Contents. xxv SECTION IV.—VARIOUS CIRCLES AFD CONICS. PAGE Neuberg's circles,.......... 423 ,, ,, equation of, in barycentric co-ordinates, . - 424 ,, „ properties of,....... 425 First and second angle of Steinor,....... 426 Nouborg's circles—different modes of derivation, .... 426 M'Cay's circles,.......... 427 ,, j, are special cases of annex circles, .... 427 Jaogonal transformation, isogonal conjugates,..... 428 ,, ,, of any diameter of circumcircle is an equi- lateral hyperbola, ......... 428' luogonal transformation of a few lines, ...... 429 Nouberg's hyperbolas,........429-431 I.'oloH, with respect to triangle of reference, of Ncuberg's hyperbolae, Kieport's liypcrbola, and circumcircle are collinear, . . • 431 lAil inn aim's circles, ........-• 431 Point of contact of nine-points circle with incircle, .... 434 Threo points on the common tangent of incircle, and nine-points circle,........... 436- Orthocentroidal circle defined and its equation found, . . . 436 ,, ,, incetu perpendiculars and medians in six points forming a harmonic hoxagon, . . . . • • .437 Tho Ih'oc.ard jiaraboho, ......... 439 Artxt'n puraboho (Hocond group), .....-• 441 Ki«porl,'H hyperbola, . . . - • • • .431, 442 ,, triunglo,.......... 443 ,, hyperbola, any two points on, whoso parametric angles diU'or by n right angle aro collinear with centre of nine-points oirolo,........... 444 Kwpwt'n Ijyporhola; propcriicH of in connexion with Noubcrg's