-^08 9rU ^8 tY jL^ s*^ aJniorp'Bfw rii £) U asoriJosub 'lonim ant 

 JlSliJ^^nWWriabiyi It is almost needless, to mention that thQ 

 distances of the common directrices and foci from the centre 



6f^4^'i^er^aarfi a cos w and -^ respectively ; hence, in 



tS^L^W!^kP^n>o% where c« = ;^;^|^^,,ordmary and 



ftrfhtft* rfiWeft-J^J^' Coincide, as do also tHe^«WrM^.bn and mino^ 

 foci ; whence we may deduce the very general and remavk- 

 k\}],(B conclusion that. 



The common directrices and foci of the equilateral hyperbola 

 possess tdoo distinct classes" of properties, t^ose ivhich belong to 

 them as being the common or ordinary directrices and foci, as 

 'also that other nerd> and equally extensive class, to 'which they 

 xtre in like manner related, as btiiig the minor directrices and 

 foci of a central coiiic section. '^ ^'^^^q rf'>iti'' «bioo sdj ,M&h 

 • In the circle the minor direciVi'^s-JifeiflfinltelydigCafle/'and 

 the minor foti coincide with the centre, as is also the case with 

 tlie ordinary directrices and foci. 



Of the following theorems, most of which are, it is believed^ 

 new, the demonstrations have been suppressed, as to any who 

 are moderately versed in analysis, and who take an interest in 

 the subject, it will give but litde trouble to supply them. It 

 may, however, be remarked, that the solutions of many of the 

 theorems may be effected with great brevity and simplicity by 

 the application of a new method in analytic geometry,— the 

 theory of tangential co-ordinates, an Outline of v^^hic^i was pub 

 lished some years ago by the author *. 



lOfiim sdJ jto ?.9ij^no'Ux*Na^f7n 3 sjafoff krfi dgnoiriT .III 

 tfilod'tsq'^d^Hl niS^Xfi o^r^7^ti^fy^d1; "Xoko (Sgqifb srfj ni axn 

 owi nv/fiib g^sLsionl Jal ^o^pm sxh noSi imo^ i^Aio \aR bnu 

 t'T? TT ginioq 9d.tTfk4 9^j;p^iib iqii istf^di !(;) 9no §ni}99ra abioa 



' , *. On the Application fcA^nfefeMl^^^c^tem^ of 



♦duV^e? aml^ CurveiT SdrfaiHie'^ f.otfaofl;"Sfi«)iI^iaiifeWiir§1iMl : dam- 

 bridge, Deiglitons. odjo dosQ oJ 89lj^nxi jdgi'i )n a ' 



