612 KEV. HUGH MARTIN ON CENTRES, FAISCEAUX 



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

 tri- tangent conies 



/ 9 h 



will envelope the straight line 



J + t + Z = o (120). 



I m ■ n 



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

 of tri-tangent conies 



* ± £ ± 7_ 



±^±S±^=o 



will envelope the circumscribing conic 



l - + f + *-' = . . . . (121). 

 a P 7 



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

 of tri-tangent conies 



± 7^ ±s f ±N f=o 



will envelope the self-conjugate conic 



a 



(? f 



^- + ^ + ^ = (122). 



I 3 m* n 



Section V. — The Faisceau of Homology being Bi-tangent Conies. 



LXIV. (1.) Required the envelope of & faisceau of bi-tangent conies when the 

 centre of homology moves in a straight line. 

 Let the faisceau be 



and the straight line la + mP + n 7 = } 



The envelope is <* 2 = (^-Y Py (124). 



LXV. (2.) Required the envelope of a faisceau of bi-tangent conies when the 

 centre of homology moves in a circumscribing conic. The envelope is 



» ! = (&)^ • < 125 >- 



LXVI. (3.) Required the envelope of a faisceau of bi-tangent conies when 

 the centre of homology moves in a self-conjugate conic. The envelope is 



