6810 



Planimetry. Regular Polygons 



6810 



equations for sides and diagonals. Badon- 



Ghijben, J. [1865] Amst. Vs. Ak. 1 (1866) 



(Nt'k.) 293-; Arch. Need. 1 (1866) 131-. 

 , and decomposition of same into equations 



of lower degrees. Schonborn, W. Arch. 



Mth. Ps. 46 (1866) 425-. 

 with half the number of sides odd, relations 



between sides and diameter. Schwarzer, A. 



Wien Sb. 53 (1866) (Ab. 2) 454-. 

 in- and circum-scribed. Azzarelli, M. Em. N. 



Line. At. 50 (1897) 69-. 

 inscription. Dickson, L. E. A. Mth. 9 (1894- 



95) 73-. 

 isoperimetrical. Ranking, W. J. M. Ph. Mg. 



34 (1867) 364-. 

 , and theorems of Chasles. Ter quern, 0. 



Liouv. J. Mth. 3 (1838) 97-. 

 linkage for describing. Everett, J. D. B. A. 



Ep. (1894) 559-. 

 mensuration. Hessel, J. F. C. Grunert Arch. 



39 (1862) 279-. 

 paving an area with. Levy, L. Par. S. Phlm. 



Bll. 3 (1891) 46-. 

 perimeter of, equal in area to given polygon. 



Cigir, G. I. Kazan S. Nt. (Ps.-Mth.) P. 2 



(1884) 92-. 

 , (Cigir). Zbikovskij, 



A. K. Kazan S. Nt. (Ps.-Mth.) P. 4 (1886) 



233-. 

 properties. Mensbrugghe, G. van der. Brux. 



Ac. Bll. 17 (1864) 153-. 

 sides and areas, method of finding. Cabreira, 



A. Lisb. J. Sc. Mth. 5 (1898) 175-. 

 theorem, general. Wallace, (Prof.) W. Edinb. 



Ph. J. 11 (1824) 377-. 

 theorems. Fran^ais, J. F. Gergonne A. Mth. 



5 (1814-15) 341-. 

 . Reinemund, F. Brux. Ac. Bll. 40 (1875) 



801- ; 43(1877)356-. 



. Meutzner, P. Mth. A. 13 (1878) 566-. 

 . Sparer, B. Z. Mth. Ps. 37 (1892) 25-. 

 5-gon (Staudt). Barral, H. N. A. Mth. 11 



(1852) 388-. 

 .formula. Tortolini,B. A. Mt. 6 (1864) 191-. 



and ' ' pentalpha ' ' area. Mobius, A. F. As. 

 Nr. 3 (1825) 131-. 



, theory. Clebsch, R. F. A. Mth. A. 4 



(1871) 284-. 

 , 6-gon, and 10-gon in circle, relation between 



sides. Grunert, J. A. Grunert Arch. 40 



(1863) 127-. 

 6-gon, in- and' circumscribed of circle, etc. 



Durrande, J. B. Gergonne A. Mth. 14 



(1823-24) 29-. 

 6-gonal facets within given circle. M,, A. J. 



Mcr. Sc. 6 (1858) 83-. 

 7-gon. Grunert, J. A. Grunert Arch. 17 



(1851) 355-. 



and circle, fractional values for. Norton, H. 

 Ph. Mg. 27 (1864) 281-. 



, Eober's construction. Hamilton, (Sir) W. R. 

 [1863] Ph. Mg. 27 (1864) 124-. 



and 9-gon, approximate construction. 

 Efremoff, D. Fschr. Mth. (1892) 531-. 



9-gon. Denys, A. Mathesis 10 (1890) 162-. 

 , inscription in circle. Encontre, D. Mntp. 

 Eec. Bll. 1 (1803) 293-. 



15-gon, 30-gon, 60-gon, etc., inscription, and 



calculation of sides. Dostor, G. Arch. Mth. 



Ps. 62 (1878) 103-. 

 20-gon, inscribed, perimeter compared with 



radius. Hamilton, (Sir) W. R. Ph. Mg. 



23 (1862) 267-. 

 30-gons, inscription of four. Dostor, G. N. A. 



Mth. 17 (1878) 370-. 

 n- and 2n-gons, relative number, for n even 



and odd. Dostor, G. [1877] Arch. Mth. 



Ps. 62 (1878) 148-. 



Eevolving polygon, curve envelopes of sides, 

 metrical relation. Olsson, 0. Ts. Mth. 4 

 (1886) 120- ; Fschr. Mth. (1886) 666. 



Self-inscribed polygons. Brunei, G. Bordeaux 

 S. Sc. PV. (1895-96) 35-. 



inscription, multiple, polygons with. Brunei, 

 G. Bordeaux S. Sc. PV. (1897-98) 43-. 



Semi-regular polygons, analytical researches. 

 Pigeon, H. Par. EC. Pol. J. Cah. 41 (1865) 

 165-. 



, area. Cabreira, A. [1897] Lisb. J. 

 Sc. Mth. 5 (1898) 43-; Fschr. Mth. (1897) 

 446. 



Series. Darboux, G. Bll. Sc. Mth. As. 2 



(1878) 298-. 

 . Ocagne, M. d\ Brux. S. Sc. A. 9 (1885) 



(Pt. 2) 231-. 

 Star polygons. Levy, M. Eouen Tr. Ac. 



(1824) 40-. 

 . Saigey, J. F. Fe"russac Bll. Sc. Mth. 



4 (1825) 201-. 



. Valat, .. Bordeaux Act. Ac. Sc. 

 (1840) 415-. 



, area. Hermes, 0. Crelle J. 65 (1866) 



174-. 



, , Jacobi's rule extended to case of 

 multiple points. Hermes, 0. [1865] Crelle 

 J. 65 (1866) 177-. 



, general theory. Dostor, G. Liouv. J. 



Mth. 6 (1880) 343-. 



, geometrical import. Schroder, E. 

 Schlomilch Z. 7 (1862) 55-. 



, regular, with continuous outline. 

 Azzarelli, M. Em. N. Line. At. 36 (1883) 

 316-. 



and rayed polygons. Dostor, G. Arch. 

 Mth. Ps. 59 (1876) 375-. 



Theorems. Fung, N. [1810] St Pet. Ac. Sc. 

 Mm. 11 (1830) 209-. 



, and application to arithmetic and trigono- 

 metry. Werner, O. [1857] St Pet. Ac. Sc. 

 Bll. 16 (1858) 1-. 



Porisms. 

 (See also 4050 and 7210.) 



Play/air, J. [1792] Edinb. E. S. T. 3 (1794) 



154-. 

 Wallace, (Prof.) W. [1796] Edinb. E. S. T. 



4 (1798) 107-. 



Breton [de Champ], P. C. E. 36 (1853) 1008-. 

 Housel, . Liouv. J. Mth. 1 (1856) 193-. 

 (Breton de Champ.) Vincent, A. J. H. Liouv. 



J. Mth. 4 (1859) 9-. 



439 



