606 REV. HUGH MARTIN ON CENTRES, FAISCEAUX. 



Giving appropriate values to s, viz., — 1 ; 3 ; — 3 : we find as follows : — 



XXXV. If the centre of homology move in a conic circumscribing the tri- 

 angle, the faisceau of self-conjugate conies 



/ 9 ■■ h 



will envelope, or inscribe, the quadrilateral represented by 



± (1)1* ± (m).*/3 ± 0)^7 = . . . . (93). 



XXXVI. If the centre of homology move in a conic circumscribing the tri- 

 angle, the faisceau of self- conjugate conies 



jfi.« + £302 + Ay = o 

 will envelope the circumscribing conic 



!i +4 + ^=0 . ■ . . (94). 



« P 7 



XXXVII. If the centre of homology move in a conic circumscribing the tri- 

 angle, the faisceau of self-conjugate conies 



will envelope the tri-tangent conic 



XXXVIII. Cor. Since the inverse centre of homology moves in a circum- 

 scribing conic when the direct centre moves in a straight line, and vice vei'sa, it 

 follows, as before, that the direct and inverse faisceaux have the same envelope. 

 Compare (89), (93) ; (90), (94) ; (91), (95). 



XXXIX. (3.) Required the envelope of a faisceau of self-conjugate conies when 

 the centre moves in a self-conjugate conic. 



Here we have / s « 2 + g s P 2 + toy* = 0, 



and p + -j + p =0; 



and, by the consideration formerly employed, reading for s in (88) ^ we nave the 



envelope 



i i 



(^«*) s + 2 + (m s ^) s + ' 2 + (™ i7 *)' + 2 = . . . (96). 



Giving appropriate values to s, viz., 2 ; — 6 ; 6 : we find as follows : — 



XL. If the centre of homology move in a self-conjugate conic, the faisceau of 



self-conjugate conies 



/ 2 « 2 + # 2 /3 2 + 7i 2 7 2 = 



will inscribe the quadrilateral 



± Via ± \/^2 18 ± \/w y = (97). 



