6810 



Planimetry. Porisms. 



Breton [de Chump], P. Liouv. J. Mth. 4 (1859) 



153- ; C. B. 51 (1860) 1034-. 

 ( ) Bertrand, J., & Serret, . C. E. 



53 (1861) 699-. 

 Circles, in- and circum-scribed, of polygon, 



relation between distance of centres and 



radii. Grunert, J. A. Grunert Arch. 32 



(1859) 68-. 



, or circum-scribed, of plane or spherical 



polygons, equations. Casey, J. As. Fr. C. 



B. 9 (1880) 230-. 

 , and e-scribed, of triangle, Beltrami's 



theorem for relation between centres, demon- 

 stration. Schmidt, C. Arch. Mth. Ps. 43 



(1865) 238- ; 44 (1865) 120- . 

 , , , circum-circles of. Jeff'ery, 



H. M. QJ. Mth. 24 (1889) 180-. 

 , porism. Larmor, J. Mess. Mth. 13 (1884) 



61-. 

 , porismatic systems. Lachlan, E. Mess. 



Mth. 16 (1887) 152-. 

 , ring of, touching 2 circles, porism. Taylor, 



H. M. Mess. Mth. 7 (1878) 148-. 

 , , , . Taylor, W. W. Mess. 



Mth. 7 (1878) 167-. 

 Euclid's porisms (Chasles), demonstration. 



Marianini, P. D. Mod. Mm. S. It. 2 (1866) 1-. 

 Fermat's fourth porism. Nagel, C. H. Arch. 



Mth. Ps. 46 (1866) 11-. 

 Functional symmetry in notation. Graves, 



J. T. Ph. Mg. 15 (1839) 129-. 

 Polygon porism of two circles. Enneper, A. 



Schlomilch Z. 7 (1862) 190-. 



. Weill, M. Liouv. J. Mth. 4 



(1878) 265- ; N. A. Mth. 19 (1880) 57-. 



. Intrigila, C. G. Mt. 21 



(1883) 323-. 

 . Dixon, A. C. Mth. Gz. 1 



(1900) 121-. 



- , maxima and minima. 



Birnbaitm, H. Grunert Arch. 29 (1857) 414-. 

 , relations. DoleZal, E. Arch. 



Mth. Ps. 15 (1897) 172-. 

 Polygons, irregular symmetrical, both in- and 



circum-scribed to circle. Fuss, N. [1798] St 



Pet. Ac. Sc. N. Acta 13 (1802) 166-. 

 , , , Fuss's problem. 



Mention, J. [1859] St Pet. Ac. Sc. Bll. 1 



(1860) 15-, 33-. 



Problems. Clifford, W. K. [1868] Camb. 



Ph. S. P. 2 (1876) 120-. 

 Triangles, in-, and circum-scribed, of circles. 



Gamier, J. G. Quetelet Cor. Mth. 1 (1825) 



179-. 

 , , , theorems. Mainardi, G. 



Brugnatelli G. 9 (1826) 119-, 181-. 



inscribed in ellipse and circumscribed to 

 concentric circle. Barisien, E. Mathesis 

 19 (1899) 224-, 247-, 269-; 20 (1900) 84-, 

 113-, 136-. 



, two, such that circum-circle of one is in- 

 circle of other, areal relation. Luchterhandt, 

 A. R. Grunert Arch. 9 (1847) 262-. 



Powers. Arndt, C. F. Grunert Arch. 5 (1844) 

 113-. 



of circles and spheres, theorems. Johnson, 

 W. W. B. A. Bp. (1890) 743-. 



Pythagorean Theorem 6810 



Powers of points. Laisant, C. A. As. Fr. C. 



B. (1875) 139-. 

 Problem. Martini, M. (vm) Bologna Opusc. 



Sc. N. Col. (1824) 251-. 



: through given point equidistant from two 

 given lines to draw intercept of given length 

 (Newton). Gergonne, J. D. Gergonne A. 

 Mth. 10 (1819-20) 204-. 



Font6, . N. A. Mth. 6 (1847) 180-. 



(Newton). Transon, (Prof.) A. N. A. Mth. 

 6 (1847) 458-. 



Problems, solutions of two. Mackay, J. S. 

 Edinb. Mth. S. P. 7 (1889) 42-. 



on triangle, circle, etc. Paque, A. Liege 

 Mm. S. Sc. 10 (1855) 199-. 



Pythagorean theorem, 



MUtter t H. K. F. von. Oken Isis (1826( 763-. 

 Gudermann, C. Crelle J. 42 (1852) 280-. 

 Vincent, A. J. H. N. A. Mth. 11 (1852) 5-. 

 De Morgan, A, QJ. Mth. 1 (1857) 236-. 

 Salmon, G. QJ. Mth. 1 (1857) 237-. 

 Richardson, J. M. Camb. (M.) Mth. M. 2 



(1860) 45-. 

 Azzarelli, M. [1873] Bm. N. Line. At. 27 



(1874) 66-. 



Harvey, W. Edinb. Mth. S. P. 4 (1886) 17-. 

 Zahradnik, K. fiasopis 25 (1896) 261- ; Fschr. 



Mth. (1896) 394. 



Confirmation. Wittstein, T. Grunert Arch. 11 

 . (1848) 152-. 

 Demonstration. Buquoy, G. von. Oken Isis 



21 (1828) 1-. 



by dissection. Perigal, H. Mess. Mth. 2 

 (1873) 103-. 



Extension to any triangle. Jelinek, V. 6aso- 



pis 28 (1899) 79-; Fschr. Mth. (1899) 456. 

 Extensions. Anglin, A. H. Edinb. E. S. P. 



12 (1884) 703-. 

 Figures for proving. Andre, H. d'. N. A. 



Mth. 5 (1846) 324-. 

 Generalisation. Umpfenbach, (Dr) . Crelle J. 



26 (1843) 92. 

 Puzzles connected with theorem. Brand, E. 



Bv. Sc. 2 (1894) 274-, 809-. 

 Pythagorean triangles. Grunert, J. A. Grunert 



Arch. 31 (1858) 472-. 

 . Cantor, M. Schlomilch Z. 4 (1859) 



306-. 



. Lewis, J. Am. Ph. S. P. 9 (1865) 415-. 



. Whitworth, W. A. Lpool. Lt. Ph. S. 



P. 29 (1875) 237-. 

 , and application to the division of the 



circumference. Graeber, . Arch. Mth. 



Ps. 15 (1897) 337-. 



, nearly isosceles. Martin, Art. Des 

 Moines Anal. 3 (1876) 47-. 



, properties. Breton, Ph. Les Mondes 6 



(1864) 401-. 

 Eight-angled triangles. Bangma, O. S. Amst. 



Vh. 4 (1818) 28-. 

 , squares on sides (Hamett). Gergonne, 



J. D. Gergonne A. Mth. 14 (1823) 334-. 





440 



