6810 Apollonian Problem 



Circle cutting 3 circles isogonally. Wageningen, 

 F. van. N. Arch. Wisk. 2 (*1876) 180-. 



at given angles. Griffiths, J. 

 L. Mth. S. P. 3 (1869-71) 269- ; 5 (1873-74) 

 33- ; QJ. Mth. 11 (1871) 366-. 



derived from seven straight lines. Serret, 

 P. C. B. 119 (1894) 474-, 493- ; 123 (1896) 

 442-. 



on diagonal of a rectangle as chord. Locus 

 problem. Siacci,F. G. Arcad. 18 (1860) 166-. 



as figure of least perimeter for given area. 

 Anon, (vi 525) Gergonne A. Mth. 4 (1813 

 -14) 338-. 



. Anon, (vi 545) 



Gergonne A. Mth. 13 (1822-23) 132-. 



. Anon, (vi 550) 



Gergonne A. Mth. 14 (1823-24) 316-. 



. Anon, (vi 555) 

 Gergonne A. Mth. 15 (1824-25) 257-. 



, completion of 



Steiner's proof. Edler, F. Gott. Nr. (1882) 

 73-. 



orthotomic to three circles. Whiticorth, 

 W. A. [1864] Mess. Mth. 3 (1866) 26-. 



through two points cutting another dia- 

 metrally. Clausen, T. Grunert Arch. 15 

 (1850) 235-. 



Circles 6810 



conjectured Apollonian solution. Flauti, V. 



Nap. At. Ac. 1 (1819) 71-. 

 construction. Turrell, I. H. Des Moines 



Anal. 5 (1878) 166-. 

 modern researches. Sqgajto, A. Par. T. 



Nauk Sc. Pam. 8 (*1876) Art. 6, 7 pp. 

 nature of solutions. Muirhead, R. F. Edinb. 



Mth. S. P. 14 (1896) 135-. 

 tangencies, problems, solution (new). Fergola, 



N. [1809] Nap. At. Ac. 1 (1819) 3-. 



Circle touching straight lines, equations. 



Cayley, A. N. A. Mth. 18 (1859) 222-. 

 Circles touching a common circle. Allardice, 



R. E. [1900] Edinb. Mth. S. P. 19 (1901) 



each other in succession, radii of systems. 



Seitz, E. B. Des Moines Anal. 1 (1874) 



173- ; 2 (1875) 74-. 

 one circle, and orthogonal to another, 



system. Aubert, P. Edinb. Mth. S. P. 6 



(1888) 33-. 

 semicircles, locus of centres. Dostor, G. 



Arch. Mth. Ps. 66 (1881) 17-. 

 three circles which touch each other. 



Dostor, G. Arch. Mth. Ps. 51 (1870) 191-. 



to replace a given curve within a finite . theorem (T 2 = id 1 d 3 ). 



space, practical tracing. Leaute, H. C. E. Turrell, I. H. Des Moines Anal. 1 (1874) 



85 (1877) 1049-. 171-. 



of similitude of two circles. Nnggerath, given circles, centres and radii, to 



find. Prange, A. J. A. N. Arch. Wisk. 15 



E. J. Grunert Arch. 33 (1859) 329-. 



Circle touching 3 given circles. 

 (Apollonian problem.) 



Cauchy, A. L. Par. EC. Pol. Cor. 1 (1804-8) 



193-. 

 Gergonne, J. D. [1814-17] Tor. Mm. Ac. 22 



(1816) 20*- ; Gergonne A. Mth. 7 (1816-17) 



289-. 

 Anon, (vi 547) Gergonne A. Mth. 13 (1822 



-23) 193- . 

 Badon Ghijben, J. (vn) Amst. N. Ws. Ntk. 



Vh. 1 (1844) 164-. 

 Kerz, F. Grunert Arch. 24 (1855) 211- ; 26 



(1856) 266-; 28 (1857) 402- ; 35 (1860) 121-. 

 Grunert, J. A. Grunert Arch. 28 (1857) 354-. 

 Kurz, A. Grunert Arch. 37 (1861) 347-. 

 Serret, P. N. A. Mth. 2 (1863) 95-. 

 Barbier, E. N. A. Mth. 4 (1865) 313- ; C. B. 



60 (1865)1076-. 



Stott, . Mth. A. 6 (1873) 613-. 

 Cayley, . QJ. Mth. 25 (1891) 104-. 

 Hioux, V. N. A. Mth. 10 (1891) 399-. 

 Langley, E. M. Mth. Gz. No. 5 (1895) 41. 

 Study, E. Mth. A. 49 (1897) 497-. 

 analytical results. Crelle, A. L. Berl. Ab. 



(1841) 65- ; Berl. B. (1841) 162-. 

 solution. Strehlke, F. Crelle J. 12 (1834) 



359-. 



. Cayley, A. Ph. Mg. 13 (1857) 507-. 



. Mertens, F. Z. Mth. Ps. 21 (1876) 



443-. 

 Casey's equation and theorem. Cayley, A. 



QJ. Mth. 8 (1867) 334- ; A. Mt. 1 (1867-68) 



132-. 



(1888) 165- ; Fschr. Mth. (1888) 731. 

 or cutting them at given angle. 



Fouche, H. N. A. Mth. 11 (1892) 227-, 



331-, 404-. 

 , system treated by trilinear 



coordinates. Caldarera, F. Palermo Cir. 



Mt. Bd. 4 (1890) 43-. 

 , (Caldarera). 



Albeggiani, M. L. Palermo Cir. Mt. Bd. 



4 (1890) 50-. 

 , 2, relation between. Cayley, A. QJ. Mth. 



11 (1871) 82-. 

 , 3, cutting at given angles, system. 



Cayley, A. Mess. Mth. 17 (1888) 60-. 

 , , , of equations. Cayley, 



A. Mess. Mth. 17 (1888) 18-. 

 , , mutually tangent, theorems. Muir, T. 



Edinb. Mth. S. P. 3 (1885) 119-. 

 , , system, deduction from properties. 



Franklin, F. [1880] (xn) J. H. Un. Cir. 



[1] (1882) 85. 



, , with three common tangents, construc- 

 tion. Dewall, (Oberst) von. Arch. Mth. Ps. 



41 (1864) 139- ; 42 (1864) 65-, 80-. 

 , 4, in contact, radii. Baur, C. W. Schlo- 



milch Z. 5 (1860) 365-. 

 , , in piano, and four powers relative to 



a point in plane, theorem. Lucas, E. N. A. 



Mth. 15 (1876) 205-. 



(Lucas). Cassani, P. G. Mt. 14 (1876) 347-. 

 , pairs, through six common points of 3 



circles. Griffiths, J. QJ. Mth. 9 (1868) 



358- ; 10 (1870) 230-. 

 , 8, touching 3. Casey, J. QJ. Mth. 5 



(1862) 318-. 



432 



