6810 



Planimetry. Triangles. Remarkable Points 



6810 



Centres of similitude of triangle of constant Point, the sum of whose distances from vertices 



form circumscribed to given triangle. Grif- is a minimum. Gergonne, J. D. Gergonne 



fiths, J. L. Mth. S. P. 24 (1893) 369-. A. Mth. 20 (1829-30) 299-. 



inscribed in given , . Azzarelli, M. 



L. Mth. S. 



24 



triangle. Griffith 



(1893) 181-. 

 Centroid. Haiti, E. [1875] Arch. Mth. Ps. 



58 (1876) 170-. 

 , distances. Dostor, G. 



N. 



A. Mth. 2 (1883) 

 Grunert, J. A. 



and in-circle, distance. 

 Arch. Mth. Ps. 52 (1871) 247-. 



, intersection of medians and other theorems. 



Burg, A. Wien Jb. Pol. I. 12 (1828) 4- ; 13 



(1828) 223-. 

 , Lemoine, and other points. DurdnLoriga, 



J. J. G. Teix. J. Sc. 11 (1892) 161- ; Fschr. 



Mth. (1893-94) 1104. 



of particular family of triangles, locus. 

 Brocard, H. Mathesis 11 (1891) 153-. 



, points whose joins are trisected by. 



Eeuschle, C. G. Z. Mth. Ps. 11 (1866) 475-. 

 Centroids, pedal and symmetrical. Neuberg, J. 



N. Arch. Wisk. 4 (1899) 192- . 

 "Cosine" orthocentres of a triangle, and a 



cubic through them. Tucker, R. Mess. 



Mth. 17 (1888) 97-. 

 Distances of point from vertices. Cayley, A. 



QJ. Mth. 5 (1862) 381-. 



. BlazeievsM, E. N. A. Mth. 



13 (1894) 28-. 



points. Thiry, C. Brux. Ac. Bll. 21 



(1891) 471-. 



from each other. Grunert, J. A. 

 Grunert Arch. 36 (1861) 325-. 



. Lemoine, E. N. A. Mth. 



9 (1870) 311-. 

 Eighty-four special points, including Jefabek's. 



Jefabek, V. Casopis 20 (1891) 141-, 237-; 



Fschr. Mth. (1891) 603-. 

 Fifth remarkable point. Hochheim,A. Arch. 



Mth. Ps. 52 (1871) 26-. 

 Four remarkable points (Euler). Grunert, J. A . 



Grunert Arch. 26 (1856) 343-. 



, analytically treated. Metzler, C. 

 Arch. Mth. Ps. 47 (1867) 243-. 



G points of circle with respect to given triangle, 



finding. Griffiths, J. [1891] L. Mth. S. P. 



23 (1892) 96-. 

 Loci. Lindman, C. F. Arch. Mth. Ps. 43 



(1865) 350-. 



. Hochheim, A. Z. Mth. Ps. 15 (1870) 33-. 

 Locus of point whose pedal triangle has given 



area. Azzarelli, M. Em. N. Line. At. 27 



(1874) 333-. 

 points, sum of whose distances from sides 



is constant (Entf ernungsort) . Grunert, J.A. 



Grunert Arch. 17 (1851) 361-. 

 , ( ). Emsmann, 



H. Arch. Mth. Ps. 46 (1866) 121-. 

 Middle points of triangles formed by in- and 



ex-centres of triangle. Noggerath, E. J. 



Schlomilch Z. 8 (1863) 394-. 

 Nagel and Gergonne points. Harnischmacher, 



F. J. Arch. Mth. Ps. 42 (1864) 90-. 

 . Mink, W. Arch. Mth. Ps. 43 



(1865) 1-. 



447 



Em. N. Line. At. 39 (1886) 95-. 

 Eeciprocal trilinear coordinates, properties of 



points with. Greiner, M. Arch. Mth. Ps. 



1 (1884) 130-. 

 Series of points. Poulain, A. Mathesis 10 



(1890) 246-. 

 Spieker's point. Hain, E. [1875] Arch. Mth. 



Ps. 58 (1876) 164-. 

 Steiner's foci of a triangle. Neuberg, J., <& 



Gob, A. As. Fr. C. E. (1889) (Ft. 2) 179-. 



point. Neuberg, J. As. Fr. C. E. (1885) 

 (Pt. 2) 89-. 



Symmedian or Lemoine point. Lemoine, E. 



N. A. Mth. 12 (1873) 364-; As. Fr. C. E. 2 



(1873) 90-; (1874) 1165-. 

 . Picquet, H. As. Fr. C. E. (1874) 



1202-. 

 . Hain, E. [1875] Arch. Mth. Ps. 



58 (1876) 84-. 

 , early history. Mackay, J. S. 



Edinb. Mth. S. P. 11 (1893) 92-. 

 point axis of system of triangles. Tucker, 



R. QJ. Mth. 20 (1885) 167-. 

 Symmetry points. Hoppe, R. Arch. Mth. 



Ps. 57 (1875) 422-. 

 . Hain, E. Arch. Mth. Ps. 58 (1876) 



176-, 385-, 394-; 59 (1876) 415-, 420- ; 60 



(1877) 71- ; 64 (1879) 398-. 

 Tarry's point. Neuberg, J. Mathesis 6 (1886) 



5-. 

 Three points (Euler). Gentil, . N. A. Mth. 



5 (1846) 28-. 



, certain groups. K$piiiski, S. Prace 

 Mt.-Fiz. 2 (1890) 169-. 



Two points. Grunert, J. A. Arch. Mth. Ps. 

 48 (1868) 37-. 



in plane of a triangle. Lemoine, E. 

 As. Fr. C. E. (1885) (Pt. 2) 23-. 



Eemarkable triangle. Barisien, (le capit.) E. N. 



As. Fr. C. E. (1897) (Pt. 2) 107-. 

 Eight angled isosceles triangle, calculation of 



angles. Voll, W. Oken Isis (1826) 490-. 

 triangles, properties. Dostor, G. Arch. 



Mth. Ps. 51 (1870) 103-. 

 , theorem. Ramus, C. Crelle J. 20 



(1840) 28. 

 , theorems, four. Lilienthal, . 



Grunert Arch. 21 (1853) 99-. 

 Scalenity. Sharpe, H. J. [1864] Mess. Mth. 



3 (1866) 52- ; 4 (1868) 177-. 

 Schroeter, theoremof , andLongchamps's line d. 



Droz-Farny, A. As. Fr. C. E. (1897) (Pt. 2) 



136- . 

 Segmentary properties. Ocagne, M. d'. N. 



A. Mth. 2 (1883) 497-. 

 Segments of sides by concurrent lines through 



vertices. Bellavitis, G. A. Sc. Lomb. Yen. 



2 (1832) 250-. 

 (Bellavitis). Fusinieri, 



A. A. Sc. Lomb. Yen. 2 (1832) 254-. 

 , geometry of certain. Ocagne, M. d'. 



G. Teix. J. Sc. 6 (1885) 125-. 



