Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

An Extension of the Harmonic Relation between Conics


     

   Subscribe/Renew Journal


If there exists one self-polar triangle of a conic S inscribed in a second conic S', then there exists an one-fold infinity and S' is out-polar or ex-harmonic to S. On the other hand it is easily seen that there always exists a finite number of self-polar triangles of S with their three vertices situated severally on three assigned conies S1, S2, S3. The object of the present note is to shew that under certain circumstances the conies S1, S2, S3 admit an infinity of such triangles. For the symbolic method which is used throughout, reference may be made to Grace and Young : Algebra of Invariants (Ternary Forms).
Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 239

PDF Views: 0




  • An Extension of the Harmonic Relation between Conics

Abstract Views: 239  |  PDF Views: 0

Authors

Abstract


If there exists one self-polar triangle of a conic S inscribed in a second conic S', then there exists an one-fold infinity and S' is out-polar or ex-harmonic to S. On the other hand it is easily seen that there always exists a finite number of self-polar triangles of S with their three vertices situated severally on three assigned conies S1, S2, S3. The object of the present note is to shew that under certain circumstances the conies S1, S2, S3 admit an infinity of such triangles. For the symbolic method which is used throughout, reference may be made to Grace and Young : Algebra of Invariants (Ternary Forms).