) 239-. 

 In-polygons. Gardiner, M. [91862-64] N. S. 



W. Ph. S. T. 1 (1866) 88-; QJ. Mth. 7 (1866) 



146-, 284-. 



In-polygons. Lucas, F. Par. S. Mth. Bll. 20 



(1892) 33-. 

 , regular, of ellipse and circle. Terquem, 0. 



Liouv. J. Mth. 3 (1838) 477-. 

 , theorem. Molins, H. Toul. Mm. Ac. 6 



(1862) 177-. 

 , theorems. Serret, P. N. A. Mth. 6 (1847) 



356-. 

 , (Serret). Catalan, E. C. N. A. Mth. 6 



(1847) 425. 

 Maximum in-, and minimum circum-polygon 



of ellipse. Spitzer, S. Grunert Arch. 30 



(1858) 352-. 

 , . Wanka, J. Lotos 39 



(1891) 33-. 



, , construction. Grunert, 



J. A. Grunert Arch. 30 (1858) 84-. 



Minimum circum-polygon of ellipse. Matheics, 

 G. B. Mess. Mth. 22 (1893) 68-. 



Pentagon theorem. Serret, P. N. A. Mth. 6 

 (1847) 21-. 



Polygon m sides circumscribable to conic, con- 

 ditions. Serret, P. N. A. Mth. 6 (1847) 

 21-. 



Property common to three groups of two poly- 

 gons inscribed, circumscribed or conjugate 

 with respect to conic. Serret, P. C. E. 114 



(1892) 1254-, 1343-. 



Schroter's heptagon circumscribed by a conic. 

 Andreev, K. A. Kharkov Mth. S. Com. 1 

 (1889) 277-; Fschr. Mth. (1891) 669. 



Variable polygon and conies, theorem. Roberts, 

 S. QJ. Mth. 4 (1861) 361-. 



PonceleCs Polygons, Porisms. 

 (See also 4050 and 6810.) 



Seydeu-itz, F. Grunert Arch. 4 (1844) 421-. 

 Bordoni, A. Tortolini A. 3 (1852) 5-. 

 Cayley, A. Ph. Mg. 6 (1853) 99-, 376-; 7 



(1854) 339-. 



Brioschi, F. N. A. Mth. 16 (1857) 421-. 

 Salmon, G. Ph. Mg. 13 (1857) 337-. 

 Mainardi, G. Mil. At. I. Lomb. 1 (1858) 



117-. 



Cayley, A. Phil. Trans. (1861) 225-. 

 Pasch, M., <& Eosanes, J. Crelle J. 64 (1865) 



126-. 



Cayley, A. QJ. Mth. 11 (1871) 83-. 

 Darboux, G. (rx) Par. S. Phlm. Bll. 8 (1872) 



100-, 128-. 

 Chelini, D. Bologna Ac. Sc. Mm. 5 (1874) 



353-. 



Czuber [or Cuter], E. Prag Sb. (1875) 156-. 

 Gundelfinger, S. Crelle J. Mth. 83 (1877) 



171-. 



Darboux, G. C. E. 90 (1880) 85-. 

 Andreev [Andreef], K. A. (xn) Kharkov 



Mth. S. Com. (1881) 91- ; (ix) As. Fr. C. 



E. 11 (1882) 96-. 

 Forsyth, A. E. [1882] Mess. Mth. 12 (1883) 



100-. 

 Eogers, L. J. L. Mth. S. P. 16 (1884-85) 



306-. 

 Berg, F. J. van den. N. Arch. Wisk. 16 (1889) 



160- ; Fschr. Mth. (1889) 719. 

 Frolov, (le gen.) M. As. Fr. C. E. (1894) 



(Pt. 2) 226-. 





494 



