36 The Rev. H. Holditch on a Property of the Parabola. 



and subtracting the latter from the former, and dividing by 

 Yij— Y23, we have 



-— «r X12--X2S xr , Y I « ^12 ~ ^23 I 7, _0' 



19 + A23. ^ -^ - + I12+ J^23 + ^' V _ V + ^ — ^> 



*12 — ^23 •*^12 ^23 



but Y.,-Y,=3^^ and ^,,-X^^.y-^MirJ^, 



• • Y — __ Y " ^/ ' ^^ *^ r • 3^1 + 3^3' 



"' anrY,+ Y, =?^i+-^|l±i^: 

 and therefore 



12 



yi -^3/3'^r2 ^ .Vi + 23/2 + 3/3 ^ ?_^2 ^. ^ = 0. 



And similarly 



y^-^yx'^ y\ , .^2 + 23/3+ 3/ 1 . ^ «y3 . ;: _ „ 



ana o- ^, ^ » 



and substituting these values in the equation X^jg + Y^ 

 + a Xj2 + b Y12 + c = 0, we have 



„_ y^y<l +^1.^3 + .^2^3 



To find where the circle cuts the axis make ?/ = ; 

 r , x^ -\- a X ■\- c — % or 



\ / 4? / * 4 ' 



- (X,,+ X,3 f X,3 + 4).^ -f ?^- -^ X^^3 + X,3 ,^^^^ 



or ^^ — X12 + X23 + X13J . ^or — — j=0; 



.♦. = x — X12 + X23 + Xi3 and = .r — — , 



and the latter factor shows that the circle passes through the 

 focus of the parabola. 



August, 13, 1836. 



or 



«.2 



